CSE_E---1.7.THM-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SWW312+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 : n010.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May  5 05:31:21 PM UTC 2026

% Result   : Theorem 31.75s 17.27s
% Output   : CNFRefutation 32.73s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_6102)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_of__int__num,axiom,
    ! [X30,X5] :
      ( class_Rings_Oring__1(X5)
     => ( ( X30 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(c_Int_Oring__1__class_Oof__int(X5),X30) = c_Groups_Ozero__class_Ozero(X5) )
        & ( X30 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
             => hAPP(c_Int_Oring__1__class_Oof__int(X5),X30) = 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),X30))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
             => hAPP(c_Int_Oring__1__class_Oof__int(X5),X30) = 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(X30,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,
    ! [X22,X14,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),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(X15),X22),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__power2__lt__zero) ).

fof(fact_power2__less__0,axiom,
    ! [X25,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__less__0) ).

fof(fact_zmod__number__of__Bit1,axiom,
    ! [X126,X132] :
      ( ( 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),X132)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X132))) = 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),X126),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)))),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),X132)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X132))) = 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),X126)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)))),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,
    ! [X132,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),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126))))
         => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132),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),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)),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),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126))))
         => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132),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(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132),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__number__of) ).

fof(fact_negDivAlg__eqn__1__number__of,axiom,
    ! [X132] :
      ( 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),X132)))
     => ( ( 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),X132))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)) = 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),X132))) )
        & ( ~ 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),X132))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)),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),X132)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg__eqn__1__number__of) ).

fof(fact_posDivAlg__eqn__number__of,axiom,
    ! [X132,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),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
         => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132),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)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
         => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132),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(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132),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__number__of) ).

fof(fact_posDivAlg__eqn__1__number__of,axiom,
    ! [X132] :
      ( 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),X132)))
     => ( ( 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),X132)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)) = 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),X132)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)),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),X132)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg__eqn__1__number__of) ).

fof(fact_negDivAlg__eqn,axiom,
    ! [X25,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__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25),X26)))
         => c_Divides_OnegDivAlg(X25,X26) = 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),X25),X26)) )
        & ( ~ 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),X25),X26)))
         => c_Divides_OnegDivAlg(X25,X26) = hAPP(c_Divides_Oadjust(X26),c_Divides_OnegDivAlg(X25,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)))),X26))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg__eqn) ).

fof(fact_posDivAlg__eqn,axiom,
    ! [X25,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),X25),X26))
         => c_Divides_OposDivAlg(X25,X26) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),X26))
         => c_Divides_OposDivAlg(X25,X26) = hAPP(c_Divides_Oadjust(X26),c_Divides_OposDivAlg(X25,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)))),X26))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg__eqn) ).

fof(fact_hd__dropWhile,axiom,
    ! [X212,X29,X5] :
      ( c_List_OdropWhile(X5,X29,X212) != c_List_Olist_ONil(X5)
     => ~ hBOOL(hAPP(X29,hAPP(c_List_Ohd(X5),c_List_OdropWhile(X5,X29,X212)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__dropWhile) ).

fof(fact_power__number__of__odd__number__of,axiom,
    ! [X56,X112,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),X112)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X56)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X112))) = hAPP(hAPP(c_HOL_OLet(X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X56)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X112))),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),X56)))),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),X112)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X56)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X112))) = 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,
    ! [X212,X29,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),c_List_OdropWhile(X5,X29,X212))))
         => ~ hBOOL(hAPP(X29,X3)) )
     => c_List_OtakeWhile(X5,X29,X212) = hAPP(c_List_Ofilter(X5,X29),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__eq__filter) ).

fof(fact_power__number__of__odd,axiom,
    ! [X37,X112,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),X112)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),X37),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X112))) = hAPP(hAPP(c_HOL_OLet(X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X37),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X112))),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),X37))),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),X112)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),X37),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X112))) = 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,
    ! [X37,X112] :
      ( ( 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),X112)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X37),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X112))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X37),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X112))),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),X37))),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),X112)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X37),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X112))) = 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,
    ! [X12,X34,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X5,X5),X34)),c_Transitive__Closure_Ortrancl(X5,X34)) = 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),X12),X12)),c_Transitive__Closure_Otrancl(X5,X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__tranclI) ).

fof(fact_dropWhile__append1,axiom,
    ! [X214,X29,X212,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => ( ~ hBOOL(hAPP(X29,X12))
       => c_List_OdropWhile(X5,X29,hAPP(hAPP(c_List_Oappend(X5),X212),X214)) = hAPP(hAPP(c_List_Oappend(X5),c_List_OdropWhile(X5,X29,X212)),X214) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__append1) ).

fof(fact_acyclic__def,axiom,
    ! [X34,X5] :
      ( c_Wellfounded_Oacyclic(X5,X34)
    <=> ! [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,X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__def) ).

fof(fact_eq__int__code_I15_J,axiom,
    ! [X265,X266] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X266)),c_Int_OBit0(X265))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__int__code_I15_J) ).

fof(fact_eq__int__code_I10_J,axiom,
    ! [X266] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X266)),c_Int_OPls)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__int__code_I10_J) ).

fof(fact_zdiv__number__of__Bit1,axiom,
    ! [X126,X132] :
      ( ( 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),X132)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X126))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X132))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)) )
      & ( ~ 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),X132)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X126))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X132))) = 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),X126)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__number__of__Bit1) ).

fof(fact_acyclicI,axiom,
    ! [X34,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,X34)))
     => c_Wellfounded_Oacyclic(X5,X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclicI) ).

fof(fact_dropWhile_Osimps_I2_J,axiom,
    ! [X212,X5,X12,X29] :
      ( ( hBOOL(hAPP(X29,X12))
       => c_List_OdropWhile(X5,X29,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = c_List_OdropWhile(X5,X29,X212) )
      & ( ~ hBOOL(hAPP(X29,X12))
       => c_List_OdropWhile(X5,X29,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile_Osimps_I2_J) ).

fof(fact_nat__number__of__Bit1,axiom,
    ! [X112] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X112)))
       => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X112)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X112)))
       => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X112)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X112)),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_eq__int__code_I14_J,axiom,
    ! [X265,X266] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X266)),c_Int_OBit1(X265))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__int__code_I14_J) ).

fof(fact_upt__rec__number__of,axiom,
    ! [X98,X99] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X98)))
       => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X98)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X98))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X98)))
       => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X98)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__rec__number__of) ).

fof(fact_eq__int__code_I4_J,axiom,
    ! [X265] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X265))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__int__code_I4_J) ).

fof(fact_iszero__number__of__Bit1,axiom,
    ! [X132,X15] :
      ( ( class_Int_Onumber__ring(X15)
        & class_Int_Oring__char__0(X15) )
     => ~ c_Int_Oiszero(X15,hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OBit1(X132))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__number__of__Bit1) ).

fof(fact_dropWhile__eq__Cons__conv,axiom,
    ! [X214,X27,X212,X29,X5] :
      ( c_List_OdropWhile(X5,X29,X212) = hAPP(hAPP(c_List_Olist_OCons(X5),X27),X214)
    <=> ( X212 = hAPP(hAPP(c_List_Oappend(X5),c_List_OtakeWhile(X5,X29,X212)),hAPP(hAPP(c_List_Olist_OCons(X5),X27),X214))
        & ~ hBOOL(hAPP(X29,X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__eq__Cons__conv) ).

fof(fact_not__iszero__Numeral1,axiom,
    ! [X15] :
      ( class_Int_Onumber__ring(X15)
     => ~ c_Int_Oiszero(X15,hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OBit1(c_Int_OPls))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__iszero__Numeral1) ).

fof(fact_removeAll__id,axiom,
    ! [X212,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => hAPP(c_List_OremoveAll(X5,X12),X212) = X212 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll__id) ).

fof(fact_removeAll__filter__not,axiom,
    ! [X212,X5,X12,X29] :
      ( ~ hBOOL(hAPP(X29,X12))
     => hAPP(c_List_OremoveAll(X5,X12),hAPP(c_List_Ofilter(X5,X29),X212)) = hAPP(c_List_Ofilter(X5,X29),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll__filter__not) ).

fof(fact_Suc__nat__number__of__add,axiom,
    ! [X98,X126] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),X98)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X98) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),X98)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X126))),X98) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__nat__number__of__add) ).

fof(fact_upt__Suc,axiom,
    ! [X101,X102] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X101))
       => c_List_Oupt(X102,hAPP(c_Nat_OSuc,X101)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X102,X101)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X101),c_List_Olist_ONil(tc_Nat_Onat))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X101))
       => c_List_Oupt(X102,hAPP(c_Nat_OSuc,X101)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__Suc) ).

fof(fact_eq__int__code_I11_J,axiom,
    ! [X266] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X266)),c_Int_OMin)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__int__code_I11_J) ).

fof(fact_upt__rec,axiom,
    ! [X101,X102] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X101))
       => c_List_Oupt(X102,X101) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X102),c_List_Oupt(hAPP(c_Nat_OSuc,X102),X101)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X101))
       => c_List_Oupt(X102,X101) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__rec) ).

fof(fact_eq__int__code_I7_J,axiom,
    ! [X265] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X265))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__int__code_I7_J) ).

fof(fact_nat__number__of__add__1,axiom,
    ! [X126] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X126),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),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),X126),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X126)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__add__1) ).

fof(fact_nat__number__of__diff__1,axiom,
    ! [X126] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X126),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),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),X126),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X126)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__diff__1) ).

fof(fact_nat__1__add__number__of,axiom,
    ! [X126] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X126),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),X126)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X126),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),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X126)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__add__number__of) ).

fof(fact_Suc__nat__number__of,axiom,
    ! [X126] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X126)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__nat__number__of) ).

fof(fact_member__rec_I2_J,axiom,
    ! [X22,X15] : ~ hBOOL(hAPP(hAPP(c_List_Omember(X15),c_List_Olist_ONil(X15)),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_member__rec_I2_J) ).

fof(fact_adjust__def,axiom,
    ! [X17] : c_Divides_Oadjust(X17) = 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)),X17))))),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)),X17))))),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,
    ! [X100] : c_Int_Osucc(c_Int_OBit0(X100)) = c_Int_OBit1(X100),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__Bit0) ).

fof(fact_Bit0__def,axiom,
    ! [X100] : c_Int_OBit0(X100) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X100),X100),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).

fof(fact_diff__bin__simps_I2_J,axiom,
    ! [X100] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X100),c_Int_OMin) = c_Int_Osucc(X100),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I2_J) ).

fof(fact_prod__fun__imageE,axiom,
    ! [X36,X1,X2,X55,X38,X21,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),X21),hAPP(c_Set_Oimage(tc_prod(X38,X55),tc_prod(X5,X16),c_Product__Type_Omap__pair(X38,X5,X55,X16,X2,X1)),X36)))
     => ~ ! [X3,X33] :
            ( X21 = hAPP(hAPP(c_Product__Type_OPair(X5,X16),hAPP(X2,X3)),hAPP(X1,X33))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X38,X55)),hAPP(hAPP(c_Product__Type_OPair(X38,X55),X3),X33)),X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod__fun__imageE) ).

fof(fact_divmod__int__pdivmod,axiom,
    ! [X97,X30] :
      ( ( X30 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odivmod__int(X30,X97) = 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)) )
      & ( X30 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( X97 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(X30,X97) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30) )
          & ( X97 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(X30,X97) = 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,X97))),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)),X97)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X97),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X30,X97)),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),X97))))),c_Divides_Opdivmod(X30,X97)))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__pdivmod) ).

fof(fact_apsnd__def,axiom,
    ! [X2,X5,X38,X16] : c_Product__Type_Oapsnd(X16,X38,X5,X2) = c_Product__Type_Omap__pair(X5,X5,X16,X38,c_Fun_Oid(X5),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__def) ).

fof(fact_divmod__int__code,axiom,
    ! [X97,X30] :
      ( ( X30 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odivmod__int(X30,X97) = 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)) )
      & ( X30 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( X97 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(X30,X97) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30) )
          & ( X97 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(X30,X97) = 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,X97))),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,X30)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X97))),c_Divides_Opdivmod(X30,X97)),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),X97))))),c_Divides_Opdivmod(X30,X97)))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__code) ).

fof(fact_Nitpick_Oplus__frac__def,axiom,
    ! [X34,X149,X5] : c_Nitpick_Oplus__frac(X5,X149,X34) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X5),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X5),X149),hAPP(c_Nitpick_Odenom(X5),X34))),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),X149))),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),X149))))),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),X34))),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),X34)))))),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,
    ! [X27,X12,X34,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)))),X34)),c_fequal),X12),X27))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),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,
    ! [X34,X149,X17] : hAPP(c_Divides_Oadjust(X17),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X149),X34)) = 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),X34),X17)),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)))),X149)),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)))),X149)),X34))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_adjust__eq) ).

fof(fact_trancl__insert,axiom,
    ! [X34,X12,X27,X5] : c_Transitive__Closure_Otrancl(X5,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X27),X12)),X34)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X34)),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)),X27))),c_Transitive__Closure_Ortrancl(X5,X34))))),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),X12))),c_Transitive__Closure_Ortrancl(X5,X34)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__insert) ).

fof(fact_trancl__unfold__left,axiom,
    ! [X34,X5] : c_Transitive__Closure_Otrancl(X5,X34) = hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X34),c_Transitive__Closure_Ortrancl(X5,X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__unfold__left) ).

fof(fact_map__add__map__of__foldr,axiom,
    ! [X211,X45,X16,X5] : c_Map_Omap__add(X5,X16,X45,hAPP(c_Map_Omap__of(X5,X16),X211)) = c_List_Ofoldr(tc_prod(X5,X16),tc_fun(X5,tc_Option_Ooption(X16)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_fun(tc_fun(X5,tc_Option_Ooption(X16)),tc_fun(X5,tc_Option_Ooption(X16)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_Option_Ooption(X16)),tc_fun(X16,tc_fun(tc_fun(X5,tc_Option_Ooption(X16)),tc_fun(X5,tc_Option_Ooption(X16))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X16),tc_fun(tc_fun(X5,tc_Option_Ooption(X16)),tc_fun(X5,tc_Option_Ooption(X16)))),tc_fun(tc_fun(X16,tc_Option_Ooption(X16)),tc_fun(X16,tc_fun(tc_fun(X5,tc_Option_Ooption(X16)),tc_fun(X5,tc_Option_Ooption(X16))))),X5),c_COMBB(tc_Option_Ooption(X16),tc_fun(tc_fun(X5,tc_Option_Ooption(X16)),tc_fun(X5,tc_Option_Ooption(X16))),X16)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_Option_Ooption(X16)),tc_fun(tc_Option_Ooption(X16),tc_fun(X5,tc_Option_Ooption(X16)))),tc_fun(tc_Option_Ooption(X16),tc_fun(tc_fun(X5,tc_Option_Ooption(X16)),tc_fun(X5,tc_Option_Ooption(X16)))),X5),c_COMBC(tc_fun(X5,tc_Option_Ooption(X16)),tc_Option_Ooption(X16),tc_fun(X5,tc_Option_Ooption(X16)))),hAPP(c_COMBC(tc_fun(X5,tc_Option_Ooption(X16)),X5,tc_fun(tc_Option_Ooption(X16),tc_fun(X5,tc_Option_Ooption(X16)))),c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)))))),c_Option_Ooption_OSome(X16))),X211,X45),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__map__of__foldr) ).

fof(fact_foldr__foldl,axiom,
    ! [X6,X212,X2,X5,X16] : c_List_Ofoldr(X16,X5,X2,X212,X6) = hAPP(c_List_Ofoldl(X5,X16,hAPP(c_COMBC(X16,X5,X5),X2),X6),hAPP(c_List_Orev(X16),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldr__foldl) ).

fof(fact_SUP2__E,axiom,
    ! [X21,X17,X13,X11,X38,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_fun(X38,tc_HOL_Obool))),X11),X13),X17),X21))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
           => ~ hBOOL(hAPP(hAPP(hAPP(X13,X3),X17),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP2__E) ).

fof(fact_sum__power2__le__zero__iff,axiom,
    ! [X27,X12,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),X12),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),X27),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)))
      <=> ( X12 = c_Groups_Ozero__class_Ozero(X5)
          & X27 = 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,
    ! [X256,X212,X12,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),X12),X212)),X256)))
     => c_List_Otranspose(X5,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)),X256)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),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))))),X256)))),c_List_Otranspose(X5,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),X212),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)))))),X256))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose_Opsimps_I3_J) ).

fof(fact_concat__conv__foldl,axiom,
    ! [X256,X5] : c_List_Oconcat(X5,X256) = hAPP(c_List_Ofoldl(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Oappend(X5),c_List_Olist_ONil(X5)),X256),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__conv__foldl) ).

fof(fact_transpose_Osimps_I3_J,axiom,
    ! [X256,X212,X12,X5] : c_List_Otranspose(X5,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)),X256)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),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))))),X256)))),c_List_Otranspose(X5,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),X212),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)))))),X256))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose_Osimps_I3_J) ).

fof(fact_odd__power__less__zero,axiom,
    ! [X98,X25,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),c_Groups_Ozero__class_Ozero(X15)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),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)))),X98)))),c_Groups_Ozero__class_Ozero(X15))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__power__less__zero) ).

fof(fact_rel__compE,axiom,
    ! [X84,X34,X38,X209,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),X209),hAPP(hAPP(c_Relation_Orel__comp(X5,X38,X16),X34),X84)))
     => ~ ! [X3,X33,X44] :
            ( X209 = hAPP(hAPP(c_Product__Type_OPair(X5,X16),X3),X44)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X38)),hAPP(hAPP(c_Product__Type_OPair(X5,X38),X3),X33)),X34))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X38,X16)),hAPP(hAPP(c_Product__Type_OPair(X38,X16),X33),X44)),X84)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__compE) ).

fof(fact_odd__0__le__power__imp__0__le,axiom,
    ! [X98,X25,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),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)))),X98)))))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__0__le__power__imp__0__le) ).

fof(fact_Cons__eq__filter__iff,axiom,
    ! [X214,X29,X212,X12,X5] :
      ( hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212) = hAPP(c_List_Ofilter(X5,X29),X214)
    <=> ? [X243,X248] :
          ( X214 = hAPP(hAPP(c_List_Oappend(X5),X243),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X248))
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X243)))
             => ~ hBOOL(hAPP(X29,X3)) )
          & hBOOL(hAPP(X29,X12))
          & X212 = hAPP(c_List_Ofilter(X5,X29),X248) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__eq__filter__iff) ).

fof(fact_filter__eq__Cons__iff,axiom,
    ! [X212,X12,X214,X29,X5] :
      ( hAPP(c_List_Ofilter(X5,X29),X214) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)
    <=> ? [X243,X248] :
          ( X214 = hAPP(hAPP(c_List_Oappend(X5),X243),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X248))
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X243)))
             => ~ hBOOL(hAPP(X29,X3)) )
          & hBOOL(hAPP(X29,X12))
          & X212 = hAPP(c_List_Ofilter(X5,X29),X248) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__eq__Cons__iff) ).

fof(fact_power2__sum,axiom,
    ! [X22,X14,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X14),X22)),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(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),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(X15),X22),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(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X14)),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__sum) ).

fof(fact_power2__diff,axiom,
    ! [X22,X14,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X14),X22)),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(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),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(X15),X22),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(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X14)),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__diff) ).

fof(fact_Nitpick_Osetsum_H__def,axiom,
    ! [X2,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
         => c_Nitpick_Osetsum_H(X5,X16,X2,X11) = hAPP(c_List_Omonoid__add__class_Olistsum(X16),hAPP(hAPP(c_List_Omap(X5,X16),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))),X11))),c_List_Odistinct(X5))))) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
         => c_Nitpick_Osetsum_H(X5,X16,X2,X11) = c_Groups_Ozero__class_Ozero(X16) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Osetsum_H__def) ).

fof(fact_sum__power2__gt__zero__iff,axiom,
    ! [X27,X12,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),X12),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),X27),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
      <=> ( X12 != c_Groups_Ozero__class_Ozero(X5)
          | X27 != 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,
    ! [X256,X16,X212,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)),X212))),c_List_Ofoldr(tc_List_Olist(X16),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X16)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X16))),X256,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)),X212)),c_List_Ofoldr(tc_List_Olist(X16),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X16)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X16),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X16)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X16)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X16),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X16)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X16),tc_List_Olist(X16),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X16)))),X256),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__aux__max) ).

fof(fact_sublist__shift__lemma,axiom,
    ! [X70,X212,X11,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))),X11)),hAPP(hAPP(c_List_Ozip(X5,tc_Nat_Onat),X212),c_List_Oupt(X70,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X70),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))))) = 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))),X70))),X11)),hAPP(hAPP(c_List_Ozip(X5,tc_Nat_Onat),X212),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__shift__lemma) ).

fof(fact_sorted__list__of__set__range,axiom,
    ! [X76,X45] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45),X76)) = c_List_Oupt(X45,X76),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__list__of__set__range) ).

fof(fact_Random_Osimps,axiom,
    ! [X263,X1,X5,X264] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X264),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(X5,X1,X264,X263) = 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),X264),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(X5,X1,X264,X263) = 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,X263)),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),X264),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X263))),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,
    ! [X126,X99] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X99)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = 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)))),X99)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__div__eq__add3__div__number__of) ).

fof(fact_Suc__div__eq__add3__div,axiom,
    ! [X98,X99] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X99)))),X98) = 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)))),X99)),X98),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__div__eq__add3__div) ).

fof(fact_New__DSequence_Opos__not__seq__def,axiom,
    ! [X70,X253] : hAPP(c_New__DSequence_Opos__not__seq(X253),X70) = c_Lazy__Sequence_Ohb__not__seq(hAPP(X253,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)))),X70))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__not__seq__def) ).

fof(fact_mem__splitE,axiom,
    ! [X161,X21,X38,X16,X37,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X37),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X16,X38,tc_fun(X5,tc_HOL_Obool)),X21),X161)))
     => ~ ! [X3,X33] :
            ( X161 = hAPP(hAPP(c_Product__Type_OPair(X16,X38),X3),X33)
           => ~ hBOOL(hAPP(hAPP(c_member(X5),X37),hAPP(hAPP(X21,X3),X33))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__splitE) ).

fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
    ! [X56,X11,X12,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X16,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X16,X2,X37,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)),X56))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ~ ! [X33] :
                ( X56 = hAPP(hAPP(X2,X12),X33)
               => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X16,X2,X37,X11),X33)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE) ).

fof(fact_int__of__code,axiom,
    ! [X100] :
      ( ( X100 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Code__Numeral_Oint__of,X100) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X100 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => ( ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X100,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,X100) = 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),X100),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,X100,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,X100) = 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),X100),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,
    ! [X22,X14,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),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(X15),X22),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,X16,X11,X5] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),hAPP(c_Set_Oimage(X5,X16,X2),X11)))
       => ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
            & ~ 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)),X11))),hAPP(hAPP(c_COMBC(X5,X16,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X16,tc_fun(X16,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,
    ! [X214,X212,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)),X212),X214))))
         => 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))),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X214)
       => ( c_List_Oconcat(X5,X212) = c_List_Oconcat(X5,X214)
        <=> X212 = X214 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__eq__concat__iff) ).

fof(fact_concat__injective,axiom,
    ! [X214,X212,X5] :
      ( c_List_Oconcat(X5,X212) = c_List_Oconcat(X5,X214)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X214)
       => ( ! [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)),X212),X214))))
             => 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)) )
         => X212 = X214 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__injective) ).

fof(fact_nat__rec__add__eq__if,axiom,
    ! [X76,X56,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),X56)),X76)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X56))),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),X76))),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)),X76))),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)),X76))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__rec__add__eq__if) ).

fof(fact_add__Min__right,axiom,
    ! [X100] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X100),c_Int_OMin) = c_Int_Opred(X100),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Min__right) ).

fof(fact_neg__zmod__mult__2,axiom,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25),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)))),X26)),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)))),X25)) = 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),X26),c_Groups_Oone__class_Oone(tc_Int_Oint)),X25))),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,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25),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)))),X26))),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)))),X25)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__zdiv__mult__2) ).

fof(fact_pos__zdiv__mult__2,axiom,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
     => 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)))),X26))),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)))),X25)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zdiv__mult__2) ).

fof(fact_eq__number__of__Suc,axiom,
    ! [X76,X56] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56) = hAPP(c_Nat_OSuc,X76)
    <=> 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(X56))),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)),X76))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__Suc) ).

fof(fact_Suc__eq__number__of,axiom,
    ! [X56,X76] :
      ( hAPP(c_Nat_OSuc,X76) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56)
    <=> 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(X56))),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)),X76))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__number__of) ).

fof(fact_Nitpick_Ocard_H__def,axiom,
    ! [X11,X5] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => c_Nitpick_Ocard_H(X5,X11) = 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))),X11))),c_List_Odistinct(X5)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => c_Nitpick_Ocard_H(X5,X11) = 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,
    ! [X70,X67] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X67))
     => 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)),X67))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X70)))) = 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)),X67))),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,X70))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__less__Suc2) ).

fof(fact_power2__less__imp__less,axiom,
    ! [X22,X14,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),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(X15),X22),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(X15),c_Groups_Ozero__class_Ozero(X15)),X22))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__less__imp__less) ).

fof(fact_power2__le__imp__le,axiom,
    ! [X22,X14,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),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(X15),X22),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(X15),c_Groups_Ozero__class_Ozero(X15)),X22))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__le__imp__le) ).

fof(fact_vimage__if,axiom,
    ! [X13,X16,X20,X11,X21,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),X11))
           => hAPP(c_Set_Ovimage(X16,X5,hAPP(hAPP(c_COMBC(X16,X5,X5),hAPP(hAPP(c_COMBC(X16,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X16),c_If(X5)),hAPP(hAPP(c_COMBC(X16,tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool),c_member(X16)),X13))),X21)),X20)),X11) = c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X11))
           => hAPP(c_Set_Ovimage(X16,X5,hAPP(hAPP(c_COMBC(X16,X5,X5),hAPP(hAPP(c_COMBC(X16,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X16),c_If(X5)),hAPP(hAPP(c_COMBC(X16,tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool),c_member(X16)),X13))),X21)),X20)),X11) = X13 ) ) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),X11))
           => hAPP(c_Set_Ovimage(X16,X5,hAPP(hAPP(c_COMBC(X16,X5,X5),hAPP(hAPP(c_COMBC(X16,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X16),c_If(X5)),hAPP(hAPP(c_COMBC(X16,tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool),c_member(X16)),X13))),X21)),X20)),X11) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X16,tc_HOL_Obool)),X13) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X11))
           => hAPP(c_Set_Ovimage(X16,X5,hAPP(hAPP(c_COMBC(X16,X5,X5),hAPP(hAPP(c_COMBC(X16,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X16),c_If(X5)),hAPP(hAPP(c_COMBC(X16,tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool),c_member(X16)),X13))),X21)),X20)),X11) = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__if) ).

fof(fact_pos__zmod__mult__2,axiom,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
     => 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)))),X26)),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)))),X25)) = 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,X26,X25))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmod__mult__2) ).

fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
    ! [X126,X99] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X99))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = 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)))),X99),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mod__eq__add3__mod__number__of) ).

fof(fact_zero__le__even__power_H,axiom,
    ! [X98,X25,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),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)))),X98)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__even__power_H) ).

fof(fact_Suc__mod__eq__add3__mod,axiom,
    ! [X98,X99] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X99))),X98) = 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)))),X99),X98),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mod__eq__add3__mod) ).

fof(fact_mod__Suc__eq__mod__add3,axiom,
    ! [X98,X99] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X98)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,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)))),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__Suc__eq__mod__add3) ).

fof(fact_div__Suc__eq__div__add3,axiom,
    ! [X98,X99] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X98)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),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)))),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__Suc__eq__div__add3) ).

fof(fact_trancl__Int__subset,axiom,
    ! [X84,X34,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),X84))
     => ( 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,X34)),X84)),X34)),X84))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X34)),X84)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__Int__subset) ).

fof(fact_setprod__gen__delta,axiom,
    ! [X21,X17,X6,X35,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X35))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X17)),X21)),X35) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(X17,X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X16),X21),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X35)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X35))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X17)),X21)),X35) = hAPP(hAPP(c_Power_Opower__class_Opower(X16),X21),hAPP(c_Finite__Set_Ocard(X5),X35)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__gen__delta) ).

fof(fact_setsum__delta,axiom,
    ! [X17,X6,X35,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X35))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X17)),c_Groups_Ozero__class_Ozero(X16))),X35) = hAPP(X17,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X35))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X17)),c_Groups_Ozero__class_Ozero(X16))),X35) = c_Groups_Ozero__class_Ozero(X16) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__delta) ).

fof(fact_setprod__delta,axiom,
    ! [X17,X6,X35,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X35))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X17)),c_Groups_Oone__class_Oone(X16))),X35) = hAPP(X17,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X35))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X17)),c_Groups_Oone__class_Oone(X16))),X35) = c_Groups_Oone__class_Oone(X16) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__delta) ).

fof(fact_less__Suc__number__of,axiom,
    ! [X56,X76] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X76)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56)))
    <=> 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(X56))),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),X76)),c_Int_Onat))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__number__of) ).

fof(fact_le__Suc__number__of,axiom,
    ! [X56,X76] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X76)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56)))
    <=> 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(X56))),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),X76)),c_Int_Onat))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__number__of) ).

fof(fact_apsnd__apfst__commute,axiom,
    ! [X161,X1,X55,X2,X5,X16,X38] : hAPP(c_Product__Type_Oapsnd(X38,X16,X5,X2),hAPP(c_Product__Type_Oapfst(X55,X5,X38,X1),X161)) = hAPP(c_Product__Type_Oapfst(X55,X5,X16,X1),hAPP(c_Product__Type_Oapsnd(X38,X16,X55,X2),X161)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__apfst__commute) ).

fof(fact_apfst__def,axiom,
    ! [X2,X16,X38,X5] : c_Product__Type_Oapfst(X5,X38,X16,X2) = c_Product__Type_Omap__pair(X5,X38,X16,X16,X2,c_Fun_Oid(X16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apfst__def) ).

fof(fact_lexord__append__leftD,axiom,
    ! [X34,X56,X66,X12,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),X12),X66)),hAPP(hAPP(c_List_Oappend(X5),X12),X56))),c_List_Olexord(X5,X34)))
     => ( ! [X74] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X74),X74)),X34))
       => 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)),X66),X56)),c_List_Olexord(X5,X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__leftD) ).

fof(fact_rel__pow__E2,axiom,
    ! [X36,X76,X37,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X37)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X76),X36)))
     => ( ( X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => X12 != X37 )
       => ~ ! [X33,X94] :
              ( X76 = hAPP(c_Nat_OSuc,X94)
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X33)),X36))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X37)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X94),X36))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__E2) ).

fof(fact_map__comp__Some__iff,axiom,
    ! [X56,X30,X202,X203,X38,X5,X16] :
      ( c_Map_Omap__comp(X16,X5,X38,X203,X202,X30) = hAPP(c_Option_Ooption_OSome(X5),X56)
    <=> ? [X217] :
          ( hAPP(X202,X30) = hAPP(c_Option_Ooption_OSome(X16),X217)
          & hAPP(X203,X217) = hAPP(c_Option_Ooption_OSome(X5),X56) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__comp__Some__iff) ).

fof(fact_map__comp__def,axiom,
    ! [X30,X1,X2,X38,X5,X16] : c_Map_Omap__comp(X16,X5,X38,X2,X1,X30) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X5),X16,c_Option_Ooption_ONone(X5),X2),hAPP(X1,X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__comp__def) ).

fof(fact_power__odd__eq,axiom,
    ! [X98,X25,X15] :
      ( class_Groups_Omonoid__mult(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),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)))),X98))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)),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,
    ! [X12,X212,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X212))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => 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),X12)),hAPP(c_List_Orev(X5),X212)) = 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),X12)),X212))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__neq__rev) ).

fof(fact_dropWhile__eq__drop,axiom,
    ! [X212,X29,X5] : c_List_OdropWhile(X5,X29,X212) = hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X29,X212))),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__eq__drop) ).

fof(fact_apsnd__compose,axiom,
    ! [X12,X1,X55,X2,X5,X16,X38] : hAPP(c_Product__Type_Oapsnd(X38,X16,X5,X2),hAPP(c_Product__Type_Oapsnd(X55,X38,X5,X1),X12)) = hAPP(c_Product__Type_Oapsnd(X55,X16,X5,hAPP(c_Fun_Ocomp(X38,X16,X55,X2),X1)),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__compose) ).

fof(fact_apfst__compose,axiom,
    ! [X12,X1,X55,X2,X16,X5,X38] : hAPP(c_Product__Type_Oapfst(X38,X5,X16,X2),hAPP(c_Product__Type_Oapfst(X55,X38,X16,X1),X12)) = hAPP(c_Product__Type_Oapfst(X55,X5,X16,hAPP(c_Fun_Ocomp(X38,X5,X55,X2),X1)),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apfst__compose) ).

fof(fact_sum__power2__eq__zero__iff,axiom,
    ! [X27,X12,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),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),X27),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)
      <=> ( X12 = c_Groups_Ozero__class_Ozero(X5)
          & X27 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__eq__zero__iff) ).

fof(fact_transpose__rectangle,axiom,
    ! [X76,X5,X212] :
      ( ( X212 = c_List_Olist_ONil(tc_List_Olist(X5))
       => X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
     => ( ! [X145] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X145),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X212)))
           => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),X212),X145)) = X76 )
       => c_List_Otranspose(X5,X212) = 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)),X212))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X212)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X76)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__rectangle) ).

fof(fact_negDivAlg_Opinduct,axiom,
    ! [X29,X47,X158] :
      ( 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),X158),X47)))
     => ( ! [X74,X52] :
            ( 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),X74),X52)))
           => ( ( ~ ( 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),X74),X52)))
                    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X52),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
               => hBOOL(hAPP(hAPP(X29,X74),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)))),X52))) )
             => hBOOL(hAPP(hAPP(X29,X74),X52)) ) )
       => hBOOL(hAPP(hAPP(X29,X158),X47)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg_Opinduct) ).

fof(fact_setsum__delta_H,axiom,
    ! [X17,X6,X35,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X35))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(c_fequal,X6))),X17)),c_Groups_Ozero__class_Ozero(X16))),X35) = hAPP(X17,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X35))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(c_fequal,X6))),X17)),c_Groups_Ozero__class_Ozero(X16))),X35) = c_Groups_Ozero__class_Ozero(X16) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__delta_H) ).

fof(fact_setprod__delta_H,axiom,
    ! [X17,X6,X35,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X35))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(c_fequal,X6))),X17)),c_Groups_Oone__class_Oone(X16))),X35) = hAPP(X17,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X35))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(c_fequal,X6))),X17)),c_Groups_Oone__class_Oone(X16))),X35) = c_Groups_Oone__class_Oone(X16) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__delta_H) ).

fof(fact_posDivAlg_Opinduct,axiom,
    ! [X29,X47,X158] :
      ( 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),X158),X47)))
     => ( ! [X74,X52] :
            ( 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),X74),X52)))
           => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X74),X52))
                    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X52),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
               => hBOOL(hAPP(hAPP(X29,X74),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)))),X52))) )
             => hBOOL(hAPP(hAPP(X29,X74),X52)) ) )
       => hBOOL(hAPP(hAPP(X29,X158),X47)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg_Opinduct) ).

fof(fact_listrel__Cons2,axiom,
    ! [X34,X214,X27,X212,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)),X212),hAPP(hAPP(c_List_Olist_OCons(X5),X27),X214))),c_List_Olistrel(X5,X34)))
     => ~ ! [X3,X228] :
            ( X212 = hAPP(hAPP(c_List_Olist_OCons(X5),X3),X228)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X27)),X34))
             => ~ 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)),X228),X214)),c_List_Olistrel(X5,X34))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Cons2) ).

fof(fact_rel__pow__Suc__E2,axiom,
    ! [X36,X76,X37,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X37)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X76)),X36)))
     => ~ ! [X33] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X33)),X36))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X37)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X76),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__Suc__E2) ).

fof(fact_Nitpick_Otimes__frac__def,axiom,
    ! [X123,X128,X15] : c_Nitpick_Otimes__frac(X15,X128,X123) = hAPP(hAPP(c_Nitpick_Ofrac(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X15),X128)),hAPP(c_Nitpick_Onum(X15),X123))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(X15),X128)),hAPP(c_Nitpick_Odenom(X15),X123))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Otimes__frac__def) ).

fof(fact_rel__pow__E,axiom,
    ! [X36,X76,X37,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X37)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X76),X36)))
     => ( ( X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => X12 != X37 )
       => ~ ! [X33,X94] :
              ( X76 = hAPP(c_Nat_OSuc,X94)
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X33)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X94),X36)))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X37)),X36)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__E) ).

fof(fact_rel__pow__Suc__E,axiom,
    ! [X36,X76,X37,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X37)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X76)),X36)))
     => ~ ! [X33] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X33)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X76),X36)))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X37)),X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__Suc__E) ).

fof(fact_negDivAlg_Opsimps,axiom,
    ! [X17,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),X17)))
     => ( ( ( 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),X17)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
         => c_Divides_OnegDivAlg(X6,X17) = 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),X17)) )
        & ( ~ ( 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),X17)))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
         => c_Divides_OnegDivAlg(X6,X17) = hAPP(c_Divides_Oadjust(X17),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)))),X17))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg_Opsimps) ).

fof(fact_posDivAlg_Opsimps,axiom,
    ! [X17,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),X17)))
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X17))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
         => c_Divides_OposDivAlg(X6,X17) = 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),X17))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
         => c_Divides_OposDivAlg(X6,X17) = hAPP(c_Divides_Oadjust(X17),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)))),X17))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg_Opsimps) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
    ! [X98,X14,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),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)))),X98))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),X98)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),X98))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) ).

fof(fact_arith__series__int,axiom,
    ! [X76,X20,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))),X20))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X76))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X76)),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),X76),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X20)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__series__int) ).

fof(fact_less__number__of__Suc,axiom,
    ! [X76,X56] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56)),hAPP(c_Nat_OSuc,X76)))
    <=> 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(X56))),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)),X76)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of__Suc) ).

fof(fact_le__number__of__Suc,axiom,
    ! [X76,X56] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56)),hAPP(c_Nat_OSuc,X76)))
    <=> 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(X56))),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)),X76)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__number__of__Suc) ).

fof(fact_of__nat__double,axiom,
    ! [X14,X15] :
      ( class_Rings_Osemiring__1(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),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)))),X14))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),hAPP(c_Int_Onat,X14))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),hAPP(c_Int_Onat,X14))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__double) ).

fof(fact_negDivAlg_Osimps,axiom,
    ! [X26,X25] :
      ( ( ( 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),X25),X26)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
       => c_Divides_OnegDivAlg(X25,X26) = 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),X25),X26)) )
      & ( ~ ( 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),X25),X26)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
       => c_Divides_OnegDivAlg(X25,X26) = hAPP(c_Divides_Oadjust(X26),c_Divides_OnegDivAlg(X25,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)))),X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg_Osimps) ).

fof(fact_posDivAlg_Osimps,axiom,
    ! [X26,X25] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),X26))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
       => c_Divides_OposDivAlg(X25,X26) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25) )
      & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),X26))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
       => c_Divides_OposDivAlg(X25,X26) = hAPP(c_Divides_Oadjust(X26),c_Divides_OposDivAlg(X25,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)))),X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg_Osimps) ).

fof(fact_power__minus1__odd,axiom,
    ! [X98,X15] :
      ( class_Rings_Oring__1(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),c_Groups_Oone__class_Oone(X15))),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)))),X98))) = hAPP(c_Groups_Ouminus__class_Ouminus(X15),c_Groups_Oone__class_Oone(X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus1__odd) ).

fof(fact_power__minus__even,axiom,
    ! [X98,X25,X15] :
      ( class_Rings_Oring__1(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)),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)))),X98)) = hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),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)))),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus__even) ).

fof(fact_power__m1__odd,axiom,
    ! [X98,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),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)))),X98))) = hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OMin) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__m1__odd) ).

fof(fact_Suc3__eq__add__3,axiom,
    ! [X98] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X98))) = 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)))),X98),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc3__eq__add__3) ).

fof(fact_ImageE,axiom,
    ! [X11,X34,X16,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(c_Relation_OImage(X16,X5,X34),X11)))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X5)),hAPP(hAPP(c_Product__Type_OPair(X16,X5),X3),X17)),X34))
           => ~ hBOOL(hAPP(hAPP(c_member(X16),X3),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ImageE) ).

fof(fact_n__lists_Osimps_I2_J,axiom,
    ! [X212,X76,X5] : c_Enum_On__lists(X5,hAPP(c_Nat_OSuc,X76),X212) = 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)))),X212)),c_Enum_On__lists(X5,X76,X212))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__lists_Osimps_I2_J) ).

fof(fact_nat__case__add__eq__if,axiom,
    ! [X76,X56,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),X56)),X76)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X56))),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,X76))),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)),X76)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__add__eq__if) ).

fof(fact_mod2__gr__0,axiom,
    ! [X45] :
      ( 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,X45,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,X45,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,X12,X2,X5,X16,X38] :
      ( hAPP(c_Product__Type_Oapsnd(X38,X16,X5,X2),X12) = hAPP(c_Product__Type_Oapsnd(X38,X16,X5,X1),X12)
    <=> hAPP(X2,hAPP(c_Product__Type_Osnd(X5,X38),X12)) = hAPP(X1,hAPP(c_Product__Type_Osnd(X5,X38),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__eq__conv) ).

fof(fact_apfst__eq__conv,axiom,
    ! [X1,X12,X2,X16,X5,X38] :
      ( hAPP(c_Product__Type_Oapfst(X38,X5,X16,X2),X12) = hAPP(c_Product__Type_Oapfst(X38,X5,X16,X1),X12)
    <=> hAPP(X2,hAPP(c_Product__Type_Ofst(X38,X16),X12)) = hAPP(X1,hAPP(c_Product__Type_Ofst(X38,X16),X12)) ),
    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,
    ! [X12,X1,X55,X2,X5,X16,X38] : hAPP(c_Product__Type_Oapsnd(X38,X16,X5,X2),hAPP(c_Product__Type_Oapfst(X55,X5,X38,X1),X12)) = hAPP(hAPP(c_Product__Type_OPair(X5,X16),hAPP(X1,hAPP(c_Product__Type_Ofst(X55,X38),X12))),hAPP(X2,hAPP(c_Product__Type_Osnd(X55,X38),X12))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__apfst) ).

fof(fact_apfst__apsnd,axiom,
    ! [X12,X1,X55,X2,X16,X5,X38] : hAPP(c_Product__Type_Oapfst(X38,X5,X16,X2),hAPP(c_Product__Type_Oapsnd(X55,X16,X38,X1),X12)) = hAPP(hAPP(c_Product__Type_OPair(X5,X16),hAPP(X2,hAPP(c_Product__Type_Ofst(X38,X55),X12))),hAPP(X1,hAPP(c_Product__Type_Osnd(X38,X55),X12))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apfst__apsnd) ).

fof(fact_half__gt__zero__iff,axiom,
    ! [X34,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),X34),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)),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_half__gt__zero__iff) ).

fof(fact_max__Suc__number__of,axiom,
    ! [X76,X56] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56)),hAPP(c_Nat_OSuc,X76)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X56))),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,X76))),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)),X76)))),
    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,
    ! [X76,X56] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56)),hAPP(c_Nat_OSuc,X76)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X56))),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)),X76)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__Suc__number__of) ).

fof(fact_nat__rec__number__of,axiom,
    ! [X56,X2,X6,X5] : hAPP(c_Nat_Onat_Onat__rec(X5,X6,X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X56))),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,
    ! [X256,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))))),X256)) = 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)))),X256)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__aux__filter__head) ).

fof(fact_transpose__aux__filter__tail,axiom,
    ! [X256,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)))))),X256)) = 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)))),X256)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__aux__filter__tail) ).

fof(fact_rtrancl__Int__subset,axiom,
    ! [X34,X84,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Relation_OId(X5)),X84))
     => ( 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,X34)),X84)),X34)),X84))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X34)),X84)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__Int__subset) ).

fof(fact_listrel__Cons1,axiom,
    ! [X34,X212,X214,X27,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),X27),X214)),X212)),c_List_Olistrel(X5,X34)))
     => ~ ! [X33,X229] :
            ( X212 = hAPP(hAPP(c_List_Olist_OCons(X5),X33),X229)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X27),X33)),X34))
             => ~ 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)),X214),X229)),c_List_Olistrel(X5,X34))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Cons1) ).

fof(fact_power__even__eq,axiom,
    ! [X98,X25,X15] :
      ( class_Groups_Omonoid__mult(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),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)))),X98)) = hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)),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,
    ! [X11,X212,X5] : c_List_Osublist(X5,X212,X11) = 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))),X11)),hAPP(hAPP(c_List_Ozip(X5,tc_Nat_Onat),X212),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__def) ).

fof(fact_fold1Set_Oequations,axiom,
    ! [X51,X46,X47,X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,hAPP(hAPP(c_Set_Oinsert(X5),X47),X46)),X51))
    <=> ? [X74,X75] :
          ( hAPP(hAPP(c_Set_Oinsert(X5),X47),X46) = hAPP(hAPP(c_Set_Oinsert(X5),X74),X75)
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,X2,X74,X75),X51))
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X74),X75)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1Set_Oequations) ).

fof(fact_Nitpick_Ouminus__frac__def,axiom,
    ! [X128,X15] : c_Nitpick_Ouminus__frac(X15,X128) = c_Nitpick_OAbs__Frac(X15,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(X15),X128))),hAPP(c_Nitpick_Odenom(X15),X128))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Ouminus__frac__def) ).

fof(fact_snd__apsnd,axiom,
    ! [X12,X2,X38,X5,X16] : hAPP(c_Product__Type_Osnd(X16,X5),hAPP(c_Product__Type_Oapsnd(X38,X5,X16,X2),X12)) = hAPP(X2,hAPP(c_Product__Type_Osnd(X16,X38),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__apsnd) ).

fof(fact_fst__apfst,axiom,
    ! [X12,X2,X38,X16,X5] : hAPP(c_Product__Type_Ofst(X5,X16),hAPP(c_Product__Type_Oapfst(X38,X5,X16,X2),X12)) = hAPP(X2,hAPP(c_Product__Type_Ofst(X38,X16),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__apfst) ).

fof(fact_fst__apsnd,axiom,
    ! [X12,X2,X38,X16,X5] : hAPP(c_Product__Type_Ofst(X5,X16),hAPP(c_Product__Type_Oapsnd(X38,X16,X5,X2),X12)) = hAPP(c_Product__Type_Ofst(X5,X38),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__apsnd) ).

fof(fact_snd__apfst,axiom,
    ! [X12,X2,X38,X5,X16] : hAPP(c_Product__Type_Osnd(X16,X5),hAPP(c_Product__Type_Oapfst(X38,X16,X5,X2),X12)) = hAPP(c_Product__Type_Osnd(X38,X5),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__apfst) ).

fof(fact_small_H_Opinduct,axiom,
    ! [X29,X46,X47,X158] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X158),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X47),X46))))
     => ( ! [X43,X125,X145] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X43),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X125),X145))))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X125),X145))
               => ( hAPP(X43,X145) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
                 => hBOOL(hAPP(hAPP(hAPP(X29,X43),X125),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X145),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) )
             => hBOOL(hAPP(hAPP(hAPP(X29,X43),X125),X145)) ) )
       => hBOOL(hAPP(hAPP(hAPP(X29,X158),X47),X46)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small_H_Opinduct) ).

fof(fact_nat__case__number__of,axiom,
    ! [X56,X2,X6,X5] : c_Nat_Onat_Onat__case(X5,X6,X2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X56))),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,
    ! [X56,X76] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X76)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X56))),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,X76))),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),X76)),c_Int_Onat)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__number__of__Suc) ).

fof(fact_min__number__of__Suc,axiom,
    ! [X56,X76] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X76)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X56))),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),X76)),c_Int_Onat)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__number__of__Suc) ).

fof(fact_Suc__n__div__2__gt__zero,axiom,
    ! [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),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),X98),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,
    ! [X123,X15] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X15)
        & class_Int_Onumber__ring(X15) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X123))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X123),hAPP(c_Int_Onumber__class_Onumber__of(X15),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,
    ! [X98,X14,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),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)))),X98)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),X98)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).

fof(fact_div__2__gt__zero,axiom,
    ! [X98] :
      ( 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(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X98),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,
    ! [X25,X15] :
      ( class_Groups_Omonoid__mult(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),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(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X25)),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power3__eq__cube) ).

fof(fact_zero__le__power2,axiom,
    ! [X25,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),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,
    ! [X98,X15] :
      ( class_Rings_Oring__1(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),c_Groups_Oone__class_Oone(X15))),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)))),X98)) = c_Groups_Oone__class_Oone(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus1__even) ).

fof(fact_power__m1__even,axiom,
    ! [X98,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),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)))),X98)) = c_Groups_Oone__class_Oone(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__m1__even) ).

fof(fact_diff__nat__number__of,axiom,
    ! [X56,X168] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X168),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X168),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)) = 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),X56),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X168)))),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,
    ! [X212,X2,X16,X29,X5] : c_List_OdropWhile(X5,X29,hAPP(hAPP(c_List_Omap(X16,X5),X2),X212)) = hAPP(hAPP(c_List_Omap(X16,X5),X2),c_List_OdropWhile(X16,hAPP(c_Fun_Ocomp(X5,tc_HOL_Obool,X16,X29),X2),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__map) ).

fof(fact_diff__nat__eq__if,axiom,
    ! [X37,X170] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X170))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X37)),hAPP(c_Int_Onat,X170)) = hAPP(c_Int_Onat,X37) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X170))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X37)),hAPP(c_Int_Onat,X170)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X37),X170)),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,
    ! [X12,X212,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X212))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => 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),X12)),hAPP(c_List_Orev(X5),X212)) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),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),X12)),X212))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__neq__rev) ).

fof(fact_fold__graph__permute__diff,axiom,
    ! [X6,X12,X11,X17,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X17,X11),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X17),X11))
           => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X6,hAPP(hAPP(c_Set_Oinsert(X5),X17),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),X12)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph__permute__diff) ).

fof(fact_concat__map__singleton,axiom,
    ! [X212,X2,X16,X5] : c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(X16,tc_List_Olist(X5)),hAPP(hAPP(c_COMBC(X16,tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),X16),c_List_Olist_OCons(X5)),X2)),c_List_Olist_ONil(X5))),X212)) = hAPP(hAPP(c_List_Omap(X16,X5),X2),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__map__singleton) ).

fof(fact_Nitpick_Oless__eq__frac__def,axiom,
    ! [X34,X149,X5] :
      ( c_Nitpick_Oless__eq__frac(X5,X149,X34)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X5),c_Nitpick_Oplus__frac(X5,X149,c_Nitpick_Ouminus__frac(X5,X34)))),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,
    ! [X34,X149,X5] :
      ( c_Nitpick_Oless__frac(X5,X149,X34)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X5),c_Nitpick_Oplus__frac(X5,X149,c_Nitpick_Ouminus__frac(X5,X34)))),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,
    ! [X22,X14,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),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(X15),X22),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(X15),c_Groups_Ozero__class_Ozero(X15)),X14))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X22))
           => X14 = X22 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__imp__eq) ).

fof(fact_less__2__cases,axiom,
    ! [X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
     => ( X98 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X98 = 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,
    ! [X99] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X99))),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),X99),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,
    ! [X25,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),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(X15),X25),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,
    ! [X128,X15,X5] :
      ( ( class_Rings_Oinverse(X5)
        & class_Rings_Oring__1(X5) )
     => c_Nitpick_Oof__frac(X15,X5,X128) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),hAPP(c_Nitpick_Onum(X15),X128))),hAPP(c_Int_Oring__1__class_Oof__int(X5),hAPP(c_Nitpick_Odenom(X15),X128))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Oof__frac__def) ).

fof(fact_converseE,axiom,
    ! [X34,X201,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),X201),hAPP(c_Relation_Oconverse(X16,X5),X34)))
     => ~ ! [X3,X33] :
            ( X201 = hAPP(hAPP(c_Product__Type_OPair(X5,X16),X33),X3)
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X5)),hAPP(hAPP(c_Product__Type_OPair(X16,X5),X3),X33)),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converseE) ).

fof(fact_setsum__natinterval__difff,axiom,
    ! [X2,X76,X45,X5] :
      ( class_Groups_Oab__group__add(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76))
         => 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,X45,X76)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(X2,X45)),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X76),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76))
         => 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,X45,X76)) = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__natinterval__difff) ).

fof(fact_map__upd__upds__conv__if,axiom,
    ! [X27,X2,X212,X214,X16,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)),X212))))
       => c_Map_Omap__upds(X5,X16,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),X2),X12),hAPP(c_Option_Ooption_OSome(X16),X27)),X212,X214) = c_Map_Omap__upds(X5,X16,X2,X212,X214) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)),X212))))
       => c_Map_Omap__upds(X5,X16,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),X2),X12),hAPP(c_Option_Ooption_OSome(X16),X27)),X212,X214) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),c_Map_Omap__upds(X5,X16,X2,X212,X214)),X12),hAPP(c_Option_Ooption_OSome(X16),X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__upd__upds__conv__if) ).

fof(fact_fold__graph__insert__swap,axiom,
    ! [X37,X27,X11,X17,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X17,X11),X27))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X17),X11))
         => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X37,hAPP(hAPP(c_Set_Oinsert(X5),X17),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X37),X27))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph__insert__swap) ).

fof(fact_fold__graph_OinsertI,axiom,
    ! [X27,X37,X2,X16,X11,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X16,X2,X37,X11),X27))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X16,X2,X37,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)),hAPP(hAPP(X2,X12),X27))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_OinsertI) ).

fof(fact_map__comp__None__iff,axiom,
    ! [X30,X202,X203,X38,X5,X16] :
      ( c_Map_Omap__comp(X16,X5,X38,X203,X202,X30) = c_Option_Ooption_ONone(X5)
    <=> ( hAPP(X202,X30) = c_Option_Ooption_ONone(X16)
        | ? [X217] :
            ( hAPP(X202,X30) = hAPP(c_Option_Ooption_OSome(X16),X217)
            & hAPP(X203,X217) = c_Option_Ooption_ONone(X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__comp__None__iff) ).

fof(fact_tranclD,axiom,
    ! [X36,X27,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_Transitive__Closure_Otrancl(X5,X36)))
     => ? [X44] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X44)),X36))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X44),X27)),c_Transitive__Closure_Ortrancl(X5,X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclD) ).

fof(fact_tranclD2,axiom,
    ! [X36,X27,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_Transitive__Closure_Otrancl(X5,X36)))
     => ? [X44] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X44)),c_Transitive__Closure_Ortrancl(X5,X36)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X44),X27)),X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclD2) ).

fof(fact_apfst__conv,axiom,
    ! [X27,X12,X2,X16,X5,X38] : hAPP(c_Product__Type_Oapfst(X38,X5,X16,X2),hAPP(hAPP(c_Product__Type_OPair(X38,X16),X12),X27)) = hAPP(hAPP(c_Product__Type_OPair(X5,X16),hAPP(X2,X12)),X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apfst__conv) ).

fof(fact_apsnd__conv,axiom,
    ! [X27,X12,X2,X5,X16,X38] : hAPP(c_Product__Type_Oapsnd(X38,X16,X5,X2),hAPP(hAPP(c_Product__Type_OPair(X5,X38),X12),X27)) = hAPP(hAPP(c_Product__Type_OPair(X5,X16),X12),hAPP(X2,X27)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__conv) ).

fof(fact_map__upds__twist,axiom,
    ! [X234,X17,X45,X16,X235,X6,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_List_Oset(X5),X235)))
     => c_Map_Omap__upds(X5,X16,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),X45),X6),hAPP(c_Option_Ooption_OSome(X16),X17)),X235,X234) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),c_Map_Omap__upds(X5,X16,X45,X235,X234)),X6),hAPP(c_Option_Ooption_OSome(X16),X17)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__upds__twist) ).

fof(fact_list__ex1__simps_I2_J,axiom,
    ! [X212,X12,X29,X5] :
      ( c_List_Olist__ex1(X5,X29,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212))
    <=> ( ( hBOOL(hAPP(X29,X12))
         => 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),X29))),hAPP(c_fequal,X12)),X212) )
        & ( ~ hBOOL(hAPP(X29,X12))
         => c_List_Olist__ex1(X5,X29,X212) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex1__simps_I2_J) ).

fof(fact_transpose__max__length,axiom,
    ! [X212,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,X212),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)))),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__max__length) ).

fof(fact_dropWhile__nth,axiom,
    ! [X212,X29,X5,X115] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X115),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OdropWhile(X5,X29,X212))))
     => hAPP(hAPP(c_List_Onth(X5),c_List_OdropWhile(X5,X29,X212)),X115) = hAPP(hAPP(c_List_Onth(X5),X212),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X115),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X29,X212)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__nth) ).

fof(fact_zmod__number__of__Bit0,axiom,
    ! [X132,X126] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X132))) = 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),X126),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__number__of__Bit0) ).

fof(fact_power2__abs,axiom,
    ! [X25,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),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(X15),X25),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,
    ! [X25,X15] :
      ( class_Rings_Oring__1(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)),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(X15),X25),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,
    ! [X99] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X99)),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,X99,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,
    ! [X29,X11,X90,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X90))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X90),X11))
       => ( hBOOL(hAPP(X29,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
         => ( ! [X74,X106] :
                ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X106))
               => ( hBOOL(hAPP(hAPP(c_member(X5),X74),X11))
                 => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X74),X106))
                   => ( hBOOL(hAPP(X29,X106))
                     => hBOOL(hAPP(X29,hAPP(hAPP(c_Set_Oinsert(X5),X74),X106))) ) ) ) )
           => hBOOL(hAPP(X29,X90)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__subset__induct) ).

fof(fact_mult__2,axiom,
    ! [X23,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X23),X23) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2) ).

fof(fact_listsum__map__filter,axiom,
    ! [X2,X29,X212,X5,X16] :
      ( class_Groups_Omonoid__add(X16)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
           => ( ~ hBOOL(hAPP(X29,X3))
             => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X16) ) )
       => hAPP(c_List_Omonoid__add__class_Olistsum(X16),hAPP(hAPP(c_List_Omap(X5,X16),X2),hAPP(c_List_Ofilter(X5,X29),X212))) = hAPP(c_List_Omonoid__add__class_Olistsum(X16),hAPP(hAPP(c_List_Omap(X5,X16),X2),X212)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__map__filter) ).

fof(fact_nat__mult__2,axiom,
    ! [X23] : 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)))),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),X23),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__2) ).

fof(fact_add__2__eq__Suc,axiom,
    ! [X98] : 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)))),X98) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__2__eq__Suc) ).

fof(fact_length__dropWhile__le,axiom,
    ! [X212,X29,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,X29,X212))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__dropWhile__le) ).

fof(fact_folding__image__simple_Oinsert,axiom,
    ! [X12,X11,X90,X1,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X16,X2,X37,X1,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X16),X12),X11))
         => hAPP(X90,hAPP(hAPP(c_Set_Oinsert(X16),X12),X11)) = hAPP(hAPP(X2,hAPP(X1,X12)),hAPP(X90,X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert) ).

fof(fact_RangeE,axiom,
    ! [X34,X16,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(c_Relation_ORange(X16,X5),X34)))
     => ~ ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X5)),hAPP(hAPP(c_Product__Type_OPair(X16,X5),X3),X17)),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeE) ).

fof(fact_trancl__trans,axiom,
    ! [X21,X34,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),c_Transitive__Closure_Otrancl(X5,X34)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X17),X21)),c_Transitive__Closure_Otrancl(X5,X34)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Otrancl(X5,X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__trans) ).

fof(fact_trancl__converseI,axiom,
    ! [X34,X27,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),hAPP(c_Relation_Oconverse(X5,X5),c_Transitive__Closure_Otrancl(X5,X34))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_Transitive__Closure_Otrancl(X5,hAPP(c_Relation_Oconverse(X5,X5),X34)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__converseI) ).

fof(fact_trancl__converseD,axiom,
    ! [X34,X27,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_Transitive__Closure_Otrancl(X5,hAPP(c_Relation_Oconverse(X5,X5),X34))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),hAPP(c_Relation_Oconverse(X5,X5),c_Transitive__Closure_Otrancl(X5,X34)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__converseD) ).

fof(fact_restrict__fun__upd,axiom,
    ! [X27,X45,X16,X18,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X18))
       => c_Map_Orestrict__map(X5,X16,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),X45),X12),X27),X18) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),c_Map_Orestrict__map(X5,X16,X45,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X18),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),X12),X27) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X18))
       => c_Map_Orestrict__map(X5,X16,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),X45),X12),X27),X18) = c_Map_Orestrict__map(X5,X16,X45,X18) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__fun__upd) ).

fof(fact_fold1Set_Ointros,axiom,
    ! [X12,X11,X6,X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,X2,X6,X11),X12))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)),X12)) ) ),
    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,
    ! [X225,X221,X14,X15] : hAPP(c_List_OremoveAll(X15,X14),hAPP(hAPP(c_List_Oappend(X15),X221),X225)) = hAPP(hAPP(c_List_Oappend(X15),hAPP(c_List_OremoveAll(X15,X14),X221)),hAPP(c_List_OremoveAll(X15,X14),X225)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll__append) ).

fof(fact_removeAll__filter__not__eq,axiom,
    ! [X12,X5] : c_List_OremoveAll(X5,X12) = c_List_Ofilter(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(c_fequal,X12))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll__filter__not__eq) ).

fof(fact_rotate__rev,axiom,
    ! [X221,X98,X15] : hAPP(c_List_Orotate(X15,X98),hAPP(c_List_Orev(X15),X221)) = hAPP(c_List_Orev(X15),hAPP(c_List_Orotate(X15,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X98,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__rev) ).

fof(fact_rotate__def,axiom,
    ! [X76,X5] : c_List_Orotate(X5,X76) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X5),tc_List_Olist(X5)),X76),c_List_Orotate1(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__def) ).

fof(fact_map__of__zip__upd,axiom,
    ! [X37,X27,X12,X227,X212,X16,X214,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X214) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X212)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X227) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X212)
       => ( ~ hBOOL(hAPP(hAPP(c_member(X16),X12),hAPP(c_List_Oset(X16),X212)))
         => ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X16,tc_Option_Ooption(X5)),hAPP(c_Map_Omap__of(X16,X5),hAPP(hAPP(c_List_Ozip(X16,X5),X212),X214))),X12),hAPP(c_Option_Ooption_OSome(X5),X27)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X16,tc_Option_Ooption(X5)),hAPP(c_Map_Omap__of(X16,X5),hAPP(hAPP(c_List_Ozip(X16,X5),X212),X227))),X12),hAPP(c_Option_Ooption_OSome(X5),X37))
           => hAPP(c_Map_Omap__of(X16,X5),hAPP(hAPP(c_List_Ozip(X16,X5),X212),X214)) = hAPP(c_Map_Omap__of(X16,X5),hAPP(hAPP(c_List_Ozip(X16,X5),X212),X227)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__zip__upd) ).

fof(fact_rtrancl__trancl__trancl,axiom,
    ! [X37,X34,X27,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_Transitive__Closure_Ortrancl(X5,X34)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X27),X37)),c_Transitive__Closure_Otrancl(X5,X34)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X37)),c_Transitive__Closure_Otrancl(X5,X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trancl__trancl) ).

fof(fact_trancl__rtrancl__trancl,axiom,
    ! [X21,X34,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),c_Transitive__Closure_Otrancl(X5,X34)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X17),X21)),c_Transitive__Closure_Ortrancl(X5,X34)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Otrancl(X5,X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__rtrancl__trancl) ).

fof(fact_trancl__into__trancl2,axiom,
    ! [X21,X34,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),X34))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X17),X21)),c_Transitive__Closure_Otrancl(X5,X34)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Otrancl(X5,X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__into__trancl2) ).

fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
    ! [X21,X34,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),c_Transitive__Closure_Otrancl(X5,X34)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X17),X21)),X34))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Otrancl(X5,X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).

fof(fact_Collect__conv__if,axiom,
    ! [X5,X6,X29] :
      ( ( hBOOL(hAPP(X29,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))),X29)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(X29,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))),X29)) = 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,X212,X2,X38,X1,X5,X16] : c_List_Ofoldr(X16,X5,X1,hAPP(hAPP(c_List_Omap(X38,X16),X2),X212),X6) = c_List_Ofoldr(X38,X5,hAPP(c_Fun_Ocomp(X16,tc_fun(X5,X5),X38,X1),X2),X212,X6),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldr__map) ).

fof(fact_trancl__subset__Sigma,axiom,
    ! [X11,X34,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X11),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X11))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X34)),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X11),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X11)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__subset__Sigma) ).

fof(fact_norm__frac_Opsimps,axiom,
    ! [X17,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),X17)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => c_Nitpick_Onorm__frac(X6,X17) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X17)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ( ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | X17 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(X6,X17) = 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)
                  | X17 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(X6,X17) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X6),X17)),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),X17))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__frac_Opsimps) ).

fof(fact_foldr__append,axiom,
    ! [X6,X214,X212,X2,X5,X16] : c_List_Ofoldr(X16,X5,X2,hAPP(hAPP(c_List_Oappend(X16),X212),X214),X6) = c_List_Ofoldr(X16,X5,X2,X212,c_List_Ofoldr(X16,X5,X2,X214,X6)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldr__append) ).

fof(fact_psubset__insert__iff,axiom,
    ! [X13,X12,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),X13)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X13))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),X13)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X13))
         => ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
             => 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)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X13)) )
            & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__insert__iff) ).

fof(fact_lexord__irreflexive,axiom,
    ! [X27,X34,X5] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X34))
     => ~ 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)),X27),X27)),c_List_Olexord(X5,X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__irreflexive) ).

fof(fact_diff__bin__simps_I8_J,axiom,
    ! [X103,X100] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X100)),c_Int_OBit1(X103)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(X100)),X103)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I8_J) ).

fof(fact_inj__on__insert,axiom,
    ! [X11,X6,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,hAPP(hAPP(c_Set_Oinsert(X5),X6),X11))
    <=> ( c_Fun_Oinj__on(X5,X16,X2,X11)
        & ~ hBOOL(hAPP(hAPP(c_member(X16),hAPP(X2,X6)),hAPP(c_Set_Oimage(X5,X16,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),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,
    ! [X16,X5] : c_Product__Type_Oapfst(X5,X5,X16,c_Fun_Oid(X5)) = c_Fun_Oid(tc_prod(X5,X16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apfst__id) ).

fof(fact_apsnd__id,axiom,
    ! [X5,X16] : c_Product__Type_Oapsnd(X16,X16,X5,c_Fun_Oid(X16)) = c_Fun_Oid(tc_prod(X5,X16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__id) ).

fof(fact_trancl__reflcl,axiom,
    ! [X34,X5] : c_Transitive__Closure_Otrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),c_Relation_OId(X5))) = c_Transitive__Closure_Ortrancl(X5,X34),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__reflcl) ).

fof(fact_subset__insert__iff,axiom,
    ! [X13,X12,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),X13)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => 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)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X13)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insert__iff) ).

fof(fact_eq__special_I4_J,axiom,
    ! [X12,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X12) = 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),X12),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,
    ! [X27,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( c_Groups_Oone__class_Oone(X5) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X27)
      <=> 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),X27)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__special_I2_J) ).

fof(fact_small_H_Opsimps,axiom,
    ! [X70,X20,X2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X20),X70))))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20),X70))
         => c_Smallcheck_Osmall_H(X2,X20,X70) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20),X70))
         => c_Smallcheck_Osmall_H(X2,X20,X70) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X2,X20,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X70),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X2,X70)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small_H_Opsimps) ).

fof(fact_norm__frac_Osimps,axiom,
    ! [X6,X17] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Nitpick_Onorm__frac(X6,X17) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X17)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              | X17 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
           => c_Nitpick_Onorm__frac(X6,X17) = 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)
                | X17 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
           => c_Nitpick_Onorm__frac(X6,X17) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X6),X17)),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),X17))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__frac_Osimps) ).

fof(fact_rtrancl__into__trancl2,axiom,
    ! [X21,X34,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),X34))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X17),X21)),c_Transitive__Closure_Ortrancl(X5,X34)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Otrancl(X5,X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__into__trancl2) ).

fof(fact_rtrancl__into__trancl1,axiom,
    ! [X21,X34,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),c_Transitive__Closure_Ortrancl(X5,X34)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X17),X21)),X34))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Otrancl(X5,X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__into__trancl1) ).

fof(fact_power2__eq__square__number__of,axiom,
    ! [X132,X5] :
      ( ( class_Groups_Omonoid__mult(X5)
        & class_Int_Onumber(X5) )
     => hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X132)),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(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X132)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X132)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__square__number__of) ).

fof(fact_r__r__into__trancl,axiom,
    ! [X21,X36,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),X36))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X17),X21)),X36))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Otrancl(X5,X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__r__into__trancl) ).

fof(fact_DomainE,axiom,
    ! [X34,X16,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Relation_ODomain(X5,X16),X34)))
     => ~ ! [X33] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X33)),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainE) ).

fof(fact_add__self__div__2,axiom,
    ! [X99] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X99)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X99,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__self__div__2) ).

fof(fact_mult__2__right,axiom,
    ! [X23,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X23),hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X23),X23) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2__right) ).

fof(fact_power2__eq__square,axiom,
    ! [X25,X15] :
      ( class_Groups_Omonoid__mult(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),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(X15),X25),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__square) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
    ! [X14,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),X14) = hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),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,X21,X17,X13,X11,X38,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_fun(X38,tc_HOL_Obool))),X11),X13),X17),X21))
     => ( ~ hBOOL(hAPP(hAPP(hAPP(X13,X6),X17),X21))
       => ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF2__E) ).

fof(fact_nat__mult__2__right,axiom,
    ! [X23] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23),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),X23),X23),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__2__right) ).

fof(fact_add__2__eq__Suc_H,axiom,
    ! [X98] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),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,X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__2__eq__Suc_H) ).

fof(fact_zero__power2,axiom,
    ! [X15] :
      ( class_Rings_Osemiring__1(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__power2) ).

fof(fact_one__power2,axiom,
    ! [X15] :
      ( class_Rings_Osemiring__1(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),c_Groups_Oone__class_Oone(X15)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__power2) ).

fof(fact_trancl__mono,axiom,
    ! [X84,X34,X161,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X161),c_Transitive__Closure_Otrancl(X5,X34)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),X84))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X161),c_Transitive__Closure_Otrancl(X5,X84))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__mono) ).

fof(fact_not__sum__squares__lt__zero,axiom,
    ! [X22,X14,X15] :
      ( class_Rings_Olinordered__ring(X15)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X22),X22))),c_Groups_Ozero__class_Ozero(X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).

fof(fact_trancl__subset__Field2,axiom,
    ! [X34,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X34)),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),hAPP(c_Relation_OField(X5),X34)),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_Relation_OField(X5),X34))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__subset__Field2) ).

fof(fact_sup2E,axiom,
    ! [X27,X12,X13,X11,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),X11),X13),X12),X27))
     => ( ~ hBOOL(hAPP(hAPP(X11,X12),X27))
       => hBOOL(hAPP(hAPP(X13,X12),X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup2E) ).

fof(fact_rtrancl__eq__or__trancl,axiom,
    ! [X36,X27,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_Transitive__Closure_Ortrancl(X5,X36)))
    <=> ( X12 = X27
        | ( X12 != X27
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_Transitive__Closure_Otrancl(X5,X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__eq__or__trancl) ).

fof(fact_trancl__into__rtrancl,axiom,
    ! [X34,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),c_Transitive__Closure_Otrancl(X5,X34)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),c_Transitive__Closure_Ortrancl(X5,X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__into__rtrancl) ).

fof(fact_inf2E,axiom,
    ! [X27,X12,X13,X11,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),X11),X13),X12),X27))
     => ~ ( hBOOL(hAPP(hAPP(X11,X12),X27))
         => ~ hBOOL(hAPP(hAPP(X13,X12),X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2E) ).

fof(fact_eq__int__code_I16_J,axiom,
    ! [X163,X164] :
      ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X164)),c_Int_OBit1(X163)))
    <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X164),X163)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__int__code_I16_J) ).

fof(fact_rel__simps_I17_J,axiom,
    ! [X97,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X30)),c_Int_OBit1(X97)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),X97)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I17_J) ).

fof(fact_less__int__code_I16_J,axiom,
    ! [X163,X164] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X164)),c_Int_OBit1(X163)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X164),X163)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I16_J) ).

fof(fact_less__eq__int__code_I16_J,axiom,
    ! [X163,X164] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X164)),c_Int_OBit1(X163)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X164),X163)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I16_J) ).

fof(fact_rel__simps_I34_J,axiom,
    ! [X97,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X30)),c_Int_OBit1(X97)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),X97)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I34_J) ).

fof(fact_distinct__removeAll,axiom,
    ! [X14,X221,X15] :
      ( hBOOL(hAPP(c_List_Odistinct(X15),X221))
     => hBOOL(hAPP(c_List_Odistinct(X15),hAPP(c_List_OremoveAll(X15,X14),X221))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__removeAll) ).

fof(fact_map__removeAll__inj__on,axiom,
    ! [X212,X12,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,hAPP(hAPP(c_Set_Oinsert(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => hAPP(hAPP(c_List_Omap(X5,X16),X2),hAPP(c_List_OremoveAll(X5,X12),X212)) = hAPP(c_List_OremoveAll(X16,hAPP(X2,X12)),hAPP(hAPP(c_List_Omap(X5,X16),X2),X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__removeAll__inj__on) ).

fof(fact_dropWhile__append2,axiom,
    ! [X214,X29,X212,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
         => hBOOL(hAPP(X29,X3)) )
     => c_List_OdropWhile(X5,X29,hAPP(hAPP(c_List_Oappend(X5),X212),X214)) = c_List_OdropWhile(X5,X29,X214) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__append2) ).

fof(fact_map__removeAll__inj,axiom,
    ! [X212,X12,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(hAPP(c_List_Omap(X5,X16),X2),hAPP(c_List_OremoveAll(X5,X12),X212)) = hAPP(c_List_OremoveAll(X16,hAPP(X2,X12)),hAPP(hAPP(c_List_Omap(X5,X16),X2),X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__removeAll__inj) ).

fof(fact_nth__length__takeWhile,axiom,
    ! [X212,X29,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,X29,X212))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
     => ~ hBOOL(hAPP(X29,hAPP(hAPP(c_List_Onth(X5),X212),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X29,X212))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__length__takeWhile) ).

fof(fact_length__transpose,axiom,
    ! [X212,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),c_List_Otranspose(X5,X212)) = 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))),X212,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__transpose) ).

fof(fact_trancl__power,axiom,
    ! [X36,X161,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X161),c_Transitive__Closure_Otrancl(X5,X36)))
    <=> ? [X107] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X107))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X161),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X107),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__power) ).

fof(fact_concat__append,axiom,
    ! [X225,X221,X15] : c_List_Oconcat(X15,hAPP(hAPP(c_List_Oappend(tc_List_Olist(X15)),X221),X225)) = hAPP(hAPP(c_List_Oappend(X15),c_List_Oconcat(X15,X221)),c_List_Oconcat(X15,X225)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__append) ).

fof(fact_distinct__list__update,axiom,
    ! [X70,X6,X212,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X212))
     => ( ~ 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),X212)),hAPP(hAPP(c_Set_Oinsert(X5),hAPP(hAPP(c_List_Onth(X5),X212),X70)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
       => hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Olist__update(X5,X212),X70),X6))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__list__update) ).

fof(fact_pigeonhole,axiom,
    ! [X11,X2,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(c_Set_Oimage(X16,X5,X2),X11))),hAPP(c_Finite__Set_Ocard(X16),X11)))
     => ~ c_Fun_Oinj__on(X16,X5,X2,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pigeonhole) ).

fof(fact_rtranclD,axiom,
    ! [X36,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),c_Transitive__Closure_Ortrancl(X5,X36)))
     => ( X6 = X17
        | ( X6 != X17
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),c_Transitive__Closure_Otrancl(X5,X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclD) ).

fof(fact_takeWhile__eq__take__P__nth,axiom,
    ! [X29,X212,X5,X76] :
      ( ! [X145] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X145),X76))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X145),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
           => hBOOL(hAPP(X29,hAPP(hAPP(c_List_Onth(X5),X212),X145))) ) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
         => ~ hBOOL(hAPP(X29,hAPP(hAPP(c_List_Onth(X5),X212),X76))) )
       => c_List_OtakeWhile(X5,X29,X212) = hAPP(hAPP(c_List_Otake(X5),X76),X212) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__eq__take__P__nth) ).

fof(fact_trancl_Or__into__trancl,axiom,
    ! [X34,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),X34))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),c_Transitive__Closure_Otrancl(X5,X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl_Or__into__trancl) ).

fof(fact_divide__less__eq__number__of,axiom,
    ! [X112,X21,X17,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),X17),X21)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
      <=> ( ( 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),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),X21))) )
          & ( ~ 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),X21),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),X112)),X21)),X17)) )
              & ( ~ 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),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq__number__of) ).

fof(fact_divide__le__eq__number__of,axiom,
    ! [X112,X21,X17,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),X17),X21)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X21))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),X21))) )
          & ( ~ 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),X21),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),X112)),X21)),X17)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),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),X112))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq__number__of) ).

fof(fact_less__divide__eq__number__of,axiom,
    ! [X21,X17,X112,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),X112)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X17),X21)))
      <=> ( ( 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),X21)),X17)) )
          & ( ~ 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),X21),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),X21))) )
              & ( ~ 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),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),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,
    ! [X21,X17,X112,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),X112)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X17),X21)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X21))
           => 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),X112)),X21)),X17)) )
          & ( ~ 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),X21),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),X21))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq__number__of) ).

fof(fact_distinct__concat,axiom,
    ! [X212,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X5)),X212))
     => ( ! [X229] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X229),hAPP(c_List_Oset(tc_List_Olist(X5)),X212)))
           => hBOOL(hAPP(c_List_Odistinct(X5),X229)) )
       => ( ! [X229] :
              ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X229),hAPP(c_List_Oset(tc_List_Olist(X5)),X212)))
             => ! [X260] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X260),hAPP(c_List_Oset(tc_List_Olist(X5)),X212)))
                 => ( X229 != X260
                   => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X229)),hAPP(c_List_Oset(X5),X260)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ) )
         => hBOOL(hAPP(c_List_Odistinct(X5),c_List_Oconcat(X5,X212))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__concat) ).

fof(fact_Collect__conv__if2,axiom,
    ! [X5,X6,X29] :
      ( ( hBOOL(hAPP(X29,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))),X29)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(X29,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))),X29)) = 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,
    ! [X221,X98,X15] : hAPP(c_List_Orotate(X15,X98),X221) = hAPP(hAPP(c_List_Oappend(X15),hAPP(hAPP(c_List_Odrop(X15),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X98,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221))),X221)),hAPP(hAPP(c_List_Otake(X15),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X98,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221))),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__drop__take) ).

fof(fact_in__set__zipE,axiom,
    ! [X214,X212,X27,X12,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X12),X27)),hAPP(c_List_Oset(tc_prod(X5,X16)),hAPP(hAPP(c_List_Ozip(X5,X16),X212),X214))))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
         => ~ hBOOL(hAPP(hAPP(c_member(X16),X27),hAPP(c_List_Oset(X16),X214))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__zipE) ).

fof(fact_removeAll_Osimps_I2_J,axiom,
    ! [X221,X15,X22,X14] :
      ( ( X14 = X22
       => hAPP(c_List_OremoveAll(X15,X14),hAPP(hAPP(c_List_Olist_OCons(X15),X22),X221)) = hAPP(c_List_OremoveAll(X15,X14),X221) )
      & ( X14 != X22
       => hAPP(c_List_OremoveAll(X15,X14),hAPP(hAPP(c_List_Olist_OCons(X15),X22),X221)) = hAPP(hAPP(c_List_Olist_OCons(X15),X22),hAPP(c_List_OremoveAll(X15,X14),X221)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll_Osimps_I2_J) ).

fof(fact_map__add__upd__left,axiom,
    ! [X198,X199,X200,X16,X45,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X45),c_Map_Odom(X5,X16,X200)))
     => c_Map_Omap__add(X5,X16,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),X199),X45),hAPP(c_Option_Ooption_OSome(X16),X198)),X200) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),c_Map_Omap__add(X5,X16,X199,X200)),X45),hAPP(c_Option_Ooption_OSome(X16),X198)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__upd__left) ).

fof(fact_acyclic__insert,axiom,
    ! [X34,X12,X27,X5] :
      ( c_Wellfounded_Oacyclic(X5,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X27),X12)),X34))
    <=> ( c_Wellfounded_Oacyclic(X5,X34)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_Transitive__Closure_Ortrancl(X5,X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__insert) ).

fof(fact_wf__insert,axiom,
    ! [X34,X12,X27,X5] :
      ( c_Wellfounded_Owf(X5,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X27),X12)),X34))
    <=> ( c_Wellfounded_Owf(X5,X34)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_Transitive__Closure_Ortrancl(X5,X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__insert) ).

fof(fact_trancl__unfold,axiom,
    ! [X34,X5] : c_Transitive__Closure_Otrancl(X5,X34) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),c_Transitive__Closure_Otrancl(X5,X34)),X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__unfold) ).

fof(fact_wf__eq__minimal,axiom,
    ! [X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
    <=> ! [X196] :
          ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),X196))
         => ? [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X196))
              & ! [X33] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X3)),X34))
                 => ~ hBOOL(hAPP(hAPP(c_member(X5),X33),X196)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__eq__minimal) ).

fof(fact_less__int__code_I15_J,axiom,
    ! [X163,X164] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X164)),c_Int_OBit0(X163)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X164),X163)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I15_J) ).

fof(fact_rel__simps_I16_J,axiom,
    ! [X97,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X30)),c_Int_OBit0(X97)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),X97)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I16_J) ).

fof(fact_rel__simps_I33_J,axiom,
    ! [X97,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X30)),c_Int_OBit0(X97)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),X97)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I33_J) ).

fof(fact_less__eq__int__code_I15_J,axiom,
    ! [X163,X164] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X164)),c_Int_OBit0(X163)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X164),X163)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I15_J) ).

fof(fact_fun__upd__None__restrict,axiom,
    ! [X45,X16,X18,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X18))
       => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),c_Map_Orestrict__map(X5,X16,X45,X18)),X12),c_Option_Ooption_ONone(X16)) = c_Map_Orestrict__map(X5,X16,X45,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X18),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X18))
       => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),c_Map_Orestrict__map(X5,X16,X45,X18)),X12),c_Option_Ooption_ONone(X16)) = c_Map_Orestrict__map(X5,X16,X45,X18) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__None__restrict) ).

fof(fact_Nitpick_Oint__lcm__def,axiom,
    ! [X22,X14] : c_Nitpick_Oint__lcm(X14,X22) = 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),X14)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X22)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Oint__lcm__def) ).

fof(fact_Nitpick_Onat__lcm__def,axiom,
    ! [X22,X14] : c_Nitpick_Onat__lcm(X14,X22) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X22)),c_Nitpick_Onat__gcd(X14,X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Onat__lcm__def) ).

fof(fact_foldr_Osimps_I2_J,axiom,
    ! [X6,X212,X12,X2,X5,X16] : c_List_Ofoldr(X16,X5,X2,hAPP(hAPP(c_List_Olist_OCons(X16),X12),X212),X6) = hAPP(hAPP(X2,X12),c_List_Ofoldr(X16,X5,X2,X212,X6)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldr_Osimps_I2_J) ).

fof(fact_wf__not__sym,axiom,
    ! [X12,X6,X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X12)),X34))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X6)),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__not__sym) ).

fof(fact_wf__asym,axiom,
    ! [X12,X6,X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X12)),X34))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X6)),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__asym) ).

fof(fact_divmod__nat__rel__def,axiom,
    ! [X162,X76,X45] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X45,X76),X162))
    <=> ( X45 = 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),X162)),X76)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X162))
        & ( X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X162) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( X76 != 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)),X76))
             => ( 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),X162)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X162)),X76)) ) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X76))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X162)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X162)),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,X112,X17,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),X17),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112))),X6))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),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),X112))),X17)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),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,X112,X17,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),X17),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112))),X6))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),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),X112))),X17)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),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,
    ! [X100] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(X100)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X100))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Bit1) ).

fof(fact_small__lazy_H_Opinduct,axiom,
    ! [X29,X47,X158] :
      ( 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),X158),X47)))
     => ( ! [X125,X145] :
            ( 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),X125),X145)))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X125),X145))
               => hBOOL(hAPP(hAPP(X29,X125),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X145),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
             => hBOOL(hAPP(hAPP(X29,X125),X145)) ) )
       => hBOOL(hAPP(hAPP(X29,X158),X47)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small__lazy_H_Opinduct) ).

fof(fact_less__eq,axiom,
    ! [X76,X45] :
      ( 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),X45),X76)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq) ).

fof(fact_quotientE,axiom,
    ! [X34,X11,X31,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X31),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X11),X34)))
     => ~ ! [X3] :
            ( X31 = hAPP(c_Relation_OImage(X5,X5,X34),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),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotientE) ).

fof(fact_divmod__nat__if,axiom,
    ! [X45,X76] :
      ( ( ( X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76)) )
       => c_Divides_Odivmod__nat(X45,X76) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X45) )
      & ( ~ ( X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76)) )
       => c_Divides_Odivmod__nat(X45,X76) = 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),X45),X76),X76)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__if) ).

fof(fact_divmod__nat__def,axiom,
    ! [X76,X45] : c_Divides_Odivmod__nat(X45,X76) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X45,X76)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__def) ).

fof(fact_bin__less__0__simps_I4_J,axiom,
    ! [X112] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X112)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X112),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,
    ! [X249,X250,X251,X252,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X252),X251) = hAPP(hAPP(c_List_Oappend(X5),X250),X249)
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X252)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X250)))
         => ( X252 = hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X252)),X250)
            & X251 = hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X252)),X250)),X249) ) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X252)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X250)))
         => ( hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X250)),X252) = X250
            & hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X250)),X252)),X251) = X249 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__append__conv__if) ).

fof(fact_eq__int__code_I12_J,axiom,
    ! [X164] :
      ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X164)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X164),c_Int_OMin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__int__code_I12_J) ).

fof(fact_rel__simps_I13_J,axiom,
    ! [X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X30)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),c_Int_OMin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I13_J) ).

fof(fact_rel__simps_I12_J,axiom,
    ! [X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X30)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I12_J) ).

fof(fact_rel__simps_I29_J,axiom,
    ! [X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X30)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I29_J) ).

fof(fact_rel__simps_I30_J,axiom,
    ! [X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X30)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),c_Int_OMin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I30_J) ).

fof(fact_neg__number__of__Bit1,axiom,
    ! [X112] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X112))))
    <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X112))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__number__of__Bit1) ).

fof(fact_imageE,axiom,
    ! [X11,X2,X16,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(c_Set_Oimage(X16,X5,X2),X11)))
     => ~ ! [X3] :
            ( X17 = hAPP(X2,X3)
           => ~ hBOOL(hAPP(hAPP(c_member(X16),X3),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_imageE) ).

fof(fact_length__remdups__concat,axiom,
    ! [X256,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremdups(X5,c_List_Oconcat(X5,X256))) = 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)),X256)),c_List_Oset(X5))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__remdups__concat) ).

fof(fact_less__special_I2_J,axiom,
    ! [X27,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),X27)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I2_J) ).

fof(fact_le__special_I2_J,axiom,
    ! [X27,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),X27)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I2_J) ).

fof(fact_less__divide__eq__number__of1,axiom,
    ! [X112,X17,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),X17),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112))))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
           => 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),X112))),X17)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),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,
    ! [X112,X17,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),X17),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112))))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
           => 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),X112))),X17)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),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,
    ! [X16,X5,X11,X27,X12,X13] :
      ( ( ~ hBOOL(hAPP(hAPP(X13,X12),X27))
       => hBOOL(hAPP(hAPP(X11,X12),X27)) )
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),X11),X13),X12),X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup2CI) ).

fof(fact_not__acc__down,axiom,
    ! [X36,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),c_Wellfounded_Oacc(X5,X36)))
     => ~ ! [X44] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X44),X12)),X36))
           => hBOOL(hAPP(hAPP(c_member(X5),X44),c_Wellfounded_Oacc(X5,X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__acc__down) ).

fof(fact_flat__lub__def,axiom,
    ! [X17,X11,X5] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X17),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(X5,X17,X11) = X17 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X17),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(X5,X17,X11) = 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)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X17),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,
    ! [X34,X212,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)),X212)),c_List_Olistrel1(X5,X34))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Nil__listrel1) ).

fof(fact_Nil__notin__lex,axiom,
    ! [X34,X214,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)),X214)),c_List_Olex(X5,X34))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__notin__lex) ).

fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
    ! [X2,X12,X5,X16,X70] :
      ( ( X70 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Oneg__decr__bind(X16,X5,X12,X2),X70) = c_Lazy__Sequence_Ohit__bound(X5) )
      & ( X70 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Oneg__decr__bind(X16,X5,X12,X2),X70) = c_Lazy__Sequence_Ohb__bind(X16,X5,hAPP(X12,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X70),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X16,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5))),X2),X70)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__decr__bind__def) ).

fof(fact_hb__bind__def,axiom,
    ! [X2,X253,X5,X16] : c_Lazy__Sequence_Ohb__bind(X16,X5,X253,X2) = c_Lazy__Sequence_Ohb__flat(X5,c_Lazy__Sequence_Ohb__map(X16,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5)),X2,X253)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hb__bind__def) ).

fof(fact_fun__upd__image,axiom,
    ! [X27,X2,X16,X11,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hAPP(c_Set_Oimage(X5,X16,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),X2),X12),X27)),X11) = hAPP(hAPP(c_Set_Oinsert(X16),X27),hAPP(c_Set_Oimage(X5,X16,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hAPP(c_Set_Oimage(X5,X16,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),X2),X12),X27)),X11) = hAPP(c_Set_Oimage(X5,X16,X2),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__image) ).

fof(fact_not__listrel1__Nil,axiom,
    ! [X34,X212,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)),X212),c_List_Olist_ONil(X5))),c_List_Olistrel1(X5,X34))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__listrel1__Nil) ).

fof(fact_lexord__Nil__right,axiom,
    ! [X34,X12,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)),X12),c_List_Olist_ONil(X5))),c_List_Olexord(X5,X34))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__Nil__right) ).

fof(fact_Nil2__notin__lex,axiom,
    ! [X34,X212,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)),X212),c_List_Olist_ONil(X5))),c_List_Olex(X5,X34))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil2__notin__lex) ).

fof(fact_foldl__foldr1__lemma,axiom,
    ! [X212,X6,X5] :
      ( class_Groups_Omonoid__add(X5)
     => hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),X6),X212) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),c_List_Ofoldr(X5,X5,c_Groups_Oplus__class_Oplus(X5),X212,c_Groups_Ozero__class_Ozero(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__foldr1__lemma) ).

fof(fact_pair__in__Id__conv,axiom,
    ! [X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),c_Relation_OId(X5)))
    <=> X6 = X17 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__in__Id__conv) ).

fof(fact_finite__induct,axiom,
    ! [X29,X90,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X90))
     => ( hBOOL(hAPP(X29,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
       => ( ! [X3,X106] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X106))
             => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X106))
               => ( hBOOL(hAPP(X29,X106))
                 => hBOOL(hAPP(X29,hAPP(hAPP(c_Set_Oinsert(X5),X3),X106))) ) ) )
         => hBOOL(hAPP(X29,X90)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__induct) ).

fof(fact_one__add__one__is__two,axiom,
    ! [X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),c_Groups_Oone__class_Oone(X15)),c_Groups_Oone__class_Oone(X15)) = hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__add__one__is__two) ).

fof(fact_map__upds__apply__nontin,axiom,
    ! [X214,X2,X16,X212,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => hAPP(c_Map_Omap__upds(X5,X16,X2,X212,X214),X12) = hAPP(X2,X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__upds__apply__nontin) ).

fof(fact_map__of__eq__None__iff,axiom,
    ! [X12,X210,X5,X16] :
      ( hAPP(hAPP(c_Map_Omap__of(X16,X5),X210),X12) = c_Option_Ooption_ONone(X5)
    <=> ~ hBOOL(hAPP(hAPP(c_member(X16),X12),hAPP(c_Set_Oimage(tc_prod(X16,X5),X16,c_Product__Type_Ofst(X16,X5)),hAPP(c_List_Oset(tc_prod(X16,X5)),X210)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__eq__None__iff) ).

fof(fact_set__removeAll,axiom,
    ! [X212,X12,X5] : hAPP(c_List_Oset(X5),hAPP(c_List_OremoveAll(X5,X12),X212)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X212)),hAPP(hAPP(c_Set_Oinsert(X5),X12),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,X16,X11,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => hAPP(c_Fun_Ooverride__on(X5,X16,X2,X1,X11),X6) = hAPP(X1,X6) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => hAPP(c_Fun_Ooverride__on(X5,X16,X2,X1,X11),X6) = hAPP(X2,X6) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_override__on__def) ).

fof(fact_divmod__nat__step,axiom,
    ! [X99,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__eq(tc_Nat_Onat),X98),X99))
       => c_Divides_Odivmod__nat(X99,X98) = 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),X99),X98)),X98))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98),X98)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__step) ).

fof(fact_foldl__foldr,axiom,
    ! [X212,X6,X2,X16,X5] : hAPP(c_List_Ofoldl(X5,X16,X2,X6),X212) = c_List_Ofoldr(X16,X5,hAPP(c_COMBC(X5,X16,X5),X2),hAPP(c_List_Orev(X16),X212),X6),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__foldr) ).

fof(fact_override__on__apply__notin,axiom,
    ! [X1,X2,X16,X11,X6,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
     => hAPP(c_Fun_Ooverride__on(X5,X16,X2,X1,X11),X6) = hAPP(X2,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_override__on__apply__notin) ).

fof(fact_distinct__dropWhile,axiom,
    ! [X29,X212,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X212))
     => hBOOL(hAPP(c_List_Odistinct(X5),c_List_OdropWhile(X5,X29,X212))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__dropWhile) ).

fof(fact_comm__monoid__big_OF__eq,axiom,
    ! [X1,X11,X90,X37,X2,X16,X5] :
      ( c_Big__Operators_Ocomm__monoid__big(X5,X16,X2,X37,X90)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11))
         => hAPP(hAPP(X90,X1),X11) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X16,X2),X1),X37),X11) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11))
         => hAPP(hAPP(X90,X1),X11) = X37 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__monoid__big_OF__eq) ).

fof(fact_in__measure,axiom,
    ! [X2,X27,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),hAPP(c_Wellfounded_Omeasure(X5),X2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X12)),hAPP(X2,X27))) ),
    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_New__DSequence_Oneg__bind__def,axiom,
    ! [X70,X2,X12,X5,X16] : hAPP(c_New__DSequence_Oneg__bind(X16,X5,X12,X2),X70) = c_Lazy__Sequence_Ohb__bind(X16,X5,hAPP(X12,X70),hAPP(hAPP(c_COMBC(X16,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5))),X2),X70)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__bind__def) ).

fof(fact_SigmaE2,axiom,
    ! [X13,X11,X17,X6,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),X13)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => ~ hBOOL(hAPP(hAPP(c_member(X16),X17),hAPP(X13,X6))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaE2) ).

fof(fact_map__concat,axiom,
    ! [X212,X2,X5,X16] : hAPP(hAPP(c_List_Omap(X16,X5),X2),c_List_Oconcat(X16,X212)) = c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X16),tc_List_Olist(X5)),hAPP(c_List_Omap(X16,X5),X2)),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__concat) ).

fof(fact_add__Bit1__Bit0,axiom,
    ! [X103,X100] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X100)),c_Int_OBit0(X103)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X100),X103)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit1__Bit0) ).

fof(fact_diff__bin__simps_I9_J,axiom,
    ! [X103,X100] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X100)),c_Int_OBit0(X103)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X100),X103)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I9_J) ).

fof(fact_insort__insert__insort__key,axiom,
    ! [X212,X16,X12,X2,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X12)),hAPP(c_Set_Oimage(X16,X5,X2),hAPP(c_List_Oset(X16),X212))))
       => c_List_Olinorder__class_Oinsort__insert__key(X16,X5,X2,X12,X212) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X16,X5,X2),X12),X212) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__insert__insort__key) ).

fof(fact_total__on__diff__Id,axiom,
    ! [X34,X11,X5] :
      ( c_Relation_Ototal__on(X5,X11,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),c_Relation_OId(X5)))
    <=> c_Relation_Ototal__on(X5,X11,X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__diff__Id) ).

fof(fact_Suc__diff__eq__diff__pred,axiom,
    ! [X99,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X98))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X99)),X98) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),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,
    ! [X103,X100] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X100)),X103) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X100),X103))),X103),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Bit1) ).

fof(fact_number__of1,axiom,
    ! [X98] :
      ( 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),X98)))
     => ( 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(X98))))
        & 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(X98)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of1) ).

fof(fact_add__Bit1__Bit1,axiom,
    ! [X103,X100] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X100)),c_Int_OBit1(X103)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X100),c_Int_Osucc(X103))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit1__Bit1) ).

fof(fact_rel__simps_I15_J,axiom,
    ! [X97,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X30)),c_Int_OBit1(X97)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),X97)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I15_J) ).

fof(fact_less__int__code_I14_J,axiom,
    ! [X163,X164] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X164)),c_Int_OBit1(X163)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X164),X163)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I14_J) ).

fof(fact_rel__simps_I32_J,axiom,
    ! [X97,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X30)),c_Int_OBit1(X97)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),X97)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I32_J) ).

fof(fact_less__eq__int__code_I14_J,axiom,
    ! [X163,X164] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X164)),c_Int_OBit1(X163)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X164),X163)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I14_J) ).

fof(fact_finite__trancl,axiom,
    ! [X34,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),c_Transitive__Closure_Otrancl(X5,X34)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__trancl) ).

fof(fact_card__Diff__insert,axiom,
    ! [X13,X6,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X13))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13))) = 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)),X11),X13))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff__insert) ).

fof(fact_rev__concat,axiom,
    ! [X212,X5] : hAPP(c_List_Orev(X5),c_List_Oconcat(X5,X212)) = 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)),X212))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__concat) ).

fof(fact_fold__image__insert,axiom,
    ! [X37,X1,X6,X11,X5,X16] :
      ( class_Groups_Oab__semigroup__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X1),X37),hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(X1,X6)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X1),X37),X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__insert) ).

fof(fact_filter__concat,axiom,
    ! [X212,X161,X5] : hAPP(c_List_Ofilter(X5,X161),c_List_Oconcat(X5,X212)) = c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Ofilter(X5,X161)),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__concat) ).

fof(fact_in__measures_I1_J,axiom,
    ! [X27,X12,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),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,X21,X17,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),X17),X21)),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),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21))) )
          & ( ~ 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),X21),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21)),X17)) )
              & ( ~ 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),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,X21,X17,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),X17),X21)),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__eq(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21))) )
          & ( ~ 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),X21),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),X21)),X17)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),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,
    ! [X212,X76,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(c_List_Orotate(X5,X76),X212)))
    <=> hBOOL(hAPP(c_List_Odistinct(X5),X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__rotate) ).

fof(fact_Not__Domain__rtrancl,axiom,
    ! [X27,X36,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_Relation_ODomain(X5,X5),X36)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_Transitive__Closure_Ortrancl(X5,X36)))
      <=> X12 = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).

fof(fact_add__Bit0__Bit1,axiom,
    ! [X103,X100] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X100)),c_Int_OBit1(X103)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X100),X103)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit0__Bit1) ).

fof(fact_comm__monoid__big_Oinfinite,axiom,
    ! [X1,X11,X90,X37,X2,X16,X5] :
      ( c_Big__Operators_Ocomm__monoid__big(X5,X16,X2,X37,X90)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11))
       => hAPP(hAPP(X90,X1),X11) = X37 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__monoid__big_Oinfinite) ).

fof(fact_diff__special_I2_J,axiom,
    ! [X126,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X126)),c_Groups_Oone__class_Oone(X15)) = hAPP(c_Int_Onumber__class_Onumber__of(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X126),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,
    ! [X212,X12,X2,X5,X16] :
      ( class_Orderings_Olinorder(X16)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X16,X2),X12),X212)))
      <=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
          & hBOOL(hAPP(c_List_Odistinct(X5),X212)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__insort) ).

fof(fact_diff__special_I1_J,axiom,
    ! [X132,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),c_Groups_Oone__class_Oone(X15)),hAPP(c_Int_Onumber__class_Onumber__of(X15),X132)) = hAPP(c_Int_Onumber__class_Onumber__of(X15),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),X132))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__special_I1_J) ).

fof(fact_r__into__trancl_H,axiom,
    ! [X34,X161,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X161),X34))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X161),c_Transitive__Closure_Otrancl(X5,X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__into__trancl_H) ).

fof(fact_concat_Osimps_I2_J,axiom,
    ! [X221,X14,X15] : c_List_Oconcat(X15,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X15)),X14),X221)) = hAPP(hAPP(c_List_Oappend(X15),X14),c_List_Oconcat(X15,X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat_Osimps_I2_J) ).

fof(fact_add__special_I2_J,axiom,
    ! [X132,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),c_Groups_Oone__class_Oone(X15)),hAPP(c_Int_Onumber__class_Onumber__of(X15),X132)) = hAPP(c_Int_Onumber__class_Onumber__of(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X132)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__special_I2_J) ).

fof(fact_atLeastatMost__psubset__iff,axiom,
    ! [X20,X21,X17,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,X17)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X21,X20)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X17))
            | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),X6))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),X20))
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),X6))
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),X20)) ) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),X20)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastatMost__psubset__iff) ).

fof(fact_insert__partition,axiom,
    ! [X90,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X12),X90))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X12),X90)))
           => ! [X39] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X39),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X12),X90)))
               => ( X3 != X39
                 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X3),X39) = 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)),X12),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X90)) = 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,
    ! [X34,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X34)),c_Relation_OId(X5)) = c_Transitive__Closure_Ortrancl(X5,X34),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reflcl__trancl) ).

fof(fact_list__update__append,axiom,
    ! [X14,X225,X221,X15,X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
       => hAPP(hAPP(c_List_Olist__update(X15,hAPP(hAPP(c_List_Oappend(X15),X221),X225)),X98),X14) = hAPP(hAPP(c_List_Oappend(X15),hAPP(hAPP(c_List_Olist__update(X15,X221),X98),X14)),X225) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
       => hAPP(hAPP(c_List_Olist__update(X15,hAPP(hAPP(c_List_Oappend(X15),X221),X225)),X98),X14) = hAPP(hAPP(c_List_Oappend(X15),X221),hAPP(hAPP(c_List_Olist__update(X15,X225),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221))),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__append) ).

fof(fact_less__divide__eq,axiom,
    ! [X21,X17,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),X17),X21)))
      <=> ( ( 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21)),X17)) )
          & ( ~ 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),X21),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21))) )
              & ( ~ 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))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq) ).

fof(fact_le__divide__eq,axiom,
    ! [X21,X17,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),X17),X21)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X21))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21)),X17)) )
          & ( ~ 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),X21),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq) ).

fof(fact_mult__numeral__1,axiom,
    ! [X25,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OBit1(c_Int_OPls))),X25) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__numeral__1) ).

fof(fact_list__ex__iff__not__all__inverval__int,axiom,
    ! [X115,X70,X29] :
      ( c_List_Olist__ex(tc_Int_Oint,X29,c_List_Oupto(X70,X115))
    <=> ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X29),X70,X115) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__iff__not__all__inverval__int) ).

fof(fact_rotate__add,axiom,
    ! [X76,X45,X5] : c_List_Orotate(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X76)) = hAPP(c_Fun_Ocomp(tc_List_Olist(X5),tc_List_Olist(X5),tc_List_Olist(X5),c_List_Orotate(X5,X45)),c_List_Orotate(X5,X76)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__add) ).

fof(fact_atLeastatMost__subset__iff,axiom,
    ! [X20,X21,X17,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,X17)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X21,X20)))
      <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X17))
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),X20)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastatMost__subset__iff) ).

fof(fact_less__special_I4_J,axiom,
    ! [X12,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),X12)),c_Groups_Oone__class_Oone(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),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,
    ! [X12,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),X12)),c_Groups_Oone__class_Oone(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12),c_Int_OBit1(c_Int_OPls))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I4_J) ).

fof(fact_IdE,axiom,
    ! [X161,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X161),c_Relation_OId(X5)))
     => ~ ! [X3] : X161 != 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,
    ! [X103] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X103)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X103)),
    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,
    ! [X256,X212,X5] : hAPP(c_List_Ofoldl(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Oappend(X5),X212),X256) = hAPP(hAPP(c_List_Oappend(X5),X212),c_List_Oconcat(X5,X256)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__conv__concat) ).

fof(fact_diff__bin__simps_I10_J,axiom,
    ! [X103,X100] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X100)),c_Int_OBit1(X103)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X100),X103)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I10_J) ).

fof(fact_insort__insert__insort,axiom,
    ! [X212,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => c_List_Olinorder__class_Oinsort__insert__key(X5,X5,c_COMBI(X5),X12,X212) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X12),X212) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__insert__insort) ).

fof(fact_irrefl__def,axiom,
    ! [X34,X5] :
      ( c_Relation_Oirrefl(X5,X34)
    <=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__def) ).

fof(fact_wf__not__refl,axiom,
    ! [X6,X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X6)),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__not__refl) ).

fof(fact_wf__irrefl,axiom,
    ! [X6,X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X6)),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__irrefl) ).

fof(fact_rtrancl__unfold,axiom,
    ! [X34,X5] : c_Transitive__Closure_Ortrancl(X5,X34) = 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,X34)),X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__unfold) ).

fof(fact_INT__E,axiom,
    ! [X6,X13,X11,X16,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X11),X13)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(X13,X6)))
       => ~ hBOOL(hAPP(hAPP(c_member(X16),X6),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__E) ).

fof(fact_eq__int__code_I8_J,axiom,
    ! [X163] :
      ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X163)))
    <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X163)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__int__code_I8_J) ).

fof(fact_rel__simps_I9_J,axiom,
    ! [X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X30)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I9_J) ).

fof(fact_rel__simps_I26_J,axiom,
    ! [X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X30)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I26_J) ).

fof(fact_rel__simps_I5_J,axiom,
    ! [X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X30)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I5_J) ).

fof(fact_rel__simps_I22_J,axiom,
    ! [X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X30)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I22_J) ).

fof(fact_power__number__of__even__number__of,axiom,
    ! [X112,X56,X5] :
      ( class_Int_Onumber__ring(X5)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X56)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X112))) = hAPP(hAPP(c_HOL_OLet(X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X56)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X112))),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_inj__on__fun__updI,axiom,
    ! [X12,X27,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X16),X27),hAPP(c_Set_Oimage(X5,X16,X2),X11)))
       => c_Fun_Oinj__on(X5,X16,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),X2),X12),X27),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__fun__updI) ).

fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
    ! [X12,X27,X21] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X27))
       => 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)),X21)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X12),X27)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X21)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X27),X21)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X27))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X27))
           => 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)),X21)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X12),X27)) = 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),X12),X27))
           => 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)),X21)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X12),X27)) = 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,
    ! [X212,X5] :
      ( class_Groups_Omonoid__add(X5)
     => hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X212) = c_List_Ofoldr(X5,X5,c_Groups_Oplus__class_Oplus(X5),X212,c_Groups_Ozero__class_Ozero(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__foldr1) ).

fof(fact_nth__map__upt,axiom,
    ! [X2,X5,X45,X76,X70] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X70),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X76),X45)))
     => hAPP(hAPP(c_List_Onth(X5),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X5),X2),c_List_Oupt(X45,X76))),X70) = hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X70)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__map__upt) ).

fof(fact_rotate__rotate,axiom,
    ! [X221,X98,X99,X15] : hAPP(c_List_Orotate(X15,X99),hAPP(c_List_Orotate(X15,X98),X221)) = hAPP(c_List_Orotate(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X98)),X221),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__rotate) ).

fof(fact_foldr__conv__foldl,axiom,
    ! [X6,X212,X5] :
      ( class_Groups_Oab__semigroup__add(X5)
     => c_List_Ofoldr(X5,X5,c_Groups_Oplus__class_Oplus(X5),X212,X6) = hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),X6),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldr__conv__foldl) ).

fof(fact_rotate__conv__mod,axiom,
    ! [X221,X98,X15] : hAPP(c_List_Orotate(X15,X98),X221) = hAPP(c_List_Orotate(X15,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X98,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221))),X221),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__conv__mod) ).

fof(fact_map__of__zip__map,axiom,
    ! [X2,X16,X212,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => hAPP(hAPP(c_Map_Omap__of(X5,X16),hAPP(hAPP(c_List_Ozip(X5,X16),X212),hAPP(hAPP(c_List_Omap(X5,X16),X2),X212))),X12) = hAPP(c_Option_Ooption_OSome(X16),hAPP(X2,X12)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => hAPP(hAPP(c_Map_Omap__of(X5,X16),hAPP(hAPP(c_List_Ozip(X5,X16),X212),hAPP(hAPP(c_List_Omap(X5,X16),X2),X212))),X12) = c_Option_Ooption_ONone(X16) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__zip__map) ).

fof(fact_image__map__upd,axiom,
    ! [X27,X45,X16,X11,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
     => hAPP(c_Set_Oimage(X5,tc_Option_Ooption(X16),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),X45),X12),hAPP(c_Option_Ooption_OSome(X16),X27))),X11) = hAPP(c_Set_Oimage(X5,tc_Option_Ooption(X16),X45),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__map__upd) ).

fof(fact_pred__Bit0,axiom,
    ! [X100] : c_Int_Opred(c_Int_OBit0(X100)) = c_Int_OBit1(c_Int_Opred(X100)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__Bit0) ).

fof(fact_setprod__diff1,axiom,
    ! [X6,X2,X11,X5,X16] :
      ( class_Fields_Ofield(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hAPP(X2,X6) != c_Groups_Ozero__class_Ozero(X16)
         => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),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(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),X11)),hAPP(X2,X6)) )
            & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),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,X16),X2),X11) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__diff1) ).

fof(fact_refl__reflcl,axiom,
    ! [X34,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)),X34),c_Relation_OId(X5))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__reflcl) ).

fof(fact_takeWhile__dropWhile__id,axiom,
    ! [X212,X29,X5] : hAPP(hAPP(c_List_Oappend(X5),c_List_OtakeWhile(X5,X29,X212)),c_List_OdropWhile(X5,X29,X212)) = X212,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__dropWhile__id) ).

fof(fact_setsum__diff1,axiom,
    ! [X2,X6,X11,X5,X16] :
      ( class_Groups_Oab__group__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),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(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X11)),hAPP(X2,X6)) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),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,X16),X2),X11) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__diff1) ).

fof(fact_set__concat,axiom,
    ! [X212,X5] : hAPP(c_List_Oset(X5),c_List_Oconcat(X5,X212)) = 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)),X212)),c_List_Oset(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__concat) ).

fof(fact_length__concat,axiom,
    ! [X256,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oconcat(X5,X256)) = 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))),X256)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__concat) ).

fof(fact_INF1__E,axiom,
    ! [X6,X17,X13,X11,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X11),X13),X17))
     => ( ~ hBOOL(hAPP(hAPP(X13,X6),X17))
       => ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF1__E) ).

fof(fact_foldr__max__sorted,axiom,
    ! [X27,X212,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(c_List_Orev(X5),X212))
       => ( ( X212 = c_List_Olist_ONil(X5)
           => c_List_Ofoldr(X5,X5,c_Orderings_Oord__class_Omax(X5),X212,X27) = X27 )
          & ( X212 != c_List_Olist_ONil(X5)
           => c_List_Ofoldr(X5,X5,c_Orderings_Oord__class_Omax(X5),X212,X27) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_List_Onth(X5),X212),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X27) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldr__max__sorted) ).

fof(fact_length__filter__less,axiom,
    ! [X29,X212,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => ( ~ hBOOL(hAPP(X29,X12))
       => 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,X29),X212))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__filter__less) ).

fof(fact_rtrancl__r__diff__Id,axiom,
    ! [X34,X5] : c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),c_Relation_OId(X5))) = c_Transitive__Closure_Ortrancl(X5,X34),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__r__diff__Id) ).

fof(fact_rtrancl__reflcl,axiom,
    ! [X36,X5] : c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X36),c_Relation_OId(X5))) = c_Transitive__Closure_Ortrancl(X5,X36),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__reflcl) ).

fof(fact_irrefl__diff__Id,axiom,
    ! [X34,X5] : c_Relation_Oirrefl(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),c_Relation_OId(X5))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__diff__Id) ).

fof(fact_divmod__int__relI,axiom,
    ! [X123,X128,X26,X25] :
      ( X25 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X128)),X123)
     => ( ( ( 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__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X123))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),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),X26),X123))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X123),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X25,X26),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X128),X123))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__relI) ).

fof(fact_diff__bin__simps_I5_J,axiom,
    ! [X103] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X103)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X103)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I5_J) ).

fof(fact_setsum__diff1__nat,axiom,
    ! [X2,X11,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => 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)),X11),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),X11)),hAPP(X2,X6)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => 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)),X11),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),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__diff1__nat) ).

fof(fact_wf__converse__trancl,axiom,
    ! [X34,X5] :
      ( c_Wellfounded_Owf(X5,hAPP(c_Relation_Oconverse(X5,X5),X34))
     => c_Wellfounded_Owf(X5,hAPP(c_Relation_Oconverse(X5,X5),c_Transitive__Closure_Otrancl(X5,X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__converse__trancl) ).

fof(fact_small_H_Osimps,axiom,
    ! [X2,X70,X20] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20),X70))
       => c_Smallcheck_Osmall_H(X2,X20,X70) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20),X70))
       => c_Smallcheck_Osmall_H(X2,X20,X70) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X2,X20,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X70),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X2,X70)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small_H_Osimps) ).

fof(fact_concat__eq__Nil__conv,axiom,
    ! [X256,X5] :
      ( c_List_Oconcat(X5,X256) = c_List_Olist_ONil(X5)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X3),hAPP(c_List_Oset(tc_List_Olist(X5)),X256)))
         => 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,
    ! [X256,X5] :
      ( c_List_Olist_ONil(X5) = c_List_Oconcat(X5,X256)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X3),hAPP(c_List_Oset(tc_List_Olist(X5)),X256)))
         => 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,
    ! [X100,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X101))
     => c_List_Oupt(X102,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),X100)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X102,X101)),c_List_Oupt(X101,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),X100))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__add__eq__append) ).

fof(fact_setsum__cl__ivl__Suc,axiom,
    ! [X2,X45,X76,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X76)),X45))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X45,hAPP(c_Nat_OSuc,X76))) = c_Groups_Ozero__class_Ozero(X5) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X76)),X45))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X45,hAPP(c_Nat_OSuc,X76))) = 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,X45,X76))),hAPP(X2,hAPP(c_Nat_OSuc,X76))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__cl__ivl__Suc) ).

fof(fact_UnE,axiom,
    ! [X13,X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
       => hBOOL(hAPP(hAPP(c_member(X5),X21),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UnE) ).

fof(fact_dropWhile__eq__Nil__conv,axiom,
    ! [X212,X29,X5] :
      ( c_List_OdropWhile(X5,X29,X212) = c_List_Olist_ONil(X5)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
         => hBOOL(hAPP(X29,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__eq__Nil__conv) ).

fof(fact_folding_Oinsert,axiom,
    ! [X12,X11,X90,X2,X16,X5] :
      ( c_Finite__Set_Ofolding(X5,X16,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(X90,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(c_Fun_Ocomp(X16,X16,X16,hAPP(X90,X11)),hAPP(X2,X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Oinsert) ).

fof(fact_sorted__dropWhile,axiom,
    ! [X29,X212,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,X212)
       => c_List_Olinorder__class_Osorted(X5,c_List_OdropWhile(X5,X29,X212)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__dropWhile) ).

fof(fact_in__set__conv__decomp__last,axiom,
    ! [X212,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
    <=> ? [X229,X260] :
          ( X212 = hAPP(hAPP(c_List_Oappend(X5),X229),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X260))
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X260))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__conv__decomp__last) ).

fof(fact_in__set__conv__decomp__first,axiom,
    ! [X212,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
    <=> ? [X229] :
          ( ? [X260] : X212 = hAPP(hAPP(c_List_Oappend(X5),X229),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X260))
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X229))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__conv__decomp__first) ).

fof(fact_succ__Bit1,axiom,
    ! [X100] : c_Int_Osucc(c_Int_OBit1(X100)) = c_Int_OBit0(c_Int_Osucc(X100)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__Bit1) ).

fof(fact_power__number__of__even,axiom,
    ! [X112,X37,X5] :
      ( class_Int_Onumber__ring(X5)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X5),X37),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X112))) = hAPP(hAPP(c_HOL_OLet(X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X37),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X112))),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,
    ! [X13,X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
        & ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__iff) ).

fof(fact_DiffD2,axiom,
    ! [X13,X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffD2) ).

fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
    ! [X99,X103] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X103),X99) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(X103)),c_List_Oembed__list(X99))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__list__functions_I1_J) ).

fof(fact_return__list__def,axiom,
    ! [X97] : c_List_Oreturn__list(X97) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X97),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_return__list__def) ).

fof(fact_embed__list__def,axiom,
    ! [X97] : c_List_Oembed__list(X97) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X97),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_embed__list__def) ).

fof(fact_card__Suc__eq,axiom,
    ! [X30,X11,X5] :
      ( hAPP(c_Finite__Set_Ocard(X5),X11) = hAPP(c_Nat_OSuc,X30)
    <=> ? [X52,X127] :
          ( X11 = hAPP(hAPP(c_Set_Oinsert(X5),X52),X127)
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X52),X127))
          & hAPP(c_Finite__Set_Ocard(X5),X127) = X30
          & ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
           => X127 = 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,
    ! [X14,X221,X15] :
      ( hBOOL(hAPP(c_List_Odistinct(X15),X221))
     => c_List_Oremove1(X15,X14,X221) = hAPP(c_List_OremoveAll(X15,X14),X221) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__remove1__removeAll) ).

fof(fact_take__upt,axiom,
    ! [X98,X99,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X99)),X98))
     => hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X99),c_List_Oupt(X102,X98)) = c_List_Oupt(X102,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X99)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__upt) ).

fof(fact_rotate__map,axiom,
    ! [X212,X2,X16,X76,X5] : hAPP(c_List_Orotate(X5,X76),hAPP(hAPP(c_List_Omap(X16,X5),X2),X212)) = hAPP(hAPP(c_List_Omap(X16,X5),X2),hAPP(c_List_Orotate(X16,X76),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__map) ).

fof(fact_trancl__converse,axiom,
    ! [X34,X5] : c_Transitive__Closure_Otrancl(X5,hAPP(c_Relation_Oconverse(X5,X5),X34)) = hAPP(c_Relation_Oconverse(X5,X5),c_Transitive__Closure_Otrancl(X5,X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__converse) ).

fof(fact_insort__key_Osimps_I2_J,axiom,
    ! [X214,X16,X27,X12,X2,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X2,X12)),hAPP(X2,X27)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X16,X5,X2),X12),hAPP(hAPP(c_List_Olist_OCons(X16),X27),X214)) = hAPP(hAPP(c_List_Olist_OCons(X16),X12),hAPP(hAPP(c_List_Olist_OCons(X16),X27),X214)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X2,X12)),hAPP(X2,X27)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X16,X5,X2),X12),hAPP(hAPP(c_List_Olist_OCons(X16),X27),X214)) = hAPP(hAPP(c_List_Olist_OCons(X16),X27),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X16,X5,X2),X12),X214)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__key_Osimps_I2_J) ).

fof(fact_upto__rec__number__of,axiom,
    ! [X98,X99] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X99)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X98)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X99),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X98)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X99)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X99)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X98))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X99)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X98)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X99),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X98)) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upto__rec__number__of) ).

fof(fact_subset__insert,axiom,
    ! [X13,X11,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),X13)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insert) ).

fof(fact_IntE,axiom,
    ! [X13,X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
         => ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntE) ).

fof(fact_upto_Opsimps,axiom,
    ! [X115,X70] :
      ( 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),X70),X115)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X70),X115))
         => c_List_Oupto(X70,X115) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X70),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X70),c_Groups_Oone__class_Oone(tc_Int_Oint)),X115)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X70),X115))
         => c_List_Oupto(X70,X115) = 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,
    ! [X37,X12,X11,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X16,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),X37),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(X2,X12),hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),X37),X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert) ).

fof(fact_small__lazy_H_Opsimps,axiom,
    ! [X70,X20] :
      ( 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),X20),X70)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20),X70))
         => c_Lazy__Sequence_Osmall__lazy_H(X20,X70) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20),X70))
         => c_Lazy__Sequence_Osmall__lazy_H(X20,X70) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X70),c_Lazy__Sequence_Osmall__lazy_H(X20,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X70),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small__lazy_H_Opsimps) ).

fof(fact_map__fun__upd,axiom,
    ! [X56,X2,X16,X212,X27,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X27),hAPP(c_List_Oset(X5),X212)))
     => hAPP(hAPP(c_List_Omap(X5,X16),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),X2),X27),X56)),X212) = hAPP(hAPP(c_List_Omap(X5,X16),X2),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__fun__upd) ).

fof(fact_notin__set__remove1,axiom,
    ! [X27,X212,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),c_List_Oremove1(X5,X27,X212)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_notin__set__remove1) ).

fof(fact_notin__set__sublistI,axiom,
    ! [X68,X212,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),c_List_Osublist(X5,X212,X68)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_notin__set__sublistI) ).

fof(fact_nth__upt,axiom,
    ! [X101,X100,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X100)),X101))
     => hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X102,X101)),X100) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X100) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__upt) ).

fof(fact_zpower__number__of__even,axiom,
    ! [X112,X37] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X37),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X112))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X37),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X112))),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,X16] :
      ( class_Orderings_Oord(X16)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,X16)),X2),X1))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X16)),X2),X1))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X16)),X1),X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).

fof(fact_pick_Osimps,axiom,
    ! [X221,X14,X15,X102] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X102),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X15),X14)))
       => hAPP(c_Random_Opick(X15,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X15)),X14),X221)),X102) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X15),X14) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X102),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X15),X14)))
       => hAPP(c_Random_Opick(X15,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X15)),X14),X221)),X102) = hAPP(c_Random_Opick(X15,X221),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X102),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X15),X14))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pick_Osimps) ).

fof(fact_map__of__zip__is__None,axiom,
    ! [X12,X214,X16,X212,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)
     => ( hAPP(hAPP(c_Map_Omap__of(X5,X16),hAPP(hAPP(c_List_Ozip(X5,X16),X212),X214)),X12) = c_Option_Ooption_ONone(X16)
      <=> ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__zip__is__None) ).

fof(fact_UnionE,axiom,
    ! [X19,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X11),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X19)))
     => ~ ! [X195] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X11),X195))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X195),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UnionE) ).

fof(fact_eq__int__code_I13_J,axiom,
    ! [X163,X164] :
      ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X164)),c_Int_OBit0(X163)))
    <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X164),X163)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__int__code_I13_J) ).

fof(fact_less__int__code_I13_J,axiom,
    ! [X163,X164] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X164)),c_Int_OBit0(X163)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X164),X163)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I13_J) ).

fof(fact_rel__simps_I14_J,axiom,
    ! [X97,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X30)),c_Int_OBit0(X97)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),X97)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I14_J) ).

fof(fact_rel__simps_I31_J,axiom,
    ! [X97,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X30)),c_Int_OBit0(X97)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),X97)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I31_J) ).

fof(fact_less__eq__int__code_I13_J,axiom,
    ! [X163,X164] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X164)),c_Int_OBit0(X163)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X164),X163)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I13_J) ).

fof(fact_removeAll_Osimps_I1_J,axiom,
    ! [X14,X15] : hAPP(c_List_OremoveAll(X15,X14),c_List_Olist_ONil(X15)) = c_List_Olist_ONil(X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll_Osimps_I1_J) ).

fof(fact_card__Diff__singleton__if,axiom,
    ! [X12,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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),X11)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(X5),X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff__singleton__if) ).

fof(fact_add__special_I3_J,axiom,
    ! [X126,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X126)),c_Groups_Oone__class_Oone(X15)) = hAPP(c_Int_Onumber__class_Onumber__of(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X126),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,
    ! [X112,X56,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),X56)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X56))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__number__of__eq__not__less) ).

fof(fact_bot2E,axiom,
    ! [X27,X12,X16,X5] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),X12),X27)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot2E) ).

fof(fact_Least__Suc,axiom,
    ! [X76,X29] :
      ( hBOOL(hAPP(X29,X76))
     => ( ~ hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
       => c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X29) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X29),c_Nat_OSuc))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Least__Suc) ).

fof(fact_divmod__int__rel__mod__eq,axiom,
    ! [X22,X151,X147,X148] :
      ( X148 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X147),X151)),X22)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X147))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22),X147)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X147))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X147),X22))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => ( X147 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => c_Divides_Odiv__class_Omod(tc_Int_Oint,X148,X147) = X22 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__mod__eq) ).

fof(fact_foldr_Osimps_I1_J,axiom,
    ! [X6,X2,X5,X16] : c_List_Ofoldr(X16,X5,X2,c_List_Olist_ONil(X16),X6) = X6,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldr_Osimps_I1_J) ).

fof(fact_concat__map__maps,axiom,
    ! [X212,X2,X16,X5] : c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(X16,tc_List_Olist(X5)),X2),X212)) = c_List_Omaps(X16,X5,X2,X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__map__maps) ).

fof(fact_maps__def,axiom,
    ! [X212,X2,X5,X16] : c_List_Omaps(X16,X5,X2,X212) = c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(X16,tc_List_Olist(X5)),X2),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_maps__def) ).

fof(fact_divmod__int__rel__div__eq,axiom,
    ! [X146,X22,X147,X148] :
      ( X148 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X147),X22)),X146)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X147))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X146))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X146),X147)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X147))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X147),X146))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X146),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => ( X147 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X148),X147) = X22 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__div__eq) ).

fof(fact_rotate__Suc,axiom,
    ! [X221,X98,X15] : hAPP(c_List_Orotate(X15,hAPP(c_Nat_OSuc,X98)),X221) = hAPP(c_List_Orotate1(X15),hAPP(c_List_Orotate(X15,X98),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__Suc) ).

fof(fact_fun__left__comm_Ofold__insert2,axiom,
    ! [X37,X12,X11,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X16,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),X37),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),hAPP(hAPP(X2,X12),X37)),X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert2) ).

fof(fact_upt__eq__Cons__conv,axiom,
    ! [X212,X12,X115,X70] :
      ( c_List_Oupt(X70,X115) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X12),X212)
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X70),X115))
        & X70 = X12
        & c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X70),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X115) = X212 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__eq__Cons__conv) ).

fof(fact_setsum__op__ivl__Suc,axiom,
    ! [X2,X45,X76,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),X45))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45),hAPP(c_Nat_OSuc,X76))) = c_Groups_Ozero__class_Ozero(X5) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),X45))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45),hAPP(c_Nat_OSuc,X76))) = 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,X45),X76))),hAPP(X2,X76)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__op__ivl__Suc) ).

fof(fact_sup1E,axiom,
    ! [X12,X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13),X12))
     => ( ~ hBOOL(hAPP(X11,X12))
       => hBOOL(hAPP(X13,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup1E) ).

fof(fact_pred__Bit1,axiom,
    ! [X100] : c_Int_Opred(c_Int_OBit1(X100)) = c_Int_OBit0(X100),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__Bit1) ).

fof(fact_nat__number__of__add__left,axiom,
    ! [X100,X169,X126] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)),X100)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)),X100) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X169)))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)),X100)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),X100) )
          & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X169)))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)),X100)) = 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),X126),X169))),X100) ) ) ) ),
    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,
    ! [X76,X45,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(X45,X76))) = hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X5),X2),c_List_Oupt(X45,X76))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__set__upt__conv__listsum__nat) ).

fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
    ! [X76,X45,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(X45,X76))) = 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(X45,X76))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_interv__listsum__conv__setsum__set__nat) ).

fof(fact_inf1E,axiom,
    ! [X12,X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13),X12))
     => ~ ( hBOOL(hAPP(X11,X12))
         => ~ hBOOL(hAPP(X13,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1E) ).

fof(fact_rotate1__rotate__swap,axiom,
    ! [X221,X98,X15] : hAPP(c_List_Orotate1(X15),hAPP(c_List_Orotate(X15,X98),X221)) = hAPP(c_List_Orotate(X15,X98),hAPP(c_List_Orotate1(X15),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__rotate__swap) ).

fof(fact_number__of__Bit1,axiom,
    ! [X132,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OBit1(X132)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),c_Groups_Oone__class_Oone(X15)),hAPP(c_Int_Onumber__class_Onumber__of(X15),X132))),hAPP(c_Int_Onumber__class_Onumber__of(X15),X132)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Bit1) ).

fof(fact_DiffI,axiom,
    ! [X13,X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X13))
       => hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffI) ).

fof(fact_code__numeral_Orecs_I2_J,axiom,
    ! [X174,X88,X89,X5] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X5,X89,X88,c_Code__Numeral_OSuc__code__numeral(X174)) = hAPP(hAPP(X88,X174),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X5,X89,X88,X174)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Orecs_I2_J) ).

fof(fact_Suc__code__numeral__def,axiom,
    ! [X100] : c_Code__Numeral_OSuc__code__numeral(X100) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X100))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__code__numeral__def) ).

fof(fact_card__def,axiom,
    ! [X11,X5] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(c_Finite__Set_Ocard(X5),X11) = 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)),X11) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(c_Finite__Set_Ocard(X5),X11) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__def) ).

fof(fact_Id__O__R,axiom,
    ! [X36,X16,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X16),c_Relation_OId(X5)),X36) = X36,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__O__R) ).

fof(fact_divide__numeral__1,axiom,
    ! [X25,X15] :
      ( ( class_Fields_Ofield(X15)
        & class_Int_Onumber__ring(X15) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OBit1(c_Int_OPls))) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__numeral__1) ).

fof(fact_divide__Numeral1,axiom,
    ! [X14,X15] :
      ( ( class_Fields_Ofield(X15)
        & class_Int_Onumber__ring(X15) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OBit1(c_Int_OPls))) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__Numeral1) ).

fof(fact_le__supE,axiom,
    ! [X14,X26,X25,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X25),X26)),X14))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X14))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__supE) ).

fof(fact_min__max_Ole__supE,axiom,
    ! [X14,X26,X25,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X25),X26)),X14))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X14))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__supE) ).

fof(fact_mult__numeral__1__right,axiom,
    ! [X25,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OBit1(c_Int_OPls))) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__numeral__1__right) ).

fof(fact_member__rec_I1_J,axiom,
    ! [X27,X212,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_List_Omember(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)),X27))
    <=> ( X12 = X27
        | hBOOL(hAPP(hAPP(c_List_Omember(X5),X212),X27)) ) ),
    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,
    ! [X98,X15,X221] :
      ( X221 != c_List_Olist_ONil(X15)
     => hAPP(c_List_Ohd(X15),hAPP(c_List_Orotate(X15,X98),X221)) = hAPP(hAPP(c_List_Onth(X15),X221),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X98,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__rotate__conv__nth) ).

fof(fact_nat__number__of__mult__left,axiom,
    ! [X100,X169,X126] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X126),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)),X100)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X126),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)),X100)) = 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),X126),X169))),X100) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__mult__left) ).

fof(fact_rotate__length01,axiom,
    ! [X98,X221,X15] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
     => hAPP(c_List_Orotate(X15,X98),X221) = X221 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__length01) ).

fof(fact_Int__insert__left,axiom,
    ! [X13,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)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13)),X19) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X13),X19)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13)),X19) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X13),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__left) ).

fof(fact_UnCI,axiom,
    ! [X11,X13,X21,X5] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X13))
       => hBOOL(hAPP(hAPP(c_member(X5),X21),X11)) )
     => hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UnCI) ).

fof(fact_map__add__dom__app__simps_I2_J,axiom,
    ! [X207,X206,X16,X45,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X45),c_Map_Odom(X5,X16,X206)))
     => hAPP(c_Map_Omap__add(X5,X16,X206,X207),X45) = hAPP(X207,X45) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__dom__app__simps_I2_J) ).

fof(fact_map__add__dom__app__simps_I3_J,axiom,
    ! [X206,X207,X16,X45,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X45),c_Map_Odom(X5,X16,X207)))
     => hAPP(c_Map_Omap__add(X5,X16,X206,X207),X45) = hAPP(X206,X45) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__dom__app__simps_I3_J) ).

fof(fact_not__square__less__zero,axiom,
    ! [X25,X15] :
      ( class_Rings_Olinordered__ring(X15)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X25)),c_Groups_Ozero__class_Ozero(X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).

fof(fact_bin__less__0__simps_I3_J,axiom,
    ! [X112] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X112)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X112),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,
    ! [X132,X126] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X126))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X132))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__number__of__Bit0) ).

fof(fact_add__leE,axiom,
    ! [X98,X100,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X100)),X98))
     => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X98))
         => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X100),X98)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).

fof(fact_eq__int__code_I9_J,axiom,
    ! [X164] :
      ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X164)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X164),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__int__code_I9_J) ).

fof(fact_rel__simps_I10_J,axiom,
    ! [X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X30)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I10_J) ).

fof(fact_rel__simps_I11_J,axiom,
    ! [X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X30)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),c_Int_OMin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I11_J) ).

fof(fact_rel__simps_I28_J,axiom,
    ! [X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X30)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),c_Int_OMin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I28_J) ).

fof(fact_rel__simps_I27_J,axiom,
    ! [X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X30)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I27_J) ).

fof(fact_neg__number__of__Bit0,axiom,
    ! [X112] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X112))))
    <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X112))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__number__of__Bit0) ).

fof(fact_Image__Id,axiom,
    ! [X11,X5] : hAPP(c_Relation_OImage(X5,X5,c_Relation_OId(X5)),X11) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Id) ).

fof(fact_insert__Diff__if,axiom,
    ! [X11,X13,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X13))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)),X13) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X13))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)),X13) = hAPP(hAPP(c_Set_Oinsert(X5),X12),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff__if) ).

fof(fact_map__comp__empty_I2_J,axiom,
    ! [X12,X45,X38,X5,X16] : c_Map_Omap__comp(X16,X5,X38,hAPP(c_COMBK(tc_Option_Ooption(X5),X16),c_Option_Ooption_ONone(X5)),X45,X12) = c_Option_Ooption_ONone(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__comp__empty_I2_J) ).

fof(fact_map__comp__empty_I1_J,axiom,
    ! [X12,X45,X38,X5,X16] : c_Map_Omap__comp(X16,X5,X38,X45,hAPP(c_COMBK(tc_Option_Ooption(X16),X38),c_Option_Ooption_ONone(X16)),X12) = c_Option_Ooption_ONone(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__comp__empty_I1_J) ).

fof(fact_le__iff__pred__less,axiom,
    ! [X97,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),X97))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X30)),X97)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__pred__less) ).

fof(fact_diff__bin__simps_I6_J,axiom,
    ! [X103] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X103)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X103)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I6_J) ).

fof(fact_div__if,axiom,
    ! [X99,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),X99),X98))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),X98) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),X98) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98)),X98)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__if) ).

fof(fact_div__geq,axiom,
    ! [X99,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),X99),X98))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),X98) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98)),X98)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__geq) ).

fof(fact_not__zle__0__negative,axiom,
    ! [X98] : ~ 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,X98))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__zle__0__negative) ).

fof(fact_rtrancl__reflcl__absorb,axiom,
    ! [X36,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X36)),c_Relation_OId(X5)) = c_Transitive__Closure_Ortrancl(X5,X36),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__reflcl__absorb) ).

fof(fact_upt__Suc__append,axiom,
    ! [X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X101))
     => c_List_Oupt(X102,hAPP(c_Nat_OSuc,X101)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X102,X101)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X101),c_List_Olist_ONil(tc_Nat_Onat))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__Suc__append) ).

fof(fact_Int__insert__right,axiom,
    ! [X13,X11,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__right) ).

fof(fact_setsum_OF__eq,axiom,
    ! [X1,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),X11) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Oplus__class_Oplus(X16)),X1),c_Groups_Ozero__class_Ozero(X16)),X11) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),X11) = c_Groups_Ozero__class_Ozero(X16) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_OF__eq) ).

fof(fact_setprod_OF__eq,axiom,
    ! [X1,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X11) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X1),c_Groups_Oone__class_Oone(X16)),X11) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X11) = c_Groups_Oone__class_Oone(X16) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_OF__eq) ).

fof(fact_nth__append,axiom,
    ! [X225,X221,X15,X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
       => hAPP(hAPP(c_List_Onth(X15),hAPP(hAPP(c_List_Oappend(X15),X221),X225)),X98) = hAPP(hAPP(c_List_Onth(X15),X221),X98) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
       => hAPP(hAPP(c_List_Onth(X15),hAPP(hAPP(c_List_Oappend(X15),X221),X225)),X98) = hAPP(hAPP(c_List_Onth(X15),X225),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__append) ).

fof(fact_Compl__iff,axiom,
    ! [X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11)))
    <=> ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__iff) ).

fof(fact_ComplD,axiom,
    ! [X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ComplD) ).

fof(fact_ComplE,axiom,
    ! [X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ComplE) ).

fof(fact_nat__number__of__Bit0,axiom,
    ! [X112] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X112)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X112)),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,
    ! [X126,X120,X5] :
      ( ( class_Int_Onumber(X5)
        & class_Orderings_Oord(X5) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X120)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X120)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X126) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X120)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X120)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X120) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__number__of) ).

fof(fact_min__number__of,axiom,
    ! [X126,X120,X5] :
      ( ( class_Int_Onumber(X5)
        & class_Orderings_Oord(X5) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X120)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X120)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X120) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X120)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X120)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X126) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__number__of) ).

fof(fact_not__add__less1,axiom,
    ! [X101,X102] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X101)),X102)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).

fof(fact_not__add__less2,axiom,
    ! [X102,X101] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),X102)),X102)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).

fof(fact_remove1__append,axiom,
    ! [X214,X212,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => c_List_Oremove1(X5,X12,hAPP(hAPP(c_List_Oappend(X5),X212),X214)) = hAPP(hAPP(c_List_Oappend(X5),c_List_Oremove1(X5,X12,X212)),X214) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => c_List_Oremove1(X5,X12,hAPP(hAPP(c_List_Oappend(X5),X212),X214)) = hAPP(hAPP(c_List_Oappend(X5),X212),c_List_Oremove1(X5,X12,X214)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__append) ).

fof(fact_neg__number__of__pred__iff__0,axiom,
    ! [X56] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X56))))
    <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56) = 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,
    ! [X12,X2,X5] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__fold1SetE) ).

fof(fact_rel__simps_I51_J,axiom,
    ! [X97,X30] :
      ( c_Int_OBit1(X30) = c_Int_OBit1(X97)
    <=> X30 = X97 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I51_J) ).

fof(fact_concat__replicate__trivial,axiom,
    ! [X102,X15] : c_List_Oconcat(X15,c_List_Oreplicate(tc_List_Olist(X15),X102,c_List_Olist_ONil(X15))) = c_List_Olist_ONil(X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__replicate__trivial) ).

fof(fact_restrict__map__def,axiom,
    ! [X45,X16,X11,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hAPP(c_Map_Orestrict__map(X5,X16,X45,X11),X12) = hAPP(X45,X12) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hAPP(c_Map_Orestrict__map(X5,X16,X45,X11),X12) = c_Option_Ooption_ONone(X16) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__map__def) ).

fof(fact_nat__diff__split__asm,axiom,
    ! [X17,X6,X29] :
      ( hBOOL(hAPP(X29,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6),X17)))
    <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X17))
            & ~ hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
          | ? [X125] :
              ( X6 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X125)
              & ~ hBOOL(hAPP(X29,X125)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).

fof(fact_distinct_Osimps_I2_J,axiom,
    ! [X212,X12,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
        & hBOOL(hAPP(c_List_Odistinct(X5),X212)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct_Osimps_I2_J) ).

fof(fact_finite__map__freshness,axiom,
    ! [X2,X16,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Map_Odom(X5,X16,X2)))
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))
       => ? [X3] : hAPP(X2,X3) = c_Option_Ooption_ONone(X16) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__map__freshness) ).

fof(fact_length__rotate,axiom,
    ! [X221,X98,X15] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),hAPP(c_List_Orotate(X15,X98),X221)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__rotate) ).

fof(fact_dropWhile_Osimps_I1_J,axiom,
    ! [X29,X5] : c_List_OdropWhile(X5,X29,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,
    ! [X11,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__insert__absorb) ).

fof(fact_setsum_Oinsert,axiom,
    ! [X1,X12,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16),hAPP(X1,X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Oinsert) ).

fof(fact_setsum__insert,axiom,
    ! [X2,X6,X90,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X90))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X90))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),hAPP(hAPP(c_Set_Oinsert(X5),X6),X90)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16),hAPP(X2,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X90)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__insert) ).

fof(fact_setprod_Oinsert,axiom,
    ! [X1,X12,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(X1,X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Oinsert) ).

fof(fact_setprod__insert,axiom,
    ! [X2,X6,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(X2,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__insert) ).

fof(fact_drop__upt,axiom,
    ! [X101,X102,X99] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X99),c_List_Oupt(X102,X101)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X99),X101),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__upt) ).

fof(fact_filter__empty__conv,axiom,
    ! [X212,X29,X5] :
      ( hAPP(c_List_Ofilter(X5,X29),X212) = c_List_Olist_ONil(X5)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
         => ~ hBOOL(hAPP(X29,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__empty__conv) ).

fof(fact_not__int__zless__negative,axiom,
    ! [X99,X98] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X98)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X99)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__int__zless__negative) ).

fof(fact_set__rotate,axiom,
    ! [X212,X76,X5] : hAPP(c_List_Oset(X5),hAPP(c_List_Orotate(X5,X76),X212)) = hAPP(c_List_Oset(X5),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rotate) ).

fof(fact_sup1CI,axiom,
    ! [X5,X11,X12,X13] :
      ( ( ~ hBOOL(hAPP(X13,X12))
       => hBOOL(hAPP(X11,X12)) )
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup1CI) ).

fof(fact_partition__P,axiom,
    ! [X258,X259,X212,X29,X5] :
      ( c_List_Opartition(X5,X29,X212) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X259),X258)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X259)))
           => hBOOL(hAPP(X29,X3)) )
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X258)))
           => ~ hBOOL(hAPP(X29,X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition__P) ).

fof(fact_trancl__domain,axiom,
    ! [X34,X5] : hAPP(c_Relation_ODomain(X5,X5),c_Transitive__Closure_Otrancl(X5,X34)) = hAPP(c_Relation_ODomain(X5,X5),X34),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__domain) ).

fof(fact_trancl__range,axiom,
    ! [X34,X5] : hAPP(c_Relation_ORange(X5,X5),c_Transitive__Closure_Otrancl(X5,X34)) = hAPP(c_Relation_ORange(X5,X5),X34),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__range) ).

fof(fact_le__nat__number__of,axiom,
    ! [X168,X56] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X56),X168))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X56),c_Int_OPls)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__nat__number__of) ).

fof(fact_add__Bit0__Bit0,axiom,
    ! [X103,X100] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X100)),c_Int_OBit0(X103)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X100),X103)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit0__Bit0) ).

fof(fact_diff__bin__simps_I7_J,axiom,
    ! [X103,X100] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X100)),c_Int_OBit0(X103)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X100),X103)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I7_J) ).

fof(fact_folding__one_Oeq__fold_H,axiom,
    ! [X12,X11,X90,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(X90,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,X2),X12),X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold_H) ).

fof(fact_Abs__Integ__cases,axiom,
    ! [X12] :
      ~ ! [X33] :
          ( X12 = hAPP(c_Int_OAbs__Integ,X33)
         => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X33),c_Int_OInteg)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Abs__Integ__cases) ).

fof(fact_upt__conv__Cons,axiom,
    ! [X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X101))
     => c_List_Oupt(X102,X101) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X102),c_List_Oupt(hAPP(c_Nat_OSuc,X102),X101)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__conv__Cons) ).

fof(fact_map__comp__simps_I2_J,axiom,
    ! [X203,X16,X38,X218,X5,X30,X202] :
      ( hAPP(X202,X30) = hAPP(c_Option_Ooption_OSome(X5),X218)
     => c_Map_Omap__comp(X5,X38,X16,X203,X202,X30) = hAPP(X203,X218) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__comp__simps_I2_J) ).

fof(fact_filter__insort__triv,axiom,
    ! [X212,X2,X5,X12,X29,X16] :
      ( class_Orderings_Olinorder(X16)
     => ( ~ hBOOL(hAPP(X29,X12))
       => hAPP(c_List_Ofilter(X5,X29),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X16,X2),X12),X212)) = hAPP(c_List_Ofilter(X5,X29),X212) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__insort__triv) ).

fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X12),X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold_H) ).

fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X12),X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold_H) ).

fof(fact_not__psubset__empty,axiom,
    ! [X11,X5] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__psubset__empty) ).

fof(fact_restrict__out,axiom,
    ! [X45,X16,X11,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
     => hAPP(c_Map_Orestrict__map(X5,X16,X45,X11),X12) = c_Option_Ooption_ONone(X16) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__out) ).

fof(fact_fold1__eq__fold,axiom,
    ! [X6,X11,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Groups_Otimes__class_Otimes(X5)),X6),X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__eq__fold) ).

fof(fact_number__of__Bit0,axiom,
    ! [X132,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OBit0(X132)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(c_Int_Onumber__class_Onumber__of(X15),X132))),hAPP(c_Int_Onumber__class_Onumber__of(X15),X132)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Bit0) ).

fof(fact_map__nth,axiom,
    ! [X212,X5] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X5),hAPP(c_List_Onth(X5),X212)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212))) = X212,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__nth) ).

fof(fact_le__infE,axiom,
    ! [X26,X25,X14,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X25),X26)))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X25))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infE) ).

fof(fact_min__max_Ole__infE,axiom,
    ! [X26,X25,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X25),X26)))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X25))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__infE) ).

fof(fact_length__remove1,axiom,
    ! [X212,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremove1(X5,X12,X212)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremove1(X5,X12,X212)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__remove1) ).

fof(fact_Int__insert__left__if0,axiom,
    ! [X13,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)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13)),X19) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X13),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__left__if0) ).

fof(fact_nat__of__aux__code,axiom,
    ! [X98,X102] :
      ( ( X102 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => c_Code__Numeral_Onat__of__aux(X102,X98) = X98 )
      & ( X102 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => c_Code__Numeral_Onat__of__aux(X102,X98) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X102),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X98)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__aux__code) ).

fof(fact_nat__of__aux__def,axiom,
    ! [X98,X102] : c_Code__Numeral_Onat__of__aux(X102,X98) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X102)),X98),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__aux__def) ).

fof(fact_wf__trancl,axiom,
    ! [X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => c_Wellfounded_Owf(X5,c_Transitive__Closure_Otrancl(X5,X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__trancl) ).

fof(fact_R__O__Id,axiom,
    ! [X36,X16,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X16,X16),X36),c_Relation_OId(X16)) = X36,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_R__O__Id) ).

fof(fact_map__comp__simps_I1_J,axiom,
    ! [X203,X16,X38,X5,X30,X202] :
      ( hAPP(X202,X30) = c_Option_Ooption_ONone(X5)
     => c_Map_Omap__comp(X5,X38,X16,X203,X202,X30) = c_Option_Ooption_ONone(X38) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__comp__simps_I1_J) ).

fof(fact_trancl__unfold__right,axiom,
    ! [X34,X5] : c_Transitive__Closure_Otrancl(X5,X34) = hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),c_Transitive__Closure_Ortrancl(X5,X34)),X34),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__unfold__right) ).

fof(fact_trancl__rtrancl__absorb,axiom,
    ! [X36,X5] : c_Transitive__Closure_Ortrancl(X5,c_Transitive__Closure_Otrancl(X5,X36)) = c_Transitive__Closure_Ortrancl(X5,X36),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__rtrancl__absorb) ).

fof(fact_concat_Osimps_I1_J,axiom,
    ! [X15] : c_List_Oconcat(X15,c_List_Olist_ONil(tc_List_Olist(X15))) = c_List_Olist_ONil(X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat_Osimps_I1_J) ).

fof(fact_Min_Oeq__fold_H,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X12),X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oeq__fold_H) ).

fof(fact_Max_Oeq__fold_H,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X12),X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oeq__fold_H) ).

fof(fact_Sup__fin_Oeq__fold_H,axiom,
    ! [X12,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X12),X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oeq__fold_H) ).

fof(fact_Inf__fin_Oeq__fold_H,axiom,
    ! [X12,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X12),X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oeq__fold_H) ).

fof(fact_eq__nat__number__of,axiom,
    ! [X168,X56] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)
    <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X168)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X56)))
         => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X168)))
             => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X56) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
            & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X168)))
             => X56 = X168 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__nat__number__of) ).

fof(fact_abs__number__of,axiom,
    ! [X14,X15] :
      ( ( class_Int_Onumber__ring(X15)
        & class_Rings_Olinordered__idom(X15) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X14)),c_Groups_Ozero__class_Ozero(X15)))
         => hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X14)) = hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X14)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X14)),c_Groups_Ozero__class_Ozero(X15)))
         => hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X14)) = hAPP(c_Int_Onumber__class_Onumber__of(X15),X14) ) ) ),
    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,
    ! [X169,X126] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X169)))
           => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = 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),X169)))
           => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X169))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__nat__number__of) ).

fof(fact_min__max_OSup__fin_Oinsert,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( X11 != 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),X12),X11)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X12),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oinsert) ).

fof(fact_min__max_OInf__fin_Oinsert,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( X11 != 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),X12),X11)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X12),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oinsert) ).

fof(fact_mult__Bit0,axiom,
    ! [X103,X100] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X100)),X103) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X100),X103)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Bit0) ).

fof(fact_takeWhile__append1,axiom,
    ! [X214,X29,X212,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => ( ~ hBOOL(hAPP(X29,X12))
       => c_List_OtakeWhile(X5,X29,hAPP(hAPP(c_List_Oappend(X5),X212),X214)) = c_List_OtakeWhile(X5,X29,X212) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__append1) ).

fof(fact_div__nat__number__of,axiom,
    ! [X169,X126] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X169))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nat__number__of) ).

fof(fact_power__nat__number__of__number__of,axiom,
    ! [X132,X126] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X132)) = 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),X132)) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X132)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X132))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__nat__number__of__number__of) ).

fof(fact_mk__less__def,axiom,
    ! [X27,X12,X36,X5] :
      ( c_Partial__Function_Omk__less(X5,X36,X12,X27)
    <=> ( hBOOL(hAPP(hAPP(X36,X12),X27))
        & ~ hBOOL(hAPP(hAPP(X36,X27),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mk__less__def) ).

fof(fact_fold1__insert,axiom,
    ! [X12,X11,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
         => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
           => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__insert) ).

fof(fact_Suc__diff__number__of,axiom,
    ! [X99,X126] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X126))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X99)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X126))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__number__of) ).

fof(fact_ex__least__nat__less,axiom,
    ! [X76,X29] :
      ( ~ hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
     => ( hBOOL(hAPP(X29,X76))
       => ? [X109] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X109),X76))
            & ! [X145] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X145),X109))
               => ~ hBOOL(hAPP(X29,X145)) )
            & hBOOL(hAPP(X29,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X109),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,
    ! [X45,X76] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X76,X45) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X76),hAPP(c_Nat_OSuc,X45))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanAtMost__upt) ).

fof(fact_eq__int__code_I3_J,axiom,
    ! [X163] :
      ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X163)))
    <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X163)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__int__code_I3_J) ).

fof(fact_rel__simps_I8_J,axiom,
    ! [X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X30)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I8_J) ).

fof(fact_rel__simps_I25_J,axiom,
    ! [X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X30)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I25_J) ).

fof(fact_rel__simps_I4_J,axiom,
    ! [X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X30)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I4_J) ).

fof(fact_rel__simps_I21_J,axiom,
    ! [X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X30)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I21_J) ).

fof(fact_Int__insert__right__if0,axiom,
    ! [X13,X11,X6,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__right__if0) ).

fof(fact_rotate__id,axiom,
    ! [X221,X15,X98] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X98,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Orotate(X15,X98),X221) = X221 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__id) ).

fof(fact_rotate__is__Nil__conv,axiom,
    ! [X212,X76,X5] :
      ( hAPP(c_List_Orotate(X5,X76),X212) = c_List_Olist_ONil(X5)
    <=> X212 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__is__Nil__conv) ).

fof(fact_simp__from__to,axiom,
    ! [X70,X115] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X115),X70))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X70,X115) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X115),X70))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X70,X115) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X70),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X70),c_Groups_Oone__class_Oone(tc_Int_Oint)),X115)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_simp__from__to) ).

fof(fact_double__number__of__Bit0,axiom,
    ! [X132,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),c_Groups_Oone__class_Oone(X15)),c_Groups_Oone__class_Oone(X15))),hAPP(c_Int_Onumber__class_Onumber__of(X15),X132)) = hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OBit0(X132)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__number__of__Bit0) ).

fof(fact_insertCI,axiom,
    ! [X17,X13,X6,X5] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X13))
       => X6 = X17 )
     => hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X17),X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertCI) ).

fof(fact_Bit1__def,axiom,
    ! [X100] : c_Int_OBit1(X100) = 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)),X100)),X100),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def) ).

fof(fact_internal__split__conv,axiom,
    ! [X17,X6,X21,X5,X38,X16] : hAPP(hAPP(c_Product__Type_Ointernal__split(X16,X38,X5),X21),hAPP(hAPP(c_Product__Type_OPair(X16,X38),X6),X17)) = hAPP(hAPP(X21,X6),X17),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_internal__split__conv) ).

fof(fact_internal__split__def,axiom,
    ! [X38,X16,X5] : c_Product__Type_Ointernal__split(X5,X16,X38) = c_Product__Type_Oprod_Oprod__case(X5,X16,X38),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_internal__split__def) ).

fof(fact_map__replicate__trivial,axiom,
    ! [X70,X12,X5] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X5),hAPP(c_COMBK(X5,tc_Nat_Onat),X12)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X70)) = c_List_Oreplicate(X5,X70,X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__replicate__trivial) ).

fof(fact_ComplI,axiom,
    ! [X11,X21,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
     => hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ComplI) ).

fof(fact_vimage__const,axiom,
    ! [X16,X11,X21,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
       => hAPP(c_Set_Ovimage(X16,X5,hAPP(c_COMBK(X5,X16),X21)),X11) = c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
       => hAPP(c_Set_Ovimage(X16,X5,hAPP(c_COMBK(X5,X16),X21)),X11) = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__const) ).

fof(fact_folding__one_Oinsert,axiom,
    ! [X12,X11,X90,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X90,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(X2,X12),hAPP(X90,X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Oinsert) ).

fof(fact_map__Suc__upt,axiom,
    ! [X76,X45] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(X45,X76)) = c_List_Oupt(hAPP(c_Nat_OSuc,X45),hAPP(c_Nat_OSuc,X76)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__Suc__upt) ).

fof(fact_divmod__int__def,axiom,
    ! [X26,X25] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
           => c_Divides_Odivmod__int(X25,X26) = c_Divides_OposDivAlg(X25,X26) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
           => ( ( X25 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
               => c_Divides_Odivmod__int(X25,X26) = 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)) )
              & ( X25 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
               => c_Divides_Odivmod__int(X25,X26) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26))) ) ) ) ) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
           => c_Divides_Odivmod__int(X25,X26) = c_Divides_OnegDivAlg(X25,X26) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
           => c_Divides_Odivmod__int(X25,X26) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__def) ).

fof(fact_takeWhile__tail,axiom,
    ! [X97,X212,X5,X12,X29] :
      ( ~ hBOOL(hAPP(X29,X12))
     => c_List_OtakeWhile(X5,X29,hAPP(hAPP(c_List_Oappend(X5),X212),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X97))) = c_List_OtakeWhile(X5,X29,X212) ),
    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,
    ! [X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__1__eq__1) ).

fof(fact_semiring__norm_I110_J,axiom,
    ! [X15] :
      ( class_Int_Onumber__ring(X15)
     => c_Groups_Oone__class_Oone(X15) = hAPP(c_Int_Onumber__class_Onumber__of(X15),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,
    ! [X76,X45] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X76)),X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).

fof(fact_abs__not__less__zero,axiom,
    ! [X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),c_Groups_Ozero__class_Ozero(X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__not__less__zero) ).

fof(fact_of__nat__less__0__iff,axiom,
    ! [X99,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),X99)),c_Groups_Ozero__class_Ozero(X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__0__iff) ).

fof(fact_iszero__number__of__Bit0,axiom,
    ! [X112,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(X112)))
      <=> c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__number__of__Bit0) ).

fof(fact_add__nat__number__of,axiom,
    ! [X169,X126] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X126),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X126),c_Int_OPls))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X169),c_Int_OPls))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X169),c_Int_OPls))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X126),X169)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nat__number__of) ).

fof(fact_power__nat__number__of,axiom,
    ! [X98,X126] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),X98) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X98) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),X98) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),X98)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__nat__number__of) ).

fof(fact_diff__bin__simps_I3_J,axiom,
    ! [X103] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X103)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X103)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I3_J) ).

fof(fact_minus__shift__def,axiom,
    ! [X123,X103,X100] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X100),X103))
       => c_Random_Ominus__shift(X123,X100,X103) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X123),X100)),X103) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X100),X103))
       => c_Random_Ominus__shift(X123,X100,X103) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X100),X103) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__shift__def) ).

fof(fact_split__zmod,axiom,
    ! [X30,X76,X29] :
      ( hBOOL(hAPP(X29,c_Divides_Odiv__class_Omod(tc_Int_Oint,X76,X30)))
    <=> ( ( X30 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(X29,X76)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))
         => ! [X145,X124] :
              ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X124))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X124),X30))
                & X76 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X145)),X124) )
             => hBOOL(hAPP(X29,X124)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [X145,X124] :
              ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),X124))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X124),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                & X76 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X145)),X124) )
             => hBOOL(hAPP(X29,X124)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__zmod) ).

fof(fact_upto_Osimps,axiom,
    ! [X101,X102] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X102),X101))
       => c_List_Oupto(X102,X101) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X102),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X102),c_Groups_Oone__class_Oone(tc_Int_Oint)),X101)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X102),X101))
       => c_List_Oupto(X102,X101) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upto_Osimps) ).

fof(fact_rel__simps_I49_J,axiom,
    ! [X103,X100] : c_Int_OBit0(X100) != c_Int_OBit1(X103),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I49_J) ).

fof(fact_rel__simps_I50_J,axiom,
    ! [X103,X100] : c_Int_OBit1(X100) != c_Int_OBit0(X103),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I50_J) ).

fof(fact_divmod__nat__div__mod,axiom,
    ! [X98,X99] : c_Divides_Odivmod__nat(X99,X98) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),X98)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__div__mod) ).

fof(fact_code__numeral_Osimps_I5_J,axiom,
    ! [X174,X88,X89,X5] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X5,X89,X88,c_Code__Numeral_OSuc__code__numeral(X174)) = hAPP(X88,X174),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I5_J) ).

fof(fact_greaterThanLessThan__upt,axiom,
    ! [X45,X76] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X76,X45) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X76),X45)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanLessThan__upt) ).

fof(fact_remdups_Osimps_I2_J,axiom,
    ! [X212,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => c_List_Oremdups(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = c_List_Oremdups(X5,X212) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => c_List_Oremdups(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Oremdups(X5,X212)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups_Osimps_I2_J) ).

fof(fact_of__int__of__nat,axiom,
    ! [X100,X15] :
      ( class_Rings_Oring__1(X15)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X100),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hAPP(c_Int_Oring__1__class_Oof__int(X15),X100) = hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X100)))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X100),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hAPP(c_Int_Oring__1__class_Oof__int(X15),X100) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),hAPP(c_Int_Onat,X100)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__of__nat) ).

fof(fact_small__lazy_H_Osimps,axiom,
    ! [X102,X41] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X41),X102))
       => c_Lazy__Sequence_Osmall__lazy_H(X41,X102) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X41),X102))
       => c_Lazy__Sequence_Osmall__lazy_H(X41,X102) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X102),c_Lazy__Sequence_Osmall__lazy_H(X41,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X102),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_Min_Oinsert,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X12),c_Big__Operators_Olinorder__class_OMin(X5,X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oinsert) ).

fof(fact_Max_Oinsert,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X12),c_Big__Operators_Olinorder__class_OMax(X5,X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oinsert) ).

fof(fact_Sup__fin_Oinsert,axiom,
    ! [X12,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( X11 != 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),X12),X11)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X12),c_Big__Operators_Olattice__class_OSup__fin(X5,X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oinsert) ).

fof(fact_Inf__fin_Oinsert,axiom,
    ! [X12,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( X11 != 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),X12),X11)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X12),c_Big__Operators_Olattice__class_OInf__fin(X5,X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oinsert) ).

fof(fact_rtrancl__trancl__absorb,axiom,
    ! [X36,X5] : c_Transitive__Closure_Otrancl(X5,c_Transitive__Closure_Ortrancl(X5,X36)) = c_Transitive__Closure_Ortrancl(X5,X36),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trancl__absorb) ).

fof(fact_sublist__singleton,axiom,
    ! [X12,X5,X11] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X11))
       => c_List_Osublist(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Olist_ONil(X5)),X11) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Olist_ONil(X5)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X11))
       => c_List_Osublist(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Olist_ONil(X5)),X11) = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__singleton) ).

fof(fact_in__set__member,axiom,
    ! [X212,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
    <=> hBOOL(hAPP(hAPP(c_List_Omember(X5),X212),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__member) ).

fof(fact_List_Omember__def,axiom,
    ! [X12,X212,X5] :
      ( hBOOL(hAPP(hAPP(c_List_Omember(X5),X212),X12))
    <=> hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Omember__def) ).

fof(fact_one__mod__nat__number__of,axiom,
    ! [X169] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X169)))
       => 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),X169)) = 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),X169)))
       => 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),X169)) = 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),X169))) ) ),
    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,
    ! [X27,X12,X5] :
      ( class_Orderings_Opreorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X12),X27))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X27),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).

fof(fact_card_Oinsert,axiom,
    ! [X12,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oinsert) ).

fof(fact_split__zdiv,axiom,
    ! [X30,X76,X29] :
      ( hBOOL(hAPP(X29,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X76),X30)))
    <=> ( ( X30 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(X29,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)),X30))
         => ! [X145] :
              ( ? [X124] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X124))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X124),X30))
                  & X76 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X145)),X124) )
             => hBOOL(hAPP(X29,X145)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [X145] :
              ( ? [X124] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),X124))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X124),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & X76 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X145)),X124) )
             => hBOOL(hAPP(X29,X145)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__zdiv) ).

fof(fact_insert__ident,axiom,
    ! [X13,X11,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X13))
       => ( hAPP(hAPP(c_Set_Oinsert(X5),X12),X11) = hAPP(hAPP(c_Set_Oinsert(X5),X12),X13)
        <=> X11 = X13 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__ident) ).

fof(fact_card__insert__if,axiom,
    ! [X12,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(c_Finite__Set_Ocard(X5),X11) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__if) ).

fof(fact_last__upt,axiom,
    ! [X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X101))
     => c_List_Olast(tc_Nat_Onat,c_List_Oupt(X102,X101)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X101),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,
    ! [X98] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X98)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X98,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__code__numeral__minus__one) ).

fof(fact_not__less__eq,axiom,
    ! [X76,X45] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),hAPP(c_Nat_OSuc,X45))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).

fof(fact_distinct__upt,axiom,
    ! [X101,X102] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X102,X101))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__upt) ).

fof(fact_relpow_Osimps_I1_J,axiom,
    ! [X36,X5] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X36) = c_Relation_OId(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_relpow_Osimps_I1_J) ).

fof(fact_takeWhile_Osimps_I2_J,axiom,
    ! [X212,X5,X12,X29] :
      ( ( hBOOL(hAPP(X29,X12))
       => c_List_OtakeWhile(X5,X29,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_OtakeWhile(X5,X29,X212)) )
      & ( ~ hBOOL(hAPP(X29,X12))
       => c_List_OtakeWhile(X5,X29,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I2_J) ).

fof(fact_int__less__0__conv,axiom,
    ! [X100] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X100)),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,
    ! [X97] :
      ( c_Int_OMin = c_Int_OBit1(X97)
    <=> c_Int_OMin = X97 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I43_J) ).

fof(fact_rel__simps_I47_J,axiom,
    ! [X30] :
      ( c_Int_OBit1(X30) = c_Int_OMin
    <=> X30 = c_Int_OMin ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I47_J) ).

fof(fact_rel__simps_I46_J,axiom,
    ! [X100] : c_Int_OBit1(X100) != c_Int_OPls,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I46_J) ).

fof(fact_rel__simps_I39_J,axiom,
    ! [X103] : c_Int_OPls != c_Int_OBit1(X103),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).

fof(fact_of__nat__number__of__lemma,axiom,
    ! [X126,X15] :
      ( class_Int_Onumber__ring(X15)
     => ( ( 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(c_Nat_Osemiring__1__class_Oof__nat(X15),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(X15),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(c_Nat_Osemiring__1__class_Oof__nat(X15),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = c_Groups_Ozero__class_Ozero(X15) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__number__of__lemma) ).

fof(fact_card__insert__disjoint,axiom,
    ! [X12,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__disjoint) ).

fof(fact_linorder__antisym__conv2,axiom,
    ! [X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X12),X27))
        <=> X12 = X27 ) ) ),
    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,
    ! [X212,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => c_List_Oinsert(X5,X12,X212) = X212 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => c_List_Oinsert(X5,X12,X212) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Oinsert__def) ).

fof(fact_xt1_I9_J,axiom,
    ! [X25,X26,X15] :
      ( class_Orderings_Oorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),X25))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).

fof(fact_not__less__iff__gr__or__eq,axiom,
    ! [X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X12),X27))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X27),X12))
          | X12 = X27 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).

fof(fact_leD,axiom,
    ! [X14,X22,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X14))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).

fof(fact_linorder__not__less,axiom,
    ! [X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X12),X27))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X27),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).

fof(fact_linorder__not__le,axiom,
    ! [X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X27),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).

fof(fact_order__less__asym,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Opreorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).

fof(fact_order__less__asym_H,axiom,
    ! [X26,X25,X15] :
      ( class_Orderings_Opreorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).

fof(fact_order__less__imp__not__less,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Opreorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).

fof(fact_order__less__not__sym,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Opreorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).

fof(fact_mult__nat__number__of,axiom,
    ! [X169,X126] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X126),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X126),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X126),X169)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nat__number__of) ).

fof(fact_hd__upt,axiom,
    ! [X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X101))
     => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(X102,X101)) = X102 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__upt) ).

fof(fact_empty__iff,axiom,
    ! [X21,X5] : ~ hBOOL(hAPP(hAPP(c_member(X5),X21),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,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),hAPP(c_Nat_OSuc,X98)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X98))
       => X99 = hAPP(c_Nat_OSuc,X98) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucE) ).

fof(fact_atLeastAtMost__upt,axiom,
    ! [X45,X76] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X76,X45) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X76,hAPP(c_Nat_OSuc,X45))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastAtMost__upt) ).

fof(fact_atLeastLessThanSuc,axiom,
    ! [X76,X45] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45),hAPP(c_Nat_OSuc,X76)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X76),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45),X76)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45),hAPP(c_Nat_OSuc,X76)) = 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,
    ! [X212,X5,X12,X29] :
      ( ( hBOOL(hAPP(X29,X12))
       => hAPP(c_List_Ofilter(X5,X29),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),hAPP(c_List_Ofilter(X5,X29),X212)) )
      & ( ~ hBOOL(hAPP(X29,X12))
       => hAPP(c_List_Ofilter(X5,X29),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = hAPP(c_List_Ofilter(X5,X29),X212) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter_Osimps_I2_J) ).

fof(fact_less__SucE,axiom,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),hAPP(c_Nat_OSuc,X98)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
       => X99 = X98 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).

fof(fact_less__antisym,axiom,
    ! [X99,X98] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X99))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_OSuc,X99)))
       => X99 = X98 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).

fof(fact_not__less__less__Suc__eq,axiom,
    ! [X45,X76] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),X45))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),hAPP(c_Nat_OSuc,X45)))
      <=> X76 = X45 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).

fof(fact_divmod__nat__rel__divmod__nat,axiom,
    ! [X98,X99] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X99,X98),c_Divides_Odivmod__nat(X99,X98))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__divmod__nat) ).

fof(fact_code__numeral_Osize_I4_J,axiom,
    ! [X172] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X172)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X172)),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,
    ! [X76] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X76) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X76))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__upto) ).

fof(fact_number__of__pred,axiom,
    ! [X132,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_Opred(X132)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),c_Groups_Oone__class_Oone(X15))),hAPP(c_Int_Onumber__class_Onumber__of(X15),X132)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__pred) ).

fof(fact_not__less__Least,axiom,
    ! [X29,X30,X5] :
      ( class_Orderings_Owellorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),c_Orderings_Oord__class_OLeast(X5,X29)))
       => ~ hBOOL(hAPP(X29,X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__Least) ).

fof(fact_atLeastatMost__empty__iff2,axiom,
    ! [X17,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X17)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastatMost__empty__iff2) ).

fof(fact_greaterThanAtMost__empty__iff2,axiom,
    ! [X97,X30,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X30,X97)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),X97)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanAtMost__empty__iff2) ).

fof(fact_atLeastatMost__empty__iff,axiom,
    ! [X17,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X17) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastatMost__empty__iff) ).

fof(fact_greaterThanAtMost__empty__iff,axiom,
    ! [X97,X30,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X30,X97) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),X97)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanAtMost__empty__iff) ).

fof(fact_divmod__nat__base,axiom,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
     => c_Divides_Odivmod__nat(X99,X98) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X99) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__base) ).

fof(fact_equalityE,axiom,
    ! [X5,X13,X11] :
      ( X11 = X13
     => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
         => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityE) ).

fof(fact_Suc__n__not__le__n,axiom,
    ! [X98] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X98)),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).

fof(fact_z3div__def,axiom,
    ! [X100,X103] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X103))
       => c_SMT_Oz3div(X100,X103) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X100),X103) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X103))
       => c_SMT_Oz3div(X100,X103) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X100),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X103))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_z3div__def) ).

fof(fact_mod__if,axiom,
    ! [X98,X99] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98) = X99 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98),X98) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__if) ).

fof(fact_mod__geq,axiom,
    ! [X98,X99] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98),X98) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__geq) ).

fof(fact_not__in__set__insert,axiom,
    ! [X212,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => c_List_Oinsert(X5,X12,X212) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__in__set__insert) ).

fof(fact_linorder__antisym__conv1,axiom,
    ! [X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X12),X27))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27))
        <=> X12 = X27 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).

fof(fact_atLeastLessThan__empty__iff,axiom,
    ! [X17,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X17) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff) ).

fof(fact_atLeastLessThan__empty__iff2,axiom,
    ! [X17,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),X17)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff2) ).

fof(fact_code__numeral_Oinject,axiom,
    ! [X173,X174] :
      ( c_Code__Numeral_OSuc__code__numeral(X174) = c_Code__Numeral_OSuc__code__numeral(X173)
    <=> X174 = X173 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Oinject) ).

fof(fact_code__numeral_Osize_I2_J,axiom,
    ! [X172] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X172)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X172)),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,
    ! [X100] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X100)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X100)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Bit0) ).

fof(fact_filter__replicate,axiom,
    ! [X76,X5,X12,X29] :
      ( ( hBOOL(hAPP(X29,X12))
       => hAPP(c_List_Ofilter(X5,X29),c_List_Oreplicate(X5,X76,X12)) = c_List_Oreplicate(X5,X76,X12) )
      & ( ~ hBOOL(hAPP(X29,X12))
       => hAPP(c_List_Ofilter(X5,X29),c_List_Oreplicate(X5,X76,X12)) = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__replicate) ).

fof(fact_transfer__nat__int__list__return__embed,axiom,
    ! [X103] :
      ( c_List_Onat__list(X103)
     => c_List_Oembed__list(c_List_Oreturn__list(X103)) = X103 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__list__return__embed) ).

fof(fact_all__not__in__conv,axiom,
    ! [X11,X5] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
    <=> X11 = 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,
    ! [X212,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => c_List_Oremove1(X5,X12,X212) = X212 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__idem) ).

fof(fact_length__upt,axiom,
    ! [X101,X102] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X102,X101)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X101),X102),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__upt) ).

fof(fact_sgn__if,axiom,
    ! [X14,X15] :
      ( class_Groups_Osgn__if(X15)
     => ( ( X14 = c_Groups_Ozero__class_Ozero(X15)
         => c_Groups_Osgn__class_Osgn(X15,X14) = c_Groups_Ozero__class_Ozero(X15) )
        & ( X14 != c_Groups_Ozero__class_Ozero(X15)
         => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X14))
             => c_Groups_Osgn__class_Osgn(X15,X14) = c_Groups_Oone__class_Oone(X15) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X14))
             => c_Groups_Osgn__class_Osgn(X15,X14) = hAPP(c_Groups_Ouminus__class_Ouminus(X15),c_Groups_Oone__class_Oone(X15)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__if) ).

fof(fact_upt__eq__Nil__conv,axiom,
    ! [X115,X70] :
      ( c_List_Oupt(X70,X115) = c_List_Olist_ONil(tc_Nat_Onat)
    <=> ( X115 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X115),X70)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__eq__Nil__conv) ).

fof(fact_upt__conv__Nil,axiom,
    ! [X102,X101] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X101),X102))
     => c_List_Oupt(X102,X101) = c_List_Olist_ONil(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__conv__Nil) ).

fof(fact_z3mod__def,axiom,
    ! [X100,X103] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X103))
       => c_SMT_Oz3mod(X100,X103) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X100,X103) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X103))
       => c_SMT_Oz3mod(X100,X103) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X100,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X103)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_z3mod__def) ).

fof(fact_abs__if,axiom,
    ! [X25,X15] :
      ( class_Groups_Oabs__if(X15)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),c_Groups_Ozero__class_Ozero(X15)))
         => hAPP(c_Groups_Oabs__class_Oabs(X15),X25) = hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),c_Groups_Ozero__class_Ozero(X15)))
         => hAPP(c_Groups_Oabs__class_Oabs(X15),X25) = X25 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__if) ).

fof(fact_not__one__less__zero,axiom,
    ! [X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Oone__class_Oone(X15)),c_Groups_Ozero__class_Ozero(X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).

fof(fact_not__one__le__zero,axiom,
    ! [X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Oone__class_Oone(X15)),c_Groups_Ozero__class_Ozero(X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).

fof(fact_add__diff__inverse,axiom,
    ! [X98,X99] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98)) = X99 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__inverse) ).

fof(fact_atLeast__upt,axiom,
    ! [X76] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X76) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X76)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast__upt) ).

fof(fact_linorder__neqE__linordered__idom,axiom,
    ! [X22,X14,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => ( X14 != X22
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).

fof(fact_linorder__cases,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
       => ( X14 != X22
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).

fof(fact_linorder__neqE,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( X14 != X22
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).

fof(fact_linorder__antisym__conv3,axiom,
    ! [X12,X27,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X27),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X12),X27))
        <=> X12 = X27 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).

fof(fact_not__leE,axiom,
    ! [X14,X22,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X14))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).

fof(fact_leI,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).

fof(fact_linorder__le__cases,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).

fof(fact_set__upt,axiom,
    ! [X115,X70] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X70,X115)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X70),X115),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__upt) ).

fof(fact_atLeastLessThan__upt,axiom,
    ! [X115,X70] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X70),X115) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X70,X115)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__upt) ).

fof(fact_succ__pred,axiom,
    ! [X14] : c_Int_Osucc(c_Int_Opred(X14)) = X14,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__pred) ).

fof(fact_number__of__succ,axiom,
    ! [X100,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_Osucc(X100)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),c_Groups_Oone__class_Oone(X15)),hAPP(c_Int_Onumber__class_Onumber__of(X15),X100)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__succ) ).

fof(fact_equals0D,axiom,
    ! [X6,X5,X11] :
      ( X11 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equals0D) ).

fof(fact_not__neg__eq__ge__0,axiom,
    ! [X12] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X12))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__eq__ge__0) ).

fof(fact_nat__eq__iff,axiom,
    ! [X45,X112] :
      ( hAPP(c_Int_Onat,X112) = X45
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X112))
         => X112 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X45) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X112))
         => X45 = 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,
    ! [X112,X45] :
      ( X45 = hAPP(c_Int_Onat,X112)
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X112))
         => X112 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X45) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X112))
         => X45 = 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,
    ! [X23] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X23)) = X23 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X23)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__nat__eq) ).

fof(fact_tsub__def,axiom,
    ! [X14,X22] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22),X14))
       => c_Nat__Transfer_Otsub(X14,X22) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X14),X22) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22),X14))
       => c_Nat__Transfer_Otsub(X14,X22) = 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,
    ! [X126,X15] :
      ( class_Int_Onumber__ring(X15)
     => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = c_Groups_Ozero__class_Ozero(X15) )
        & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(X15),X126) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__number__of__eq) ).

fof(fact_mod__nat__def,axiom,
    ! [X98,X99] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X99,X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__nat__def) ).

fof(fact_remove1__filter__not,axiom,
    ! [X212,X5,X12,X29] :
      ( ~ hBOOL(hAPP(X29,X12))
     => c_List_Oremove1(X5,X12,hAPP(c_List_Ofilter(X5,X29),X212)) = hAPP(c_List_Ofilter(X5,X29),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__filter__not) ).

fof(fact_div__nat__def,axiom,
    ! [X98,X99] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),X98) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X99,X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nat__def) ).

fof(fact_int__nat__number__of,axiom,
    ! [X126] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__nat__number__of) ).

fof(fact_zabs__def,axiom,
    ! [X102] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X102),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X102) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X102) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X102),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X102) = X102 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zabs__def) ).

fof(fact_linorder__neqE__nat,axiom,
    ! [X22,X14] :
      ( X14 != X22
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),X22))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).

fof(fact_divmod__nat__eq,axiom,
    ! [X159,X98,X99] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X99,X98),X159))
     => c_Divides_Odivmod__nat(X99,X98) = X159 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__eq) ).

fof(fact_zsgn__def,axiom,
    ! [X102] :
      ( ( X102 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X102) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X102 != 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)),X102))
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X102) = 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)),X102))
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X102) = 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,
    ! [X101,X102] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X102,X101)),
    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,
    ! [X14,X15] :
      ( class_Orderings_Opreorder(X15)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).

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,
    ! [X98] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),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,
    ! [X98] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).

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

fof(fact_divmod__nat__zero,axiom,
    ! [X99] : c_Divides_Odivmod__nat(X99,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)),X99),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__zero) ).

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

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

fof(fact_rel__simps_I48_J,axiom,
    ! [X97,X30] :
      ( c_Int_OBit0(X30) = c_Int_OBit0(X97)
    <=> X30 = X97 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I48_J) ).

fof(fact_setsum__infinite,axiom,
    ! [X2,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X11) = c_Groups_Ozero__class_Ozero(X16) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__infinite) ).

fof(fact_setsum_Oinfinite,axiom,
    ! [X1,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),X11) = c_Groups_Ozero__class_Ozero(X16) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Oinfinite) ).

fof(fact_setprod_Oinfinite,axiom,
    ! [X1,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X11) = c_Groups_Oone__class_Oone(X16) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Oinfinite) ).

fof(fact_setprod__infinite,axiom,
    ! [X2,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),X11) = c_Groups_Oone__class_Oone(X16) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__infinite) ).

fof(fact_not__neg__int,axiom,
    ! [X98] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X98))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__int) ).

fof(fact_code__numeral_Osimps_I3_J,axiom,
    ! [X175] : c_Code__Numeral_OSuc__code__numeral(X175) != 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,
    ! [X176] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X176),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I2_J) ).

fof(help_c__fimplies__3,axiom,
    ! [X28,X29] :
      ( ~ hBOOL(hAPP(hAPP(c_fimplies,X29),X28))
      | ~ hBOOL(X29)
      | hBOOL(X28) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__3) ).

fof(fact_card__eq__0__iff,axiom,
    ! [X11,X5] :
      ( hAPP(c_Finite__Set_Ocard(X5),X11) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X11 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__eq__0__iff) ).

fof(help_c__fdisj__3,axiom,
    ! [X28,X29] :
      ( ~ hBOOL(hAPP(hAPP(c_fdisj,X29),X28))
      | hBOOL(X29)
      | hBOOL(X28) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__3) ).

fof(help_c__fconj__2,axiom,
    ! [X28,X29] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X29),X28))
      | hBOOL(X29) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__2) ).

fof(help_c__fconj__3,axiom,
    ! [X28,X29] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X29),X28))
      | hBOOL(X28) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__3) ).

fof(fact_empty__Collect__eq,axiom,
    ! [X29,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),X29)
    <=> ! [X3] : ~ hBOOL(hAPP(X29,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__Collect__eq) ).

fof(fact_Collect__empty__eq,axiom,
    ! [X29,X5] :
      ( hAPP(c_Set_OCollect(X5),X29) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] : ~ hBOOL(hAPP(X29,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).

fof(help_c__fequal__1,axiom,
    ! [X27,X12] :
      ( ~ hBOOL(hAPP(hAPP(c_fequal,X12),X27))
      | X12 = X27 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).

fof(fact_nat__of__code,axiom,
    ! [X102] : hAPP(c_Code__Numeral_Onat__of,X102) = c_Code__Numeral_Onat__of__aux(X102,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,
    ! [X29,X5] : ~ c_List_Olist__ex1(X5,X29,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,
    ! [X29,X5] : ~ c_List_Olist__ex(X5,X29,c_List_Olist_ONil(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__simps_I2_J) ).

fof(fact_pred__def,axiom,
    ! [X100] : c_Int_Opred(X100) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X100),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__def) ).

fof(fact_succ__def,axiom,
    ! [X100] : c_Int_Osucc(X100) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X100),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__def) ).

fof(fact_upt__0,axiom,
    ! [X102] : c_List_Oupt(X102,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,
    ! [X28,X29] :
      ( ~ hBOOL(X29)
      | ~ hBOOL(X28)
      | hBOOL(hAPP(hAPP(c_fconj,X29),X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__1) ).

fof(fact_add__Min,axiom,
    ! [X100] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X100) = c_Int_Opred(X100),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Min) ).

fof(fact_nonzero__number__of__Min,axiom,
    ! [X15] :
      ( class_Int_Onumber__ring(X15)
     => ~ c_Int_Oiszero(X15,hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OMin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__number__of__Min) ).

fof(help_c__fdisj__1,axiom,
    ! [X28,X29] :
      ( ~ hBOOL(X29)
      | hBOOL(hAPP(hAPP(c_fdisj,X29),X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__1) ).

fof(help_c__fdisj__2,axiom,
    ! [X29,X28] :
      ( ~ hBOOL(X28)
      | hBOOL(hAPP(hAPP(c_fdisj,X29),X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__2) ).

fof(help_c__fimplies__2,axiom,
    ! [X29,X28] :
      ( ~ hBOOL(X28)
      | hBOOL(hAPP(hAPP(c_fimplies,X29),X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__2) ).

fof(fact_rel__simps_I38_J,axiom,
    ! [X97] :
      ( c_Int_OPls = c_Int_OBit0(X97)
    <=> c_Int_OPls = X97 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I38_J) ).

fof(fact_rel__simps_I44_J,axiom,
    ! [X30] :
      ( c_Int_OBit0(X30) = c_Int_OPls
    <=> X30 = c_Int_OPls ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I44_J) ).

fof(fact_rel__simps_I45_J,axiom,
    ! [X100] : c_Int_OBit0(X100) != c_Int_OMin,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I45_J) ).

fof(fact_rel__simps_I42_J,axiom,
    ! [X103] : c_Int_OMin != c_Int_OBit0(X103),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I42_J) ).

fof(fact_not__neg__nat,axiom,
    ! [X23] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X23))
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X23)) = X23 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__nat) ).

fof(fact_card__infinite,axiom,
    ! [X11,X5] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => hAPP(c_Finite__Set_Ocard(X5),X11) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__infinite) ).

fof(help_c__fNot__1,axiom,
    ! [X29] :
      ( ~ hBOOL(hAPP(c_fNot,X29))
      | ~ hBOOL(X29) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).

fof(fact_not__iszero__1,axiom,
    ! [X15] :
      ( class_Rings_Osemiring__1(X15)
     => ~ c_Int_Oiszero(X15,c_Groups_Oone__class_Oone(X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__iszero__1) ).

fof(help_c__fNot__2,axiom,
    ! [X29] :
      ( ~ ~ hBOOL(X29)
      | hBOOL(hAPP(c_fNot,X29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__2) ).

fof(fact_UN__equiv__class__type2,axiom,
    ! [X13,X71,X72,X2,X38,X62,X63,X16,X64,X65,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X65,X64)
     => ( c_Equiv__Relations_Oequiv(X16,X63,X62)
       => ( c_Equiv__Relations_Ocongruent2(X5,X16,tc_fun(X38,tc_HOL_Obool),X64,X62,X2)
         => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X72),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X65),X64)))
           => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X16,tc_HOL_Obool)),X71),hAPP(hAPP(c_Equiv__Relations_Oquotient(X16),X63),X62)))
             => ( ! [X32] :
                    ( hBOOL(hAPP(hAPP(c_member(X5),X32),X65))
                   => ! [X73] :
                        ( hBOOL(hAPP(hAPP(c_member(X16),X73),X63))
                       => hBOOL(hAPP(hAPP(c_member(tc_fun(X38,tc_HOL_Obool)),hAPP(hAPP(X2,X32),X73)),X13)) ) )
               => hBOOL(hAPP(hAPP(c_member(tc_fun(X38,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X38,tc_HOL_Obool)),X72),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_fun(X38,tc_HOL_Obool)),tc_fun(X38,tc_HOL_Obool),X5),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X38,tc_HOL_Obool)),X71)),X2))),X13)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__equiv__class__type2) ).

fof(fact_setsum__mult__setsum__if__inj,axiom,
    ! [X13,X11,X1,X2,X16,X5,X38] :
      ( class_Rings_Osemiring__0(X38)
     => ( c_Fun_Oinj__on(tc_prod(X5,X16),X38,hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,X38),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,X38),tc_fun(X16,X38)),hAPP(hAPP(c_COMBB(tc_fun(X38,X38),tc_fun(tc_fun(X16,X38),tc_fun(X16,X38)),X5),c_COMBB(X38,X38,X16)),hAPP(hAPP(c_COMBB(X38,tc_fun(X38,X38),X5),c_Groups_Otimes__class_Otimes(X38)),X2))),X1)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X13)))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X38),X2),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X38),X1),X13)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X38,X38),c_Fun_Oid(X38)),hAPP(c_Set_OCollect(X38),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X38),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X16,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X38),hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X16))),hAPP(hAPP(c_COMBC(X38,tc_fun(X5,tc_fun(X16,tc_HOL_Obool)),tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool))),tc_fun(tc_fun(X5,tc_fun(X16,tc_HOL_Obool)),tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),X38),c_COMBS(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X16,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X5,tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool))),X38),hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBS(X16,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X16,tc_HOL_Obool)),tc_fun(X5,tc_fun(X16,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X38),hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X16),c_fconj))),hAPP(hAPP(c_COMBC(X38,tc_fun(X5,tc_fun(X16,X38)),tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X16,X38),tc_fun(X16,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(X16,X38)),tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),X38),c_COMBB(tc_fun(X16,X38),tc_fun(X16,tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(X38,tc_HOL_Obool),tc_fun(tc_fun(X16,X38),tc_fun(X16,tc_HOL_Obool)),X38),c_COMBB(X38,tc_HOL_Obool,X16)),c_fequal))),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,X38),tc_fun(X16,X38)),hAPP(hAPP(c_COMBB(tc_fun(X38,X38),tc_fun(tc_fun(X16,X38),tc_fun(X16,X38)),X5),c_COMBB(X38,X38,X16)),hAPP(hAPP(c_COMBB(X38,tc_fun(X38,X38),X5),c_Groups_Otimes__class_Otimes(X38)),X2))),X1)))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X16)),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)),X11)))),hAPP(hAPP(c_COMBC(X16,tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool),c_member(X16)),X13))))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__mult__setsum__if__inj) ).

fof(fact_rel__comp__def,axiom,
    ! [X84,X34,X16,X38,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X38,X16),X34),X84) = hAPP(c_Set_OCollect(tc_prod(X5,X16)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_fun(X38,tc_HOL_Obool)),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_fun(X38,tc_HOL_Obool),tc_HOL_Obool,X16),c_HOL_OEx(X38))),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_fun(X38,tc_HOL_Obool)),tc_fun(X16,tc_fun(X38,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X38,tc_HOL_Obool),tc_fun(X38,tc_HOL_Obool)),tc_fun(tc_fun(X16,tc_fun(X38,tc_HOL_Obool)),tc_fun(X16,tc_fun(X38,tc_HOL_Obool))),X5),c_COMBB(tc_fun(X38,tc_HOL_Obool),tc_fun(X38,tc_HOL_Obool),X16)),hAPP(hAPP(c_COMBB(tc_fun(X38,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X38,tc_HOL_Obool),tc_fun(X38,tc_HOL_Obool)),X5),c_COMBS(X38,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X38,tc_HOL_Obool),tc_fun(X38,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X38),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X38),tc_HOL_Obool),tc_fun(X38,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X38,tc_fun(tc_fun(tc_prod(X5,X38),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X38),tc_HOL_Obool),tc_fun(X38,tc_HOL_Obool)),X5),c_COMBC(X38,tc_fun(tc_prod(X5,X38),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X38,tc_prod(X5,X38)),tc_fun(X38,tc_fun(tc_fun(tc_prod(X5,X38),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X38),tc_fun(tc_fun(tc_prod(X5,X38),tc_HOL_Obool),tc_HOL_Obool),X38),c_member(tc_prod(X5,X38)))),c_Product__Type_OPair(X5,X38)))),X34))))),hAPP(hAPP(c_COMBC(X16,tc_fun(tc_prod(X38,X16),tc_HOL_Obool),tc_fun(X38,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X38,tc_fun(tc_fun(tc_prod(X38,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X38,X16),tc_HOL_Obool),tc_fun(X38,tc_HOL_Obool)),X16),c_COMBC(X38,tc_fun(tc_prod(X38,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X38,tc_prod(X38,X16)),tc_fun(X38,tc_fun(tc_fun(tc_prod(X38,X16),tc_HOL_Obool),tc_HOL_Obool)),X16),hAPP(c_COMBB(tc_prod(X38,X16),tc_fun(tc_fun(tc_prod(X38,X16),tc_HOL_Obool),tc_HOL_Obool),X38),c_member(tc_prod(X38,X16)))),hAPP(c_COMBC(X38,X16,tc_prod(X38,X16)),c_Product__Type_OPair(X38,X16))))),X84))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__def) ).

fof(fact_min__max_Osup__Inf2__distrib,axiom,
    ! [X13,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
           => ( X13 != 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),X11)),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X13)) = 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)),X11)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X13))))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__Inf2__distrib) ).

fof(fact_min__max_Oinf__Sup2__distrib,axiom,
    ! [X13,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
           => ( X13 != 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),X11)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X13)) = 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)),X11)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X13))))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__Sup2__distrib) ).

fof(fact_inf__Sup2__distrib,axiom,
    ! [X13,X11,X5] :
      ( class_Lattices_Odistrib__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
           => ( X13 != 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,X11)),c_Big__Operators_Olattice__class_OSup__fin(X5,X13)) = 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)),X11)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X13))))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Sup2__distrib) ).

fof(fact_sup__Inf2__distrib,axiom,
    ! [X13,X11,X5] :
      ( class_Lattices_Odistrib__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
           => ( X13 != 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,X11)),c_Big__Operators_Olattice__class_OInf__fin(X5,X13)) = 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)),X11)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X13))))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__Inf2__distrib) ).

fof(fact_set__Cons__def,axiom,
    ! [X166,X11,X5] : c_List_Oset__Cons(X5,X11,X166) = 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)),X11)))),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))),X166)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__Cons__def) ).

fof(fact_image__INT,axiom,
    ! [X115,X13,X11,X38,X19,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X19)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X38),X3),X11))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(X13,X3)),X19)) )
       => ( hBOOL(hAPP(hAPP(c_member(X38),X115),X11))
         => hAPP(c_Set_Oimage(X5,X16,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X38,tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X38,tc_fun(X16,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X38),c_Set_Oimage(X5,X16,X2)),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__INT) ).

fof(fact_inf__Int__eq2,axiom,
    ! [X27,X12,X35,X36,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBC(X16,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X16),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool),X16),c_member(tc_prod(X5,X16)))),c_Product__Type_OPair(X5,X16)))),X36)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBC(X16,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X16),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool),X16),c_member(tc_prod(X5,X16)))),c_Product__Type_OPair(X5,X16)))),X35)),X12),X27))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X12),X27)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X36),X35))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Int__eq2) ).

fof(fact_sup__Un__eq2,axiom,
    ! [X27,X12,X35,X36,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBC(X16,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X16),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool),X16),c_member(tc_prod(X5,X16)))),c_Product__Type_OPair(X5,X16)))),X36)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBC(X16,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X16),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool),X16),c_member(tc_prod(X5,X16)))),c_Product__Type_OPair(X5,X16)))),X35)),X12),X27))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X12),X27)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X36),X35))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__Un__eq2) ).

fof(fact_lenlex__conv,axiom,
    ! [X34,X5] : c_List_Olenlex(X5,X34) = 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,X34)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lenlex__conv) ).

fof(fact_foldl__apply,axiom,
    ! [X84,X1,X48,X2,X16,X38,X212,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
         => hAPP(c_Fun_Ocomp(X38,X38,X16,hAPP(X2,X3)),X48) = hAPP(c_Fun_Ocomp(X16,X38,X16,X48),hAPP(X1,X3)) )
     => hAPP(c_List_Ofoldl(X38,X5,hAPP(c_COMBC(X5,X38,X38),X2),hAPP(X48,X84)),X212) = hAPP(X48,hAPP(c_List_Ofoldl(X16,X5,hAPP(c_COMBC(X5,X16,X16),X1),X84),X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__apply) ).

fof(fact_INF__INT__eq2,axiom,
    ! [X27,X12,X34,X38,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_fun(X38,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X16,X38),tc_HOL_Obool),tc_fun(X16,tc_fun(X38,tc_HOL_Obool)),X5),hAPP(c_COMBC(X16,tc_fun(tc_prod(X16,X38),tc_HOL_Obool),tc_fun(X38,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X38,tc_fun(tc_fun(tc_prod(X16,X38),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X16,X38),tc_HOL_Obool),tc_fun(X38,tc_HOL_Obool)),X16),c_COMBC(X38,tc_fun(tc_prod(X16,X38),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X38,tc_prod(X16,X38)),tc_fun(X38,tc_fun(tc_fun(tc_prod(X16,X38),tc_HOL_Obool),tc_HOL_Obool)),X16),hAPP(c_COMBB(tc_prod(X16,X38),tc_fun(tc_fun(tc_prod(X16,X38),tc_HOL_Obool),tc_HOL_Obool),X38),c_member(tc_prod(X16,X38)))),c_Product__Type_OPair(X16,X38))))),X34)),X12),X27))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X38)),hAPP(hAPP(c_Product__Type_OPair(X16,X38),X12),X27)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(tc_prod(X16,X38),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__INT__eq2) ).

fof(fact_SUP__UN__eq2,axiom,
    ! [X27,X12,X34,X38,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_fun(X38,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X16,X38),tc_HOL_Obool),tc_fun(X16,tc_fun(X38,tc_HOL_Obool)),X5),hAPP(c_COMBC(X16,tc_fun(tc_prod(X16,X38),tc_HOL_Obool),tc_fun(X38,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X38,tc_fun(tc_fun(tc_prod(X16,X38),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X16,X38),tc_HOL_Obool),tc_fun(X38,tc_HOL_Obool)),X16),c_COMBC(X38,tc_fun(tc_prod(X16,X38),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X38,tc_prod(X16,X38)),tc_fun(X38,tc_fun(tc_fun(tc_prod(X16,X38),tc_HOL_Obool),tc_HOL_Obool)),X16),hAPP(c_COMBB(tc_prod(X16,X38),tc_fun(tc_fun(tc_prod(X16,X38),tc_HOL_Obool),tc_HOL_Obool),X38),c_member(tc_prod(X16,X38)))),c_Product__Type_OPair(X16,X38))))),X34)),X12),X27))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X38)),hAPP(hAPP(c_Product__Type_OPair(X16,X38),X12),X27)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X16,X38),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__UN__eq2) ).

fof(fact_pred__comp__rel__comp__eq,axiom,
    ! [X27,X12,X84,X34,X38,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X16,X38,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBC(X16,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X16),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool),X16),c_member(tc_prod(X5,X16)))),c_Product__Type_OPair(X5,X16)))),X34),hAPP(hAPP(c_COMBC(X16,tc_fun(tc_prod(X16,X38),tc_HOL_Obool),tc_fun(X38,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X38,tc_fun(tc_fun(tc_prod(X16,X38),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X16,X38),tc_HOL_Obool),tc_fun(X38,tc_HOL_Obool)),X16),c_COMBC(X38,tc_fun(tc_prod(X16,X38),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X38,tc_prod(X16,X38)),tc_fun(X38,tc_fun(tc_fun(tc_prod(X16,X38),tc_HOL_Obool),tc_HOL_Obool)),X16),hAPP(c_COMBB(tc_prod(X16,X38),tc_fun(tc_fun(tc_prod(X16,X38),tc_HOL_Obool),tc_HOL_Obool),X38),c_member(tc_prod(X16,X38)))),c_Product__Type_OPair(X16,X38)))),X84)),X12),X27))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X38)),hAPP(hAPP(c_Product__Type_OPair(X5,X38),X12),X27)),hAPP(hAPP(c_Relation_Orel__comp(X5,X16,X38),X34),X84))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp__rel__comp__eq) ).

fof(fact_coinduct3__lemma,axiom,
    ! [X2,X31,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X31),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),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)),tc_fun(X5,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),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)),tc_fun(X5,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X2)),X31))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),X2))))))
     => ( c_Orderings_Oorder__class_Omono(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),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)),tc_fun(X5,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),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)),tc_fun(X5,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X2)),X31))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),X2)))),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),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)),tc_fun(X5,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),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)),tc_fun(X5,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X2)),X31))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),X2)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coinduct3__lemma) ).

fof(fact_UN__equiv__class__inject,axiom,
    ! [X42,X31,X2,X16,X34,X11,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X11,X34)
     => ( c_Equiv__Relations_Ocongruent(X5,tc_fun(X16,tc_HOL_Obool),X34,X2)
       => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X31),X2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X42),X2)
         => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X31),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X11),X34)))
           => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X42),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X11),X34)))
             => ( ! [X3] :
                    ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
                   => ! [X33] :
                        ( hBOOL(hAPP(hAPP(c_member(X5),X33),X11))
                       => ( hAPP(X2,X3) = hAPP(X2,X33)
                         => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X33)),X34)) ) ) )
               => X31 = X42 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__equiv__class__inject) ).

fof(fact_finite__image__set,axiom,
    ! [X2,X16,X29,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),X29)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X16),hAPP(c_Set_OCollect(X16),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X16),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X16,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)),X16),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)),X16),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X16,tc_fun(X5,X16),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X5,X16),tc_fun(X5,tc_HOL_Obool)),X16),c_COMBB(X16,tc_HOL_Obool,X5)),c_fequal)),X2)))),X29))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__image__set) ).

fof(fact_setsum__reindex__cong,axiom,
    ! [X48,X1,X13,X11,X2,X16,X5,X38] :
      ( class_Groups_Ocomm__monoid__add(X38)
     => ( c_Fun_Oinj__on(X5,X16,X2,X11)
       => ( X13 = hAPP(c_Set_Oimage(X5,X16,X2),X11)
         => ( ! [X74] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X74),X11))
               => hAPP(X1,X74) = hAPP(X48,hAPP(X2,X74)) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X38),X48),X13) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X38),X1),X11) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__reindex__cong) ).

fof(fact_conversep__converse__eq,axiom,
    ! [X27,X12,X34,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5,X16,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBC(X16,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X16),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool),X16),c_member(tc_prod(X5,X16)))),c_Product__Type_OPair(X5,X16)))),X34)),X12),X27))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X5)),hAPP(hAPP(c_Product__Type_OPair(X16,X5),X12),X27)),hAPP(c_Relation_Oconverse(X5,X16),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__converse__eq) ).

fof(fact_strong__setprod__reindex__cong,axiom,
    ! [X48,X1,X13,X11,X2,X16,X5,X38] :
      ( class_Groups_Ocomm__monoid__mult(X38)
     => ( c_Fun_Oinj__on(X5,X16,X2,X11)
       => ( X13 = hAPP(c_Set_Oimage(X5,X16,X2),X11)
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
               => hAPP(X1,X3) = hAPP(hAPP(c_Fun_Ocomp(X16,X38,X5,X48),X2),X3) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16,X38),X48),X13) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X38),X1),X11) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_strong__setprod__reindex__cong) ).

fof(fact_setsum__ivl__cong,axiom,
    ! [X1,X2,X20,X17,X21,X6,X5,X16] :
      ( ( class_Groups_Ocomm__monoid__add(X16)
        & class_Orderings_Oord(X5) )
     => ( X6 = X21
       => ( X17 = X20
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),X3))
               => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X3),X20))
                 => hAPP(X2,X3) = hAPP(X1,X3) ) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X17)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X21),X20)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__ivl__cong) ).

fof(fact_lazy__sequence__size__code,axiom,
    ! [X253,X84,X5] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X5,X84),X253) = hAPP(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)),X84))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X5,X84))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(X5),X253)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence__size__code) ).

fof(fact_minus__int__def,axiom,
    ! [X37] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X37) = 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,X37)),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_rp__inv__image__def,axiom,
    ! [X16,X5] : c_FunDef_Orp__inv__image(X5,X16) = 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(X16,X5),tc_prod(tc_fun(tc_prod(X16,X16),tc_HOL_Obool),tc_fun(tc_prod(X16,X16),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(X16,X5),tc_fun(tc_prod(X16,X16),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X16,X5),tc_prod(tc_fun(tc_prod(X16,X16),tc_HOL_Obool),tc_fun(tc_prod(X16,X16),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X16,X5),tc_fun(tc_prod(X16,X16),tc_HOL_Obool)),tc_fun(tc_fun(X16,X5),tc_prod(tc_fun(tc_prod(X16,X16),tc_HOL_Obool),tc_fun(tc_prod(X16,X16),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X16,X5),tc_fun(tc_prod(X16,X16),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X16,X5),tc_prod(tc_fun(tc_prod(X16,X16),tc_HOL_Obool),tc_fun(tc_prod(X16,X16),tc_HOL_Obool))))),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X16,X5),tc_fun(tc_prod(X16,X16),tc_HOL_Obool)),tc_fun(tc_fun(X16,X5),tc_prod(tc_fun(tc_prod(X16,X16),tc_HOL_Obool),tc_fun(tc_prod(X16,X16),tc_HOL_Obool))),tc_fun(tc_prod(X5,X5),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X16,X5),tc_fun(tc_fun(tc_prod(X16,X16),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X16,X16),tc_HOL_Obool),tc_fun(tc_prod(X16,X16),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X16,X5),tc_fun(tc_prod(X16,X16),tc_HOL_Obool)),tc_fun(tc_fun(X16,X5),tc_prod(tc_fun(tc_prod(X16,X16),tc_HOL_Obool),tc_fun(tc_prod(X16,X16),tc_HOL_Obool)))),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_COMBS(tc_fun(X16,X5),tc_fun(tc_prod(X16,X16),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X16,X16),tc_HOL_Obool),tc_fun(tc_prod(X16,X16),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X16,X5),tc_fun(tc_prod(X16,X16),tc_HOL_Obool)),tc_fun(tc_fun(X16,X5),tc_fun(tc_fun(tc_prod(X16,X16),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X16,X16),tc_HOL_Obool),tc_fun(tc_prod(X16,X16),tc_HOL_Obool)))),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X16,X16),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X16,X16),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X16,X16),tc_HOL_Obool),tc_fun(tc_prod(X16,X16),tc_HOL_Obool))),tc_fun(X16,X5)),c_Product__Type_OPair(tc_fun(tc_prod(X16,X16),tc_HOL_Obool),tc_fun(tc_prod(X16,X16),tc_HOL_Obool)))),c_Relation_Oinv__image(X5,X16))))),c_Relation_Oinv__image(X5,X16))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp__inv__image__def) ).

fof(fact_coinduct3,axiom,
    ! [X31,X6,X2,X5] :
      ( c_Orderings_Oorder__class_Omono(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X2)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X31))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X31),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),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)),tc_fun(X5,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),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)),tc_fun(X5,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X2)),X31))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),X2))))))
         => hBOOL(hAPP(hAPP(c_member(X5),X6),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),X2))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coinduct3) ).

fof(fact_def__coinduct3,axiom,
    ! [X31,X6,X2,X5,X11] :
      ( X11 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),X2)
     => ( c_Orderings_Oorder__class_Omono(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X2)
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X31))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X31),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),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)),tc_fun(X5,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),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)),tc_fun(X5,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X2)),X31))),X11)))))
           => hBOOL(hAPP(hAPP(c_member(X5),X6),X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__coinduct3) ).

fof(fact_inv__image__def,axiom,
    ! [X2,X34,X5,X16] : hAPP(hAPP(c_Relation_Oinv__image(X16,X5),X34),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(X16,X16),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X16,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X16,X16),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X16,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X16,X16)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X16,X16),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X16,X16),tc_fun(tc_fun(tc_prod(X16,X16),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X16,X16)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X16),tc_fun(X5,tc_prod(X16,X16))),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X16,X16)),tc_fun(tc_fun(X5,X16),tc_fun(X5,tc_prod(X16,X16))),X5),c_COMBB(X16,tc_prod(X16,X16),X5)),hAPP(hAPP(c_COMBB(X16,tc_fun(X16,tc_prod(X16,X16)),X5),c_Product__Type_OPair(X16,X16)),X2))),X2)))),X34))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__image__def) ).

fof(fact_set__zip,axiom,
    ! [X214,X212,X16,X5] : hAPP(c_List_Oset(tc_prod(X5,X16)),hAPP(hAPP(c_List_Ozip(X5,X16),X212),X214)) = hAPP(c_Set_OCollect(tc_prod(X5,X16)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X5,X16)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X5,X16),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,X16)),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,X16)),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,X16),tc_fun(tc_Nat_Onat,tc_prod(X5,X16)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X5,X16)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X5,X16)),c_COMBB(tc_prod(X5,X16),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X16,tc_prod(X5,X16)),hAPP(hAPP(c_COMBB(X5,tc_fun(X16,tc_prod(X5,X16)),tc_Nat_Onat),c_Product__Type_OPair(X5,X16)),hAPP(c_List_Onth(X5),X212))),hAPP(c_List_Onth(X16),X214)))))),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)),X212)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__zip) ).

fof(fact_pred__subset__eq2,axiom,
    ! [X35,X36,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBC(X16,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X16),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool),X16),c_member(tc_prod(X5,X16)))),c_Product__Type_OPair(X5,X16)))),X36)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBC(X16,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X16),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool),X16),c_member(tc_prod(X5,X16)))),c_Product__Type_OPair(X5,X16)))),X35)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X36),X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).

fof(fact_Pow__Compl,axiom,
    ! [X11,X5] : hAPP(c_Set_OPow(X5),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11)) = 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)),X11)),c_Set_OPow(X5))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__Compl) ).

fof(fact_map__upds__fold__map__upd,axiom,
    ! [X245,X219,X45,X16,X5] : c_Map_Omap__upds(X5,X16,X45,X219,X245) = hAPP(c_List_Ofoldl(tc_fun(X5,tc_Option_Ooption(X16)),tc_prod(X5,X16),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X16,tc_fun(X5,tc_Option_Ooption(X16)))),tc_fun(tc_prod(X5,X16),tc_fun(X5,tc_Option_Ooption(X16))),tc_fun(X5,tc_Option_Ooption(X16))),c_Product__Type_Oprod_Oprod__case(X5,X16,tc_fun(X5,tc_Option_Ooption(X16)))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_Option_Ooption(X16)),tc_fun(X16,tc_Option_Ooption(X16)),tc_fun(X5,tc_fun(X16,tc_fun(X5,tc_Option_Ooption(X16))))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(X16,tc_Option_Ooption(X16)),tc_fun(X16,tc_fun(X5,tc_Option_Ooption(X16))))),tc_fun(tc_fun(X16,tc_Option_Ooption(X16)),tc_fun(X5,tc_fun(X16,tc_fun(X5,tc_Option_Ooption(X16))))),tc_fun(X5,tc_Option_Ooption(X16))),c_COMBC(X5,tc_fun(X16,tc_Option_Ooption(X16)),tc_fun(X16,tc_fun(X5,tc_Option_Ooption(X16))))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_Option_Ooption(X16),tc_fun(X5,tc_Option_Ooption(X16)))),tc_fun(X5,tc_fun(tc_fun(X16,tc_Option_Ooption(X16)),tc_fun(X16,tc_fun(X5,tc_Option_Ooption(X16))))),tc_fun(X5,tc_Option_Ooption(X16))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X16),tc_fun(X5,tc_Option_Ooption(X16))),tc_fun(tc_fun(X16,tc_Option_Ooption(X16)),tc_fun(X16,tc_fun(X5,tc_Option_Ooption(X16)))),X5),c_COMBB(tc_Option_Ooption(X16),tc_fun(X5,tc_Option_Ooption(X16)),X16))),c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16))))),c_Option_Ooption_OSome(X16))),X45),hAPP(hAPP(c_List_Ozip(X5,X16),X219),X245)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__upds__fold__map__upd) ).

fof(fact_UN__equiv__class__type,axiom,
    ! [X13,X31,X2,X16,X34,X11,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X11,X34)
     => ( c_Equiv__Relations_Ocongruent(X5,tc_fun(X16,tc_HOL_Obool),X34,X2)
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X31),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X11),X34)))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
               => hBOOL(hAPP(hAPP(c_member(tc_fun(X16,tc_HOL_Obool)),hAPP(X2,X3)),X13)) )
           => hBOOL(hAPP(hAPP(c_member(tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X31),X2)),X13)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__equiv__class__type) ).

fof(fact_INF2__I,axiom,
    ! [X38,X16,X21,X17,X13,X11,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
         => hBOOL(hAPP(hAPP(hAPP(X13,X3),X17),X21)) )
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_fun(X38,tc_HOL_Obool))),X11),X13),X17),X21)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF2__I) ).

fof(fact_INF2__iff,axiom,
    ! [X21,X17,X13,X11,X38,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_fun(X38,tc_HOL_Obool))),X11),X13),X17),X21))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
         => hBOOL(hAPP(hAPP(hAPP(X13,X3),X17),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF2__iff) ).

fof(fact_min__max_Osup__Inf1__distrib,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X12),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X11)) = 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),X12))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X11))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__Inf1__distrib) ).

fof(fact_min__max_Oinf__Sup1__distrib,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X12),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X11)) = 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),X12))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X11))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__Sup1__distrib) ).

fof(fact_add__Min__commute,axiom,
    ! [X30,X93,X5] :
      ( class_Groups_Olinordered__ab__semigroup__add(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X93))
       => ( X93 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),c_Big__Operators_Olinorder__class_OMin(X5,X93)) = 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),X30))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X93))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Min__commute) ).

fof(fact_add__Max__commute,axiom,
    ! [X30,X93,X5] :
      ( class_Groups_Olinordered__ab__semigroup__add(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X93))
       => ( X93 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),c_Big__Operators_Olinorder__class_OMax(X5,X93)) = 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),X30))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X93))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Max__commute) ).

fof(fact_inf__Sup1__distrib,axiom,
    ! [X12,X11,X5] :
      ( class_Lattices_Odistrib__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X12),c_Big__Operators_Olattice__class_OSup__fin(X5,X11)) = 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),X12))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X11))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Sup1__distrib) ).

fof(fact_sup__Inf1__distrib,axiom,
    ! [X12,X11,X5] :
      ( class_Lattices_Odistrib__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X12),c_Big__Operators_Olattice__class_OInf__fin(X5,X11)) = 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),X12))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X11))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__Inf1__distrib) ).

fof(fact_anamorph_Osimps,axiom,
    ! [X12,X2,X5,X16,X30] :
      ( ( X30 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X16,X5,X2),X30),X12) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),X16),c_List_Olist_ONil(X5)),X12) )
      & ( X30 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X16,X5,X2),X30),X12) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X5),X16),tc_prod(X5,X16),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),X16),c_List_Olist_ONil(X5)),X12),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_prod(tc_List_Olist(X5),X16)),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_prod(tc_List_Olist(X5),X16)),tc_fun(X16,tc_prod(tc_List_Olist(X5),X16))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X5),X16),tc_prod(tc_List_Olist(X5),X16)),tc_fun(tc_fun(X16,tc_prod(tc_List_Olist(X5),X16)),tc_fun(X16,tc_prod(tc_List_Olist(X5),X16))),X5),c_COMBB(tc_prod(tc_List_Olist(X5),X16),tc_prod(tc_List_Olist(X5),X16),X16)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_fun(X16,tc_prod(tc_List_Olist(X5),X16))),tc_fun(tc_prod(tc_List_Olist(X5),X16),tc_prod(tc_List_Olist(X5),X16)),X5),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5),X16,tc_prod(tc_List_Olist(X5),X16))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_fun(X16,tc_prod(tc_List_Olist(X5),X16))),X5),hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(X16,tc_prod(tc_List_Olist(X5),X16)),tc_List_Olist(X5)),c_Product__Type_OPair(tc_List_Olist(X5),X16))),c_List_Olist_OCons(X5))))),hAPP(c_Lazy__Sequence_Oanamorph(X16,X5,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X30),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(X2,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_anamorph_Osimps) ).

fof(fact_listrel__iff__zip,axiom,
    ! [X34,X214,X212,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)),X212),X214)),c_List_Olistrel(X5,X34)))
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X214)
        & ! [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),X212),X214))))
           => 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)))),X34)),X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__iff__zip) ).

fof(fact_DomainP__Domain__eq,axiom,
    ! [X12,X34,X16,X5] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(X5,X16,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBC(X16,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X16),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool),X16),c_member(tc_prod(X5,X16)))),c_Product__Type_OPair(X5,X16)))),X34)),X12))
    <=> hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_Relation_ODomain(X5,X16),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP__Domain__eq) ).

fof(fact_RangeP__Range__eq,axiom,
    ! [X12,X34,X16,X5] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(X5,X16,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBC(X16,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X16),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool),X16),c_member(tc_prod(X5,X16)))),c_Product__Type_OPair(X5,X16)))),X34)),X12))
    <=> hBOOL(hAPP(hAPP(c_member(X16),X12),hAPP(c_Relation_ORange(X5,X16),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP__Range__eq) ).

fof(fact_accp__acc__eq,axiom,
    ! [X12,X34,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)))),X34)),X12))
    <=> hBOOL(hAPP(hAPP(c_member(X5),X12),c_Wellfounded_Oacc(X5,X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__acc__eq) ).

fof(fact_fold__graph_H_Oequations_I2_J,axiom,
    ! [X49,X47,X46,X50,X51,X16,X5] :
      ( c_Nitpick_Ofold__graph_H(X5,X16,X51,X50,X46,hAPP(hAPP(X51,X47),X49))
    <=> ( ( X46 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
          & hAPP(hAPP(X51,X47),X49) = X50 )
        | ? [X3,X33] :
            ( hAPP(hAPP(X51,X47),X49) = hAPP(hAPP(X51,X3),X33)
            & hBOOL(hAPP(hAPP(c_member(X5),X3),X46))
            & c_Nitpick_Ofold__graph_H(X5,X16,X51,X50,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X46),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X33) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I2_J) ).

fof(fact_SUP2__iff,axiom,
    ! [X21,X17,X13,X11,X38,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_fun(X38,tc_HOL_Obool))),X11),X13),X17),X21))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
          & hBOOL(hAPP(hAPP(hAPP(X13,X3),X17),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP2__iff) ).

fof(fact_partition_Osimps_I2_J,axiom,
    ! [X212,X12,X29,X5] : c_List_Opartition(X5,X29,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = 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(X29,X12)))),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),X12))))),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),X12)))),c_List_Opartition(X5,X29,X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition_Osimps_I2_J) ).

fof(fact_lexn_Osimps_I2_J,axiom,
    ! [X76,X34,X5] : hAPP(c_List_Olexn(X5,X34),hAPP(c_Nat_OSuc,X76)) = 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),X34,hAPP(c_List_Olexn(X5,X34),X76)))),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,X76))))),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,X76)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexn_Osimps_I2_J) ).

fof(fact_set__sublist,axiom,
    ! [X68,X212,X5] : hAPP(c_List_Oset(X5),c_List_Osublist(X5,X212,X68)) = 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),X212))))),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)),X212)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X68))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__sublist) ).

fof(fact_setsum__multicount__gen,axiom,
    ! [X30,X36,X10,X16,X84,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X84))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X10))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X16),X3),X10))
             => 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)),X84))),hAPP(hAPP(c_COMBC(X5,X16,tc_HOL_Obool),X36),X3)))) = hAPP(X30,X3) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_Nat_Onat,X5),c_Finite__Set_Ocard(X16)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),c_Set_OCollect(X16)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_COMBS(X16,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X16),c_fconj),hAPP(hAPP(c_COMBC(X16,tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool),c_member(X16)),X10)))),X36)))),X84) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,tc_Nat_Onat),X30),X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__multicount__gen) ).

fof(fact_set__conv__nth,axiom,
    ! [X212,X5] : hAPP(c_List_Oset(X5),X212) = 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),X212))))),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)),X212))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__conv__nth) ).

fof(fact_Sigma__def,axiom,
    ! [X13,X11,X16,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),X13) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBS(X5,tc_fun(X16,tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(tc_prod(X5,X16),tc_HOL_Obool))),X13)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_fun(tc_prod(X5,X16),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(tc_prod(X5,X16),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_fun(tc_prod(X5,X16),tc_HOL_Obool))),X5),c_COMBC(X16,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(tc_prod(X5,X16),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(tc_prod(X5,X16),tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_prod(X5,X16),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X16),c_Set_Oinsert(tc_prod(X5,X16)))),c_Product__Type_OPair(X5,X16)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X16),tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__def) ).

fof(fact_setsum__multicount,axiom,
    ! [X30,X36,X108,X16,X35,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X108))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X16),X3),X108))
             => 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)),X35))),hAPP(hAPP(c_COMBC(X5,X16,tc_HOL_Obool),X36),X3)))) = X30 )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_Nat_Onat,X5),c_Finite__Set_Ocard(X16)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),c_Set_OCollect(X16)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_COMBS(X16,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X16),c_fconj),hAPP(hAPP(c_COMBC(X16,tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool),c_member(X16)),X108)))),X36)))),X35) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),hAPP(c_Finite__Set_Ocard(X16),X108)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__multicount) ).

fof(fact_setsum__setsum__restrict,axiom,
    ! [X36,X2,X108,X16,X35,X5,X38] :
      ( class_Groups_Ocomm__monoid__add(X38)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X108))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X38),hAPP(hAPP(c_COMBS(X5,tc_fun(X16,tc_HOL_Obool),X38),hAPP(hAPP(c_COMBB(tc_fun(X16,X38),tc_fun(tc_fun(X16,tc_HOL_Obool),X38),X5),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X38)),X2)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),c_Set_OCollect(X16)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_COMBS(X16,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X16),c_fconj),hAPP(hAPP(c_COMBC(X16,tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool),c_member(X16)),X108)))),X36)))),X35) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X38),hAPP(hAPP(c_COMBS(X16,tc_fun(X5,tc_HOL_Obool),X38),hAPP(hAPP(c_COMBB(tc_fun(X5,X38),tc_fun(tc_fun(X5,tc_HOL_Obool),X38),X16),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X38)),hAPP(c_COMBC(X5,X16,X38),X2))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X16),c_Set_OCollect(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X16),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)),X35)))),hAPP(c_COMBC(X5,X16,tc_HOL_Obool),X36))))),X108) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__setsum__restrict) ).

fof(fact_sequence__trans,axiom,
    ! [X30,X70,X34,X2,X5] :
      ( ! [X145] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(X2,hAPP(c_Nat_OSuc,X145))),hAPP(X2,X145))),c_Transitive__Closure_Ortrancl(X5,X34)))
     => 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),X70),X30))),hAPP(X2,X70))),c_Transitive__Closure_Ortrancl(X5,X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sequence__trans) ).

fof(fact_lfp__induct2,axiom,
    ! [X29,X2,X17,X6,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),X2)))
     => ( c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(tc_prod(X5,X16),tc_HOL_Obool),X2)
       => ( ! [X74,X52] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X74),X52)),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),X2)),hAPP(c_Set_OCollect(tc_prod(X5,X16)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_HOL_Obool),X29))))))
             => hBOOL(hAPP(hAPP(X29,X74),X52)) )
         => hBOOL(hAPP(hAPP(X29,X6),X17)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lfp__induct2) ).

fof(fact_divmod__int__rel__def,axiom,
    ! [X17,X6] : c_Divides_Odivmod__int__rel(X6,X17) = 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),X17)))))),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)),X17))),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)),X17))))),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)),X17)))),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),X17))),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,
    ! [X13,X1,X38,X11,X2,X16,X5] :
      ( class_Rings_Osemiring__0(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),X2),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X38,X5),X1),X13)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),hAPP(hAPP(c_COMBC(X16,tc_fun(X38,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBB(tc_fun(X38,X5),tc_fun(tc_fun(X38,tc_HOL_Obool),X5),X16),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X38,X5)),hAPP(hAPP(c_COMBC(X16,tc_fun(X38,X5),tc_fun(X38,X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,X5),tc_fun(tc_fun(X38,X5),tc_fun(X38,X5)),X16),c_COMBB(X5,X5,X38)),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X16),c_Groups_Otimes__class_Otimes(X5)),X2))),X1))),X13)),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__product) ).

fof(fact_fold__image__Sigma,axiom,
    ! [X1,X13,X16,X11,X5,X38] :
      ( class_Groups_Ocomm__monoid__mult(X38)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(X16),hAPP(X13,X3))) )
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X38,X5,c_Groups_Otimes__class_Otimes(X38)),hAPP(hAPP(c_COMBS(X5,tc_fun(X16,tc_HOL_Obool),X38),hAPP(hAPP(c_COMBC(X5,X38,tc_fun(tc_fun(X16,tc_HOL_Obool),X38)),hAPP(hAPP(c_COMBB(tc_fun(X16,X38),tc_fun(X38,tc_fun(tc_fun(X16,tc_HOL_Obool),X38)),X5),c_Finite__Set_Ofold__image(X38,X16,c_Groups_Otimes__class_Otimes(X38))),X1)),c_Groups_Oone__class_Oone(X38))),X13)),c_Groups_Oone__class_Oone(X38)),X11) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X38,tc_prod(X5,X16),c_Groups_Otimes__class_Otimes(X38)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,X38),X1)),c_Groups_Oone__class_Oone(X38)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__Sigma) ).

fof(fact_finite__lists__length__le,axiom,
    ! [X76,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => 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))),X11))),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)))),X76))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__lists__length__le) ).

fof(fact_finite__lists__length__eq,axiom,
    ! [X76,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => 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))),X11))),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)))),X76))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__lists__length__eq) ).

fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
    ! [X13,X11,X90,X1,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X16,X2,X37,X1,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X13))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X16),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),X11),X13)))
               => hAPP(X1,X3) = X37 )
           => hAPP(X90,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(X2,hAPP(X90,X11)),hAPP(X90,X13)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__inter__neutral) ).

fof(fact_nat__def,axiom,
    ! [X37] : hAPP(c_Int_Onat,X37) = 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,X37)),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_nat__intermed__int__val,axiom,
    ! [X30,X2,X76,X45] :
      ( ! [X145] :
          ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X145))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X145),X76)) )
         => 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),X145),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,X145)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X45)),X30))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),hAPP(X2,X76)))
           => ? [X145] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X145))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X145),X76))
                & hAPP(X2,X145) = X30 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__intermed__int__val) ).

fof(fact_Sigma__mono,axiom,
    ! [X18,X13,X16,X19,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X19))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),hAPP(X13,X3)),hAPP(X18,X3))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),X13)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X19),X18))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__mono) ).

fof(fact_mem__splitI2,axiom,
    ! [X21,X37,X38,X16,X5,X161] :
      ( ! [X74,X52] :
          ( X161 = hAPP(hAPP(c_Product__Type_OPair(X5,X16),X74),X52)
         => hBOOL(hAPP(hAPP(c_member(X38),X37),hAPP(hAPP(X21,X74),X52))) )
     => hBOOL(hAPP(hAPP(c_member(X38),X37),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_fun(X38,tc_HOL_Obool)),X21),X161))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__splitI2) ).

fof(fact_converse__def,axiom,
    ! [X34,X5,X16] : hAPP(c_Relation_Oconverse(X16,X5),X34) = hAPP(c_Set_OCollect(tc_prod(X5,X16)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X16,X5),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X16,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X16,X5),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBC(X16,tc_fun(tc_prod(X16,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X16,X5)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X16,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X16,X5),tc_fun(tc_fun(tc_prod(X16,X5),tc_HOL_Obool),tc_HOL_Obool),X16),c_member(tc_prod(X16,X5)))),hAPP(c_COMBC(X16,X5,tc_prod(X16,X5)),c_Product__Type_OPair(X16,X5))))),X34))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__def) ).

fof(fact_card__less__Suc,axiom,
    ! [X70,X67] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X67))
     => 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)),X67))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X70))))) = 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)),X67))),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,X70))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__less__Suc) ).

fof(fact_setsum__image__gen,axiom,
    ! [X2,X38,X1,X35,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),X35) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X38,X16),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),X16,X38),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X38),c_Set_OCollect(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X38),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)),X35)))),hAPP(c_COMBC(X5,X38,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X38,tc_fun(X38,tc_HOL_Obool),X5),c_fequal),X2)))))),hAPP(c_Set_Oimage(X5,X38,X2),X35)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__image__gen) ).

fof(fact_refl__on__def_H,axiom,
    ! [X34,X11,X5] :
      ( c_Relation_Orefl__on(X5,X11,X34)
    <=> ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X3),X34))
           => 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)),X11)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X11))),X3)) )
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X34)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__def_H) ).

fof(fact_zip__Cons,axiom,
    ! [X214,X27,X212,X16,X5] : hAPP(hAPP(c_List_Ozip(X5,X16),X212),hAPP(hAPP(c_List_Olist_OCons(X16),X27),X214)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X5,X16)),X5,c_List_Olist_ONil(tc_prod(X5,X16)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_prod(X5,X16))),tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_prod(X5,X16)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X5,X16)),tc_List_Olist(tc_prod(X5,X16))),tc_fun(tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_prod(X5,X16))),tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_prod(X5,X16)))),X5),c_COMBB(tc_List_Olist(tc_prod(X5,X16)),tc_List_Olist(tc_prod(X5,X16)),tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_prod(X5,X16),tc_fun(tc_List_Olist(tc_prod(X5,X16)),tc_List_Olist(tc_prod(X5,X16))),X5),c_List_Olist_OCons(tc_prod(X5,X16))),hAPP(hAPP(c_COMBC(X5,X16,tc_prod(X5,X16)),c_Product__Type_OPair(X5,X16)),X27)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X16),tc_List_Olist(tc_prod(X5,X16))),c_List_Ozip(X5,X16)),X214))),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__Cons) ).

fof(fact_max__extp__max__ext__eq,axiom,
    ! [X59,X12,X36,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)))),X36),X12,X59)
    <=> 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)),X12),X59)),c_Wellfounded_Omax__ext(X5,X36))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__extp__max__ext__eq) ).

fof(fact_listrelp__listrel__eq,axiom,
    ! [X59,X12,X34,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)))),X34),X12,X59)
    <=> 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)),X12),X59)),c_List_Olistrel(X5,X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp__listrel__eq) ).

fof(fact_UN__Times__distrib,axiom,
    ! [X90,X184,X13,X11,X16,X5,X55,X38] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X38,X55),tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X38,X55),X11),hAPP(c_COMBK(tc_fun(X55,tc_HOL_Obool),X38),X13))),hAPP(c_Product__Type_Oprod_Oprod__case(X38,X55,tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X38,tc_fun(X55,tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),tc_fun(X55,tc_fun(tc_prod(X5,X16),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_fun(X16,tc_HOL_Obool)),tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),tc_fun(tc_fun(X55,tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),tc_fun(X55,tc_fun(tc_prod(X5,X16),tc_HOL_Obool))),X38),c_COMBB(tc_fun(X5,tc_fun(X16,tc_HOL_Obool)),tc_fun(tc_prod(X5,X16),tc_HOL_Obool),X55)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_fun(X16,tc_HOL_Obool)),tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X38),c_Product__Type_OSigma(X5,X16)),X184))),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X5,tc_fun(X16,tc_HOL_Obool)),X55),c_COMBK(tc_fun(X16,tc_HOL_Obool),X5)),X90)))) = hAPP(hAPP(c_Product__Type_OSigma(X5,X16),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,tc_fun(X5,tc_HOL_Obool)),X11),X184)),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X55,tc_fun(X16,tc_HOL_Obool)),X13),X90))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__Times__distrib) ).

fof(fact_equivp__equiv,axiom,
    ! [X11,X5] :
      ( c_Equiv__Relations_Oequiv(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X11)
    <=> 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)))),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__equiv) ).

fof(fact_wfP__wf__eq,axiom,
    ! [X34,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)))),X34))
    <=> c_Wellfounded_Owf(X5,X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__wf__eq) ).

fof(fact_pred__equals__eq2,axiom,
    ! [X35,X36,X16,X5] :
      ( hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBC(X16,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X16),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool),X16),c_member(tc_prod(X5,X16)))),c_Product__Type_OPair(X5,X16)))),X36) = hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBC(X16,tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X16),tc_fun(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_HOL_Obool),X16),c_member(tc_prod(X5,X16)))),c_Product__Type_OPair(X5,X16)))),X35)
    <=> X36 = X35 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).

fof(fact_map__zip__map2,axiom,
    ! [X214,X1,X55,X212,X2,X5,X38,X16] : hAPP(hAPP(c_List_Omap(tc_prod(X16,X38),X5),X2),hAPP(hAPP(c_List_Ozip(X16,X38),X212),hAPP(hAPP(c_List_Omap(X55,X38),X1),X214))) = hAPP(hAPP(c_List_Omap(tc_prod(X16,X55),X5),hAPP(c_Product__Type_Oprod_Oprod__case(X16,X55,X5),hAPP(hAPP(c_COMBB(tc_fun(X55,tc_prod(X16,X38)),tc_fun(X55,X5),X16),hAPP(c_COMBB(tc_prod(X16,X38),X5,X55),X2)),hAPP(hAPP(c_COMBC(X16,tc_fun(X55,X38),tc_fun(X55,tc_prod(X16,X38))),hAPP(hAPP(c_COMBB(tc_fun(X38,tc_prod(X16,X38)),tc_fun(tc_fun(X55,X38),tc_fun(X55,tc_prod(X16,X38))),X16),c_COMBB(X38,tc_prod(X16,X38),X55)),c_Product__Type_OPair(X16,X38))),X1)))),hAPP(hAPP(c_List_Ozip(X16,X55),X212),X214)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__zip__map2) ).

fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
    ! [X6,X27,X11,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X16,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X16,X2,X37,X11),X27))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => ? [X190] :
              ( X27 = hAPP(hAPP(X2,X6),X190)
              & hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X16,X2,X37,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X190)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE__aux) ).

fof(fact_map__of__map,axiom,
    ! [X212,X2,X38,X16,X5] : hAPP(c_Map_Omap__of(X5,X16),hAPP(hAPP(c_List_Omap(tc_prod(X5,X38),tc_prod(X5,X16)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X38,tc_prod(X5,X16)),hAPP(hAPP(c_COMBC(X5,tc_fun(X38,X16),tc_fun(X38,tc_prod(X5,X16))),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(tc_fun(X38,X16),tc_fun(X38,tc_prod(X5,X16))),X5),c_COMBB(X16,tc_prod(X5,X16),X38)),c_Product__Type_OPair(X5,X16))),X2))),X212)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(X38),tc_Option_Ooption(X16),X5,hAPP(c_Option_Omap(X38,X16),X2)),hAPP(c_Map_Omap__of(X5,X38),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__map) ).

fof(fact_zip__Cons1,axiom,
    ! [X214,X212,X12,X16,X5] : hAPP(hAPP(c_List_Ozip(X5,X16),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)),X214) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X5,X16)),X16,c_List_Olist_ONil(tc_prod(X5,X16)),hAPP(hAPP(c_COMBC(X16,tc_fun(tc_List_Olist(X16),tc_List_Olist(tc_prod(X5,X16))),tc_fun(tc_List_Olist(X16),tc_List_Olist(tc_prod(X5,X16)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X5,X16)),tc_List_Olist(tc_prod(X5,X16))),tc_fun(tc_fun(tc_List_Olist(X16),tc_List_Olist(tc_prod(X5,X16))),tc_fun(tc_List_Olist(X16),tc_List_Olist(tc_prod(X5,X16)))),X16),c_COMBB(tc_List_Olist(tc_prod(X5,X16)),tc_List_Olist(tc_prod(X5,X16)),tc_List_Olist(X16))),hAPP(hAPP(c_COMBB(tc_prod(X5,X16),tc_fun(tc_List_Olist(tc_prod(X5,X16)),tc_List_Olist(tc_prod(X5,X16))),X16),c_List_Olist_OCons(tc_prod(X5,X16))),hAPP(c_Product__Type_OPair(X5,X16),X12)))),hAPP(c_List_Ozip(X5,X16),X212))),X214),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__Cons1) ).

fof(fact_wf__if__measure,axiom,
    ! [X5,X1,X2,X29] :
      ( ! [X3] :
          ( hBOOL(hAPP(X29,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),X29))),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_min__ext__compat,axiom,
    ! [X35,X36,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),X36),X35)),X36))
     => 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,X36)),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,X35)),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,X36))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__ext__compat) ).

fof(fact_max__ext__compat,axiom,
    ! [X35,X36,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),X36),X35)),X36))
     => 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,X36)),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,X35)),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,X36))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ext__compat) ).

fof(fact_setsum__restrict__set_H,axiom,
    ! [X13,X2,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),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)),X11))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X13)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X13))),X2)),c_Groups_Ozero__class_Ozero(X16))),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__restrict__set_H) ).

fof(fact_zip__map__map,axiom,
    ! [X214,X1,X55,X212,X2,X38,X16,X5] : hAPP(hAPP(c_List_Ozip(X5,X16),hAPP(hAPP(c_List_Omap(X38,X5),X2),X212)),hAPP(hAPP(c_List_Omap(X55,X16),X1),X214)) = hAPP(hAPP(c_List_Omap(tc_prod(X38,X55),tc_prod(X5,X16)),hAPP(c_Product__Type_Oprod_Oprod__case(X38,X55,tc_prod(X5,X16)),hAPP(hAPP(c_COMBC(X38,tc_fun(X55,X16),tc_fun(X55,tc_prod(X5,X16))),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(tc_fun(X55,X16),tc_fun(X55,tc_prod(X5,X16))),X38),c_COMBB(X16,tc_prod(X5,X16),X55)),hAPP(hAPP(c_COMBB(X5,tc_fun(X16,tc_prod(X5,X16)),X38),c_Product__Type_OPair(X5,X16)),X2))),X1))),hAPP(hAPP(c_List_Ozip(X38,X55),X212),X214)),
    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,X55,X38,X36,X17,X6,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17)),X36))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X38,X55)),hAPP(hAPP(c_Product__Type_OPair(X38,X55),hAPP(X2,X6)),hAPP(X1,X17))),hAPP(c_Set_Oimage(tc_prod(X5,X16),tc_prod(X38,X55),c_Product__Type_Omap__pair(X5,X38,X16,X55,X2,X1)),X36))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__imageI) ).

fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
    ! [X262,X263,X264,X2,X36,X5,X16] : c_New__Random__Sequence_Oneg__decr__bind(X16,X5,X36,X2,X264,X263,X262) = c_New__DSequence_Oneg__decr__bind(X16,X5,hAPP(hAPP(hAPP(X36,X264),X263),X262),hAPP(hAPP(c_COMBC(X16,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(X16,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(X16,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),X264)),X263)),X262)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__Random__Sequence_Oneg__decr__bind__def) ).

fof(fact_INTER__def,axiom,
    ! [X13,X11,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X11),X13) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OAll(X16)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_COMBS(X16,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X16),c_fimplies),hAPP(hAPP(c_COMBC(X16,tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool),c_member(X16)),X11)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_fun(X5,tc_HOL_Obool)),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X16,tc_fun(X5,tc_HOL_Obool)),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X16)),c_member(X5))),X13)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INTER__def) ).

fof(fact_congruent__def,axiom,
    ! [X2,X34,X16,X5] :
      ( c_Equiv__Relations_Ocongruent(X5,X16,X34,X2)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X3),X34))
         => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X16),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X5,X16),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X16,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(X16,tc_fun(X16,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,
    ! [X28,X16,X29,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),X29)))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),hAPP(c_Set_OCollect(X16),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X16),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X16),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))),X28)))))
      <=> ! [X33] :
            ( hBOOL(hAPP(X29,X33))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X16),hAPP(c_Set_OCollect(X16),hAPP(hAPP(c_COMBC(X16,X5,tc_HOL_Obool),X28),X33)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__bounded__ex) ).

fof(fact_setsum__Sigma,axiom,
    ! [X2,X13,X16,X11,X5,X38] :
      ( class_Groups_Ocomm__monoid__add(X38)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(X16),hAPP(X13,X3))) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X38),hAPP(hAPP(c_COMBS(X5,tc_fun(X16,tc_HOL_Obool),X38),hAPP(hAPP(c_COMBB(tc_fun(X16,X38),tc_fun(tc_fun(X16,tc_HOL_Obool),X38),X5),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X38)),X2)),X13)),X11) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X5,X16),X38),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,X38),X2)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__Sigma) ).

fof(fact_setprod__Sigma,axiom,
    ! [X2,X13,X16,X11,X5,X38] :
      ( class_Groups_Ocomm__monoid__mult(X38)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(X16),hAPP(X13,X3))) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X38),hAPP(hAPP(c_COMBS(X5,tc_fun(X16,tc_HOL_Obool),X38),hAPP(hAPP(c_COMBB(tc_fun(X16,X38),tc_fun(tc_fun(X16,tc_HOL_Obool),X38),X5),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16,X38)),X2)),X13)),X11) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X5,X16),X38),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,X38),X2)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__Sigma) ).

fof(fact_setsum__restrict__set,axiom,
    ! [X13,X2,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X13))),X2)),c_Groups_Ozero__class_Ozero(X16))),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__restrict__set) ).

fof(fact_UN__finite2__subset,axiom,
    ! [X13,X30,X11,X5] :
      ( ! [X107] : 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)),X107)),X11)),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),X107),X30))),X13)))
     => 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))),X11)),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))),X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__finite2__subset) ).

fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
    ! [X262,X263,X264,X2,X36,X5,X16] : c_New__Random__Sequence_Opos__decr__bind(X16,X5,X36,X2,X264,X263,X262) = c_New__DSequence_Opos__decr__bind(X16,X5,hAPP(hAPP(hAPP(X36,X264),X263),X262),hAPP(hAPP(c_COMBC(X16,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(X16,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(X16,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),X264)),X263)),X262)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__Random__Sequence_Opos__decr__bind__def) ).

fof(fact_image__split__eq__Sigma,axiom,
    ! [X11,X1,X2,X16,X5,X38] : hAPP(c_Set_Oimage(X38,tc_prod(X5,X16),hAPP(hAPP(c_COMBS(X38,X16,tc_prod(X5,X16)),hAPP(hAPP(c_COMBB(X5,tc_fun(X16,tc_prod(X5,X16)),X38),c_Product__Type_OPair(X5,X16)),X2)),X1)),X11) = hAPP(hAPP(c_Product__Type_OSigma(X5,X16),hAPP(c_Set_Oimage(X38,X5,X2),X11)),hAPP(hAPP(c_COMBB(tc_fun(X38,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),c_Set_Oimage(X38,X16,X1)),hAPP(hAPP(c_COMBC(X5,tc_fun(X38,tc_HOL_Obool),tc_fun(X38,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X38,tc_HOL_Obool),tc_fun(tc_fun(X38,tc_HOL_Obool),tc_fun(X38,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X38,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X38,tc_HOL_Obool),X5),c_Set_Ovimage(X38,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)))))),X11))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__split__eq__Sigma) ).

fof(fact_small__lazy__list_Osimps,axiom,
    ! [X20,X5] :
      ( class_Lazy__Sequence_Osmall__lazy(X5)
     => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X5),X20) = 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)),X20)),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),X20),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),X20),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,
    ! [X11,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OSup__class_OSup(X5,X11) = 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)),X11)))),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,
    ! [X70,X13,X2,X84,X5,X16] :
      ( class_Groups_Oordered__ab__group__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X84))
       => ( ! [X145] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X145),X84))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),c_Groups_Ozero__class_Ozero(X16)),hAPP(X2,X145))) )
         => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X84) = X13
           => ( hBOOL(hAPP(hAPP(c_member(X5),X70),X84))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(X2,X70)),X13)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__nonneg__leq__bound) ).

fof(fact_coinduct3__mono__lemma,axiom,
    ! [X13,X31,X2,X16,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Oorder__class_Omono(X5,tc_fun(X16,tc_HOL_Obool),X2)
       => c_Orderings_Oorder__class_Omono(X5,tc_fun(X16,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool))),X2)),X31))),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coinduct3__mono__lemma) ).

fof(fact_Inf__Sup,axiom,
    ! [X11,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OInf__class_OInf(X5,X11) = 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)),X11)))),c_Orderings_Oord__class_Oless__eq(X5))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__Sup) ).

fof(fact_Int__UN__distrib2,axiom,
    ! [X13,X69,X38,X11,X68,X16,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X68),X11)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,tc_fun(X5,tc_HOL_Obool)),X69),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X68),hAPP(hAPP(c_COMBB(tc_fun(X38,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X16),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,tc_fun(X5,tc_HOL_Obool)),X69)),hAPP(hAPP(c_COMBC(X16,tc_fun(X38,tc_fun(X5,tc_HOL_Obool)),tc_fun(X38,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(X38,tc_fun(X5,tc_HOL_Obool)),tc_fun(X38,tc_fun(X5,tc_HOL_Obool))),X16),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X38)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X16),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool))),X11))),X13))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__UN__distrib2) ).

fof(fact_Un__INT__distrib2,axiom,
    ! [X13,X69,X38,X11,X68,X16,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X68),X11)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X38,tc_fun(X5,tc_HOL_Obool)),X69),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X68),hAPP(hAPP(c_COMBB(tc_fun(X38,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X16),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X38,tc_fun(X5,tc_HOL_Obool)),X69)),hAPP(hAPP(c_COMBC(X16,tc_fun(X38,tc_fun(X5,tc_HOL_Obool)),tc_fun(X38,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(X38,tc_fun(X5,tc_HOL_Obool)),tc_fun(X38,tc_fun(X5,tc_HOL_Obool))),X16),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X38)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X16),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X11))),X13))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__INT__distrib2) ).

fof(fact_neg__bind__def,axiom,
    ! [X262,X263,X264,X2,X36,X5,X16] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X16,X5,X36,X2),X264),X263),X262) = c_New__DSequence_Oneg__bind(X16,X5,hAPP(hAPP(hAPP(X36,X264),X263),X262),hAPP(hAPP(c_COMBC(X16,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(X16,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(X16,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),X264)),X263)),X262)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__bind__def) ).

fof(fact_Inter__eq,axiom,
    ! [X11,X5] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X11) = 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))),X11)))),c_member(X5)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__eq) ).

fof(fact_rtrancl__Un__separatorE,axiom,
    ! [X28,X29,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X29),X28))))
     => ( ! [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,X29)))
           => ! [X33] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X33)),X28))
               => X3 = X33 ) )
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),c_Transitive__Closure_Ortrancl(X5,X29))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__Un__separatorE) ).

fof(fact_rtrancl__Un__separator__converseE,axiom,
    ! [X28,X29,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X29),X28))))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X17)),c_Transitive__Closure_Ortrancl(X5,X29)))
           => ! [X33] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X3)),X28))
               => X33 = X3 ) )
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),c_Transitive__Closure_Ortrancl(X5,X29))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).

fof(fact_zip__map2,axiom,
    ! [X214,X2,X38,X212,X16,X5] : hAPP(hAPP(c_List_Ozip(X5,X16),X212),hAPP(hAPP(c_List_Omap(X38,X16),X2),X214)) = hAPP(hAPP(c_List_Omap(tc_prod(X5,X38),tc_prod(X5,X16)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X38,tc_prod(X5,X16)),hAPP(hAPP(c_COMBC(X5,tc_fun(X38,X16),tc_fun(X38,tc_prod(X5,X16))),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(tc_fun(X38,X16),tc_fun(X38,tc_prod(X5,X16))),X5),c_COMBB(X16,tc_prod(X5,X16),X38)),c_Product__Type_OPair(X5,X16))),X2))),hAPP(hAPP(c_List_Ozip(X5,X38),X212),X214)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__map2) ).

fof(fact_nat0__intermed__int__val,axiom,
    ! [X30,X2,X76] :
      ( ! [X145] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X145),X76))
         => 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),X145),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,X145)))),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))),X30))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),hAPP(X2,X76)))
         => ? [X145] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X145),X76))
              & hAPP(X2,X145) = X30 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat0__intermed__int__val) ).

fof(fact_int__val__lemma,axiom,
    ! [X30,X2,X76] :
      ( ! [X145] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X145),X76))
         => 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),X145),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,X145)))),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))),X30))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),hAPP(X2,X76)))
         => ? [X145] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X145),X76))
              & hAPP(X2,X145) = X30 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__val__lemma) ).

fof(fact_small__prod__def,axiom,
    ! [X20,X2,X5,X16] :
      ( ( class_Smallcheck_Osmall(X16)
        & class_Smallcheck_Osmall(X5) )
     => hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(X5,X16)),X2),X20) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(X5),hAPP(hAPP(c_COMBC(X5,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X5),c_Smallcheck_Osmall__class_Osmall(X16)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(X16,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X5),hAPP(c_COMBB(tc_prod(X5,X16),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),X16),X2)),c_Product__Type_OPair(X5,X16)))),X20)),X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small__prod__def) ).

fof(fact_inj__vimage__singleton,axiom,
    ! [X6,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,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,X16,X2),hAPP(hAPP(c_Set_Oinsert(X16),X6),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X5),c_HOL_OThe(X5,hAPP(hAPP(c_COMBC(X5,X16,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X16,tc_fun(X16,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,
    ! [X262,X263,X264,X2,X36,X5,X16] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X16,X5,X36,X2),X264),X263),X262) = c_New__DSequence_Opos__bind(X16,X5,hAPP(hAPP(hAPP(X36,X264),X263),X262),hAPP(hAPP(c_COMBC(X16,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(X16,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(X16,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),X264)),X263)),X262)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__bind__def) ).

fof(fact_Nitpick_Oprod__def,axiom,
    ! [X13,X11,X16,X5] : c_Nitpick_Oprod(X5,X16,X11,X13) = hAPP(c_Set_OCollect(tc_prod(X5,X16)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X16)),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)),X11)))),hAPP(hAPP(c_COMBC(X16,tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool),c_member(X16)),X13)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Oprod__def) ).

fof(fact_map__pair_Ocompositionality,axiom,
    ! [X186,X70,X48,X91,X85,X1,X2,X16,X55,X5,X38] : hAPP(c_Product__Type_Omap__pair(X38,X5,X55,X16,X2,X1),hAPP(c_Product__Type_Omap__pair(X85,X38,X91,X55,X48,X70),X186)) = hAPP(c_Product__Type_Omap__pair(X85,X5,X91,X16,hAPP(c_Fun_Ocomp(X38,X5,X85,X2),X48),hAPP(c_Fun_Ocomp(X55,X16,X91,X1),X70)),X186),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair_Ocompositionality) ).

fof(fact_less,axiom,
    ! [X56,X66,X27,X12] :
      ( 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),X12),X27)),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),X66),X56)),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),X12),X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X66),X27))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less) ).

fof(fact_le,axiom,
    ! [X56,X66,X27,X12] :
      ( 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),X12),X27)),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),X66),X56)),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),X12),X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X66),X27))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le) ).

fof(fact_setsum__reindex__nonzero,axiom,
    ! [X16,X48,X2,X35,X5,X38] :
      ( class_Groups_Ocomm__monoid__add(X38)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X35))
             => ! [X33] :
                  ( hBOOL(hAPP(hAPP(c_member(X5),X33),X35))
                 => ( X3 != X33
                   => ( hAPP(X2,X3) = hAPP(X2,X33)
                     => hAPP(X48,hAPP(X2,X3)) = c_Groups_Ozero__class_Ozero(X38) ) ) ) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X38),X48),hAPP(c_Set_Oimage(X5,X16,X2),X35)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X38),hAPP(c_Fun_Ocomp(X16,X38,X5,X48),X2)),X35) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__reindex__nonzero) ).

fof(fact_if__image__distrib,axiom,
    ! [X35,X1,X2,X29,X5,X16] : hAPP(c_Set_Oimage(X16,X5,hAPP(hAPP(c_COMBS(X16,X5,X5),hAPP(hAPP(c_COMBS(X16,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X16),c_If(X5)),X29)),X2)),X1)),X35) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X16,X5,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),X35),hAPP(c_Set_OCollect(X16),X29)))),hAPP(c_Set_Oimage(X16,X5,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),X35),hAPP(c_Set_OCollect(X16),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X16),c_fNot),X29))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_if__image__distrib) ).

fof(fact_mult,axiom,
    ! [X56,X66,X27,X12] : 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),X12),X27)),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),X66),X56)),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),X12),X66)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X56))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X66)))),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,
    ! [X37,X48,X1,X11,X5,X16] :
      ( class_Groups_Oab__semigroup__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
             => hAPP(X1,X3) = hAPP(X48,X3) )
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X1),X37),X11) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X48),X37),X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__cong) ).

fof(fact_wf__map__pair__image,axiom,
    ! [X2,X16,X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
       => c_Wellfounded_Owf(X16,hAPP(c_Set_Oimage(tc_prod(X5,X5),tc_prod(X16,X16),c_Product__Type_Omap__pair(X5,X16,X5,X16,X2,X2)),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__map__pair__image) ).

fof(fact_inj__on__INTER,axiom,
    ! [X11,X2,X38,X16,X5,X68] :
      ( X68 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
     => ( ! [X145] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X145),X68))
           => c_Fun_Oinj__on(X16,X38,X2,hAPP(X11,X145)) )
       => c_Fun_Oinj__on(X16,X38,X2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X68),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__INTER) ).

fof(fact_listsum__mono,axiom,
    ! [X1,X2,X212,X5,X16] :
      ( ( class_Groups_Omonoid__add(X16)
        & class_Groups_Oordered__ab__semigroup__add(X16) )
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(X2,X3)),hAPP(X1,X3))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(c_List_Omonoid__add__class_Olistsum(X16),hAPP(hAPP(c_List_Omap(X5,X16),X2),X212))),hAPP(c_List_Omonoid__add__class_Olistsum(X16),hAPP(hAPP(c_List_Omap(X5,X16),X1),X212)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__mono) ).

fof(fact_list__all2__all__nthI,axiom,
    ! [X29,X17,X16,X6,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X6) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X17)
     => ( ! [X107] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X6)))
           => hBOOL(hAPP(hAPP(X29,hAPP(hAPP(c_List_Onth(X5),X6),X107)),hAPP(hAPP(c_List_Onth(X16),X17),X107))) )
       => c_List_Olist__all2(X5,X16,X29,X6,X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__all__nthI) ).

fof(fact_list__all2__conv__all__nth,axiom,
    ! [X214,X212,X29,X16,X5] :
      ( c_List_Olist__all2(X5,X16,X29,X212,X214)
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)
        & ! [X145] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X145),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
           => hBOOL(hAPP(hAPP(X29,hAPP(hAPP(c_List_Onth(X5),X212),X145)),hAPP(hAPP(c_List_Onth(X16),X214),X145))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__conv__all__nth) ).

fof(fact_setsum__strict__mono,axiom,
    ! [X1,X2,X11,X5,X16] :
      ( ( class_Groups_Ocomm__monoid__add(X16)
        & class_Groups_Oordered__cancel__ab__semigroup__add(X16) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16),hAPP(X2,X3)),hAPP(X1,X3))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),X11))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__strict__mono) ).

fof(fact_setsum__cases,axiom,
    ! [X1,X2,X29,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),hAPP(hAPP(c_COMBS(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),X29)),X2)),X1)),X11) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Set_OCollect(X5),X29)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X29))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__cases) ).

fof(fact_folding__one__idem_Ohom__commute,axiom,
    ! [X93,X48,X90,X2,X5] :
      ( c_Finite__Set_Ofolding__one__idem(X5,X2,X90)
     => ( ! [X3,X33] : hAPP(X48,hAPP(hAPP(X2,X3),X33)) = hAPP(hAPP(X2,hAPP(X48,X3)),hAPP(X48,X33))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X93))
         => ( X93 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X48,hAPP(X90,X93)) = hAPP(X90,hAPP(c_Set_Oimage(X5,X5,X48),X93)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Ohom__commute) ).

fof(fact_set__n__lists,axiom,
    ! [X212,X76,X5] : hAPP(c_List_Oset(tc_List_Olist(X5)),c_Enum_On__lists(X5,X76,X212)) = 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)))),X76))),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),X212)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__n__lists) ).

fof(fact_map__pair_Ocomp,axiom,
    ! [X70,X48,X1,X2,X16,X5,X55,X38,X91,X85] : hAPP(c_Fun_Ocomp(tc_prod(X85,X91),tc_prod(X38,X55),tc_prod(X5,X16),c_Product__Type_Omap__pair(X85,X38,X91,X55,X2,X1)),c_Product__Type_Omap__pair(X5,X85,X16,X91,X48,X70)) = c_Product__Type_Omap__pair(X5,X38,X16,X55,hAPP(c_Fun_Ocomp(X85,X38,X5,X2),X48),hAPP(c_Fun_Ocomp(X91,X55,X16,X1),X70)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair_Ocomp) ).

fof(fact_map__pair__compose,axiom,
    ! [X187,X188,X91,X88,X89,X85,X55,X16,X38,X5] : c_Product__Type_Omap__pair(X5,X38,X16,X55,hAPP(c_Fun_Ocomp(X85,X38,X5,X89),X88),hAPP(c_Fun_Ocomp(X91,X55,X16,X188),X187)) = hAPP(c_Fun_Ocomp(tc_prod(X85,X91),tc_prod(X38,X55),tc_prod(X5,X16),c_Product__Type_Omap__pair(X85,X38,X91,X55,X89,X188)),c_Product__Type_Omap__pair(X5,X85,X16,X91,X88,X187)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__compose) ).

fof(fact_listrel__iff__nth,axiom,
    ! [X34,X214,X212,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)),X212),X214)),c_List_Olistrel(X5,X34)))
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X214)
        & ! [X107] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(hAPP(c_List_Onth(X5),X212),X107)),hAPP(hAPP(c_List_Onth(X5),X214),X107))),X34)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__iff__nth) ).

fof(fact_rel__pow__Suc__D2,axiom,
    ! [X36,X76,X37,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X37)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X76)),X36)))
     => ? [X33] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X33)),X36))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X37)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X76),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__Suc__D2) ).

fof(fact_quotient__def,axiom,
    ! [X34,X11,X5] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X11),X34) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X11),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,X34)),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,
    ! [X11,X34,X16,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(c_Relation_OImage(X16,X5,X34),X11)))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X16),X3),X11))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X5)),hAPP(hAPP(c_Product__Type_OPair(X16,X5),X3),X17)),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__iff) ).

fof(fact_folding__one_Oclosed,axiom,
    ! [X11,X90,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X33] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(X2,X3),X33)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X33),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X5),hAPP(X90,X11)),X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Oclosed) ).

fof(fact_set__map__of__compr,axiom,
    ! [X212,X16,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Omap(tc_prod(X5,X16),X5),c_Product__Type_Ofst(X5,X16)),X212)))
     => hAPP(c_List_Oset(tc_prod(X5,X16)),X212) = hAPP(c_Set_OCollect(tc_prod(X5,X16)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_Option_Ooption(X16)),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X16),tc_HOL_Obool),tc_fun(tc_fun(X16,tc_Option_Ooption(X16)),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBB(tc_Option_Ooption(X16),tc_HOL_Obool,X16)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X16),tc_fun(tc_Option_Ooption(X16),tc_HOL_Obool),X5),c_fequal),hAPP(c_Map_Omap__of(X5,X16),X212)))),c_Option_Ooption_OSome(X16)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__map__of__compr) ).

fof(fact_quotient__diff1,axiom,
    ! [X6,X11,X34,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))))),X34),X11)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X34) = 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),X11),X34)),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)))),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__diff1) ).

fof(fact_Collect__ball__eq,axiom,
    ! [X29,X11,X16,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OAll(X16)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_COMBS(X16,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X16),c_fimplies),hAPP(hAPP(c_COMBC(X16,tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool),c_member(X16)),X11)))),X29))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X16),c_Set_OCollect(X5)),hAPP(c_COMBC(X5,X16,tc_HOL_Obool),X29))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__ball__eq) ).

fof(fact_sublist__append,axiom,
    ! [X11,X247,X97,X5] : c_List_Osublist(X5,hAPP(hAPP(c_List_Oappend(X5),X97),X247),X11) = hAPP(hAPP(c_List_Oappend(X5),c_List_Osublist(X5,X97,X11)),c_List_Osublist(X5,X247,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)),X97)))),X11)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__append) ).

fof(fact_zip__obtain__same__length,axiom,
    ! [X29,X214,X16,X212,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)),X212)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214))),X212)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),hAPP(hAPP(c_List_Otake(X16),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214))),X214))
       => hBOOL(hAPP(X29,hAPP(hAPP(c_List_Ozip(X5,X16),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)),X212)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214))),X212)),hAPP(hAPP(c_List_Otake(X16),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214))),X214)))) )
     => hBOOL(hAPP(X29,hAPP(hAPP(c_List_Ozip(X5,X16),X212),X214))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__obtain__same__length) ).

fof(fact_map__filter__map__filter,axiom,
    ! [X212,X29,X2,X5,X16] : hAPP(hAPP(c_List_Omap(X16,X5),X2),hAPP(c_List_Ofilter(X16,X29),X212)) = c_List_Omap__filter(X16,X5,hAPP(hAPP(c_COMBC(X16,tc_Option_Ooption(X5),tc_Option_Ooption(X5)),hAPP(hAPP(c_COMBS(X16,tc_Option_Ooption(X5),tc_fun(tc_Option_Ooption(X5),tc_Option_Ooption(X5))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X5),tc_fun(tc_Option_Ooption(X5),tc_Option_Ooption(X5))),X16),c_If(tc_Option_Ooption(X5))),X29)),hAPP(hAPP(c_COMBB(X5,tc_Option_Ooption(X5),X16),c_Option_Ooption_OSome(X5)),X2))),c_Option_Ooption_ONone(X5)),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__filter__map__filter) ).

fof(fact_card__quotient__disjoint,axiom,
    ! [X34,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( 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))))),X34),X11)
       => hAPP(c_Finite__Set_Ocard(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X11),X34)) = hAPP(c_Finite__Set_Ocard(X5),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__quotient__disjoint) ).

fof(fact_dom__if,axiom,
    ! [X1,X2,X29,X16,X5] : c_Map_Odom(X5,X16,hAPP(hAPP(c_COMBS(X5,tc_Option_Ooption(X16),tc_Option_Ooption(X16)),hAPP(hAPP(c_COMBS(X5,tc_Option_Ooption(X16),tc_fun(tc_Option_Ooption(X16),tc_Option_Ooption(X16))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X16),tc_fun(tc_Option_Ooption(X16),tc_Option_Ooption(X16))),X5),c_If(tc_Option_Ooption(X16))),X29)),X2)),X1)) = 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)),c_Map_Odom(X5,X16,X2)),hAPP(c_Set_OCollect(X5),X29))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Map_Odom(X5,X16,X1)),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X29)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dom__if) ).

fof(fact_map__filter__def,axiom,
    ! [X212,X2,X5,X16] : c_List_Omap__filter(X16,X5,X2,X212) = hAPP(hAPP(c_List_Omap(X16,X5),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X5),X5,X16,c_Option_Othe(X5)),X2)),hAPP(c_List_Ofilter(X16,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X16),c_fNot),hAPP(hAPP(c_COMBC(X16,tc_Option_Ooption(X5),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X5),tc_fun(tc_Option_Ooption(X5),tc_HOL_Obool),X16),c_fequal),X2)),c_Option_Ooption_ONone(X5)))),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__filter__def) ).

fof(fact_arith__series__general,axiom,
    ! [X76,X20,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))),X20))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X76))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X76)),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),X76),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X20)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__series__general) ).

fof(fact_reduction__pair__def,axiom,
    ! [X29,X5] :
      ( c_FunDef_Oreduction__pair(X5,X29)
    <=> ( 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)),X29))
        & 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)),X29)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X29))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X29))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reduction__pair__def) ).

fof(fact_UN__subset__iff,axiom,
    ! [X13,X11,X68,X16,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(X16,tc_fun(X5,tc_HOL_Obool)),X68),X11)),X13))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X16),X3),X68))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(X11,X3)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__subset__iff) ).

fof(fact_setsum__bounded,axiom,
    ! [X180,X2,X11,X5,X16] :
      ( ( class_Groups_Oordered__ab__semigroup__add(X16)
        & class_Rings_Osemiring__1(X16) )
     => ( ! [X145] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X145),X11))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(X2,X145)),X180)) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X16),hAPP(c_Finite__Set_Ocard(X5),X11))),X180))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__bounded) ).

fof(fact_map__pair__def,axiom,
    ! [X1,X2,X55,X16,X38,X5] : c_Product__Type_Omap__pair(X5,X38,X16,X55,X2,X1) = hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_prod(X38,X55)),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,X55),tc_fun(X16,tc_prod(X38,X55))),hAPP(hAPP(c_COMBB(tc_fun(X55,tc_prod(X38,X55)),tc_fun(tc_fun(X16,X55),tc_fun(X16,tc_prod(X38,X55))),X5),c_COMBB(X55,tc_prod(X38,X55),X16)),hAPP(hAPP(c_COMBB(X38,tc_fun(X55,tc_prod(X38,X55)),X5),c_Product__Type_OPair(X38,X55)),X2))),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__def) ).

fof(fact_image__subsetI,axiom,
    ! [X13,X2,X16,X11,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
         => hBOOL(hAPP(hAPP(c_member(X16),hAPP(X2,X3)),X13)) )
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X16,X2),X11)),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__subsetI) ).

fof(fact_decr__lemma,axiom,
    ! [X23,X14,X41] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X41))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X14),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),X14),X23))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X41))),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decr__lemma) ).

fof(fact_SUP__le__iff,axiom,
    ! [X66,X67,X11,X16,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(X16,X5),X11),X67)),X66))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X16),X3),X11))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X67,X3)),X66)) ) ) ),
    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_size__code,axiom,
    ! [X253,X5] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X5)),X253) = hAPP(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),X253)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_size__code) ).

fof(fact_lexord__take__index__conv,axiom,
    ! [X34,X27,X12,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)),X12),X27)),c_List_Olexord(X5,X34)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X12)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X27)))
          & hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X12)),X27) = X12 )
        | ? [X145] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X145),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X12)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X27))))
            & hAPP(hAPP(c_List_Otake(X5),X145),X12) = hAPP(hAPP(c_List_Otake(X5),X145),X27)
            & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(hAPP(c_List_Onth(X5),X12),X145)),hAPP(hAPP(c_List_Onth(X5),X27),X145))),X34)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__take__index__conv) ).

fof(fact_SetCompr__Sigma__eq,axiom,
    ! [X28,X29,X16,X5] : hAPP(c_Set_OCollect(tc_prod(X5,X16)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X29))),X28))) = hAPP(hAPP(c_Product__Type_OSigma(X5,X16),hAPP(c_Set_OCollect(X5),X29)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),c_Set_OCollect(X16)),X28)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SetCompr__Sigma__eq) ).

fof(fact_card__less,axiom,
    ! [X70,X67] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X67))
     => 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)),X67))),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,X70))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__less) ).

fof(fact_Eps__split__eq,axiom,
    ! [X27,X12,X16,X5] : c_Hilbert__Choice_OEps(tc_prod(X5,X16),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(c_fequal,X12)))),hAPP(c_fequal,X27)))) = hAPP(hAPP(c_Product__Type_OPair(X5,X16),X12),X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Eps__split__eq) ).

fof(fact_The__split__eq,axiom,
    ! [X27,X12,X16,X5] : c_HOL_OThe(tc_prod(X5,X16),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(c_fequal,X12)))),hAPP(c_fequal,X27)))) = hAPP(hAPP(c_Product__Type_OPair(X5,X16),X12),X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_The__split__eq) ).

fof(fact_setsum__commute,axiom,
    ! [X11,X13,X2,X38,X16,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),hAPP(hAPP(c_COMBC(X16,tc_fun(X38,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBB(tc_fun(X38,X5),tc_fun(tc_fun(X38,tc_HOL_Obool),X5),X16),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X38,X5)),X2)),X13)),X11) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X38,X5),hAPP(hAPP(c_COMBC(X38,tc_fun(X16,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBB(tc_fun(X16,X5),tc_fun(tc_fun(X16,tc_HOL_Obool),X5),X38),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5)),hAPP(c_COMBC(X16,X38,X5),X2))),X11)),X13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__commute) ).

fof(fact_Collect__split,axiom,
    ! [X28,X29,X16,X5] : hAPP(c_Set_OCollect(tc_prod(X5,X16)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X29))),X28))) = hAPP(hAPP(c_Product__Type_OSigma(X5,X16),hAPP(c_Set_OCollect(X5),X29)),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_Set_OCollect(X16),X28))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__split) ).

fof(fact_image__eq__fold__image,axiom,
    ! [X2,X16,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => hAPP(c_Set_Oimage(X5,X16,X2),X11) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X16,tc_HOL_Obool),X5,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X16,tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_Set_Oinsert(X16)),X2)),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eq__fold__image) ).

fof(fact_card__Diff2__less,axiom,
    ! [X27,X12,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X27),X11))
         => 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)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X5),X27),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X5),X11))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff2__less) ).

fof(fact_Id__on__def_H,axiom,
    ! [X11,X5] : c_Relation_OId__on(X5,X11) = 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))),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__def_H) ).

fof(fact_int__ge__less__than__def,axiom,
    ! [X20] : c_Int_Oint__ge__less__than(X20) = 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),X20)))),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,
    ! [X48,X1,X2,X91,X85,X16,X55,X38,X5] : hAPP(hAPP(c_Product__Type_Oscomp(X5,X38,X55,X16),hAPP(hAPP(c_Product__Type_Oscomp(X5,X85,X91,tc_prod(X38,X55)),X2),X1)),X48) = hAPP(hAPP(c_Product__Type_Oscomp(X5,X85,X91,X16),X2),hAPP(hAPP(c_COMBC(X85,tc_fun(X38,tc_fun(X55,X16)),tc_fun(X91,X16)),hAPP(hAPP(c_COMBB(tc_fun(X91,tc_prod(X38,X55)),tc_fun(tc_fun(X38,tc_fun(X55,X16)),tc_fun(X91,X16)),X85),c_Product__Type_Oscomp(X91,X38,X55,X16)),X1)),X48)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_scomp__scomp) ).

fof(fact_wmax__insertI,axiom,
    ! [X166,X12,X165,X27] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27),X165))
     => ( 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)),X12),X27)),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)),X166),X165)),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)),X12),X166)),X165)),c_FunDef_Omax__weak)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wmax__insertI) ).

fof(fact_smax__insertI,axiom,
    ! [X31,X12,X42,X27] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27),X42))
     => ( 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)),X12),X27)),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)),X31),X42)),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)),X12),X31)),X42)),c_FunDef_Omax__strict)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smax__insertI) ).

fof(fact_sorted__map__same,axiom,
    ! [X212,X1,X2,X16,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X16,X5),X2),hAPP(c_List_Ofilter(X16,hAPP(hAPP(c_COMBC(X16,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,tc_HOL_Obool),X16),c_fequal),X2)),hAPP(X1,X212))),X212))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__map__same) ).

fof(fact_max__ext_Osimps,axiom,
    ! [X36,X46,X47,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)),X47),X46)),c_Wellfounded_Omax__ext(X5,X36)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X47))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X46))
        & X46 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X47))
           => ? [X39] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X39),X46))
                & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X39)),X36)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ext_Osimps) ).

fof(fact_wf__union__merge,axiom,
    ! [X35,X36,X5] :
      ( c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X36),X35))
    <=> 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),X36),X36)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X35),X36))),X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__union__merge) ).

fof(fact_map__pair__surj__on,axiom,
    ! [X60,X13,X1,X38,X55,X53,X11,X2,X5,X16] :
      ( hAPP(c_Set_Oimage(X16,X5,X2),X11) = X53
     => ( hAPP(c_Set_Oimage(X55,X38,X1),X13) = X60
       => hAPP(c_Set_Oimage(tc_prod(X16,X55),tc_prod(X5,X38),c_Product__Type_Omap__pair(X16,X5,X55,X38,X2,X1)),hAPP(hAPP(c_Product__Type_OSigma(X16,X55),X11),hAPP(c_COMBK(tc_fun(X55,tc_HOL_Obool),X16),X13))) = hAPP(hAPP(c_Product__Type_OSigma(X5,X38),X53),hAPP(c_COMBK(tc_fun(X38,tc_HOL_Obool),X5),X60)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__surj__on) ).

fof(fact_wmin__insertI,axiom,
    ! [X165,X27,X166,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X12),X166))
     => ( 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)),X12),X27)),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)),X166),X165)),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)),X166),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27),X165))),c_FunDef_Omin__weak)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wmin__insertI) ).

fof(fact_smin__insertI,axiom,
    ! [X165,X27,X166,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X12),X166))
     => ( 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)),X12),X27)),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)),X166),X165)),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)),X166),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X27),X165))),c_FunDef_Omin__strict)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smin__insertI) ).

fof(fact_insert__fold1SetE,axiom,
    ! [X12,X31,X6,X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,hAPP(hAPP(c_Set_Oinsert(X5),X6),X31)),X12))
     => ~ ! [X74,X75] :
            ( hAPP(hAPP(c_Set_Oinsert(X5),X6),X31) = hAPP(hAPP(c_Set_Oinsert(X5),X74),X75)
           => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,X2,X74,X75),X12))
             => hBOOL(hAPP(hAPP(c_member(X5),X74),X75)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__fold1SetE) ).

fof(fact_listrel1__iff__update,axiom,
    ! [X34,X214,X212,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)),X212),X214)),c_List_Olistrel1(X5,X34)))
    <=> ? [X33,X107] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(hAPP(c_List_Onth(X5),X212),X107)),X33)),X34))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
          & X214 = hAPP(hAPP(c_List_Olist__update(X5,X212),X107),X33) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__iff__update) ).

fof(fact_map__pair__surj,axiom,
    ! [X1,X38,X55,X2,X5,X16] :
      ( hAPP(c_Set_Oimage(X16,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => ( hAPP(c_Set_Oimage(X55,X38,X1),c_Orderings_Otop__class_Otop(tc_fun(X55,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X38,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(X16,X55),tc_prod(X5,X38),c_Product__Type_Omap__pair(X16,X5,X55,X38,X2,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X16,X55),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X5,X38),tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__surj) ).

fof(fact_minus__fold__remove,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X13),X11) = 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))))),X13),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__fold__remove) ).

fof(fact_map__of__mapk__SomeI,axiom,
    ! [X12,X30,X10,X38,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hAPP(hAPP(c_Map_Omap__of(X5,X38),X10),X30) = hAPP(c_Option_Ooption_OSome(X38),X12)
       => hAPP(hAPP(c_Map_Omap__of(X16,X38),hAPP(hAPP(c_List_Omap(tc_prod(X5,X38),tc_prod(X16,X38)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X38,tc_prod(X16,X38)),hAPP(hAPP(c_COMBB(X16,tc_fun(X38,tc_prod(X16,X38)),X5),c_Product__Type_OPair(X16,X38)),X2))),X10)),hAPP(X2,X30)) = hAPP(c_Option_Ooption_OSome(X38),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__mapk__SomeI) ).

fof(fact_fst__map__pair,axiom,
    ! [X12,X1,X2,X55,X38,X16,X5] : hAPP(c_Product__Type_Ofst(X5,X16),hAPP(c_Product__Type_Omap__pair(X38,X5,X55,X16,X2,X1),X12)) = hAPP(X2,hAPP(c_Product__Type_Ofst(X38,X55),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__map__pair) ).

fof(fact_snd__prod__fun,axiom,
    ! [X12,X1,X2,X55,X38,X5,X16] : hAPP(c_Product__Type_Osnd(X16,X5),hAPP(c_Product__Type_Omap__pair(X38,X16,X55,X5,X2,X1),X12)) = hAPP(X1,hAPP(c_Product__Type_Osnd(X38,X55),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__prod__fun) ).

fof(fact_lexord__linear,axiom,
    ! [X27,X12,X34,X5] :
      ( ! [X74,X52] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X74),X52)),X34))
          | X74 = X52
          | hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X52),X74)),X34)) )
     => ( 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)),X12),X27)),c_List_Olexord(X5,X34)))
        | X12 = X27
        | 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)),X27),X12)),c_List_Olexord(X5,X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__linear) ).

fof(fact_add,axiom,
    ! [X56,X66,X27,X12] : 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),X12),X27)),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),X66),X56)),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),X12),X66)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),X56))),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,
    ! [X11,X5] : c_Relation_OId__on(X5,X11) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X11),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,
    ! [X27,X12,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)),X12),X27))
    <=> X12 != X27 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__noteq) ).

fof(fact_map__zip__map,axiom,
    ! [X214,X212,X1,X55,X2,X5,X38,X16] : hAPP(hAPP(c_List_Omap(tc_prod(X16,X38),X5),X2),hAPP(hAPP(c_List_Ozip(X16,X38),hAPP(hAPP(c_List_Omap(X55,X16),X1),X212)),X214)) = hAPP(hAPP(c_List_Omap(tc_prod(X55,X38),X5),hAPP(c_Product__Type_Oprod_Oprod__case(X55,X38,X5),hAPP(hAPP(c_COMBB(tc_fun(X38,tc_prod(X16,X38)),tc_fun(X38,X5),X55),hAPP(c_COMBB(tc_prod(X16,X38),X5,X38),X2)),hAPP(hAPP(c_COMBB(X16,tc_fun(X38,tc_prod(X16,X38)),X55),c_Product__Type_OPair(X16,X38)),X1)))),hAPP(hAPP(c_List_Ozip(X55,X38),X212),X214)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__zip__map) ).

fof(fact_order__fun_I2_J,axiom,
    ! [X1,X2,X5,X16] :
      ( ( class_Orderings_Oorder(X16)
        & class_Enum_Oenum(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,X16)),X2),X1))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X16)),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,X16,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X16,tc_fun(X16,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,
    ! [X11,X97,X12,X5] : c_List_Osublist(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X97),X11) = 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)),X11)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Olist_ONil(X5))),c_List_Olist_ONil(X5))),c_List_Osublist(X5,X97,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)),X11)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__Cons) ).

fof(fact_enum__ex__fun__code,axiom,
    ! [X29,X5,X16] :
      ( ( class_Enum_Oenum(X16)
        & class_Enum_Oenum(X5)
        & class_HOL_Oequal(X5) )
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X5,X16)),X29))
      <=> c_Enum_Oex__n__lists(X16,hAPP(hAPP(c_COMBB(tc_fun(X5,X16),tc_HOL_Obool,tc_List_Olist(X16)),X29),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_Option_Ooption(X16)),tc_fun(X5,X16),tc_List_Olist(X16)),c_Fun_Ocomp(tc_Option_Ooption(X16),X16,X5,c_Option_Othe(X16))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X5,X16)),tc_fun(X5,tc_Option_Ooption(X16)),tc_List_Olist(X16)),c_Map_Omap__of(X5,X16)),hAPP(c_List_Ozip(X5,X16),c_Enum_Oenum__class_Oenum(X5))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_Enum_Oenum__class_Oenum(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__ex__fun__code) ).

fof(fact_enum__all__fun__code,axiom,
    ! [X29,X5,X16] :
      ( ( class_Enum_Oenum(X16)
        & class_Enum_Oenum(X5)
        & class_HOL_Oequal(X5) )
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X5,X16)),X29))
      <=> c_Enum_Oall__n__lists(X16,hAPP(hAPP(c_COMBB(tc_fun(X5,X16),tc_HOL_Obool,tc_List_Olist(X16)),X29),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_Option_Ooption(X16)),tc_fun(X5,X16),tc_List_Olist(X16)),c_Fun_Ocomp(tc_Option_Ooption(X16),X16,X5,c_Option_Othe(X16))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X5,X16)),tc_fun(X5,tc_Option_Ooption(X16)),tc_List_Olist(X16)),c_Map_Omap__of(X5,X16)),hAPP(c_List_Ozip(X5,X16),c_Enum_Oenum__class_Oenum(X5))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_Enum_Oenum__class_Oenum(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__all__fun__code) ).

fof(fact_enum__ex__fun__def,axiom,
    ! [X29,X5,X16] :
      ( ( class_Enum_Oenum(X16)
        & class_Enum_Oenum(X5) )
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X5,X16)),X29))
      <=> c_Enum_Oex__n__lists(X16,hAPP(hAPP(c_COMBB(tc_fun(X5,X16),tc_HOL_Obool,tc_List_Olist(X16)),X29),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_Option_Ooption(X16)),tc_fun(X5,X16),tc_List_Olist(X16)),c_Fun_Ocomp(tc_Option_Ooption(X16),X16,X5,c_Option_Othe(X16))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X5,X16)),tc_fun(X5,tc_Option_Ooption(X16)),tc_List_Olist(X16)),c_Map_Omap__of(X5,X16)),hAPP(c_List_Ozip(X5,X16),c_Enum_Oenum__class_Oenum(X5))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_Enum_Oenum__class_Oenum(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__ex__fun__def) ).

fof(fact_enum__all__fun__def,axiom,
    ! [X29,X5,X16] :
      ( ( class_Enum_Oenum(X16)
        & class_Enum_Oenum(X5) )
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X5,X16)),X29))
      <=> c_Enum_Oall__n__lists(X16,hAPP(hAPP(c_COMBB(tc_fun(X5,X16),tc_HOL_Obool,tc_List_Olist(X16)),X29),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_Option_Ooption(X16)),tc_fun(X5,X16),tc_List_Olist(X16)),c_Fun_Ocomp(tc_Option_Ooption(X16),X16,X5,c_Option_Othe(X16))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X5,X16)),tc_fun(X5,tc_Option_Ooption(X16)),tc_List_Olist(X16)),c_Map_Omap__of(X5,X16)),hAPP(c_List_Ozip(X5,X16),c_Enum_Oenum__class_Oenum(X5))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_Enum_Oenum__class_Oenum(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__all__fun__def) ).

fof(fact_dom__override__on,axiom,
    ! [X11,X1,X2,X16,X5] : c_Map_Odom(X5,X16,c_Fun_Ooverride__on(X5,tc_Option_Ooption(X16),X2,X1,X11)) = 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)),c_Map_Odom(X5,X16,X2)),hAPP(c_Set_OCollect(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)),X11),c_Map_Odom(X5,X16,X1)))))),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),c_Map_Odom(X5,X16,X1))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dom__override__on) ).

fof(fact_nth__nth__transpose__sorted,axiom,
    ! [X115,X70,X212,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))),X212)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X70),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),c_List_Otranspose(X5,X212))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X115),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),X70)),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X212))))
         => hAPP(hAPP(c_List_Onth(X5),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),c_List_Otranspose(X5,X212)),X70)),X115) = hAPP(hAPP(c_List_Onth(X5),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),X212),X115)),X70) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__nth__transpose__sorted) ).

fof(fact_INF__less__iff,axiom,
    ! [X6,X2,X11,X16,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(X16,X5),X11),X2)),X6))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X16),X3),X11))
            & 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,
    ! [X29,X13,X11,X16,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X11),X13)))
         => hBOOL(hAPP(X29,X3)) )
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X16),X3),X11))
         => ! [X39] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X39),hAPP(X13,X3)))
             => hBOOL(hAPP(X29,X39)) ) ) ),
    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,
    ! [X18,X19,X36,X13,X11,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)),X11),X13)),c_Wellfounded_Omax__ext(X5,X36)))
     => ( 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),X18)),c_Wellfounded_Omax__ext(X5,X36)))
       => 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)),X11),X19)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X13),X18))),c_Wellfounded_Omax__ext(X5,X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ext__additive) ).

fof(fact_SigmaE,axiom,
    ! [X13,X11,X21,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),X21),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),X13)))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
           => ! [X33] :
                ( hBOOL(hAPP(hAPP(c_member(X16),X33),hAPP(X13,X3)))
               => X21 != hAPP(hAPP(c_Product__Type_OPair(X5,X16),X3),X33) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaE) ).

fof(fact_foldl__map,axiom,
    ! [X212,X2,X38,X6,X1,X16,X5] : hAPP(c_List_Ofoldl(X5,X16,X1,X6),hAPP(hAPP(c_List_Omap(X38,X16),X2),X212)) = hAPP(c_List_Ofoldl(X5,X38,hAPP(hAPP(c_COMBC(X5,tc_fun(X38,X16),tc_fun(X38,X5)),hAPP(hAPP(c_COMBB(tc_fun(X16,X5),tc_fun(tc_fun(X38,X16),tc_fun(X38,X5)),X5),c_COMBB(X16,X5,X38)),X1)),X2),X6),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__map) ).

fof(fact_rel__comp__UNION__distrib2,axiom,
    ! [X84,X34,X68,X55,X16,X38,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X38,X16),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X55,tc_fun(tc_prod(X5,X38),tc_HOL_Obool)),X68),X34)),X84) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X55,tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X68),hAPP(hAPP(c_COMBC(X55,tc_fun(tc_prod(X38,X16),tc_HOL_Obool),tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X5,X38),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X38,X16),tc_HOL_Obool),tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X55),c_Relation_Orel__comp(X5,X38,X16)),X34)),X84)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__UNION__distrib2) ).

fof(fact_finite__Collect__disjI,axiom,
    ! [X28,X29,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),X29)),X28))))
    <=> ( 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),X28))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__disjI) ).

fof(fact_inj__transfer,axiom,
    ! [X12,X29,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( ! [X33] :
            ( hBOOL(hAPP(hAPP(c_member(X16),X33),hAPP(c_Set_Oimage(X5,X16,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
           => hBOOL(hAPP(X29,hAPP(c_Hilbert__Choice_Oinv__into(X5,X16,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),X33))) )
       => hBOOL(hAPP(X29,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__transfer) ).

fof(fact_enum__ex__prod__def,axiom,
    ! [X29,X5,X16] :
      ( ( class_Enum_Oenum(X16)
        & class_Enum_Oenum(X5) )
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X5,X16)),X29))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X5),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool,X5),c_Enum_Oenum__class_Oenum__ex(X16)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_prod(X5,X16),tc_HOL_Obool,X16),X29)),c_Product__Type_OPair(X5,X16))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__ex__prod__def) ).

fof(fact_enum__all__prod__def,axiom,
    ! [X29,X5,X16] :
      ( ( class_Enum_Oenum(X16)
        & class_Enum_Oenum(X5) )
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X5,X16)),X29))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X5),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool,X5),c_Enum_Oenum__class_Oenum__all(X16)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_prod(X5,X16),tc_HOL_Obool,X16),X29)),c_Product__Type_OPair(X5,X16))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__all__prod__def) ).

fof(fact_listsp__conj__eq,axiom,
    ! [X12,X13,X11,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),X11)),X13)),X12))
    <=> ( hBOOL(hAPP(c_List_Olistsp(X5,X11),X12))
        & hBOOL(hAPP(c_List_Olistsp(X5,X13),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__conj__eq) ).

fof(fact_lists__IntI,axiom,
    ! [X13,X11,X97,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X97),c_List_Olists(X5,X11)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X97),c_List_Olists(X5,X13)))
       => 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)),X11)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X13))),X97)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__IntI) ).

fof(fact_UN__equiv__class2,axiom,
    ! [X46,X47,X2,X38,X62,X63,X16,X64,X65,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X65,X64)
     => ( c_Equiv__Relations_Oequiv(X16,X63,X62)
       => ( c_Equiv__Relations_Ocongruent2(X5,X16,tc_fun(X38,tc_HOL_Obool),X64,X62,X2)
         => ( hBOOL(hAPP(hAPP(c_member(X5),X47),X65))
           => ( hBOOL(hAPP(hAPP(c_member(X16),X46),X63))
             => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X38,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X64),hAPP(hAPP(c_Set_Oinsert(X5),X47),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_fun(X38,tc_HOL_Obool)),tc_fun(X38,tc_HOL_Obool),X5),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X38,tc_HOL_Obool)),hAPP(c_Relation_OImage(X16,X16,X62),hAPP(hAPP(c_Set_Oinsert(X16),X46),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)))))),X2)) = hAPP(hAPP(X2,X47),X46) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__equiv__class2) ).

fof(fact_length__sublist,axiom,
    ! [X68,X212,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Osublist(X5,X212,X68)) = 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)),X212)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X68)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__sublist) ).

fof(fact_length__filter__conv__card,axiom,
    ! [X212,X161,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X161),X212)) = 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)),X212)))),hAPP(hAPP(c_COMBB(X5,tc_HOL_Obool,tc_Nat_Onat),X161),hAPP(c_List_Onth(X5),X212))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__filter__conv__card) ).

fof(fact_fold__image__distrib,axiom,
    ! [X48,X1,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),hAPP(hAPP(c_COMBS(X5,X16,X16),hAPP(hAPP(c_COMBB(X16,tc_fun(X16,X16),X5),c_Groups_Otimes__class_Otimes(X16)),X1)),X48)),c_Groups_Oone__class_Oone(X16)),X11) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X1),c_Groups_Oone__class_Oone(X16)),X11)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X48),c_Groups_Oone__class_Oone(X16)),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__distrib) ).

fof(fact_snoc__listrel1__snoc__iff,axiom,
    ! [X34,X27,X214,X12,X212,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),X212),hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Olist_ONil(X5)))),hAPP(hAPP(c_List_Oappend(X5),X214),hAPP(hAPP(c_List_Olist_OCons(X5),X27),c_List_Olist_ONil(X5))))),c_List_Olistrel1(X5,X34)))
    <=> ( ( 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)),X212),X214)),c_List_Olistrel1(X5,X34)))
          & X12 = X27 )
        | ( X212 = X214
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),X34)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snoc__listrel1__snoc__iff) ).

fof(fact_list__all2__map2,axiom,
    ! [X234,X2,X38,X235,X29,X16,X5] :
      ( c_List_Olist__all2(X5,X16,X29,X235,hAPP(hAPP(c_List_Omap(X38,X16),X2),X234))
    <=> c_List_Olist__all2(X5,X38,hAPP(hAPP(c_COMBC(X5,tc_fun(X38,X16),tc_fun(X38,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X38,X16),tc_fun(X38,tc_HOL_Obool)),X5),c_COMBB(X16,tc_HOL_Obool,X38)),X29)),X2),X235,X234) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__map2) ).

fof(fact_UN__finite2__eq,axiom,
    ! [X13,X30,X11,X5] :
      ( ! [X107] : 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)),X107)),X11) = 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),X107),X30))),X13)
     => 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))),X11) = 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))),X13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__finite2__eq) ).

fof(fact_max__ext_Ointros,axiom,
    ! [X36,X42,X31,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X31))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X42))
       => ( X42 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X31))
               => ? [X39] :
                    ( hBOOL(hAPP(hAPP(c_member(X5),X39),X42))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X39)),X36)) ) )
           => 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)),X31),X42)),c_Wellfounded_Omax__ext(X5,X36))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ext_Ointros) ).

fof(fact_ran__def,axiom,
    ! [X45,X5,X16] : c_Map_Oran(X16,X5,X45) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X16)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X5),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_COMBC(X16,tc_Option_Ooption(X5),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X5),tc_fun(tc_Option_Ooption(X5),tc_HOL_Obool),X16),c_fequal),X45))),c_Option_Ooption_OSome(X5)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ran__def) ).

fof(fact_pred__comp_Oequations,axiom,
    ! [X51,X47,X84,X34,X38,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X16,X38,X34,X84),X47),X51))
    <=> ? [X52] :
          ( hBOOL(hAPP(hAPP(X34,X47),X52))
          & hBOOL(hAPP(hAPP(X84,X52),X51)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp_Oequations) ).

fof(fact_wf__no__infinite__down__chainE,axiom,
    ! [X2,X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => ~ ! [X109] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(X2,hAPP(c_Nat_OSuc,X109))),hAPP(X2,X109))),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__no__infinite__down__chainE) ).

fof(fact_wf__iff__no__infinite__down__chain,axiom,
    ! [X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
    <=> ~ ? [X43] :
          ! [X145] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(X43,hAPP(c_Nat_OSuc,X145))),hAPP(X43,X145))),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__iff__no__infinite__down__chain) ).

fof(fact_congruent2__implies__congruent__UN,axiom,
    ! [X6,X2,X38,X62,X63,X16,X64,X65,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X65,X64)
     => ( c_Equiv__Relations_Oequiv(X16,X63,X62)
       => ( c_Equiv__Relations_Ocongruent2(X5,X16,tc_fun(X38,tc_HOL_Obool),X64,X62,X2)
         => ( hBOOL(hAPP(hAPP(c_member(X16),X6),X63))
           => c_Equiv__Relations_Ocongruent(X5,tc_fun(X38,tc_HOL_Obool),X64,hAPP(hAPP(c_COMBB(tc_fun(X16,tc_fun(X38,tc_HOL_Obool)),tc_fun(X38,tc_HOL_Obool),X5),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X38,tc_HOL_Obool)),hAPP(c_Relation_OImage(X16,X16,X62),hAPP(hAPP(c_Set_Oinsert(X16),X6),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)))))),X2)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruent2__implies__congruent__UN) ).

fof(fact_Diff1__fold__graph,axiom,
    ! [X27,X12,X11,X37,X2,X16,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X16,X2,X37,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X27))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X16,X2,X37,X11),hAPP(hAPP(X2,X12),X27))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff1__fold__graph) ).

fof(fact_setsum__mono3,axiom,
    ! [X2,X11,X13,X5,X16] :
      ( ( class_Groups_Ocomm__monoid__add(X16)
        & class_Groups_Oordered__ab__semigroup__add(X16) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X13),X11)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),c_Groups_Ozero__class_Ozero(X16)),hAPP(X2,X3))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X13))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__mono3) ).

fof(fact_setsum__mono2,axiom,
    ! [X2,X11,X13,X5,X16] :
      ( class_Groups_Oordered__comm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
         => ( ! [X52] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X52),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X13),X11)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),c_Groups_Ozero__class_Ozero(X16)),hAPP(X2,X52))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X13))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__mono2) ).

fof(fact_INF__INT__eq,axiom,
    ! [X12,X34,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_COMBC(X16,tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool),c_member(X16))),X34)),X12))
    <=> hBOOL(hAPP(hAPP(c_member(X16),X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__INT__eq) ).

fof(fact_SUP__UN__eq,axiom,
    ! [X12,X34,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_COMBC(X16,tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool),c_member(X16))),X34)),X12))
    <=> hBOOL(hAPP(hAPP(c_member(X16),X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__UN__eq) ).

fof(fact_less__add__iff1,axiom,
    ! [X20,X17,X21,X114,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),X114)),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X114)),X20)))
      <=> 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),X17)),X114)),X21)),X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff1) ).

fof(fact_le__add__iff1,axiom,
    ! [X20,X17,X21,X114,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),X114)),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X114)),X20)))
      <=> 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),X17)),X114)),X21)),X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff1) ).

fof(fact_fold__graph_H_Ointros_I2_J,axiom,
    ! [X27,X37,X2,X16,X11,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
     => ( c_Nitpick_Ofold__graph_H(X5,X16,X2,X37,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X27)
       => c_Nitpick_Ofold__graph_H(X5,X16,X2,X37,X11,hAPP(hAPP(X2,X12),X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I2_J) ).

fof(fact_INT__subset__iff,axiom,
    ! [X11,X68,X16,X13,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X68),X11)))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X16),X3),X68))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),hAPP(X11,X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__subset__iff) ).

fof(fact_refl__on__INTER,axiom,
    ! [X34,X11,X16,X35,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X35))
         => c_Relation_Orefl__on(X16,hAPP(X11,X3),hAPP(X34,X3)) )
     => c_Relation_Orefl__on(X16,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X35),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(tc_prod(X16,X16),tc_HOL_Obool)),X35),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__INTER) ).

fof(fact_zminus1__lemma,axiom,
    ! [X34,X149,X17,X6] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X6,X17),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X149),X34)))
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6),X17),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X34),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X149)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X149)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X34),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),X17),X34))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus1__lemma) ).

fof(fact_INT__iff,axiom,
    ! [X13,X11,X16,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X11),X13)))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X16),X3),X11))
         => hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(X13,X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__iff) ).

fof(fact_vimage__Times,axiom,
    ! [X13,X11,X2,X38,X16,X5] : hAPP(c_Set_Ovimage(X5,tc_prod(X16,X38),X2),hAPP(hAPP(c_Product__Type_OSigma(X16,X38),X11),hAPP(c_COMBK(tc_fun(X38,tc_HOL_Obool),X16),X13))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X16,hAPP(c_Fun_Ocomp(tc_prod(X16,X38),X16,X5,c_Product__Type_Ofst(X16,X38)),X2)),X11)),hAPP(c_Set_Ovimage(X5,X38,hAPP(c_Fun_Ocomp(tc_prod(X16,X38),X38,X5,c_Product__Type_Osnd(X16,X38)),X2)),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Times) ).

fof(fact_in__lex__prod,axiom,
    ! [X84,X34,X138,X82,X17,X6,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X16),tc_prod(X5,X16))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X16),tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X82),X138))),c_Wellfounded_Olex__prod(X5,X16,X34,X84)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X82)),X34))
        | ( X6 = X82
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X16)),hAPP(hAPP(c_Product__Type_OPair(X16,X16),X17),X138)),X84)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__lex__prod) ).

fof(fact_INF1__iff,axiom,
    ! [X17,X13,X11,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X11),X13),X17))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
         => hBOOL(hAPP(hAPP(X13,X3),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF1__iff) ).

fof(fact_finite__M__bounded__by__nat,axiom,
    ! [X70,X29] : 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),X29)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X70))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__M__bounded__by__nat) ).

fof(fact_incr__lemma,axiom,
    ! [X14,X23,X41] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X41))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X14),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),X14),X23))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X41)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__lemma) ).

fof(fact_le__INF__iff,axiom,
    ! [X67,X11,X16,X66,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X66),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,X5),X11),X67)))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X16),X3),X11))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X66),hAPP(X67,X3))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__INF__iff) ).

fof(fact_insort__is__Cons,axiom,
    ! [X6,X2,X212,X5,X16] :
      ( class_Orderings_Olinorder(X16)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(X2,X6)),hAPP(X2,X3))) )
       => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X16,X2),X6),X212) = hAPP(hAPP(c_List_Olist_OCons(X5),X6),X212) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__is__Cons) ).

fof(fact_setsum__nonneg__0,axiom,
    ! [X70,X2,X84,X5,X16] :
      ( class_Groups_Oordered__ab__group__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X84))
       => ( ! [X145] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X145),X84))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),c_Groups_Ozero__class_Ozero(X16)),hAPP(X2,X145))) )
         => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X84) = c_Groups_Ozero__class_Ozero(X16)
           => ( hBOOL(hAPP(hAPP(c_member(X5),X70),X84))
             => hAPP(X2,X70) = c_Groups_Ozero__class_Ozero(X16) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__nonneg__0) ).

fof(fact_inv__into__def,axiom,
    ! [X12,X2,X11,X16,X5] : hAPP(c_Hilbert__Choice_Oinv__into(X5,X16,X11,X2),X12) = 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)),X11))),hAPP(hAPP(c_COMBC(X5,X16,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X16,tc_fun(X16,tc_HOL_Obool),X5),c_fequal),X2)),X12))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__def) ).

fof(fact_the__inv__into__def,axiom,
    ! [X12,X2,X11,X16,X5] : hAPP(c_Fun_Othe__inv__into(X5,X16,X11,X2),X12) = 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)),X11))),hAPP(hAPP(c_COMBC(X5,X16,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X16,tc_fun(X16,tc_HOL_Obool),X5),c_fequal),X2)),X12))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__def) ).

fof(fact_listrel1E,axiom,
    ! [X34,X214,X212,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)),X212),X214)),c_List_Olistrel1(X5,X34)))
     => ~ ! [X3,X33] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X33)),X34))
           => ! [X243,X248] :
                ( X212 = hAPP(hAPP(c_List_Oappend(X5),X243),hAPP(hAPP(c_List_Olist_OCons(X5),X3),X248))
               => X214 != hAPP(hAPP(c_List_Oappend(X5),X243),hAPP(hAPP(c_List_Olist_OCons(X5),X33),X248)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1E) ).

fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
    ! [X27,X12,X11,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X16,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X16,X2,X37,X11),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X16,X2,X37,X11),X27))
         => X27 = X12 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__determ) ).

fof(fact_listsum__addf,axiom,
    ! [X212,X1,X2,X16,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X16,X5),hAPP(hAPP(c_COMBS(X16,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X16),c_Groups_Oplus__class_Oplus(X5)),X2)),X1)),X212)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X16,X5),X2),X212))),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X16,X5),X1),X212))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__addf) ).

fof(fact_listsum__subtractf,axiom,
    ! [X212,X1,X2,X16,X5] :
      ( class_Groups_Oab__group__add(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X16,X5),hAPP(hAPP(c_COMBS(X16,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X16),c_Groups_Ominus__class_Ominus(X5)),X2)),X1)),X212)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X16,X5),X2),X212))),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X16,X5),X1),X212))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__subtractf) ).

fof(fact_UN__Pow__subset,axiom,
    ! [X13,X11,X16,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(X16,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),X16),c_Set_OPow(X5)),X13))),hAPP(c_Set_OPow(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X11),X13)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__Pow__subset) ).

fof(fact_nat__less__add__iff1,axiom,
    ! [X76,X45,X66,X70,X115] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X115),X70))
     => ( 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),X70),X66)),X45)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X115),X66)),X76)))
      <=> 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),X70),X115)),X66)),X45)),X76)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).

fof(fact_nat__le__add__iff1,axiom,
    ! [X76,X45,X66,X70,X115] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X115),X70))
     => ( 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),X70),X66)),X45)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X115),X66)),X76)))
      <=> 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),X70),X115)),X66)),X45)),X76)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).

fof(fact_listsum__mult__const,axiom,
    ! [X212,X21,X2,X16,X5] :
      ( class_Rings_Osemiring__0(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X16,X5),hAPP(hAPP(c_COMBC(X16,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X16),c_Groups_Otimes__class_Otimes(X5)),X2)),X21)),X212)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X16,X5),X2),X212))),X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__mult__const) ).

fof(fact_int__ge__less__than2__def,axiom,
    ! [X20] : c_Int_Oint__ge__less__than2(X20) = 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),X20)))),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,X108,X35,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X108))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X35),X108)))
               => hAPP(X2,X3) = c_Groups_Oone__class_Oone(X16) )
           => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X2),c_Groups_Oone__class_Oone(X16)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X35),X108)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X2),c_Groups_Oone__class_Oone(X16)),X35)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X2),c_Groups_Oone__class_Oone(X16)),X108)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__Un__one) ).

fof(fact_inf__Int__eq,axiom,
    ! [X12,X35,X36,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)),X36)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X35)),X12))
    <=> hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X36),X35))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Int__eq) ).

fof(fact_sup__Un__eq,axiom,
    ! [X12,X35,X36,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)),X36)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X35)),X12))
    <=> hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X36),X35))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__Un__eq) ).

fof(fact_insert__Collect,axiom,
    ! [X29,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(c_Set_OCollect(X5),X29)) = 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)))),X29)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Collect) ).

fof(fact_equiv__class__nondisjoint,axiom,
    ! [X17,X6,X12,X34,X11,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X11,X34)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X34),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X5,X5,X34),hAPP(hAPP(c_Set_Oinsert(X5),X17),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),X17)),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__nondisjoint) ).

fof(fact_measures__def,axiom,
    ! [X261,X5] : c_List_Omeasures(X5,X261) = 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))))),X261)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measures__def) ).

fof(fact_divmod__nat__rel__add1__eq,axiom,
    ! [X152,X153,X26,X154,X155,X24,X25] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X25,X24),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X155),X154)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X26,X24),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X153),X152)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24))
         => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X26),X24),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),X155),X153)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X154),X152)),X24))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X154),X152),X24)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__add1__eq) ).

fof(fact_Random__Sequence_Omap__def,axiom,
    ! [X29,X2,X5,X16] : c_Random__Sequence_Omap(X16,X5,X2,X29) = c_Random__Sequence_Obind(X16,X5,X29,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))))),X16,c_Random__Sequence_Osingle(X5)),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Random__Sequence_Omap__def) ).

fof(fact_setprod__Un,axiom,
    ! [X2,X13,X11,X5,X16] :
      ( class_Fields_Ofield(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
               => hAPP(X2,X3) != c_Groups_Ozero__class_Ozero(X16) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),X13))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__Un) ).

fof(fact_zadd1__lemma,axiom,
    ! [X152,X153,X26,X154,X155,X24,X25] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X25,X24),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X155),X154)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26,X24),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X153),X152)))
       => ( X24 != 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),X25),X26),X24),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),X155),X153)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X154),X152)),X24))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X154),X152),X24)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd1__lemma) ).

fof(fact_setsum__cartesian__product,axiom,
    ! [X11,X13,X2,X38,X16,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),hAPP(hAPP(c_COMBC(X16,tc_fun(X38,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBB(tc_fun(X38,X5),tc_fun(tc_fun(X38,tc_HOL_Obool),X5),X16),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X38,X5)),X2)),X13)),X11) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X16,X38),X5),hAPP(c_Product__Type_Oprod_Oprod__case(X16,X38,X5),X2)),hAPP(hAPP(c_Product__Type_OSigma(X16,X38),X11),hAPP(c_COMBK(tc_fun(X38,tc_HOL_Obool),X16),X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__cartesian__product) ).

fof(fact_setprod__cartesian__product,axiom,
    ! [X11,X13,X2,X38,X16,X5] :
      ( class_Groups_Ocomm__monoid__mult(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16,X5),hAPP(hAPP(c_COMBC(X16,tc_fun(X38,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBB(tc_fun(X38,X5),tc_fun(tc_fun(X38,tc_HOL_Obool),X5),X16),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X38,X5)),X2)),X13)),X11) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X16,X38),X5),hAPP(c_Product__Type_Oprod_Oprod__case(X16,X38,X5),X2)),hAPP(hAPP(c_Product__Type_OSigma(X16,X38),X11),hAPP(c_COMBK(tc_fun(X38,tc_HOL_Obool),X16),X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__cartesian__product) ).

fof(fact_def__Collect__coinduct,axiom,
    ! [X31,X6,X29,X5,X11] :
      ( X11 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_OCollect(X5)),X29))
     => ( c_Orderings_Oorder__class_Omono(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_OCollect(X5)),X29))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X31))
         => ( ! [X44] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X44),X31))
               => hBOOL(hAPP(hAPP(X29,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X31),X11)),X44)) )
           => hBOOL(hAPP(hAPP(c_member(X5),X6),X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__Collect__coinduct) ).

fof(fact_map__pair__inj__on,axiom,
    ! [X13,X1,X55,X38,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => ( c_Fun_Oinj__on(X38,X55,X1,X13)
       => c_Fun_Oinj__on(tc_prod(X5,X38),tc_prod(X16,X55),c_Product__Type_Omap__pair(X5,X16,X38,X55,X2,X1),hAPP(hAPP(c_Product__Type_OSigma(X5,X38),X11),hAPP(c_COMBK(tc_fun(X38,tc_HOL_Obool),X5),X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__inj__on) ).

fof(fact_divmod__nat__rel__mult1__eq,axiom,
    ! [X25,X123,X128,X24,X26] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X26,X24),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X128),X123)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24))
       => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X26),X24),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),X25),X128)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X123)),X24))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X123),X24)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__mult1__eq) ).

fof(fact_ran__restrictD,axiom,
    ! [X11,X45,X16,X27,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X27),c_Map_Oran(X16,X5,c_Map_Orestrict__map(X16,X5,X45,X11))))
     => ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X16),X3),X11))
          & hAPP(X45,X3) = hAPP(c_Option_Ooption_OSome(X5),X27) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ran__restrictD) ).

fof(fact_zmult1__lemma,axiom,
    ! [X25,X123,X128,X24,X26] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26,X24),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X128),X123)))
     => ( X24 != 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),X25),X26),X24),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),X25),X128)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X123)),X24))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X123),X24)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult1__lemma) ).

fof(fact__02,axiom,
    ! [X272,X273,X16,X5] : c_Lazy__Sequence_Oproduct(X5,X16,X273,X272) = hAPP(c_Lazy__Sequence_Obind(X5,tc_prod(X5,X16),X273),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X5,X16))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X5,X16)),X5),c_Lazy__Sequence_Obind(X16,tc_prod(X5,X16),X272)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(X16,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X5,X16))),X5),hAPP(c_COMBB(tc_prod(X5,X16),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X5,X16)),X16),c_Lazy__Sequence_Osingle(tc_prod(X5,X16)))),c_Product__Type_OPair(X5,X16)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__02) ).

fof(fact_Ex__inj__on__UNION__Sigma,axiom,
    ! [X11,X68,X16,X5] :
    ? [X43] :
      ( c_Fun_Oinj__on(X5,tc_prod(X16,X5),X43,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X68),X11))
      & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X16,X5),tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,tc_prod(X16,X5),X43),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X68),X11))),hAPP(hAPP(c_Product__Type_OSigma(X16,X5),X68),X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ex__inj__on__UNION__Sigma) ).

fof(fact_enum__fun__code,axiom,
    ! [X16,X5] :
      ( ( class_Enum_Oenum(X5)
        & class_HOL_Oequal(X5)
        & class_Enum_Oenum(X16) )
     => c_Enum_Oenum__class_Oenum(tc_fun(X5,X16)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X16),tc_fun(X5,X16)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_Option_Ooption(X16)),tc_fun(X5,X16),tc_List_Olist(X16)),c_Fun_Ocomp(tc_Option_Ooption(X16),X16,X5,c_Option_Othe(X16))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X5,X16)),tc_fun(X5,tc_Option_Ooption(X16)),tc_List_Olist(X16)),c_Map_Omap__of(X5,X16)),hAPP(c_List_Ozip(X5,X16),c_Enum_Oenum__class_Oenum(X5))))),c_Enum_On__lists(X16,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_Enum_Oenum__class_Oenum(X5)),c_Enum_Oenum__class_Oenum(X16))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__fun__code) ).

fof(fact_enum__fun__def,axiom,
    ! [X16,X5] :
      ( ( class_Enum_Oenum(X5)
        & class_Enum_Oenum(X16) )
     => c_Enum_Oenum__class_Oenum(tc_fun(X5,X16)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X16),tc_fun(X5,X16)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_Option_Ooption(X16)),tc_fun(X5,X16),tc_List_Olist(X16)),c_Fun_Ocomp(tc_Option_Ooption(X16),X16,X5,c_Option_Othe(X16))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X5,X16)),tc_fun(X5,tc_Option_Ooption(X16)),tc_List_Olist(X16)),c_Map_Omap__of(X5,X16)),hAPP(c_List_Ozip(X5,X16),c_Enum_Oenum__class_Oenum(X5))))),c_Enum_On__lists(X16,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_Enum_Oenum__class_Oenum(X5)),c_Enum_Oenum__class_Oenum(X16))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__fun__def) ).

fof(fact_sublist__shift__lemma__Suc,axiom,
    ! [X257,X212,X29,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)),X29),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),X212),X257))) = 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)),X29),c_Product__Type_Osnd(X5,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X5,tc_Nat_Onat),X212),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X257)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__shift__lemma__Suc) ).

fof(fact_fst__comp__map__pair,axiom,
    ! [X1,X2,X16,X5,X55,X38] : hAPP(c_Fun_Ocomp(tc_prod(X38,X55),X38,tc_prod(X5,X16),c_Product__Type_Ofst(X38,X55)),c_Product__Type_Omap__pair(X5,X38,X16,X55,X2,X1)) = hAPP(c_Fun_Ocomp(X5,X38,tc_prod(X5,X16),X2),c_Product__Type_Ofst(X5,X16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__comp__map__pair) ).

fof(fact_snd__comp__map__pair,axiom,
    ! [X1,X2,X16,X5,X38,X55] : hAPP(c_Fun_Ocomp(tc_prod(X55,X38),X38,tc_prod(X5,X16),c_Product__Type_Osnd(X55,X38)),c_Product__Type_Omap__pair(X5,X55,X16,X38,X2,X1)) = hAPP(c_Fun_Ocomp(X16,X38,tc_prod(X5,X16),X1),c_Product__Type_Osnd(X5,X16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__comp__map__pair) ).

fof(fact_INT__extend__simps_I9_J,axiom,
    ! [X19,X13,X38,X11,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBC(X16,tc_fun(X38,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X38,tc_HOL_Obool),tc_fun(tc_fun(X38,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),X16),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X38,tc_fun(X5,tc_HOL_Obool))),X13)),X19)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X38,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X38,tc_HOL_Obool)),X11),X13)),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I9_J) ).

fof(fact_UN__extend__simps_I9_J,axiom,
    ! [X19,X13,X38,X11,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBC(X16,tc_fun(X38,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X38,tc_HOL_Obool),tc_fun(tc_fun(X38,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),X16),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,tc_fun(X5,tc_HOL_Obool))),X13)),X19)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X38,tc_HOL_Obool)),X11),X13)),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I9_J) ).

fof(fact_INT__simps_I9_J,axiom,
    ! [X19,X13,X11,X38,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,tc_fun(X16,tc_HOL_Obool)),X11),X13)),X19) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X38,tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBC(X38,tc_fun(X16,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),X38),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool))),X13)),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I9_J) ).

fof(fact_UN__UN__flatten,axiom,
    ! [X19,X13,X11,X38,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,tc_fun(X16,tc_HOL_Obool)),X11),X13)),X19) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBC(X38,tc_fun(X16,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),X38),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool))),X13)),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__UN__flatten) ).

fof(fact_UN__simps_I9_J,axiom,
    ! [X19,X13,X11,X38,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,tc_fun(X16,tc_HOL_Obool)),X11),X13)),X19) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBC(X38,tc_fun(X16,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),X38),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool))),X13)),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I9_J) ).

fof(fact_finite__less__ub,axiom,
    ! [X66,X2] :
      ( ! [X107] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X107),hAPP(X2,X107)))
     => 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)),X66)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__less__ub) ).

fof(fact_congruent2D,axiom,
    ! [X77,X78,X79,X80,X2,X62,X64,X38,X16,X5] :
      ( c_Equiv__Relations_Ocongruent2(X5,X16,X38,X64,X62,X2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X80),X79)),X64))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X16)),hAPP(hAPP(c_Product__Type_OPair(X16,X16),X78),X77)),X62))
         => hAPP(hAPP(X2,X80),X78) = hAPP(hAPP(X2,X79),X77) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruent2D) ).

fof(fact_Int__Collect__mono,axiom,
    ! [X28,X29,X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
           => ( hBOOL(hAPP(X29,X3))
             => hBOOL(hAPP(X28,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)),X11),hAPP(c_Set_OCollect(X5),X29))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X13),hAPP(c_Set_OCollect(X5),X28)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Collect__mono) ).

fof(fact_map__upds__append1,axiom,
    ! [X12,X45,X214,X16,X212,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)))
     => c_Map_Omap__upds(X5,X16,X45,hAPP(hAPP(c_List_Oappend(X5),X212),hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Olist_ONil(X5))),X214) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),c_Map_Omap__upds(X5,X16,X45,X212,X214)),X12),hAPP(c_Option_Ooption_OSome(X16),hAPP(hAPP(c_List_Onth(X16),X214),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__upds__append1) ).

fof(fact_Least__mono,axiom,
    ! [X35,X2,X5,X16] :
      ( ( class_Orderings_Oorder(X16)
        & class_Orderings_Oorder(X5) )
     => ( c_Orderings_Oorder__class_Omono(X5,X16,X2)
       => ( ? [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X35))
              & ! [X39] :
                  ( hBOOL(hAPP(hAPP(c_member(X5),X39),X35))
                 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X39)) ) )
         => c_Orderings_Oord__class_OLeast(X16,hAPP(hAPP(c_COMBC(X16,tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool),c_member(X16)),hAPP(c_Set_Oimage(X5,X16,X2),X35))) = hAPP(X2,c_Orderings_Oord__class_OLeast(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X35))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Least__mono) ).

fof(fact_UN__finite__subset,axiom,
    ! [X19,X11,X5] :
      ( ! [X107] : 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)),X107)),X11)),X19))
     => 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))),X11)),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__finite__subset) ).

fof(fact_set__diff__eq,axiom,
    ! [X13,X11,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13) = 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)),X11))),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)),X13)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__diff__eq) ).

fof(fact_finite__Collect__conjI,axiom,
    ! [X28,X29,X5] :
      ( ( 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),X28))) )
     => 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),X29)),X28)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__conjI) ).

fof(fact_UN__UN__finite__eq,axiom,
    ! [X11,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)))),X11)) = 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))),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__UN__finite__eq) ).

fof(fact_map__pair__simp,axiom,
    ! [X17,X6,X1,X2,X16,X55,X5,X38] : hAPP(c_Product__Type_Omap__pair(X38,X5,X55,X16,X2,X1),hAPP(hAPP(c_Product__Type_OPair(X38,X55),X6),X17)) = hAPP(hAPP(c_Product__Type_OPair(X5,X16),hAPP(X2,X6)),hAPP(X1,X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__simp) ).

fof(fact_list__all2I,axiom,
    ! [X29,X17,X6,X16,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),X3),hAPP(c_List_Oset(tc_prod(X5,X16)),hAPP(hAPP(c_List_Ozip(X5,X16),X6),X17))))
         => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_HOL_Obool),X29),X3)) )
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X6) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X17)
       => c_List_Olist__all2(X5,X16,X29,X6,X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2I) ).

fof(fact_list__all2__def,axiom,
    ! [X214,X212,X29,X16,X5] :
      ( c_List_Olist__all2(X5,X16,X29,X212,X214)
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),X3),hAPP(c_List_Oset(tc_prod(X5,X16)),hAPP(hAPP(c_List_Ozip(X5,X16),X212),X214))))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_HOL_Obool),X29),X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__def) ).

fof(fact_map__pair__ident,axiom,
    ! [X37,X16,X5] : hAPP(c_Product__Type_Omap__pair(X5,X5,X16,X16,c_COMBI(X5),c_COMBI(X16)),X37) = X37,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__ident) ).

fof(fact_def__lfp__induct__set,axiom,
    ! [X29,X6,X2,X5,X11] :
      ( X11 = c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X5,tc_HOL_Obool),X2)
     => ( c_Orderings_Oorder__class_Omono(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X2)
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Set_OCollect(X5),X29)))))
               => hBOOL(hAPP(X29,X3)) )
           => hBOOL(hAPP(X29,X6)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__lfp__induct__set) ).

fof(fact_folding__image__simple_Ounion__inter,axiom,
    ! [X13,X11,X90,X1,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X16,X2,X37,X1,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X13))
         => hAPP(hAPP(X2,hAPP(X90,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),X11),X13))),hAPP(X90,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),X11),X13))) = hAPP(hAPP(X2,hAPP(X90,X11)),hAPP(X90,X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__inter) ).

fof(fact_setsum__Un__zero,axiom,
    ! [X2,X108,X35,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X108))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X35),X108)))
               => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X16) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X35),X108)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X35)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X108)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__Un__zero) ).

fof(fact_setsum_Ounion__inter__neutral,axiom,
    ! [X1,X13,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
               => hAPP(X1,X3) = c_Groups_Ozero__class_Ozero(X16) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),X13)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Ounion__inter__neutral) ).

fof(fact_setprod_Ounion__inter__neutral,axiom,
    ! [X1,X13,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
               => hAPP(X1,X3) = c_Groups_Oone__class_Oone(X16) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X13)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Ounion__inter__neutral) ).

fof(fact_setprod__Un__one,axiom,
    ! [X2,X108,X35,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X108))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X35),X108)))
               => hAPP(X2,X3) = c_Groups_Oone__class_Oone(X16) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X35),X108)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),X35)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),X108)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__Un__one) ).

fof(fact_Image__singleton,axiom,
    ! [X6,X34,X5,X16] : hAPP(c_Relation_OImage(X16,X5,X34),hAPP(hAPP(c_Set_Oinsert(X16),X6),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X16,X5),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X16,X5),tc_fun(tc_fun(tc_prod(X16,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X16,X5))),hAPP(c_Product__Type_OPair(X16,X5),X6))),X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__singleton) ).

fof(fact_folding__image__simple_Oremove,axiom,
    ! [X12,X11,X90,X1,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X16,X2,X37,X1,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X16),X12),X11))
         => hAPP(X90,X11) = hAPP(hAPP(X2,hAPP(X1,X12)),hAPP(X90,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X16),X12),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oremove) ).

fof(fact_subset__image__iff,axiom,
    ! [X11,X2,X16,X13,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),hAPP(c_Set_Oimage(X16,X5,X2),X11)))
    <=> ? [X40] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),X40),X11))
          & X13 = hAPP(c_Set_Oimage(X16,X5,X2),X40) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__image__iff) ).

fof(fact_UN__iff,axiom,
    ! [X13,X11,X16,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X11),X13)))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X16),X3),X11))
          & hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(X13,X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__iff) ).

fof(fact_folding__image__simple_Oinsert__remove,axiom,
    ! [X12,X11,X90,X1,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X16,X2,X37,X1,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11))
       => hAPP(X90,hAPP(hAPP(c_Set_Oinsert(X16),X12),X11)) = hAPP(hAPP(X2,hAPP(X1,X12)),hAPP(X90,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X16),X12),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert__remove) ).

fof(fact_inv__into__comp,axiom,
    ! [X12,X11,X1,X38,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,hAPP(c_Set_Oimage(X38,X5,X1),X11))
     => ( c_Fun_Oinj__on(X38,X5,X1,X11)
       => ( hBOOL(hAPP(hAPP(c_member(X16),X12),hAPP(c_Set_Oimage(X5,X16,X2),hAPP(c_Set_Oimage(X38,X5,X1),X11))))
         => hAPP(c_Hilbert__Choice_Oinv__into(X38,X16,X11,hAPP(c_Fun_Ocomp(X5,X16,X38,X2),X1)),X12) = hAPP(hAPP(c_Fun_Ocomp(X5,X38,X16,c_Hilbert__Choice_Oinv__into(X38,X5,X11,X1)),c_Hilbert__Choice_Oinv__into(X5,X16,hAPP(c_Set_Oimage(X38,X5,X1),X11),X2)),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__comp) ).

fof(fact_the__inv__into__comp,axiom,
    ! [X12,X11,X1,X38,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,hAPP(c_Set_Oimage(X38,X5,X1),X11))
     => ( c_Fun_Oinj__on(X38,X5,X1,X11)
       => ( hBOOL(hAPP(hAPP(c_member(X16),X12),hAPP(c_Set_Oimage(X5,X16,X2),hAPP(c_Set_Oimage(X38,X5,X1),X11))))
         => hAPP(c_Fun_Othe__inv__into(X38,X16,X11,hAPP(c_Fun_Ocomp(X5,X16,X38,X2),X1)),X12) = hAPP(hAPP(c_Fun_Ocomp(X5,X38,X16,c_Fun_Othe__inv__into(X38,X5,X11,X1)),c_Fun_Othe__inv__into(X5,X16,hAPP(c_Set_Oimage(X38,X5,X1),X11),X2)),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__comp) ).

fof(fact_setsum__mono__zero__left,axiom,
    ! [X2,X35,X108,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X108))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X35),X108))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X108),X35)))
               => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X16) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X35) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X108) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__mono__zero__left) ).

fof(fact_setsum__mono__zero__right,axiom,
    ! [X2,X35,X108,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X108))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X35),X108))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X108),X35)))
               => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X16) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X108) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X35) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__mono__zero__right) ).

fof(fact_setprod__mono__one__right,axiom,
    ! [X2,X35,X108,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X108))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X35),X108))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X108),X35)))
               => hAPP(X2,X3) = c_Groups_Oone__class_Oone(X16) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),X108) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),X35) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__mono__one__right) ).

fof(fact_setprod__mono__one__left,axiom,
    ! [X2,X35,X108,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X108))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X35),X108))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X108),X35)))
               => hAPP(X2,X3) = c_Groups_Oone__class_Oone(X16) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),X35) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),X108) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__mono__one__left) ).

fof(fact_SUP1__iff,axiom,
    ! [X17,X13,X11,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X11),X13),X17))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
          & hBOOL(hAPP(hAPP(X13,X3),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP1__iff) ).

fof(fact_order__fun_I1_J,axiom,
    ! [X1,X2,X5,X16] :
      ( ( class_Orderings_Oorder(X16)
        & class_Enum_Oenum(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X16)),X2),X1))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X5),hAPP(hAPP(c_COMBS(X5,X16,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X16,tc_fun(X16,tc_HOL_Obool),X5),c_Orderings_Oord__class_Oless__eq(X16)),X2)),X1))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__fun_I1_J) ).

fof(fact_rtrancl__imp__UN__rel__pow,axiom,
    ! [X36,X161,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X161),c_Transitive__Closure_Ortrancl(X5,X36)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X161),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)),X36)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__imp__UN__rel__pow) ).

fof(fact_Int__Inter__image,axiom,
    ! [X13,X11,X19,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBS(X16,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)),X16),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool))),X11)),X13)) = 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(X16,tc_fun(X5,tc_HOL_Obool),X11),X19))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X16,tc_fun(X5,tc_HOL_Obool),X13),X19))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Inter__image) ).

fof(fact_Un__Union__image,axiom,
    ! [X13,X11,X19,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBS(X16,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)),X16),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X11)),X13)) = 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(X16,tc_fun(X5,tc_HOL_Obool),X11),X19))),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X16,tc_fun(X5,tc_HOL_Obool),X13),X19))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Union__image) ).

fof(fact_lexord__append__left__rightI,axiom,
    ! [X27,X12,X66,X34,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),X34))
     => 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),X66),hAPP(hAPP(c_List_Olist_OCons(X5),X6),X12))),hAPP(hAPP(c_List_Oappend(X5),X66),hAPP(hAPP(c_List_Olist_OCons(X5),X17),X27)))),c_List_Olexord(X5,X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__left__rightI) ).

fof(fact_intrel__iff,axiom,
    ! [X56,X66,X27,X12] :
      ( 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),X12),X27)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X66),X56))),c_Int_Ointrel))
    <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X56) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X66),X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_intrel__iff) ).

fof(fact_same__fstI,axiom,
    ! [X5,X36,X27,X144,X16,X12,X29] :
      ( hBOOL(hAPP(X29,X12))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X16)),hAPP(hAPP(c_Product__Type_OPair(X16,X16),X144),X27)),hAPP(X36,X12)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X16),tc_prod(X5,X16))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X16),tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X12),X144)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X12),X27))),c_Recdef_Osame__fst(X5,X16,X29,X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__fstI) ).

fof(fact_less__SUP__iff,axiom,
    ! [X2,X11,X16,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(X16,X5),X11),X2)))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X16),X3),X11))
            & 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,
    ! [X161,X1,X85,X55,X2,X5,X38,X16] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X16,X38,X5),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X55,X85,tc_prod(X16,X38)),X1),X161)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X55,X85,X5),hAPP(hAPP(c_COMBB(tc_fun(X85,tc_prod(X16,X38)),tc_fun(X85,X5),X55),hAPP(c_COMBB(tc_prod(X16,X38),X5,X85),hAPP(c_Product__Type_Oprod_Oprod__case(X16,X38,X5),X2))),X1)),X161),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__twice) ).

fof(fact_list__size__pointwise,axiom,
    ! [X1,X2,X212,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
         => 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,X212)),c_List_Olist_Olist__size(X5,X1,X212))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__size__pointwise) ).

fof(fact_inj__graph,axiom,
    ! [X16,X5] : c_Fun_Oinj__on(tc_fun(X5,X16),tc_fun(tc_prod(X5,X16),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X5,X16)),c_Set_OCollect(tc_prod(X5,X16))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X16,tc_HOL_Obool)),tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X5,X16)),c_Product__Type_Oprod_Oprod__case(X5,X16,tc_HOL_Obool)),hAPP(c_COMBB(X16,tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_COMBC(X16,X16,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,X16),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_Oequations,axiom,
    ! [X46,X47,X36,X5] :
      ( c_Wellfounded_Omax__extp(X5,X36,X47,X46)
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X47))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X46))
        & X46 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X47))
           => ? [X39] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X39),X46))
                & hBOOL(hAPP(hAPP(X36,X3),X39)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__extp_Oequations) ).

fof(fact_Int__def,axiom,
    ! [X13,X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) = 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)),X11))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X13))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__def) ).

fof(fact_Un__def,axiom,
    ! [X13,X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13) = 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)),X11))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X13))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__def) ).

fof(fact_folding__image__simple_Ounion__disjoint,axiom,
    ! [X13,X11,X90,X1,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X16,X2,X37,X1,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X13))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),X11),X13) = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))
           => hAPP(X90,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(X2,hAPP(X90,X11)),hAPP(X90,X13)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__disjoint) ).

fof(fact_fun__upd__restrict__conv,axiom,
    ! [X27,X45,X16,X18,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),X18))
     => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),c_Map_Orestrict__map(X5,X16,X45,X18)),X12),X27) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),c_Map_Orestrict__map(X5,X16,X45,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X18),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),X12),X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__restrict__conv) ).

fof(fact_less__add__iff2,axiom,
    ! [X20,X17,X21,X114,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),X114)),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X114)),X20)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X17),X6)),X114)),X20))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff2) ).

fof(fact_le__add__iff2,axiom,
    ! [X20,X17,X21,X114,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),X114)),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X114)),X20)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X17),X6)),X114)),X20))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff2) ).

fof(fact_Image__INT__subset,axiom,
    ! [X13,X11,X38,X34,X16,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X16,X5,X34),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X38,tc_fun(X16,tc_HOL_Obool)),X11),X13))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X38,tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X38),c_Relation_OImage(X16,X5,X34)),X13)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__INT__subset) ).

fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
    ! [X13,X11,X90,X1,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X5,X16,X2,X37,X1,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),X13),X11))
         => hAPP(hAPP(X2,hAPP(X90,X13)),hAPP(X90,X11)) = hAPP(X90,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).

fof(fact_le__funI,axiom,
    ! [X5,X1,X2,X16] :
      ( class_Orderings_Oord(X16)
     => ( ! [X3] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(X2,X3)),hAPP(X1,X3)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X16)),X2),X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funI) ).

fof(fact_le__fun__def,axiom,
    ! [X1,X2,X5,X16] :
      ( class_Orderings_Oord(X16)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X16)),X2),X1))
      <=> ! [X3] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(X2,X3)),hAPP(X1,X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).

fof(fact_fun__upd__restrict,axiom,
    ! [X27,X12,X18,X45,X16,X5] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),c_Map_Orestrict__map(X5,X16,X45,X18)),X12),X27) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),c_Map_Orestrict__map(X5,X16,X45,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X18),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),X12),X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__restrict) ).

fof(fact_folding__image__simple_Oeq__fold__g,axiom,
    ! [X11,X90,X1,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X16,X2,X37,X1,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11))
       => hAPP(X90,X11) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X16,X2),X1),X37),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).

fof(fact_map__eq__conv,axiom,
    ! [X1,X212,X2,X5,X16] :
      ( hAPP(hAPP(c_List_Omap(X16,X5),X2),X212) = hAPP(hAPP(c_List_Omap(X16,X5),X1),X212)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X16),X3),hAPP(c_List_Oset(X16),X212)))
         => hAPP(X2,X3) = hAPP(X1,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__eq__conv) ).

fof(fact_pred__comp_Ointros,axiom,
    ! [X38,X16,X5,X21,X84,X17,X6,X34] :
      ( hBOOL(hAPP(hAPP(X34,X6),X17))
     => ( hBOOL(hAPP(hAPP(X84,X17),X21))
       => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X16,X38,X34,X84),X6),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp_Ointros) ).

fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
    ! [X13,X11,X90,X1,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X5,X16,X2,X37,X1,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X13))
         => hAPP(X90,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(X2,hAPP(X90,X11)),hAPP(X90,X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Ounion__idem) ).

fof(fact_congruent2__implies__congruent,axiom,
    ! [X6,X2,X62,X38,X16,X64,X11,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X11,X64)
     => ( c_Equiv__Relations_Ocongruent2(X5,X16,X38,X64,X62,X2)
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => c_Equiv__Relations_Ocongruent(X16,X38,X62,hAPP(X2,X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruent2__implies__congruent) ).

fof(fact_append__eq__append__conv2,axiom,
    ! [X7,X227,X214,X212,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X212),X214) = hAPP(hAPP(c_List_Oappend(X5),X227),X7)
    <=> ? [X243] :
          ( ( X212 = hAPP(hAPP(c_List_Oappend(X5),X227),X243)
            & hAPP(hAPP(c_List_Oappend(X5),X243),X214) = X7 )
          | ( hAPP(hAPP(c_List_Oappend(X5),X212),X243) = X227
            & X214 = hAPP(hAPP(c_List_Oappend(X5),X243),X7) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__append__conv2) ).

fof(fact_inj__on__iff__card__le,axiom,
    ! [X13,X16,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X13))
       => ( ? [X43] :
              ( c_Fun_Oinj__on(X5,X16,X43,X11)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X16,X43),X11)),X13)) )
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X11)),hAPP(c_Finite__Set_Ocard(X16),X13))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff__card__le) ).

fof(fact_folding__image__simple__idem_Oin__idem,axiom,
    ! [X12,X11,X90,X1,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X5,X16,X2,X37,X1,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X16),X12),X11))
         => hAPP(hAPP(X2,hAPP(X1,X12)),hAPP(X90,X11)) = hAPP(X90,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).

fof(fact_sublists_Osimps_I2_J,axiom,
    ! [X212,X12,X5] : c_Enum_Osublists(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(X5)),tc_List_Olist(tc_List_Olist(X5))),c_Enum_Osublists(X5,X212)),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),X12)))),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,
    ! [X12,X11,X90,X1,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X5,X16,X2,X37,X1,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11))
       => hAPP(X90,hAPP(hAPP(c_Set_Oinsert(X16),X12),X11)) = hAPP(hAPP(X2,hAPP(X1,X12)),hAPP(X90,X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).

fof(fact_INT__Int__distrib,axiom,
    ! [X13,X11,X68,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X68),hAPP(hAPP(c_COMBS(X16,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)),X16),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool))),X11)),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X68),X11)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X68),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__Int__distrib) ).

fof(fact_UN__Un__distrib,axiom,
    ! [X13,X11,X68,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X68),hAPP(hAPP(c_COMBS(X16,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)),X16),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X11)),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X68),X11)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X68),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__Un__distrib) ).

fof(fact_in__inv__imagep,axiom,
    ! [X27,X12,X2,X34,X16,X5] :
      ( c_Predicate_Oinv__imagep(X5,X16,X34,X2,X12,X27)
    <=> hBOOL(hAPP(hAPP(X34,hAPP(X2,X12)),hAPP(X2,X27))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__inv__imagep) ).

fof(fact_inv__imagep__def,axiom,
    ! [X27,X12,X2,X34,X16,X5] :
      ( c_Predicate_Oinv__imagep(X5,X16,X34,X2,X12,X27)
    <=> hBOOL(hAPP(hAPP(X34,hAPP(X2,X12)),hAPP(X2,X27))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__imagep__def) ).

fof(fact_folding__image__simple_Oempty,axiom,
    ! [X90,X1,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X16,X2,X37,X1,X90)
     => hAPP(X90,c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oempty) ).

fof(fact_folding__image__simple__idem_Oidem,axiom,
    ! [X12,X90,X1,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X5,X16,X2,X37,X1,X90)
     => hAPP(hAPP(X2,X12),X12) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).

fof(fact_smax__emptyI,axiom,
    ! [X42] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X42))
     => ( X42 != 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))),X42)),c_FunDef_Omax__strict)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smax__emptyI) ).

fof(fact_set__filter,axiom,
    ! [X212,X29,X5] : hAPP(c_List_Oset(X5),hAPP(c_List_Ofilter(X5,X29),X212)) = 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),X212)))),X29)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__filter) ).

fof(fact_sum__diff__distrib,axiom,
    ! [X76,X29,X28] :
      ( ! [X3] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X28,X3)),hAPP(X29,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),X29),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X76))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X28),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X76))) = 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)),X29)),X28)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__diff__distrib) ).

fof(fact_inj__on__iff__surj,axiom,
    ! [X53,X16,X5,X11] :
      ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
     => ( ? [X43] :
            ( c_Fun_Oinj__on(X5,X16,X43,X11)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X16,X43),X11)),X53)) )
      <=> ? [X54] : hAPP(c_Set_Oimage(X16,X5,X54),X53) = X11 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff__surj) ).

fof(fact_Range__iff,axiom,
    ! [X34,X16,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Relation_ORange(X16,X5),X34)))
    <=> ? [X33] : hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X5)),hAPP(hAPP(c_Product__Type_OPair(X16,X5),X33),X6)),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__iff) ).

fof(fact_wmax__emptyI,axiom,
    ! [X31] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X31))
     => 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))),X31)),c_FunDef_Omax__weak)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wmax__emptyI) ).

fof(fact_INT__simps_I1_J,axiom,
    ! [X13,X11,X16,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(X16,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool))),X11)),X13)) = c_Orderings_Otop__class_Otop(tc_fun(X16,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(X16,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool))),X11)),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X19),X11)),X13) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I1_J) ).

fof(fact_INT__simps_I3_J,axiom,
    ! [X13,X11,X16,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(X16,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool))),X11)),X13)) = c_Orderings_Otop__class_Otop(tc_fun(X16,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(X16,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool))),X11)),X13)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X19),X11)),X13) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I3_J) ).

fof(fact_UN__simps_I2_J,axiom,
    ! [X13,X11,X16,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(X16,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool))),X11)),X13)) = c_Orderings_Obot__class_Obot(tc_fun(X16,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(X16,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool))),X11)),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X19),X11)),X13) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I2_J) ).

fof(fact_INT__extend__simps_I1_J,axiom,
    ! [X13,X11,X16,X5,X19] :
      ( ( X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X19),X11)),X13) = X13 )
      & ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X19),X11)),X13) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool))),X11)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I1_J) ).

fof(fact_INT__extend__simps_I3_J,axiom,
    ! [X13,X11,X16,X5,X19] :
      ( ( X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X19),X11)),X13) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))),X13) )
      & ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X19),X11)),X13) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool))),X11)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I3_J) ).

fof(fact_UN__extend__simps_I2_J,axiom,
    ! [X13,X11,X16,X5,X19] :
      ( ( X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X19),X11)),X13) = X13 )
      & ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X19),X11)),X13) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool))),X11)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I2_J) ).

fof(fact_INT__simps_I6_J,axiom,
    ! [X13,X11,X19,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X16,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)),X16),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X11)),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X19),X11)),X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I6_J) ).

fof(fact_UN__simps_I4_J,axiom,
    ! [X13,X11,X19,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X16,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)),X16),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool))),X11)),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X19),X11)),X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I4_J) ).

fof(fact_UN__simps_I6_J,axiom,
    ! [X13,X11,X19,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X16,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)),X16),c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool))),X11)),X13)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X19),X11)),X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I6_J) ).

fof(fact_UN__extend__simps_I4_J,axiom,
    ! [X13,X11,X19,X16,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X19),X11)),X13) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X16,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)),X16),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool))),X11)),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I4_J) ).

fof(fact_UN__extend__simps_I6_J,axiom,
    ! [X13,X11,X19,X16,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X19),X11)),X13) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X16,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)),X16),c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool))),X11)),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I6_J) ).

fof(fact_INT__extend__simps_I6_J,axiom,
    ! [X13,X11,X19,X16,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X19),X11)),X13) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBC(X16,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)),X16),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X11)),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I6_J) ).

fof(fact_rel__comp__subset__Sigma,axiom,
    ! [X19,X84,X38,X13,X11,X34,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X34),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X13))))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X16,X38),tc_HOL_Obool)),X84),hAPP(hAPP(c_Product__Type_OSigma(X16,X38),X13),hAPP(c_COMBK(tc_fun(X38,tc_HOL_Obool),X16),X19))))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X38),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X16,X38),X34),X84)),hAPP(hAPP(c_Product__Type_OSigma(X5,X38),X11),hAPP(c_COMBK(tc_fun(X38,tc_HOL_Obool),X5),X19)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__subset__Sigma) ).

fof(fact_Cons__listrel1__Cons,axiom,
    ! [X34,X214,X27,X212,X12,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),X12),X212)),hAPP(hAPP(c_List_Olist_OCons(X5),X27),X214))),c_List_Olistrel1(X5,X34)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),X34))
          & X212 = X214 )
        | ( X12 = X27
          & 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)),X212),X214)),c_List_Olistrel1(X5,X34))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__listrel1__Cons) ).

fof(fact_lexord__cons__cons,axiom,
    ! [X34,X27,X17,X12,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),X12)),hAPP(hAPP(c_List_Olist_OCons(X5),X17),X27))),c_List_Olexord(X5,X34)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),X34))
        | ( X6 = X17
          & 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)),X12),X27)),c_List_Olexord(X5,X34))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__cons__cons) ).

fof(fact_Cons__in__lex,axiom,
    ! [X34,X214,X27,X212,X12,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),X12),X212)),hAPP(hAPP(c_List_Olist_OCons(X5),X27),X214))),c_List_Olex(X5,X34)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),X34))
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X214) )
        | ( X12 = X27
          & 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)),X212),X214)),c_List_Olex(X5,X34))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__in__lex) ).

fof(fact_Sigma__Int__distrib2,axiom,
    ! [X13,X11,X68,X16,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X68),hAPP(hAPP(c_COMBS(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool))),X11)),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X68),X11)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X68),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Int__distrib2) ).

fof(fact_Sigma__Diff__distrib2,axiom,
    ! [X13,X11,X68,X16,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X68),hAPP(hAPP(c_COMBS(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool))),X11)),X13)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X68),X11)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X68),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Diff__distrib2) ).

fof(fact_Sigma__Un__distrib2,axiom,
    ! [X13,X11,X68,X16,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X68),hAPP(hAPP(c_COMBS(X5,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool))),X11)),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X68),X11)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X68),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Un__distrib2) ).

fof(fact_abs__diff__triangle__ineq,axiom,
    ! [X41,X24,X26,X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X24),X41)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X25),X24))),hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X26),X41))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__diff__triangle__ineq) ).

fof(fact_nat__less__add__iff2,axiom,
    ! [X76,X45,X66,X115,X70] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X70),X115))
     => ( 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),X70),X66)),X45)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X115),X66)),X76)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),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),X115),X70)),X66)),X76))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).

fof(fact_nat__le__add__iff2,axiom,
    ! [X76,X45,X66,X115,X70] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X70),X115))
     => ( 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),X70),X66)),X45)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X115),X66)),X76)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),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),X115),X70)),X66)),X76))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).

fof(fact_folding__image_Odistrib,axiom,
    ! [X48,X1,X11,X90,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__image(X5,X16,X2,X37,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11))
       => hAPP(hAPP(X90,hAPP(hAPP(c_COMBS(X16,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X16),X2),X1)),X48)),X11) = hAPP(hAPP(X2,hAPP(hAPP(X90,X1),X11)),hAPP(hAPP(X90,X48),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image_Odistrib) ).

fof(fact_fold__image__Un__Int,axiom,
    ! [X1,X13,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X1),c_Groups_Oone__class_Oone(X16)),X11)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X1),c_Groups_Oone__class_Oone(X16)),X13)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X1),c_Groups_Oone__class_Oone(X16)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X1),c_Groups_Oone__class_Oone(X16)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__Un__Int) ).

fof(fact_arith__series__nat,axiom,
    ! [X76,X20,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)),X20))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X76))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X76),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),X76),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X20)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__series__nat) ).

fof(fact_Un__Int__crazy,axiom,
    ! [X19,X13,X11,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)),X11),X13)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X13),X19))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X11)) = 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)),X11),X13)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X13),X19))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Int__crazy) ).

fof(fact_rtrancl__listrel1__ConsI2,axiom,
    ! [X214,X212,X34,X27,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_Transitive__Closure_Ortrancl(X5,X34)))
     => ( 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)),X212),X214)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X34))))
       => 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),X12),X212)),hAPP(hAPP(c_List_Olist_OCons(X5),X27),X214))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X34)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI2) ).

fof(fact_image__diff__subset,axiom,
    ! [X13,X11,X2,X16,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(X16,X5,X2),X11)),hAPP(c_Set_Oimage(X16,X5,X2),X13))),hAPP(c_Set_Oimage(X16,X5,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool)),X11),X13)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__diff__subset) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
    ! [X29] : hAPP(c_Set_OCollect(tc_Nat_Onat),X29) = 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),X29),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,
    ! [X34,X5] : c_List_Olenlex(X5,X34) = 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,X34))),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_refl__onI,axiom,
    ! [X11,X34,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X11),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X11))))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X34)) )
       => c_Relation_Orefl__on(X5,X11,X34) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onI) ).

fof(fact_refl__on__def,axiom,
    ! [X34,X11,X5] :
      ( c_Relation_Orefl__on(X5,X11,X34)
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X11),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X11))))
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X34)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__def) ).

fof(fact_map__of__map__keys,axiom,
    ! [X45,X16,X212,X5] :
      ( hAPP(c_List_Oset(X5),X212) = c_Map_Odom(X5,X16,X45)
     => hAPP(c_Map_Omap__of(X5,X16),hAPP(hAPP(c_List_Omap(X5,tc_prod(X5,X16)),hAPP(hAPP(c_COMBS(X5,X16,tc_prod(X5,X16)),c_Product__Type_OPair(X5,X16)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X16),X16,X5),c_Option_Othe(X16)),X45))),X212)) = X45 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__map__keys) ).

fof(fact_insert__compr__raw,axiom,
    ! [X13,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),X13) = 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)),X13))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__compr__raw) ).

fof(fact_insert__compr,axiom,
    ! [X13,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),X13) = 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)),X13))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__compr) ).

fof(fact_listrel_OCons,axiom,
    ! [X214,X212,X34,X27,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),X34))
     => ( 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)),X212),X214)),c_List_Olistrel(X5,X34)))
       => 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),X12),X212)),hAPP(hAPP(c_List_Olist_OCons(X5),X27),X214))),c_List_Olistrel(X5,X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel_OCons) ).

fof(fact_dom__def,axiom,
    ! [X45,X16,X5] : c_Map_Odom(X5,X16,X45) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,tc_Option_Ooption(X16),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X16),tc_fun(tc_Option_Ooption(X16),tc_HOL_Obool),X5),c_fequal),X45)),c_Option_Ooption_ONone(X16)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dom__def) ).

fof(fact_smin__emptyI,axiom,
    ! [X31] :
      ( X31 != 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)),X31),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,
    ! [X27,X12] : 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),X12),X27)),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),X27),X12)),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,
    ! [X31] : 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)),X31),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,
    ! [X27,X11,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X16,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X16,X2,X37,X11),X27))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),X37),X11) = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__equality) ).

fof(fact_empty__fold__graphE,axiom,
    ! [X12,X37,X2,X16,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X16,X2,X37,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X12))
     => X12 = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__fold__graphE) ).

fof(fact_subset__equiv__class,axiom,
    ! [X6,X17,X34,X11,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X11,X34)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X34),hAPP(hAPP(c_Set_Oinsert(X5),X17),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X5,X5,X34),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X17),X11))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),X34)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__equiv__class) ).

fof(fact_ord_OatLeastLessThan__iff,axiom,
    ! [X66,X97,X96,X95,X70,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X70),c_SetInterval_Oord_OatLeastLessThan(X5,X95,X96,X97,X66)))
    <=> ( hBOOL(hAPP(hAPP(X95,X97),X70))
        & hBOOL(hAPP(hAPP(X96,X70),X66)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).

fof(fact_ord_OgreaterThanAtMost__iff,axiom,
    ! [X66,X97,X96,X95,X70,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X70),c_SetInterval_Oord_OgreaterThanAtMost(X5,X95,X96,X97,X66)))
    <=> ( hBOOL(hAPP(hAPP(X96,X97),X70))
        & hBOOL(hAPP(hAPP(X95,X70),X66)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).

fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
    ! [X1,X2,X13,X11,X5] :
      ( ( class_Groups_Ocomm__monoid__add(X5)
        & class_Groups_Ocomm__monoid__mult(X5) )
     => ( X11 = X13
       => ( c_Nat__Transfer_Onat__set(X13)
         => ( ! [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),X11) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X1),X13) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I1_J) ).

fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
    ! [X1,X2,X13,X11,X5] :
      ( ( class_Groups_Ocomm__monoid__add(X5)
        & class_Groups_Ocomm__monoid__mult(X5) )
     => ( X11 = X13
       => ( c_Nat__Transfer_Onat__set(X13)
         => ( ! [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),X11) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X1),X13) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I2_J) ).

fof(fact_select__weigth__drop__zero,axiom,
    ! [X212,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))))),X212)) = c_Random_Oselect__weight(X5,X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_select__weigth__drop__zero) ).

fof(fact_pick__drop__zero,axiom,
    ! [X212,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))))),X212)) = c_Random_Opick(X5,X212),
    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_Domain__Int__subset,axiom,
    ! [X13,X11,X16,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X16),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X11),X13))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X16),X11)),hAPP(c_Relation_ODomain(X5,X16),X13)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Int__subset) ).

fof(fact_Range__Int__subset,axiom,
    ! [X13,X11,X16,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ORange(X16,X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X16,X5),tc_HOL_Obool)),X11),X13))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ORange(X16,X5),X11)),hAPP(c_Relation_ORange(X16,X5),X13)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Int__subset) ).

fof(fact_setsum_Odistrib,axiom,
    ! [X48,X1,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),hAPP(hAPP(c_COMBS(X5,X16,X16),hAPP(hAPP(c_COMBB(X16,tc_fun(X16,X16),X5),c_Groups_Oplus__class_Oplus(X16)),X1)),X48)),X11) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X48),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Odistrib) ).

fof(fact_setprod__dividef,axiom,
    ! [X1,X2,X11,X5,X16] :
      ( class_Fields_Ofield__inverse__zero(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),hAPP(hAPP(c_COMBS(X5,X16,X16),hAPP(hAPP(c_COMBB(X16,tc_fun(X16,X16),X5),c_Rings_Oinverse__class_Odivide(X16)),X2)),X1)),X11) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__dividef) ).

fof(fact_setprod_Odistrib,axiom,
    ! [X48,X1,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),hAPP(hAPP(c_COMBS(X5,X16,X16),hAPP(hAPP(c_COMBB(X16,tc_fun(X16,X16),X5),c_Groups_Otimes__class_Otimes(X16)),X1)),X48)),X11) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X48),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Odistrib) ).

fof(fact_fold__graph__imp__finite,axiom,
    ! [X12,X11,X37,X2,X16,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X16,X2,X37,X11),X12))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph__imp__finite) ).

fof(fact_rotate1__def,axiom,
    ! [X212,X5] : hAPP(c_List_Orotate1(X5),X212) = 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)))),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__def) ).

fof(fact_setsum__addf,axiom,
    ! [X11,X1,X2,X16,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),hAPP(hAPP(c_COMBS(X16,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X16),c_Groups_Oplus__class_Oplus(X5)),X2)),X1)),X11) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),X2),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),X1),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__addf) ).

fof(fact_setsum__subtractf,axiom,
    ! [X11,X1,X2,X16,X5] :
      ( class_Groups_Oab__group__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),hAPP(hAPP(c_COMBS(X16,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X16),c_Groups_Ominus__class_Ominus(X5)),X2)),X1)),X11) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),X2),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),X1),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__subtractf) ).

fof(fact_setprod__timesf,axiom,
    ! [X11,X1,X2,X16,X5] :
      ( class_Groups_Ocomm__monoid__mult(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16,X5),hAPP(hAPP(c_COMBS(X16,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X16),c_Groups_Otimes__class_Otimes(X5)),X2)),X1)),X11) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16,X5),X2),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16,X5),X1),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__timesf) ).

fof(fact_divmod__nat__rel__mult2__eq,axiom,
    ! [X24,X123,X128,X26,X25] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X25,X26),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X128),X123)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24))
         => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X24)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X128),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X128,X24))),X123)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__mult2__eq) ).

fof(fact_lists__Int__eq,axiom,
    ! [X13,X11,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)),X11)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X13))) = 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,X11))),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,X13))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__Int__eq) ).

fof(fact_select__weight__def,axiom,
    ! [X212,X5] : c_Random_Oselect__weight(X5,X212) = 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)),X212)))),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,X212))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_select__weight__def) ).

fof(fact_insert__times__insert,axiom,
    ! [X13,X17,X11,X6,X16,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X16),hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),hAPP(hAPP(c_Set_Oinsert(X16),X17),X13))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),hAPP(hAPP(c_Set_Oinsert(X16),X17),X13)))),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X13)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__times__insert) ).

fof(fact_setsum__divide__distrib,axiom,
    ! [X34,X11,X2,X16,X5] :
      ( class_Fields_Ofield(X5)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),X2),X11)),X34) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),hAPP(hAPP(c_COMBC(X16,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X16),c_Rings_Oinverse__class_Odivide(X5)),X2)),X34)),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__divide__distrib) ).

fof(fact_setsum__left__distrib,axiom,
    ! [X34,X11,X2,X16,X5] :
      ( class_Rings_Osemiring__0(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),X2),X11)),X34) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),hAPP(hAPP(c_COMBC(X16,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X16),c_Groups_Otimes__class_Otimes(X5)),X2)),X34)),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__left__distrib) ).

fof(fact_zmult2__lemma,axiom,
    ! [X24,X123,X128,X26,X25] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X25,X26),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X128),X123)))
     => ( X26 != 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)),X24))
         => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X24)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X128),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),c_Divides_Odiv__class_Omod(tc_Int_Oint,X128,X24))),X123)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma) ).

fof(fact_listrel__rtrancl__trans,axiom,
    ! [X227,X34,X214,X212,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)),X212),X214)),c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X34))))
     => ( 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)),X214),X227)),c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X34))))
       => 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)),X212),X227)),c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X34)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__trans) ).

fof(fact_pred__subset__eq,axiom,
    ! [X35,X36,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)),X36)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X35)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X36),X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq) ).

fof(fact_finite__range__map__of__map__add,axiom,
    ! [X97,X2,X16,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X5)),hAPP(c_Set_Oimage(X16,tc_Option_Ooption(X5),X2),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)))))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X5)),hAPP(c_Set_Oimage(X16,tc_Option_Ooption(X5),c_Map_Omap__add(X16,X5,X2,hAPP(c_Map_Omap__of(X16,X5),X97))),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__range__map__of__map__add) ).

fof(fact_reduction__pair__lemma,axiom,
    ! [X35,X36,X29,X5] :
      ( c_FunDef_Oreduction__pair(X5,X29)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X36),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X29)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X35),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X29)))
         => ( c_Wellfounded_Owf(X5,X35)
           => c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X36),X35)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reduction__pair__lemma) ).

fof(fact_Union__Int__subset,axiom,
    ! [X13,X11,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)),X11),X13))),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),X11)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X13)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__Int__subset) ).

fof(fact_Image__subset__eq,axiom,
    ! [X13,X11,X34,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X16,X5,X34),X11)),X13))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),X11),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X16,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X16,hAPP(c_Relation_Oconverse(X16,X5),X34)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X13))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__subset__eq) ).

fof(fact_image__eq__UN,axiom,
    ! [X11,X2,X5,X16] : hAPP(c_Set_Oimage(X16,X5,X2),X11) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBC(X16,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)),X16),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_option__map__o__sum__case,axiom,
    ! [X48,X1,X2,X16,X5,X38,X55] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(X55),tc_Option_Ooption(X38),tc_sum(X5,X16),hAPP(c_Option_Omap(X55,X38),X2)),c_Sum__Type_Osum_Osum__case(X5,tc_Option_Ooption(X55),X16,X1,X48)) = c_Sum__Type_Osum_Osum__case(X5,tc_Option_Ooption(X38),X16,hAPP(c_Fun_Ocomp(tc_Option_Ooption(X55),tc_Option_Ooption(X38),X5,hAPP(c_Option_Omap(X55,X38),X2)),X1),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X55),tc_Option_Ooption(X38),X16,hAPP(c_Option_Omap(X55,X38),X2)),X48)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option__map__o__sum__case) ).

fof(fact_rtrancl__listrel1__ConsI1,axiom,
    ! [X12,X34,X214,X212,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)),X212),X214)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X34))))
     => 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),X12),X212)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X214))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X34)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI1) ).

fof(fact_option__map__o__map__upd,axiom,
    ! [X17,X6,X45,X2,X5,X16,X38] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(X38),tc_Option_Ooption(X16),X5,hAPP(c_Option_Omap(X38,X16),X2)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X38)),X45),X6),hAPP(c_Option_Ooption_OSome(X38),X17))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X38),tc_Option_Ooption(X16),X5,hAPP(c_Option_Omap(X38,X16),X2)),X45)),X6),hAPP(c_Option_Ooption_OSome(X16),hAPP(X2,X17))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option__map__o__map__upd) ).

fof(fact_pair__leqI2,axiom,
    ! [X10,X84,X17,X6] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6),X17))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X84),X10))
       => 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),X84)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X17),X10))),c_FunDef_Opair__leq)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__leqI2) ).

fof(fact_pair__lessI2,axiom,
    ! [X10,X84,X17,X6] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6),X17))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X84),X10))
       => 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),X84)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X17),X10))),c_FunDef_Opair__less)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__lessI2) ).

fof(fact_rtrancl__Un__subset,axiom,
    ! [X35,X36,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,X36)),c_Transitive__Closure_Ortrancl(X5,X35))),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X36),X35)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__Un__subset) ).

fof(fact_Image__Int__subset,axiom,
    ! [X13,X11,X36,X16,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X16,X5,X36),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),X11),X13))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X16,X5,X36),X11)),hAPP(c_Relation_OImage(X16,X5,X36),X13)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Int__subset) ).

fof(fact_image__Int__subset,axiom,
    ! [X13,X11,X2,X16,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X16,X5,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),X11),X13))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X16,X5,X2),X11)),hAPP(c_Set_Oimage(X16,X5,X2),X13)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Int__subset) ).

fof(fact_transfer__nat__int__set__cong,axiom,
    ! [X197,X29] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
         => ( hBOOL(hAPP(X29,X3))
          <=> hBOOL(hAPP(X197,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)))),X29)) = 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)))),X197)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__set__cong) ).

fof(fact_pair__leqI1,axiom,
    ! [X10,X84,X17,X6] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X17))
     => 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),X84)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X17),X10))),c_FunDef_Opair__leq)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__leqI1) ).

fof(fact_pair__lessI1,axiom,
    ! [X10,X84,X17,X6] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X17))
     => 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),X84)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X17),X10))),c_FunDef_Opair__less)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__lessI1) ).

fof(fact_lists__eq__set,axiom,
    ! [X11,X5] : c_List_Olists(X5,X11) = 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))),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__eq__set) ).

fof(fact_append__listrel1I,axiom,
    ! [X245,X246,X34,X214,X212,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)),X212),X214)),c_List_Olistrel1(X5,X34)))
          & X246 = X245 )
        | ( X212 = X214
          & 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)),X246),X245)),c_List_Olistrel1(X5,X34))) ) )
     => 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),X212),X246)),hAPP(hAPP(c_List_Oappend(X5),X214),X245))),c_List_Olistrel1(X5,X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__listrel1I) ).

fof(fact_lexord__append__leftI,axiom,
    ! [X12,X34,X56,X66,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)),X66),X56)),c_List_Olexord(X5,X34)))
     => 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),X12),X66)),hAPP(hAPP(c_List_Oappend(X5),X12),X56))),c_List_Olexord(X5,X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__leftI) ).

fof(fact_listrel1I2,axiom,
    ! [X12,X34,X214,X212,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)),X212),X214)),c_List_Olistrel1(X5,X34)))
     => 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),X12),X212)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X214))),c_List_Olistrel1(X5,X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1I2) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
    ! [X29] : 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)))),X29))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J) ).

fof(fact_finite__range__updI,axiom,
    ! [X17,X6,X2,X16,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X5)),hAPP(c_Set_Oimage(X16,tc_Option_Ooption(X5),X2),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)))))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X5)),hAPP(c_Set_Oimage(X16,tc_Option_Ooption(X5),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X16,tc_Option_Ooption(X5)),X2),X6),hAPP(c_Option_Ooption_OSome(X5),X17))),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__range__updI) ).

fof(fact_zip__map1,axiom,
    ! [X214,X212,X2,X38,X16,X5] : hAPP(hAPP(c_List_Ozip(X5,X16),hAPP(hAPP(c_List_Omap(X38,X5),X2),X212)),X214) = hAPP(hAPP(c_List_Omap(tc_prod(X38,X16),tc_prod(X5,X16)),hAPP(c_Product__Type_Oprod_Oprod__case(X38,X16,tc_prod(X5,X16)),hAPP(hAPP(c_COMBB(X5,tc_fun(X16,tc_prod(X5,X16)),X38),c_Product__Type_OPair(X5,X16)),X2))),hAPP(hAPP(c_List_Ozip(X38,X16),X212),X214)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__map1) ).

fof(fact_mlex__prod__def,axiom,
    ! [X36,X2,X5] : c_Wellfounded_Omlex__prod(X5,X2,X36) = 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,X36)),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,
    ! [X29,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(X29,X11))
       => ( ! [X74,X75] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X75))
             => ( hBOOL(hAPP(hAPP(c_member(X5),X74),X75))
               => ( hBOOL(hAPP(X29,X75))
                 => hBOOL(hAPP(X29,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X75),hAPP(hAPP(c_Set_Oinsert(X5),X74),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) )
         => hBOOL(hAPP(X29,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,
    ! [X13,X11,X16,X19,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),X19))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X16,X5),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X16,X5),X11),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X16),X19))),hAPP(hAPP(c_Product__Type_OSigma(X16,X5),X13),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X16),X19))))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),X11),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Times__subset__cancel2) ).

fof(fact_rel__pow__Suc__I2,axiom,
    ! [X76,X37,X36,X27,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),X36))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X27),X37)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X76),X36)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X37)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X76)),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__Suc__I2) ).

fof(fact_rel__pow__Suc__I,axiom,
    ! [X37,X36,X76,X27,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X76),X36)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X27),X37)),X36))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X37)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X76)),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__Suc__I) ).

fof(fact_image__Pow__mono,axiom,
    ! [X13,X11,X2,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X16,X5,X2),X11)),X13))
     => 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(X16,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),c_Set_Oimage(X16,X5,X2)),hAPP(c_Set_OPow(X16),X11))),hAPP(c_Set_OPow(X5),X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Pow__mono) ).

fof(fact_select__weight__member,axiom,
    ! [X84,X212,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)),X212))))
     => 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,X212),X84))),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)),X212)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_select__weight__member) ).

fof(fact_setsum__abs,axiom,
    ! [X11,X2,X16,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(X16,X5),X2),X11))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),hAPP(hAPP(c_COMBB(X5,X5,X16),c_Groups_Oabs__class_Oabs(X5)),X2)),X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__abs) ).

fof(fact_set__minus__filter__out,axiom,
    ! [X27,X212,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X212)),hAPP(hAPP(c_Set_Oinsert(X5),X27),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),X27))),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__minus__filter__out) ).

fof(fact_filter__filter,axiom,
    ! [X212,X28,X29,X5] : hAPP(c_List_Ofilter(X5,X29),hAPP(c_List_Ofilter(X5,X28),X212)) = 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),X28)),X29)),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__filter) ).

fof(fact_Domain__Diff__subset,axiom,
    ! [X13,X11,X16,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,X16),X11)),hAPP(c_Relation_ODomain(X5,X16),X13))),hAPP(c_Relation_ODomain(X5,X16),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X11),X13)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Diff__subset) ).

fof(fact_Range__Diff__subset,axiom,
    ! [X13,X11,X16,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(X16,X5),X11)),hAPP(c_Relation_ORange(X16,X5),X13))),hAPP(c_Relation_ORange(X16,X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X16,X5),tc_HOL_Obool)),X11),X13)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Diff__subset) ).

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,
    ! [X12,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => 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)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X5),X11))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff1__less) ).

fof(fact_split__comp__eq,axiom,
    ! [X1,X2,X55,X38,X16,X5] : hAPP(hAPP(c_COMBS(tc_prod(X5,X16),X16,X38),hAPP(hAPP(c_COMBB(X55,tc_fun(X16,X38),tc_prod(X5,X16)),X2),hAPP(hAPP(c_COMBB(X5,X55,tc_prod(X5,X16)),X1),c_Product__Type_Ofst(X5,X16)))),c_Product__Type_Osnd(X5,X16)) = hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,X38),hAPP(hAPP(c_COMBB(X55,tc_fun(X16,X38),X5),X2),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__comp__eq) ).

fof(fact_insort__key__remove1,axiom,
    ! [X2,X212,X6,X5,X16] :
      ( class_Orderings_Olinorder(X16)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_List_Oset(X5),X212)))
       => ( c_List_Olinorder__class_Osorted(X16,hAPP(hAPP(c_List_Omap(X5,X16),X2),X212))
         => ( hAPP(c_List_Ohd(X5),hAPP(c_List_Ofilter(X5,hAPP(hAPP(c_COMBB(X16,tc_HOL_Obool,X5),hAPP(c_fequal,hAPP(X2,X6))),X2)),X212)) = X6
           => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X16,X2),X6),c_List_Oremove1(X5,X6,X212)) = X212 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__key__remove1) ).

fof(fact_equiv__intrel__iff,axiom,
    ! [X27,X12] :
      ( 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)),X12),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)),X27),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)),X12),X27)),c_Int_Ointrel)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__intrel__iff) ).

fof(fact_setsum__UNION__zero,axiom,
    ! [X2,X35,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),X35))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X3),X35))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3)) )
         => ( ! [X281] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X281),X35))
               => ! [X282] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X282),X35))
                   => ( X281 != X282
                     => ! [X3] :
                          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X281))
                         => ( hBOOL(hAPP(hAPP(c_member(X5),X3),X282))
                           => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X16) ) ) ) ) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X35)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X5,tc_HOL_Obool),X16),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2)),X35) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__UNION__zero) ).

fof(fact_fold__graph_H_Ointros_I1_J,axiom,
    ! [X37,X2,X16,X5] : c_Nitpick_Ofold__graph_H(X5,X16,X2,X37,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),X37),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I1_J) ).

fof(fact_fold__graph_H_Oequations_I1_J,axiom,
    ! [X46,X47,X16,X5] : c_Nitpick_Ofold__graph_H(X5,X16,X47,X46,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),X46),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).

fof(fact_map__pair_Oid,axiom,
    ! [X16,X5] : c_Product__Type_Omap__pair(X5,X5,X16,X16,c_Fun_Oid(X5),c_Fun_Oid(X16)) = c_Fun_Oid(tc_prod(X5,X16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair_Oid) ).

fof(fact_map__pair_Oidentity,axiom,
    ! [X16,X5] : c_Product__Type_Omap__pair(X5,X5,X16,X16,c_COMBI(X5),c_COMBI(X16)) = c_Fun_Oid(tc_prod(X5,X16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair_Oidentity) ).

fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
    ! [X37,X11,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X16,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X16,X2,X37,X11),hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),X37),X11))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__fold) ).

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,
    ! [X12,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => 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)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X5),X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff1__le) ).

fof(fact_rel__comp__mono,axiom,
    ! [X84,X181,X38,X34,X61,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X61),X34))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X16,X38),tc_HOL_Obool)),X181),X84))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X38),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X16,X38),X61),X181)),hAPP(hAPP(c_Relation_Orel__comp(X5,X16,X38),X34),X84))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__mono) ).

fof(fact_equiv__class__subset,axiom,
    ! [X17,X6,X34,X11,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X11,X34)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),X34))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X34),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X5,X5,X34),hAPP(hAPP(c_Set_Oinsert(X5),X17),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,
    ! [X13,X12,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => ( hBOOL(hAPP(hAPP(c_member(X16),X12),hAPP(c_Set_Oimage(X5,X16,X2),X11)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
         => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Fun_Othe__inv__into(X5,X16,X11,X2),X12)),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__into) ).

fof(fact_finite__range__imageI,axiom,
    ! [X2,X38,X1,X16,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_Oimage(X16,X5,X1),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)))))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X38),hAPP(c_Set_Oimage(X16,X38,hAPP(hAPP(c_COMBB(X5,X38,X16),X2),X1)),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__range__imageI) ).

fof(fact_Inter__Un__subset,axiom,
    ! [X13,X11,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),X11)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X13))),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)),X11),X13)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__Un__subset) ).

fof(fact_listrel__subset,axiom,
    ! [X11,X34,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X11),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X11))))
     => 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,X34)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olists(X5,X11)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_List_Olist(X5)),c_List_Olists(X5,X11))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__subset) ).

fof(fact_fold__image__reindex,axiom,
    ! [X37,X1,X48,X16,X11,X5,X38] :
      ( class_Groups_Oab__semigroup__mult(X38)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( c_Fun_Oinj__on(X5,X16,X48,X11)
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X38,X16,c_Groups_Otimes__class_Otimes(X38)),X1),X37),hAPP(c_Set_Oimage(X5,X16,X48),X11)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X38,X5,c_Groups_Otimes__class_Otimes(X38)),hAPP(c_Fun_Ocomp(X16,X38,X5,X1),X48)),X37),X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__reindex) ).

fof(fact_zmult2__lemma__aux4,axiom,
    ! [X128,X26,X123,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X123))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),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_Otimes__class_Otimes(tc_Int_Oint),X26),c_Divides_Odiv__class_Omod(tc_Int_Oint,X128,X24))),X123)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X24))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma__aux4) ).

fof(fact_restrict__map__upds,axiom,
    ! [X45,X18,X214,X16,X212,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X212)),X18))
       => c_Map_Orestrict__map(X5,X16,c_Map_Omap__upds(X5,X16,X45,X212,X214),X18) = c_Map_Omap__upds(X5,X16,c_Map_Orestrict__map(X5,X16,X45,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X18),hAPP(c_List_Oset(X5),X212))),X212,X214) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__map__upds) ).

fof(fact_min__max_Ofold__sup__le__sup,axiom,
    ! [X21,X17,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X17)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X21),X11)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X17),X21))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ofold__sup__le__sup) ).

fof(fact_fold__sup__le__sup,axiom,
    ! [X21,X17,X11,X5] :
      ( class_Lattices_Osemilattice__sup(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X17)) )
         => 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)),X21),X11)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X17),X21))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__sup__le__sup) ).

fof(fact_map__of__eqI,axiom,
    ! [X214,X212,X16,X5] :
      ( hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Omap(tc_prod(X5,X16),X5),c_Product__Type_Ofst(X5,X16)),X212)) = hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Omap(tc_prod(X5,X16),X5),c_Product__Type_Ofst(X5,X16)),X214))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Omap(tc_prod(X5,X16),X5),c_Product__Type_Ofst(X5,X16)),X212))))
           => hAPP(hAPP(c_Map_Omap__of(X5,X16),X212),X3) = hAPP(hAPP(c_Map_Omap__of(X5,X16),X214),X3) )
       => hAPP(c_Map_Omap__of(X5,X16),X212) = hAPP(c_Map_Omap__of(X5,X16),X214) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__eqI) ).

fof(fact_listrel1I1,axiom,
    ! [X212,X34,X27,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),X34))
     => 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),X12),X212)),hAPP(hAPP(c_List_Olist_OCons(X5),X27),X212))),c_List_Olistrel1(X5,X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1I1) ).

fof(fact_transpose__column,axiom,
    ! [X70,X212,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))),X212)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X70),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X212)))
       => 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)),X70)),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),X70)),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),c_List_Otranspose(X5,X212))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),X212),X70) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__column) ).

fof(fact_split__paired__Eps,axiom,
    ! [X29,X16,X5] : c_Hilbert__Choice_OEps(tc_prod(X5,X16),X29) = c_Hilbert__Choice_OEps(tc_prod(X5,X16),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_prod(X5,X16),tc_HOL_Obool,X16),X29)),c_Product__Type_OPair(X5,X16)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__Eps) ).

fof(fact_split__paired__The,axiom,
    ! [X29,X16,X5] : c_HOL_OThe(tc_prod(X5,X16),X29) = c_HOL_OThe(tc_prod(X5,X16),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_prod(X5,X16),tc_HOL_Obool,X16),X29)),c_Product__Type_OPair(X5,X16)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__The) ).

fof(fact_total__on__def,axiom,
    ! [X34,X11,X5] :
      ( c_Relation_Ototal__on(X5,X11,X34)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
         => ! [X39] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X39),X11))
             => ( X3 != X39
               => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X39)),X34))
                  | hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X39),X3)),X34)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__def) ).

fof(fact_mod__lemma,axiom,
    ! [X128,X26,X123,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X123),X26))
       => 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),X26),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X128,X24))),X123)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X24))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__lemma) ).

fof(fact_single__valued__confluent,axiom,
    ! [X37,X27,X12,X34,X5] :
      ( c_Relation_Osingle__valued(X5,X5,X34)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_Transitive__Closure_Ortrancl(X5,X34)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X37)),c_Transitive__Closure_Ortrancl(X5,X34)))
         => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X27),X37)),c_Transitive__Closure_Ortrancl(X5,X34)))
            | hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X37),X27)),c_Transitive__Closure_Ortrancl(X5,X34))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__confluent) ).

fof(fact_reduction__pairI,axiom,
    ! [X35,X36,X5] :
      ( 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),X36),X35)),X36))
       => 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)),X36),X35)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reduction__pairI) ).

fof(fact_zmult2__lemma__aux2,axiom,
    ! [X128,X123,X26,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),X123))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X123),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),X26),c_Divides_Odiv__class_Omod(tc_Int_Oint,X128,X24))),X123)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma__aux2) ).

fof(fact_select__def,axiom,
    ! [X212,X5] : c_Random_Oselect(X5,X212) = 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)),X212)))),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),X212)),c_Code__Numeral_Onat__of))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_select__def) ).

fof(fact_of__int,axiom,
    ! [X115,X70,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),X70),X115)),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),X70)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X115)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int) ).

fof(fact_dom__option__map,axiom,
    ! [X45,X2,X38,X16,X5] : c_Map_Odom(X5,X16,hAPP(hAPP(c_COMBS(X5,tc_Option_Ooption(X38),tc_Option_Ooption(X16)),hAPP(hAPP(c_COMBB(tc_fun(X38,X16),tc_fun(tc_Option_Ooption(X38),tc_Option_Ooption(X16)),X5),c_Option_Omap(X38,X16)),X2)),X45)) = c_Map_Odom(X5,X38,X45),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dom__option__map) ).

fof(fact_diff__single__insert,axiom,
    ! [X13,X12,X11,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)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X13))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__single__insert) ).

fof(fact_nat,axiom,
    ! [X27,X12] : 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),X12),X27)),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),X12),X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat) ).

fof(fact_inj__on__Un,axiom,
    ! [X13,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13))
    <=> ( c_Fun_Oinj__on(X5,X16,X2,X11)
        & c_Fun_Oinj__on(X5,X16,X2,X13)
        & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X16,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13))),hAPP(c_Set_Oimage(X5,X16,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X13),X11))) = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__Un) ).

fof(fact_in__finite__psubset,axiom,
    ! [X13,X11,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)),X11),X13)),c_Wellfounded_Ofinite__psubset(X5)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),X13))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__finite__psubset) ).

fof(fact_Domain__iff,axiom,
    ! [X34,X16,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Relation_ODomain(X5,X16),X34)))
    <=> ? [X33] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X33)),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__iff) ).

fof(fact_Un__Pow__subset,axiom,
    ! [X13,X11,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),X11)),hAPP(c_Set_OPow(X5),X13))),hAPP(c_Set_OPow(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Pow__subset) ).

fof(fact_o__inv__o__cancel,axiom,
    ! [X1,X38,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Fun_Ocomp(X16,X38,X5,hAPP(c_Fun_Ocomp(X5,X38,X16,X1),c_Hilbert__Choice_Oinv__into(X5,X16,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,
    ! [X98,X99,X120,X102,X101] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X101),X102))
     => 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),X102),X120)),X99)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X120)),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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X102),X101)),X120)),X99)),X98) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).

fof(fact_pick__member,axiom,
    ! [X212,X5,X70] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X70),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)),X212))))
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Random_Opick(X5,X212),X70)),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)),X212)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pick__member) ).

fof(fact_rel__compI,axiom,
    ! [X84,X21,X38,X34,X17,X6,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17)),X34))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X38)),hAPP(hAPP(c_Product__Type_OPair(X16,X38),X17),X21)),X84))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X38)),hAPP(hAPP(c_Product__Type_OPair(X5,X38),X6),X21)),hAPP(hAPP(c_Relation_Orel__comp(X5,X16,X38),X34),X84))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__compI) ).

fof(fact_sorted__insort__insert__key,axiom,
    ! [X12,X212,X2,X16,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X16,X5),X2),X212))
       => c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X16,X5),X2),c_List_Olinorder__class_Oinsort__insert__key(X16,X5,X2,X12,X212))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__insort__insert__key) ).

fof(fact_lfp__induct__set,axiom,
    ! [X29,X2,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X5,tc_HOL_Obool),X2)))
     => ( c_Orderings_Oorder__class_Omono(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X2)
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X5,tc_HOL_Obool),X2)),hAPP(c_Set_OCollect(X5),X29)))))
             => hBOOL(hAPP(X29,X3)) )
         => hBOOL(hAPP(X29,X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lfp__induct__set) ).

fof(fact_list__all2__append,axiom,
    ! [X245,X246,X29,X214,X16,X212,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)
     => ( c_List_Olist__all2(X5,X16,X29,hAPP(hAPP(c_List_Oappend(X5),X212),X246),hAPP(hAPP(c_List_Oappend(X16),X214),X245))
      <=> ( c_List_Olist__all2(X5,X16,X29,X212,X214)
          & c_List_Olist__all2(X5,X16,X29,X246,X245) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__append) ).

fof(fact_bex__Un,axiom,
    ! [X29,X13,X11,X5] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
          & hBOOL(hAPP(X29,X3)) )
    <=> ( ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
            & hBOOL(hAPP(X29,X3)) )
        | ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X13))
            & hBOOL(hAPP(X29,X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bex__Un) ).

fof(fact_ball__Un,axiom,
    ! [X29,X13,X11,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
         => hBOOL(hAPP(X29,X3)) )
    <=> ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
           => hBOOL(hAPP(X29,X3)) )
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X13))
           => hBOOL(hAPP(X29,X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ball__Un) ).

fof(fact_INF2__D,axiom,
    ! [X6,X21,X17,X13,X11,X38,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_fun(X38,tc_HOL_Obool))),X11),X13),X17),X21))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => hBOOL(hAPP(hAPP(hAPP(X13,X6),X17),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF2__D) ).

fof(fact_list__all2__appendI,axiom,
    ! [X20,X21,X17,X6,X29,X16,X5] :
      ( c_List_Olist__all2(X5,X16,X29,X6,X17)
     => ( c_List_Olist__all2(X5,X16,X29,X21,X20)
       => c_List_Olist__all2(X5,X16,X29,hAPP(hAPP(c_List_Oappend(X5),X6),X21),hAPP(hAPP(c_List_Oappend(X16),X17),X20)) ) ),
    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,
    ! [X27,X12,X1,X2,X5,X16,X38] : hAPP(c_Fun_Ocomp(X38,X16,X5,X2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X38),X1),X12),X27)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),hAPP(c_Fun_Ocomp(X38,X16,X5,X2),X1)),X12),hAPP(X2,X27)),
    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,
    ! [X13,X2,X16,X5] : hAPP(c_Set_Ovimage(X5,X16,X2),X13) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X16,tc_fun(tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool),X5),c_member(X16)),X2)),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__def) ).

fof(fact_zip__append2,axiom,
    ! [X242,X225,X221,X5,X15] : hAPP(hAPP(c_List_Ozip(X15,X5),X221),hAPP(hAPP(c_List_Oappend(X5),X225),X242)) = hAPP(hAPP(c_List_Oappend(tc_prod(X15,X5)),hAPP(hAPP(c_List_Ozip(X15,X5),hAPP(hAPP(c_List_Otake(X15),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X225)),X221)),X225)),hAPP(hAPP(c_List_Ozip(X15,X5),hAPP(hAPP(c_List_Odrop(X15),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X225)),X221)),X242)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__append2) ).

fof(fact_in__listrel1__converse,axiom,
    ! [X34,X27,X12,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)),X12),X27)),c_List_Olistrel1(X5,hAPP(c_Relation_Oconverse(X5,X5),X34))))
    <=> 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)),X12),X27)),hAPP(c_Relation_Oconverse(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel1(X5,X34)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__listrel1__converse) ).

fof(fact_map__filter__simps_I1_J,axiom,
    ! [X212,X12,X2,X5,X16] : c_List_Omap__filter(X16,X5,X2,hAPP(hAPP(c_List_Olist_OCons(X16),X12),X212)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(X5),X5,c_List_Omap__filter(X16,X5,X2,X212),hAPP(hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),c_List_Omap__filter(X16,X5,X2,X212))),hAPP(X2,X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__filter__simps_I1_J) ).

fof(fact_Cons__eq__append__conv,axiom,
    ! [X227,X214,X212,X12,X5] :
      ( hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212) = hAPP(hAPP(c_List_Oappend(X5),X214),X227)
    <=> ( ( X214 = c_List_Olist_ONil(X5)
          & hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212) = X227 )
        | ? [X239] :
            ( hAPP(hAPP(c_List_Olist_OCons(X5),X12),X239) = X214
            & X212 = hAPP(hAPP(c_List_Oappend(X5),X239),X227) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__eq__append__conv) ).

fof(fact_append__eq__Cons__conv,axiom,
    ! [X212,X12,X227,X214,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X214),X227) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)
    <=> ( ( X214 = c_List_Olist_ONil(X5)
          & X227 = hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212) )
        | ? [X239] :
            ( X214 = hAPP(hAPP(c_List_Olist_OCons(X5),X12),X239)
            & hAPP(hAPP(c_List_Oappend(X5),X239),X227) = X212 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__Cons__conv) ).

fof(fact_inv__into__into,axiom,
    ! [X11,X2,X16,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_Set_Oimage(X16,X5,X2),X11)))
     => hBOOL(hAPP(hAPP(c_member(X16),hAPP(c_Hilbert__Choice_Oinv__into(X16,X5,X11,X2),X12)),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__into) ).

fof(fact_min__max_OSup__fin_Oclosed,axiom,
    ! [X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X33] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X3),X33)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X33),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),X11)),X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oclosed) ).

fof(fact_min__max_OInf__fin_Oclosed,axiom,
    ! [X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X33] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X3),X33)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X33),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),X11)),X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oclosed) ).

fof(fact_card__SigmaI,axiom,
    ! [X13,X16,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X16),hAPP(X13,X3))) )
       => hAPP(c_Finite__Set_Ocard(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),X13)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_Nat_Onat,X5),c_Finite__Set_Ocard(X16)),X13)),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__SigmaI) ).

fof(fact_fold__graph_Oequations_I1_J,axiom,
    ! [X37,X2,X16,X5] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X16,X2,X37,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X37)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_Oequations_I1_J) ).

fof(fact_fold__graph_OemptyI,axiom,
    ! [X37,X2,X16,X5] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X16,X2,X37,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X37)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_OemptyI) ).

fof(fact_wf__union__compatible,axiom,
    ! [X35,X36,X5] :
      ( c_Wellfounded_Owf(X5,X36)
     => ( c_Wellfounded_Owf(X5,X35)
       => ( 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),X36),X35)),X36))
         => c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X36),X35)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__union__compatible) ).

fof(fact_map__of__map__restrict,axiom,
    ! [X219,X2,X16,X5] : hAPP(c_Map_Omap__of(X5,X16),hAPP(hAPP(c_List_Omap(X5,tc_prod(X5,X16)),hAPP(hAPP(c_COMBS(X5,X16,tc_prod(X5,X16)),c_Product__Type_OPair(X5,X16)),X2)),X219)) = c_Map_Orestrict__map(X5,X16,hAPP(c_Fun_Ocomp(X16,tc_Option_Ooption(X16),X5,c_Option_Ooption_OSome(X16)),X2),hAPP(c_List_Oset(X5),X219)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__map__restrict) ).

fof(fact_fold1__in,axiom,
    ! [X11,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X33] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X33)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X33),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)),X11)),X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__in) ).

fof(fact_unique__quotient__lemma,axiom,
    ! [X123,X128,X141,X142,X26] :
      ( 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),X26),X142)),X141)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X128)),X123)))
     => ( 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),X26))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),X26))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X142),X128)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).

fof(fact_unique__quotient__lemma__neg,axiom,
    ! [X123,X128,X141,X142,X26] :
      ( 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),X26),X142)),X141)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X128)),X123)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X123),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),X123))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),X141))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X128),X142)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).

fof(fact_distinct__insort__insert,axiom,
    ! [X12,X2,X212,X5,X16] :
      ( class_Orderings_Olinorder(X16)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),X212))
       => hBOOL(hAPP(c_List_Odistinct(X5),c_List_Olinorder__class_Oinsort__insert__key(X5,X16,X2,X12,X212))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__insort__insert) ).

fof(fact_nth__transpose,axiom,
    ! [X212,X5,X70] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X70),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),c_List_Otranspose(X5,X212))))
     => hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),c_List_Otranspose(X5,X212)),X70) = 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)),X70)),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),X70)),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__transpose) ).

fof(fact_Powp__Pow__eq,axiom,
    ! [X12,X11,X5] :
      ( hBOOL(hAPP(c_Predicate_OPowp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X11)),X12))
    <=> hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X12),hAPP(c_Set_OPow(X5),X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Powp__Pow__eq) ).

fof(fact_card__bij__eq,axiom,
    ! [X1,X13,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X16,X2),X11)),X13))
       => ( c_Fun_Oinj__on(X16,X5,X1,X13)
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X16,X5,X1),X13)),X11))
           => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
             => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X13))
               => hAPP(c_Finite__Set_Ocard(X5),X11) = hAPP(c_Finite__Set_Ocard(X16),X13) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__bij__eq) ).

fof(fact_Eps__split,axiom,
    ! [X29,X16,X5] : c_Hilbert__Choice_OEps(tc_prod(X5,X16),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_HOL_Obool),X29)) = c_Hilbert__Choice_OEps(tc_prod(X5,X16),hAPP(hAPP(c_COMBS(tc_prod(X5,X16),X16,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X5,tc_fun(X16,tc_HOL_Obool),tc_prod(X5,X16)),X29),c_Product__Type_Ofst(X5,X16))),c_Product__Type_Osnd(X5,X16))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Eps__split) ).

fof(fact_The__split,axiom,
    ! [X29,X16,X5] : c_HOL_OThe(tc_prod(X5,X16),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_HOL_Obool),X29)) = c_HOL_OThe(tc_prod(X5,X16),hAPP(hAPP(c_COMBS(tc_prod(X5,X16),X16,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X5,tc_fun(X16,tc_HOL_Obool),tc_prod(X5,X16)),X29),c_Product__Type_Ofst(X5,X16))),c_Product__Type_Osnd(X5,X16))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_The__split) ).

fof(fact_in__measures_I2_J,axiom,
    ! [X261,X2,X27,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_List_Omeasures(X5,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X5,tc_Nat_Onat)),X2),X261))))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X12)),hAPP(X2,X27)))
        | ( hAPP(X2,X12) = hAPP(X2,X27)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_List_Omeasures(X5,X261))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measures_I2_J) ).

fof(fact_div__mod__equality,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),X25),X26)),X26)),c_Divides_Odiv__class_Omod(X15,X25,X26))),X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mod__equality) ).

fof(fact_fold__Un__disjoint,axiom,
    ! [X1,X13,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X1),c_Groups_Oone__class_Oone(X16)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X1),c_Groups_Oone__class_Oone(X16)),X11)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X1),c_Groups_Oone__class_Oone(X16)),X13)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__Un__disjoint) ).

fof(fact_uminus__listsum__map,axiom,
    ! [X212,X2,X16,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(X16,X5),X2),X212))) = hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X16,X5),hAPP(c_Fun_Ocomp(X5,X5,X16,c_Groups_Ouminus__class_Ouminus(X5)),X2)),X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__listsum__map) ).

fof(fact_neg__map__def,axiom,
    ! [X29,X2,X5,X16] : c_New__Random__Sequence_Oneg__map(X16,X5,X2,X29) = c_New__Random__Sequence_Oneg__bind(X16,X5,X29,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)))))),X16,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,
    ! [X12,X11,X5] :
      ( hBOOL(hAPP(c_List_Olistsp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X11)),X12))
    <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X12),c_List_Olists(X5,X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__lists__eq) ).

fof(fact_setsum__abs__ge__zero,axiom,
    ! [X11,X2,X16,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(X16,X5),hAPP(hAPP(c_COMBB(X5,X5,X16),c_Groups_Oabs__class_Oabs(X5)),X2)),X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__abs__ge__zero) ).

fof(fact_finite__Collect__subsets,axiom,
    ! [X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => 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))),X11)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__subsets) ).

fof(fact_sum__squares__le__zero__iff,axiom,
    ! [X27,X12,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),X12),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X27),X27))),c_Groups_Ozero__class_Ozero(X5)))
      <=> ( X12 = c_Groups_Ozero__class_Ozero(X5)
          & X27 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).

fof(fact_Min_Oclosed,axiom,
    ! [X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X33] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X3),X33)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X33),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olinorder__class_OMin(X5,X11)),X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oclosed) ).

fof(fact_Max_Oclosed,axiom,
    ! [X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X33] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X3),X33)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X33),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olinorder__class_OMax(X5,X11)),X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oclosed) ).

fof(fact_Sup__fin_Oclosed,axiom,
    ! [X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X33] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X3),X33)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X33),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,X11)),X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oclosed) ).

fof(fact_Inf__fin_Oclosed,axiom,
    ! [X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X33] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X3),X33)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X33),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,X11)),X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oclosed) ).

fof(fact_folding__image_Oreindex,axiom,
    ! [X1,X48,X11,X90,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__image(X5,X16,X2,X37,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11))
       => ( c_Fun_Oinj__on(X16,X16,X48,X11)
         => hAPP(hAPP(X90,X1),hAPP(c_Set_Oimage(X16,X16,X48),X11)) = hAPP(hAPP(X90,hAPP(c_Fun_Ocomp(X16,X5,X16,X1),X48)),X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image_Oreindex) ).

fof(fact_transpose__column__length,axiom,
    ! [X70,X212,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))),X212)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X70),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X212)))
       => 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),X70)),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),c_List_Otranspose(X5,X212))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),X212),X70)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__column__length) ).

fof(fact_pair__imageI,axiom,
    ! [X2,X38,X11,X17,X6,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17)),X11))
     => hBOOL(hAPP(hAPP(c_member(X38),hAPP(hAPP(X2,X6),X17)),hAPP(c_Set_Oimage(tc_prod(X5,X16),X38,hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,X38),X2)),X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__imageI) ).

fof(fact_length__filter__map,axiom,
    ! [X212,X2,X16,X29,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X29),hAPP(hAPP(c_List_Omap(X16,X5),X2),X212))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),hAPP(c_List_Ofilter(X16,hAPP(c_Fun_Ocomp(X5,tc_HOL_Obool,X16,X29),X2)),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__filter__map) ).

fof(fact_weak__map__of__SomeI,axiom,
    ! [X97,X12,X30,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X30),X12)),hAPP(c_List_Oset(tc_prod(X5,X16)),X97)))
     => ? [X3] : hAPP(hAPP(c_Map_Omap__of(X5,X16),X97),X30) = hAPP(c_Option_Ooption_OSome(X16),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_weak__map__of__SomeI) ).

fof(fact_trancl__subset__Sigma__aux,axiom,
    ! [X11,X34,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),c_Transitive__Closure_Ortrancl(X5,X34)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X11),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X11))))
       => ( X6 = X17
          | hBOOL(hAPP(hAPP(c_member(X5),X6),X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__subset__Sigma__aux) ).

fof(fact_sum__length__filter__compl,axiom,
    ! [X212,X29,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,X29),X212))),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),X29)),X212))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__length__filter__compl) ).

fof(fact_rtrancl__trans,axiom,
    ! [X21,X34,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),c_Transitive__Closure_Ortrancl(X5,X34)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X17),X21)),c_Transitive__Closure_Ortrancl(X5,X34)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Ortrancl(X5,X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trans) ).

fof(fact_zdiv__zadd1__eq,axiom,
    ! [X24,X26,X25] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25),X26)),X24) = 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),X25),X24)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26),X24))),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,X25,X24)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X26,X24))),X24)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zadd1__eq) ).

fof(fact_div__add1__eq,axiom,
    ! [X24,X26,X25] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X26)),X24) = 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),X25),X24)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X26),X24))),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,X25,X24)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X24))),X24)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add1__eq) ).

fof(fact_inf2D1,axiom,
    ! [X27,X12,X13,X11,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),X11),X13),X12),X27))
     => hBOOL(hAPP(hAPP(X11,X12),X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2D1) ).

fof(fact_inf2D2,axiom,
    ! [X27,X12,X13,X11,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),X11),X13),X12),X27))
     => hBOOL(hAPP(hAPP(X13,X12),X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2D2) ).

fof(fact_length__takeWhile__less__P__nth,axiom,
    ! [X212,X5,X29,X115] :
      ( ! [X145] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X145),X115))
         => hBOOL(hAPP(X29,hAPP(hAPP(c_List_Onth(X5),X212),X145))) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X115),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X115),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X29,X212)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__takeWhile__less__P__nth) ).

fof(fact_converse__rtrancl__into__rtrancl,axiom,
    ! [X21,X34,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),X34))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X17),X21)),c_Transitive__Closure_Ortrancl(X5,X34)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Ortrancl(X5,X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).

fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [X21,X34,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),c_Transitive__Closure_Ortrancl(X5,X34)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X17),X21)),X34))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X21)),c_Transitive__Closure_Ortrancl(X5,X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).

fof(fact_rtrancl__listrel1__if__listrel,axiom,
    ! [X34,X214,X212,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)),X212),X214)),c_List_Olistrel(X5,X34)))
     => 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)),X212),X214)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X34)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__if__listrel) ).

fof(fact_folding_Ocommute__comps_I1_J,axiom,
    ! [X48,X1,X91,X2,X38,X55,X85,X90,X92,X16,X5] :
      ( c_Finite__Set_Ofolding(X5,X16,X92,X90)
     => hAPP(c_Fun_Ocomp(X85,X55,X38,X2),hAPP(c_Fun_Ocomp(X91,X85,X38,X1),X48)) = hAPP(c_Fun_Ocomp(X91,X55,X38,hAPP(c_Fun_Ocomp(X85,X55,X91,X2),X1)),X48) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ocommute__comps_I1_J) ).

fof(fact_zdiv__mono2__neg__lemma,axiom,
    ! [X141,X142,X143,X123,X128,X26] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X128)),X123) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X143),X142)),X141)
     => ( 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),X143),X142)),X141)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),X26))
         => ( 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),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X143))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X143),X26))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X142),X128)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
    ! [X29] : 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)))),X29)) = 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),X29),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,
    ! [X34,X214,X212,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)),X212),X214)),c_List_Olistrel1(X5,X34)))
     => 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)),X212),X214)),c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X34)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__reflcl__if__listrel1) ).

fof(fact_lexord__lex,axiom,
    ! [X34,X27,X12,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)),X12),X27)),c_List_Olex(X5,X34)))
    <=> ( 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)),X12),X27)),c_List_Olexord(X5,X34)))
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X12) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X27) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__lex) ).

fof(fact_filter__map,axiom,
    ! [X212,X2,X16,X29,X5] : hAPP(c_List_Ofilter(X5,X29),hAPP(hAPP(c_List_Omap(X16,X5),X2),X212)) = hAPP(hAPP(c_List_Omap(X16,X5),X2),hAPP(c_List_Ofilter(X16,hAPP(c_Fun_Ocomp(X5,tc_HOL_Obool,X16,X29),X2)),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__map) ).

fof(fact_wfP__SUP,axiom,
    ! [X5,X34,X16] :
      ( ! [X145] : c_Wellfounded_OwfP(X16,hAPP(X34,X145))
     => ( ! [X145,X124] :
            ( hAPP(X34,X145) != hAPP(X34,X124)
           => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),c_Predicate_ODomainP(X16,X16,hAPP(X34,X145))),c_Predicate_ORangeP(X16,X16,hAPP(X34,X124))) = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)) )
       => c_Wellfounded_OwfP(X16,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_fun(X16,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__SUP) ).

fof(fact_partition__filter__conv,axiom,
    ! [X212,X2,X5] : c_List_Opartition(X5,X2,X212) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X2),X212)),hAPP(c_List_Ofilter(X5,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X5,c_fNot),X2)),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition__filter__conv) ).

fof(fact_upto_Opinduct,axiom,
    ! [X29,X47,X158] :
      ( 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),X158),X47)))
     => ( ! [X145,X124] :
            ( 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),X145),X124)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X145),X124))
               => hBOOL(hAPP(hAPP(X29,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X145),c_Groups_Oone__class_Oone(tc_Int_Oint))),X124)) )
             => hBOOL(hAPP(hAPP(X29,X145),X124)) ) )
       => hBOOL(hAPP(hAPP(X29,X158),X47)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upto_Opinduct) ).

fof(fact_list__all2__map1,axiom,
    ! [X234,X235,X2,X38,X29,X16,X5] :
      ( c_List_Olist__all2(X5,X16,X29,hAPP(hAPP(c_List_Omap(X38,X5),X2),X235),X234)
    <=> c_List_Olist__all2(X38,X16,hAPP(hAPP(c_COMBB(X5,tc_fun(X16,tc_HOL_Obool),X38),X29),X2),X235,X234) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__map1) ).

fof(fact_map__add__upds,axiom,
    ! [X214,X212,X202,X203,X16,X5] : c_Map_Omap__add(X5,X16,X203,c_Map_Omap__upds(X5,X16,X202,X212,X214)) = c_Map_Omap__upds(X5,X16,c_Map_Omap__add(X5,X16,X203,X202),X212,X214),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__upds) ).

fof(fact_measures__lesseq,axiom,
    ! [X261,X5,X27,X12,X2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X2,X12)),hAPP(X2,X27)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_List_Omeasures(X5,X261)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_List_Omeasures(X5,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X5,tc_Nat_Onat)),X2),X261)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measures__lesseq) ).

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,
    ! [X100,X26,X25] : 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),X25),X26)),X26)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26))),X100) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25),X100),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmod__equality2) ).

fof(fact_dom__map__upds,axiom,
    ! [X214,X212,X45,X16,X5] : c_Map_Odom(X5,X16,c_Map_Omap__upds(X5,X16,X45,X212,X214)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)),X212))),c_Map_Odom(X5,X16,X45)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dom__map__upds) ).

fof(fact_INFI__set__fold,axiom,
    ! [X2,X212,X16,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,X5),hAPP(c_List_Oset(X16),X212)),X2) = hAPP(c_List_Ofoldl(X5,X16,hAPP(c_COMBC(X16,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X16),c_Lattices_Osemilattice__inf__class_Oinf(X5)),X2)),c_Orderings_Otop__class_Otop(X5)),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INFI__set__fold) ).

fof(fact_SUPR__set__fold,axiom,
    ! [X2,X212,X16,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,X5),hAPP(c_List_Oset(X16),X212)),X2) = hAPP(c_List_Ofoldl(X5,X16,hAPP(c_COMBC(X16,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X16),c_Lattices_Osemilattice__sup__class_Osup(X5)),X2)),c_Orderings_Obot__class_Obot(X5)),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUPR__set__fold) ).

fof(fact_finite__UN__I,axiom,
    ! [X13,X16,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( ! [X74] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X74),X11))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X16),hAPP(X13,X74))) )
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X16),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X11),X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UN__I) ).

fof(fact_finite__UN,axiom,
    ! [X13,X16,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X11),X13)))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X16),hAPP(X13,X3))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UN) ).

fof(fact_rel__comp__UNION__distrib,axiom,
    ! [X34,X68,X55,X84,X16,X38,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X38,X16),X84),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X55,tc_fun(tc_prod(X38,X16),tc_HOL_Obool)),X68),X34)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X55,tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X68),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X38,X16),tc_HOL_Obool),tc_fun(tc_prod(X5,X16),tc_HOL_Obool),X55),hAPP(c_Relation_Orel__comp(X5,X38,X16),X84)),X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__UNION__distrib) ).

fof(fact_weak__coinduct__image,axiom,
    ! [X2,X1,X16,X31,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X31))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X16,X1),X31)),hAPP(X2,hAPP(c_Set_Oimage(X5,X16,X1),X31))))
       => hBOOL(hAPP(hAPP(c_member(X16),hAPP(X1,X6)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X16,tc_HOL_Obool),X2))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_weak__coinduct__image) ).

fof(fact_o__assoc,axiom,
    ! [X48,X1,X55,X2,X5,X16,X38] : hAPP(c_Fun_Ocomp(X38,X16,X5,X2),hAPP(c_Fun_Ocomp(X55,X38,X5,X1),X48)) = hAPP(c_Fun_Ocomp(X55,X16,X5,hAPP(c_Fun_Ocomp(X38,X16,X55,X2),X1)),X48),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__assoc) ).

fof(fact_surj__Compl__image__subset,axiom,
    ! [X11,X2,X5,X16] :
      ( hAPP(c_Set_Oimage(X16,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X16,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(X16,X5,X2),X11))),hAPP(c_Set_Oimage(X16,X5,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X16,tc_HOL_Obool)),X11)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__Compl__image__subset) ).

fof(fact_in__inv__image,axiom,
    ! [X2,X34,X16,X27,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),hAPP(hAPP(c_Relation_Oinv__image(X16,X5),X34),X2)))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X16)),hAPP(hAPP(c_Product__Type_OPair(X16,X16),hAPP(X2,X12)),hAPP(X2,X27))),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__inv__image) ).

fof(fact_folding_Oremove,axiom,
    ! [X12,X11,X90,X2,X16,X5] :
      ( c_Finite__Set_Ofolding(X5,X16,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(X90,X11) = hAPP(c_Fun_Ocomp(X16,X16,X16,hAPP(X90,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),hAPP(X2,X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Oremove) ).

fof(fact_Image__subset,axiom,
    ! [X19,X13,X11,X34,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X34),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X13))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X16,X34),X19)),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__subset) ).

fof(fact_tl__append,axiom,
    ! [X214,X212,X5] : hAPP(c_List_Otl(X5),hAPP(hAPP(c_List_Oappend(X5),X212),X214)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X5),X5,hAPP(c_List_Otl(X5),X214),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)),X214))),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl__append) ).

fof(fact_pos__map__def,axiom,
    ! [X29,X2,X5,X16] : c_New__Random__Sequence_Opos__map(X16,X5,X2,X29) = c_New__Random__Sequence_Opos__bind(X16,X5,X29,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))))),X16,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,
    ! [X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X16,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X16,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X16,X2),X11)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__Compl__subset) ).

fof(fact_folding_Oinsert__remove,axiom,
    ! [X12,X11,X90,X2,X16,X5] :
      ( c_Finite__Set_Ofolding(X5,X16,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(X90,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(c_Fun_Ocomp(X16,X16,X16,hAPP(X90,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),hAPP(X2,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Oinsert__remove) ).

fof(fact_list__all2__update__cong2,axiom,
    ! [X70,X27,X12,X214,X212,X29,X16,X5] :
      ( c_List_Olist__all2(X5,X16,X29,X212,X214)
     => ( hBOOL(hAPP(hAPP(X29,X12),X27))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X70),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)))
         => c_List_Olist__all2(X5,X16,X29,hAPP(hAPP(c_List_Olist__update(X5,X212),X70),X12),hAPP(hAPP(c_List_Olist__update(X16,X214),X70),X27)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__update__cong2) ).

fof(fact_list__all2__update__cong,axiom,
    ! [X27,X12,X214,X29,X16,X212,X5,X70] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X70),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
     => ( c_List_Olist__all2(X5,X16,X29,X212,X214)
       => ( hBOOL(hAPP(hAPP(X29,X12),X27))
         => c_List_Olist__all2(X5,X16,X29,hAPP(hAPP(c_List_Olist__update(X5,X212),X70),X12),hAPP(hAPP(c_List_Olist__update(X16,X214),X70),X27)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__update__cong) ).

fof(fact_setprod__pos,axiom,
    ! [X2,X11,X5,X16] :
      ( class_Rings_Olinordered__semidom(X16)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16),c_Groups_Ozero__class_Ozero(X16)),hAPP(X2,X3))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16),c_Groups_Ozero__class_Ozero(X16)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),X11))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__pos) ).

fof(fact_setprod__nonneg,axiom,
    ! [X2,X11,X5,X16] :
      ( class_Rings_Olinordered__semidom(X16)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),c_Groups_Ozero__class_Ozero(X16)),hAPP(X2,X3))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),c_Groups_Ozero__class_Ozero(X16)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),X11))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__nonneg) ).

fof(fact_converse__pred__comp,axiom,
    ! [X84,X34,X38,X5,X16] : c_Predicate_Oconversep(X16,X5,c_Predicate_Opred__comp(X16,X38,X5,X34,X84)) = c_Predicate_Opred__comp(X5,X38,X16,c_Predicate_Oconversep(X38,X5,X84),c_Predicate_Oconversep(X16,X38,X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__pred__comp) ).

fof(fact_folding_Ocommute__left__comp_H_H,axiom,
    ! [X1,X38,X13,X11,X90,X2,X16,X5] :
      ( c_Finite__Set_Ofolding(X5,X16,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => hAPP(c_Fun_Ocomp(X16,X16,X38,hAPP(X90,X13)),hAPP(c_Fun_Ocomp(X16,X16,X38,hAPP(X90,X11)),X1)) = hAPP(c_Fun_Ocomp(X16,X16,X38,hAPP(X90,X11)),hAPP(c_Fun_Ocomp(X16,X16,X38,hAPP(X90,X13)),X1)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp_H_H) ).

fof(fact_inv__def,axiom,
    ! [X27,X2,X16,X5] : hAPP(c_Hilbert__Choice_Oinv__into(X5,X16,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),X27) = c_Hilbert__Choice_OEps(X5,hAPP(hAPP(c_COMBC(X5,X16,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X16,tc_fun(X16,tc_HOL_Obool),X5),c_fequal),X2)),X27)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__def) ).

fof(fact_finite__SigmaI,axiom,
    ! [X13,X16,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( ! [X74] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X74),X11))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X16),hAPP(X13,X74))) )
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__SigmaI) ).

fof(fact_convex__bound__lt,axiom,
    ! [X126,X120,X22,X25,X14,X15] :
      ( class_Rings_Olinordered__semiring__1__strict(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),X25))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X120))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X126))
             => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X120),X126) = c_Groups_Oone__class_Oone(X15)
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X120),X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X126),X22))),X25)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__lt) ).

fof(fact_convex__bound__le,axiom,
    ! [X126,X120,X22,X25,X14,X15] :
      ( class_Rings_Olinordered__semiring__1(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X25))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X120))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X126))
             => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X120),X126) = c_Groups_Oone__class_Oone(X15)
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X120),X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X126),X22))),X25)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__le) ).

fof(fact_aset_I6_J,axiom,
    ! [X11,X10,X18] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10),c_Groups_Oone__class_Oone(tc_Int_Oint))),X11))
       => ! [X3] :
            ( ! [X39] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X39),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X18)))
               => ! [X179] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X179),X11))
                   => X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X179),X39) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X10))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X18)),X10)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I6_J) ).

fof(fact_map__of__is__SomeI,axiom,
    ! [X27,X12,X210,X16,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Omap(tc_prod(X5,X16),X5),c_Product__Type_Ofst(X5,X16)),X210)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X12),X27)),hAPP(c_List_Oset(tc_prod(X5,X16)),X210)))
       => hAPP(hAPP(c_Map_Omap__of(X5,X16),X210),X12) = hAPP(c_Option_Ooption_OSome(X16),X27) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__is__SomeI) ).

fof(fact_map__of__eq__Some__iff,axiom,
    ! [X27,X12,X210,X16,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Omap(tc_prod(X5,X16),X5),c_Product__Type_Ofst(X5,X16)),X210)))
     => ( hAPP(hAPP(c_Map_Omap__of(X5,X16),X210),X12) = hAPP(c_Option_Ooption_OSome(X16),X27)
      <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X12),X27)),hAPP(c_List_Oset(tc_prod(X5,X16)),X210))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__eq__Some__iff) ).

fof(fact_Some__eq__map__of__iff,axiom,
    ! [X12,X27,X210,X16,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Omap(tc_prod(X5,X16),X5),c_Product__Type_Ofst(X5,X16)),X210)))
     => ( hAPP(c_Option_Ooption_OSome(X16),X27) = hAPP(hAPP(c_Map_Omap__of(X5,X16),X210),X12)
      <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X12),X27)),hAPP(c_List_Oset(tc_prod(X5,X16)),X210))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Some__eq__map__of__iff) ).

fof(fact_coinduct__set,axiom,
    ! [X31,X6,X2,X5] :
      ( c_Orderings_Oorder__class_Omono(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X2)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X31))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X31),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X31),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),X2)))))
         => hBOOL(hAPP(hAPP(c_member(X5),X6),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),X2))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coinduct__set) ).

fof(fact_folding_Ocommute__left__comp_H,axiom,
    ! [X1,X12,X38,X11,X90,X2,X16,X5] :
      ( c_Finite__Set_Ofolding(X5,X16,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(c_Fun_Ocomp(X16,X16,X38,hAPP(X2,X12)),hAPP(c_Fun_Ocomp(X16,X16,X38,hAPP(X90,X11)),X1)) = hAPP(c_Fun_Ocomp(X16,X16,X38,hAPP(X90,X11)),hAPP(c_Fun_Ocomp(X16,X16,X38,hAPP(X2,X12)),X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp_H) ).

fof(fact_listrel1I,axiom,
    ! [X214,X245,X246,X212,X34,X27,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),X34))
     => ( X212 = hAPP(hAPP(c_List_Oappend(X5),X246),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X245))
       => ( X214 = hAPP(hAPP(c_List_Oappend(X5),X246),hAPP(hAPP(c_List_Olist_OCons(X5),X27),X245))
         => 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)),X212),X214)),c_List_Olistrel1(X5,X34))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1I) ).

fof(fact_all__nth__imp__all__set,axiom,
    ! [X12,X29,X212,X5] :
      ( ! [X145] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X145),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
         => hBOOL(hAPP(X29,hAPP(hAPP(c_List_Onth(X5),X212),X145))) )
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => hBOOL(hAPP(X29,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nth__imp__all__set) ).

fof(fact_sum__case__inject,axiom,
    ! [X187,X188,X88,X89,X16,X38,X5] :
      ( c_Sum__Type_Osum_Osum__case(X5,X38,X16,X89,X88) = c_Sum__Type_Osum_Osum__case(X5,X38,X16,X188,X187)
     => ~ ( X89 = X188
         => X88 != X187 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__case__inject) ).

fof(fact_inf__le__fold__inf,axiom,
    ! [X21,X17,X11,X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),X3)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X17),X21)),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X21),X11))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le__fold__inf) ).

fof(fact_min__max_Oinf__le__fold__inf,axiom,
    ! [X21,X17,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),X3)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X17),X21)),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X21),X11))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__le__fold__inf) ).

fof(fact_setsum__shift__bounds__nat__ivl,axiom,
    ! [X76,X30,X45,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),X45),X30)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X76),X30))) = 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)),X30))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__shift__bounds__nat__ivl) ).

fof(fact_in__rtrancl__UnI,axiom,
    ! [X35,X36,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X12),c_Transitive__Closure_Ortrancl(X5,X36)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X12),c_Transitive__Closure_Ortrancl(X5,X35))) )
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X12),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X36),X35)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__rtrancl__UnI) ).

fof(fact_folding_Ocommute__left__comp,axiom,
    ! [X1,X12,X27,X38,X90,X2,X16,X5] :
      ( c_Finite__Set_Ofolding(X5,X16,X2,X90)
     => hAPP(c_Fun_Ocomp(X16,X16,X38,hAPP(X2,X27)),hAPP(c_Fun_Ocomp(X16,X16,X38,hAPP(X2,X12)),X1)) = hAPP(c_Fun_Ocomp(X16,X16,X38,hAPP(X2,X12)),hAPP(c_Fun_Ocomp(X16,X16,X38,hAPP(X2,X27)),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp) ).

fof(fact_mono__Int,axiom,
    ! [X13,X11,X2,X16,X5] :
      ( c_Orderings_Oorder__class_Omono(tc_fun(X5,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X2)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),hAPP(X2,X11)),hAPP(X2,X13)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mono__Int) ).

fof(fact_range__ex1__eq,axiom,
    ! [X17,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_member(X16),X17),hAPP(c_Set_Oimage(X5,X16,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
      <=> ? [X3] :
            ( X17 = hAPP(X2,X3)
            & ! [X33] :
                ( X17 = hAPP(X2,X33)
               => X33 = X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__ex1__eq) ).

fof(fact_setsum__Un,axiom,
    ! [X2,X13,X11,X5,X16] :
      ( class_Groups_Oab__group__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X16),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X13))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__Un) ).

fof(fact_rev__update,axiom,
    ! [X22,X221,X15,X100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X100),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
     => hAPP(c_List_Orev(X15),hAPP(hAPP(c_List_Olist__update(X15,X221),X100),X22)) = hAPP(hAPP(c_List_Olist__update(X15,hAPP(c_List_Orev(X15),X221)),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(X15)),X221)),X100)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__update) ).

fof(fact_Collect__imp__eq,axiom,
    ! [X28,X29,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),X29)),X28)) = 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),X29))),hAPP(c_Set_OCollect(X5),X28)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__imp__eq) ).

fof(fact_single__valued__def,axiom,
    ! [X34,X16,X5] :
      ( c_Relation_Osingle__valued(X5,X16,X34)
    <=> ! [X3,X33] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X3),X33)),X34))
         => ! [X44] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X3),X44)),X34))
             => X33 = X44 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__def) ).

fof(fact_prod__size__simp,axiom,
    ! [X161,X1,X2,X16,X5] : c_Product__Type_Oprod_Oprod__size(X5,X16,X2,X1,X161) = 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,X16),X161))),hAPP(X1,hAPP(c_Product__Type_Osnd(X5,X16),X161)))),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,
    ! [X76,X30,X45,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),X45),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X76),X30))) = 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)),X30))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X45,X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__shift__bounds__cl__nat__ivl) ).

fof(fact_bset_I8_J,axiom,
    ! [X13,X10,X18] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10),c_Groups_Oone__class_Oone(tc_Int_Oint))),X13))
       => ! [X3] :
            ( ! [X39] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X39),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X18)))
               => ! [X179] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X179),X13))
                   => X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X179),X39) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10),X3))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X18))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I8_J) ).

fof(fact_finite__equiv__class,axiom,
    ! [X31,X34,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X11),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X11))))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X31),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X11),X34)))
         => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X31)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__equiv__class) ).

fof(fact_quotient__eqI,axiom,
    ! [X27,X12,X42,X31,X34,X11,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X11,X34)
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X31),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X11),X34)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X42),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X11),X34)))
         => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X31))
           => ( hBOOL(hAPP(hAPP(c_member(X5),X27),X42))
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),X34))
               => X31 = X42 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__eqI) ).

fof(fact_quotient__eq__iff,axiom,
    ! [X27,X12,X42,X31,X34,X11,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X11,X34)
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X31),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X11),X34)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X42),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X11),X34)))
         => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X31))
           => ( hBOOL(hAPP(hAPP(c_member(X5),X27),X42))
             => ( X31 = X42
              <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),X34)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__eq__iff) ).

fof(fact_field__le__mult__one__interval,axiom,
    ! [X22,X14,X15] :
      ( class_Fields_Olinordered__field__inverse__zero(X15)
     => ( ! [X44] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X44))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X44),c_Groups_Oone__class_Oone(X15)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X44),X14)),X22)) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__le__mult__one__interval) ).

fof(fact_eq__comp__r,axiom,
    ! [X36,X5] : c_Predicate_Opred__comp(X5,X5,X5,c_fequal,c_Predicate_Opred__comp(X5,X5,X5,X36,c_fequal)) = X36,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__comp__r) ).

fof(fact_vimage__eq__UN,axiom,
    ! [X13,X2,X16,X5] : hAPP(c_Set_Ovimage(X5,X16,X2),X13) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X13),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X16),c_Set_Ovimage(X5,X16,X2)),hAPP(hAPP(c_COMBC(X16,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),c_Set_Oinsert(X16)),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__eq__UN) ).

fof(fact_Image__eq__UN,axiom,
    ! [X13,X34,X5,X16] : hAPP(c_Relation_OImage(X16,X5,X34),X13) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X13),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X16),c_Relation_OImage(X16,X5,X34)),hAPP(hAPP(c_COMBC(X16,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),c_Set_Oinsert(X16)),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__eq__UN) ).

fof(fact_min__max_Odistrib__inf__le,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),X22)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),X23))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X22),X23)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Odistrib__inf__le) ).

fof(fact_distrib__inf__le,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Lattices_Olattice(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X22)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X23))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X22),X23)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distrib__inf__le) ).

fof(fact_SUP2__I,axiom,
    ! [X38,X16,X21,X17,X13,X11,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
     => ( hBOOL(hAPP(hAPP(hAPP(X13,X6),X17),X21))
       => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_fun(X38,tc_HOL_Obool))),X11),X13),X17),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP2__I) ).

fof(fact_map__of__inject__set,axiom,
    ! [X214,X212,X16,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Omap(tc_prod(X5,X16),X5),c_Product__Type_Ofst(X5,X16)),X212)))
     => ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Omap(tc_prod(X5,X16),X5),c_Product__Type_Ofst(X5,X16)),X214)))
       => ( hAPP(c_Map_Omap__of(X5,X16),X212) = hAPP(c_Map_Omap__of(X5,X16),X214)
        <=> hAPP(c_List_Oset(tc_prod(X5,X16)),X212) = hAPP(c_List_Oset(tc_prod(X5,X16)),X214) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__inject__set) ).

fof(fact_splitD_H,axiom,
    ! [X21,X17,X6,X36,X38,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_fun(X38,tc_HOL_Obool)),X36),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17)),X21))
     => hBOOL(hAPP(hAPP(hAPP(X36,X6),X17),X21)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splitD_H) ).

fof(fact_rel__comp__distrib2,axiom,
    ! [X36,X108,X35,X16,X38,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X38,X16),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X38),tc_HOL_Obool)),X35),X108)),X36) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X38,X16),X35),X36)),hAPP(hAPP(c_Relation_Orel__comp(X5,X38,X16),X108),X36)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__distrib2) ).

fof(fact_inf__INFI__fold__inf,axiom,
    ! [X2,X13,X11,X5,X16] :
      ( class_Complete__Lattice_Ocomplete__lattice(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16),X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X16),X11),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,hAPP(hAPP(c_COMBB(X16,tc_fun(X16,X16),X5),c_Lattices_Osemilattice__inf__class_Oinf(X16)),X2)),X13),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__INFI__fold__inf) ).

fof(fact_sup__SUPR__fold__sup,axiom,
    ! [X2,X13,X11,X5,X16] :
      ( class_Complete__Lattice_Ocomplete__lattice(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X16),X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X16),X11),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,hAPP(hAPP(c_COMBB(X16,tc_fun(X16,X16),X5),c_Lattices_Osemilattice__sup__class_Osup(X16)),X2)),X13),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__SUPR__fold__sup) ).

fof(fact_fun__upd__twist,axiom,
    ! [X20,X17,X45,X16,X5,X21,X6] :
      ( X6 != X21
     => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),X45),X6),X17)),X21),X20) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),X45),X21),X20)),X6),X17) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__twist) ).

fof(fact_setsum__Un__nat,axiom,
    ! [X2,X13,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
       => 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)),X11),X13)) = 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),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X13))),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)),X11),X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__Un__nat) ).

fof(fact_finite__Collect__not,axiom,
    ! [X29,X5] :
      ( 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_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X29))))
      <=> 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_zmult2__lemma__aux1,axiom,
    ! [X128,X123,X26,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),X123))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X123),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),X26),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),c_Divides_Odiv__class_Omod(tc_Int_Oint,X128,X24))),X123))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma__aux1) ).

fof(fact_nat__diff__add__eq2,axiom,
    ! [X98,X99,X120,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X101))
     => 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),X102),X120)),X99)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X120)),X98)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),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),X101),X102)),X120)),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).

fof(fact_abs__setsum__abs,axiom,
    ! [X11,X2,X16,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(X16,X5),hAPP(hAPP(c_COMBB(X5,X5,X16),c_Groups_Oabs__class_Oabs(X5)),X2)),X11)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),hAPP(hAPP(c_COMBB(X5,X5,X16),c_Groups_Oabs__class_Oabs(X5)),X2)),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__setsum__abs) ).

fof(fact_map__upds__list__update2__drop,axiom,
    ! [X27,X45,X214,X16,X70,X212,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)),X70))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X70),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)))
       => c_Map_Omap__upds(X5,X16,X45,X212,hAPP(hAPP(c_List_Olist__update(X16,X214),X70),X27)) = c_Map_Omap__upds(X5,X16,X45,X212,X214) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__upds__list__update2__drop) ).

fof(fact_inj__image__subset__iff,axiom,
    ! [X13,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X16,X2),X11)),hAPP(c_Set_Oimage(X5,X16,X2),X13)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).

fof(fact_map__of__zip__enum__inject,axiom,
    ! [X214,X212,X5,X16] :
      ( ( class_Enum_Oenum(X16)
        & class_Enum_Oenum(X5) )
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),c_Enum_Oenum__class_Oenum(X16))
       => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X214) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),c_Enum_Oenum__class_Oenum(X16))
         => ( hAPP(c_Fun_Ocomp(tc_Option_Ooption(X5),X5,X16,c_Option_Othe(X5)),hAPP(c_Map_Omap__of(X16,X5),hAPP(hAPP(c_List_Ozip(X16,X5),c_Enum_Oenum__class_Oenum(X16)),X212))) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(X5),X5,X16,c_Option_Othe(X5)),hAPP(c_Map_Omap__of(X16,X5),hAPP(hAPP(c_List_Ozip(X16,X5),c_Enum_Oenum__class_Oenum(X16)),X214)))
           => X212 = X214 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__zip__enum__inject) ).

fof(fact_gt__half__sum,axiom,
    ! [X26,X25,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),c_Groups_Oone__class_Oone(X15)),c_Groups_Oone__class_Oone(X15)))),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gt__half__sum) ).

fof(fact_inv__into__injective,axiom,
    ! [X27,X12,X2,X11,X16,X5] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(X5,X16,X11,X2),X12) = hAPP(c_Hilbert__Choice_Oinv__into(X5,X16,X11,X2),X27)
     => ( hBOOL(hAPP(hAPP(c_member(X16),X12),hAPP(c_Set_Oimage(X5,X16,X2),X11)))
       => ( hBOOL(hAPP(hAPP(c_member(X16),X27),hAPP(c_Set_Oimage(X5,X16,X2),X11)))
         => X12 = X27 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__injective) ).

fof(fact_list__all2__Cons,axiom,
    ! [X214,X27,X212,X12,X29,X16,X5] :
      ( c_List_Olist__all2(X5,X16,X29,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212),hAPP(hAPP(c_List_Olist_OCons(X16),X27),X214))
    <=> ( hBOOL(hAPP(hAPP(X29,X12),X27))
        & c_List_Olist__all2(X5,X16,X29,X212,X214) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__Cons) ).

fof(fact_q__neg__lemma,axiom,
    ! [X141,X142,X143] :
      ( 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),X143),X142)),X141)),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)),X141))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X143))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X142),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__neg__lemma) ).

fof(fact_zip__same,axiom,
    ! [X212,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),hAPP(c_List_Oset(tc_prod(X5,X5)),hAPP(hAPP(c_List_Ozip(X5,X5),X212),X212))))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_List_Oset(X5),X212)))
        & X6 = X17 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__same) ).

fof(fact_set__zip__leftD,axiom,
    ! [X214,X212,X27,X12,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X12),X27)),hAPP(c_List_Oset(tc_prod(X5,X16)),hAPP(hAPP(c_List_Ozip(X5,X16),X212),X214))))
     => hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__zip__leftD) ).

fof(fact_set__zip__rightD,axiom,
    ! [X214,X212,X27,X12,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X12),X27)),hAPP(c_List_Oset(tc_prod(X5,X16)),hAPP(hAPP(c_List_Ozip(X5,X16),X212),X214))))
     => hBOOL(hAPP(hAPP(c_member(X16),X27),hAPP(c_List_Oset(X16),X214))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__zip__rightD) ).

fof(fact_folding_Ounion__inter,axiom,
    ! [X13,X11,X90,X2,X16,X5] :
      ( c_Finite__Set_Ofolding(X5,X16,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => hAPP(c_Fun_Ocomp(X16,X16,X16,hAPP(X90,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13))),hAPP(X90,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13))) = hAPP(c_Fun_Ocomp(X16,X16,X16,hAPP(X90,X11)),hAPP(X90,X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ounion__inter) ).

fof(fact_mono__Un,axiom,
    ! [X13,X11,X2,X16,X5] :
      ( c_Orderings_Oorder__class_Omono(tc_fun(X5,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X2)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),hAPP(X2,X11)),hAPP(X2,X13))),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mono__Un) ).

fof(fact_abs__triangle__ineq3,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),hAPP(c_Groups_Oabs__class_Oabs(X15),X26)))),hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X25),X26)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq3) ).

fof(fact_odd__less__0,axiom,
    ! [X37] :
      ( 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)),X37)),X37)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),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,X11,X5,X16] :
      ( class_Complete__Lattice_Ocomplete__lattice(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X16),X11),X2) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,hAPP(hAPP(c_COMBB(X16,tc_fun(X16,X16),X5),c_Lattices_Osemilattice__inf__class_Oinf(X16)),X2)),c_Orderings_Otop__class_Otop(X16)),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INFI__fold__inf) ).

fof(fact_SUPR__fold__sup,axiom,
    ! [X2,X11,X5,X16] :
      ( class_Complete__Lattice_Ocomplete__lattice(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X16),X11),X2) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,hAPP(hAPP(c_COMBB(X16,tc_fun(X16,X16),X5),c_Lattices_Osemilattice__sup__class_Osup(X16)),X2)),c_Orderings_Obot__class_Obot(X16)),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUPR__fold__sup) ).

fof(fact_single__valuedD,axiom,
    ! [X37,X27,X12,X34,X16,X5] :
      ( c_Relation_Osingle__valued(X5,X16,X34)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X12),X27)),X34))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X12),X37)),X34))
         => X27 = X37 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valuedD) ).

fof(fact_Collect__disj__eq,axiom,
    ! [X28,X29,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),X29)),X28)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X29)),hAPP(c_Set_OCollect(X5),X28)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__disj__eq) ).

fof(fact_Collect__conj__eq,axiom,
    ! [X28,X29,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),X29)),X28)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X29)),hAPP(c_Set_OCollect(X5),X28)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__conj__eq) ).

fof(fact_list__all2__dropI,axiom,
    ! [X76,X234,X235,X29,X16,X5] :
      ( c_List_Olist__all2(X5,X16,X29,X235,X234)
     => c_List_Olist__all2(X5,X16,X29,hAPP(hAPP(c_List_Odrop(X5),X76),X235),hAPP(hAPP(c_List_Odrop(X16),X76),X234)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__dropI) ).

fof(fact_list__all2__takeI,axiom,
    ! [X76,X214,X212,X29,X16,X5] :
      ( c_List_Olist__all2(X5,X16,X29,X212,X214)
     => c_List_Olist__all2(X5,X16,X29,hAPP(hAPP(c_List_Otake(X5),X76),X212),hAPP(hAPP(c_List_Otake(X16),X76),X214)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__takeI) ).

fof(fact_rtrancl__converseD,axiom,
    ! [X34,X27,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_Transitive__Closure_Ortrancl(X5,hAPP(c_Relation_Oconverse(X5,X5),X34))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X27),X12)),c_Transitive__Closure_Ortrancl(X5,X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__converseD) ).

fof(fact_listsum__const__mult,axiom,
    ! [X212,X2,X21,X16,X5] :
      ( class_Rings_Osemiring__0(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X16,X5),hAPP(hAPP(c_COMBB(X5,X5,X16),hAPP(c_Groups_Otimes__class_Otimes(X5),X21)),X2)),X212)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X16,X5),X2),X212))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__const__mult) ).

fof(fact_Image__mono,axiom,
    ! [X11,X53,X34,X61,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X61),X34))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X53),X11))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X16,X61),X53)),hAPP(c_Relation_OImage(X5,X16,X34),X11))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__mono) ).

fof(fact_mlex__leq,axiom,
    ! [X36,X5,X27,X12,X2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X2,X12)),hAPP(X2,X27)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),X36))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_Wellfounded_Omlex__prod(X5,X2,X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__leq) ).

fof(fact_swap__product,axiom,
    ! [X13,X11,X5,X16] : hAPP(c_Set_Oimage(tc_prod(X16,X5),tc_prod(X5,X16),hAPP(c_Product__Type_Oprod_Oprod__case(X16,X5,tc_prod(X5,X16)),hAPP(c_COMBC(X5,X16,tc_prod(X5,X16)),c_Product__Type_OPair(X5,X16)))),hAPP(hAPP(c_Product__Type_OSigma(X16,X5),X11),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X16),X13))) = hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X13),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_swap__product) ).

fof(fact_map__of__zip__is__Some,axiom,
    ! [X12,X214,X16,X212,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
      <=> ? [X33] : hAPP(hAPP(c_Map_Omap__of(X5,X16),hAPP(hAPP(c_List_Ozip(X5,X16),X212),X214)),X12) = hAPP(c_Option_Ooption_OSome(X16),X33) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__zip__is__Some) ).

fof(fact_quotientI,axiom,
    ! [X34,X11,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
     => hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X34),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X11),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotientI) ).

fof(fact_Image__singleton__iff,axiom,
    ! [X6,X34,X16,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(c_Relation_OImage(X16,X5,X34),hAPP(hAPP(c_Set_Oinsert(X16),X6),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))))))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X5)),hAPP(hAPP(c_Product__Type_OPair(X16,X5),X6),X17)),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__singleton__iff) ).

fof(fact_lfp__induct,axiom,
    ! [X29,X2,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( c_Orderings_Oorder__class_Omono(X5,X5,X2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Inductive_Ocomplete__lattice__class_Olfp(X5,X2)),X29))),X29))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Inductive_Ocomplete__lattice__class_Olfp(X5,X2)),X29)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lfp__induct) ).

fof(fact_list__all2__rev,axiom,
    ! [X214,X212,X29,X16,X5] :
      ( c_List_Olist__all2(X5,X16,X29,hAPP(c_List_Orev(X5),X212),hAPP(c_List_Orev(X16),X214))
    <=> c_List_Olist__all2(X5,X16,X29,X212,X214) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__rev) ).

fof(fact_norm__frac_Opinduct,axiom,
    ! [X29,X47,X158] :
      ( 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),X158),X47)))
     => ( ! [X74,X52] :
            ( 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),X74),X52)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X52),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
               => hBOOL(hAPP(hAPP(X29,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X74)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X52))) )
             => hBOOL(hAPP(hAPP(X29,X74),X52)) ) )
       => hBOOL(hAPP(hAPP(X29,X158),X47)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__frac_Opinduct) ).

fof(fact_aset_I5_J,axiom,
    ! [X11,X10,X18] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X10),X11))
       => ! [X3] :
            ( ! [X39] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X39),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X18)))
               => ! [X179] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X179),X11))
                   => X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X179),X39) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X10))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X18)),X10)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I5_J) ).

fof(fact_div__mod__equality2,axiom,
    ! [X24,X25,X26,X15] :
      ( class_Divides_Osemiring__div(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),X25),X26))),c_Divides_Odiv__class_Omod(X15,X25,X26))),X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mod__equality2) ).

fof(fact_list__all2__rev1,axiom,
    ! [X214,X212,X29,X16,X5] :
      ( c_List_Olist__all2(X5,X16,X29,hAPP(c_List_Orev(X5),X212),X214)
    <=> c_List_Olist__all2(X5,X16,X29,X212,hAPP(c_List_Orev(X16),X214)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__rev1) ).

fof(fact_map__upds__Cons,axiom,
    ! [X234,X17,X235,X6,X45,X16,X5] : c_Map_Omap__upds(X5,X16,X45,hAPP(hAPP(c_List_Olist_OCons(X5),X6),X235),hAPP(hAPP(c_List_Olist_OCons(X16),X17),X234)) = c_Map_Omap__upds(X5,X16,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),X45),X6),hAPP(c_Option_Ooption_OSome(X16),X17)),X235,X234),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__upds__Cons) ).

fof(fact_lexord__Nil__left,axiom,
    ! [X34,X27,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)),X27)),c_List_Olexord(X5,X34)))
    <=> ? [X74,X3] : X27 = hAPP(hAPP(c_List_Olist_OCons(X5),X74),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__Nil__left) ).

fof(fact_image__vimage__subset,axiom,
    ! [X11,X2,X16,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X16,X5,X2),hAPP(c_Set_Ovimage(X16,X5,X2),X11))),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__vimage__subset) ).

fof(fact_map__sorted__distinct__set__unique,axiom,
    ! [X214,X212,X2,X5,X16] :
      ( class_Orderings_Olinorder(X16)
     => ( c_Fun_Oinj__on(X5,X16,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X212)),hAPP(c_List_Oset(X5),X214)))
       => ( c_List_Olinorder__class_Osorted(X16,hAPP(hAPP(c_List_Omap(X5,X16),X2),X212))
         => ( hBOOL(hAPP(c_List_Odistinct(X16),hAPP(hAPP(c_List_Omap(X5,X16),X2),X212)))
           => ( c_List_Olinorder__class_Osorted(X16,hAPP(hAPP(c_List_Omap(X5,X16),X2),X214))
             => ( hBOOL(hAPP(c_List_Odistinct(X16),hAPP(hAPP(c_List_Omap(X5,X16),X2),X214)))
               => ( hAPP(c_List_Oset(X5),X212) = hAPP(c_List_Oset(X5),X214)
                 => X212 = X214 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__sorted__distinct__set__unique) ).

fof(fact_zmult2__lemma__aux3,axiom,
    ! [X128,X26,X123,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X123))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),X26))
         => 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),X26),c_Divides_Odiv__class_Omod(tc_Int_Oint,X128,X24))),X123))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma__aux3) ).

fof(fact_finite__quotient,axiom,
    ! [X34,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X11),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X11))))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X11),X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__quotient) ).

fof(fact_foldl__append,axiom,
    ! [X214,X212,X6,X2,X16,X5] : hAPP(c_List_Ofoldl(X5,X16,X2,X6),hAPP(hAPP(c_List_Oappend(X16),X212),X214)) = hAPP(c_List_Ofoldl(X5,X16,X2,hAPP(c_List_Ofoldl(X5,X16,X2,X6),X212)),X214),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__append) ).

fof(fact_rtrancl__converseI,axiom,
    ! [X34,X12,X27,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X27),X12)),c_Transitive__Closure_Ortrancl(X5,X34)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_Transitive__Closure_Ortrancl(X5,hAPP(c_Relation_Oconverse(X5,X5),X34)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__converseI) ).

fof(fact_zip__append1,axiom,
    ! [X242,X225,X221,X5,X15] : hAPP(hAPP(c_List_Ozip(X15,X5),hAPP(hAPP(c_List_Oappend(X15),X221),X225)),X242) = hAPP(hAPP(c_List_Oappend(tc_prod(X15,X5)),hAPP(hAPP(c_List_Ozip(X15,X5),X221),hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),X242))),hAPP(hAPP(c_List_Ozip(X15,X5),X225),hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),X242))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__append1) ).

fof(fact_Diff__subset__conv,axiom,
    ! [X19,X13,X11,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)),X11),X13)),X19))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X13),X19))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__subset__conv) ).

fof(fact_map__add__upd,axiom,
    ! [X27,X12,X1,X2,X16,X5] : c_Map_Omap__add(X5,X16,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),X1),X12),hAPP(c_Option_Ooption_OSome(X16),X27))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),c_Map_Omap__add(X5,X16,X2,X1)),X12),hAPP(c_Option_Ooption_OSome(X16),X27)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__upd) ).

fof(fact_image__surj__f__inv__f,axiom,
    ! [X11,X2,X5,X16] :
      ( hAPP(c_Set_Oimage(X16,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => hAPP(c_Set_Oimage(X16,X5,X2),hAPP(c_Set_Oimage(X5,X16,c_Hilbert__Choice_Oinv__into(X16,X5,c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)),X2)),X11)) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__surj__f__inv__f) ).

fof(fact_bset_I5_J,axiom,
    ! [X10,X13,X18] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18))
     => ! [X3] :
          ( ! [X39] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X39),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X18)))
             => ! [X179] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X179),X13))
                 => X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X179),X39) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X10))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X18)),X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I5_J) ).

fof(fact_bset_I6_J,axiom,
    ! [X10,X13,X18] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18))
     => ! [X3] :
          ( ! [X39] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X39),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X18)))
             => ! [X179] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X179),X13))
                 => X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X179),X39) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X10))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X18)),X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I6_J) ).

fof(fact_setsum__Un__Int,axiom,
    ! [X1,X13,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__Un__Int) ).

fof(fact_setprod_Ounion__inter,axiom,
    ! [X1,X13,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Ounion__inter) ).

fof(fact_setprod__Un__Int,axiom,
    ! [X1,X13,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__Un__Int) ).

fof(fact_inf2I,axiom,
    ! [X16,X5,X13,X27,X12,X11] :
      ( hBOOL(hAPP(hAPP(X11,X12),X27))
     => ( hBOOL(hAPP(hAPP(X13,X12),X27))
       => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),X11),X13),X12),X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2I) ).

fof(fact_vimage__subsetD,axiom,
    ! [X11,X13,X2,X5,X16] :
      ( hAPP(c_Set_Oimage(X16,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X16,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(X16,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X16,X5,X2),X13)),X11))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),hAPP(c_Set_Oimage(X16,X5,X2),X11))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__subsetD) ).

fof(fact_bset_I7_J,axiom,
    ! [X13,X10,X18] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X10),X13))
       => ! [X3] :
            ( ! [X39] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X39),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X18)))
               => ! [X179] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X179),X13))
                   => X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X179),X39) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10),X3))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X18))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I7_J) ).

fof(fact_zdiv__mono2__lemma,axiom,
    ! [X141,X142,X143,X123,X128,X26] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X128)),X123) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X143),X142)),X141)
     => ( 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),X143),X142)),X141)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X141),X143))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X123))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X143))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X143),X26))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X128),X142)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).

fof(fact_converse__INTER,axiom,
    ! [X34,X35,X38,X5,X16] : hAPP(c_Relation_Oconverse(X16,X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X38,tc_fun(tc_prod(X16,X5),tc_HOL_Obool)),X35),X34)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X38,tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X35),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X16,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X16),tc_HOL_Obool),X38),c_Relation_Oconverse(X16,X5)),X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__INTER) ).

fof(fact_converse__UNION,axiom,
    ! [X34,X35,X38,X5,X16] : hAPP(c_Relation_Oconverse(X16,X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,tc_fun(tc_prod(X16,X5),tc_HOL_Obool)),X35),X34)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X35),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X16,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X16),tc_HOL_Obool),X38),c_Relation_Oconverse(X16,X5)),X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__UNION) ).

fof(fact_eq__Abs__Integ,axiom,
    ! [X37] :
      ~ ! [X3,X33] : X37 != 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),X33)),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,
    ! [X11,X2,X16,X37,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X37),hAPP(c_Set_Oimage(X16,X5,X2),X11)))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X16),X3),X11))
          & X37 = hAPP(X2,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__iff) ).

fof(fact_eq__equiv__class__iff2,axiom,
    ! [X27,X12,X34,X11,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X11,X34)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X27),X11))
         => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X34) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),hAPP(hAPP(c_Set_Oinsert(X5),X27),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X34)
          <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),X34)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__equiv__class__iff2) ).

fof(fact_image__inv__into__cancel,axiom,
    ! [X60,X53,X11,X2,X5,X16] :
      ( hAPP(c_Set_Oimage(X16,X5,X2),X11) = X53
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X60),X53))
       => hAPP(c_Set_Oimage(X16,X5,X2),hAPP(c_Set_Oimage(X5,X16,c_Hilbert__Choice_Oinv__into(X16,X5,X11,X2)),X60)) = X60 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__inv__into__cancel) ).

fof(fact_inj__iff,axiom,
    ! [X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
    <=> hAPP(c_Fun_Ocomp(X16,X5,X5,c_Hilbert__Choice_Oinv__into(X5,X16,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,
    ! [X12,X1,X2,X55,X5,X38,X16] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X16,X38,X5),hAPP(c_Fun_Ocomp(X55,tc_fun(X38,X5),X16,X2),X1)),X12) = hAPP(hAPP(X2,hAPP(X1,hAPP(c_Product__Type_Ofst(X16,X38),X12))),hAPP(c_Product__Type_Osnd(X16,X38),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__comp) ).

fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
    ! [X13,X11] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X11),X13))
    <=> 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)),X11)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X13))) ),
    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,
    ! [X13,X11] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X11),X13))
    <=> 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)),X11)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I5_J) ).

fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
    ! [X93,X48,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ! [X3,X33] : hAPP(X48,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X3),X33)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(X48,X3)),hAPP(X48,X33))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X93))
         => ( X93 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X48,c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X93)) = c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(c_Set_Oimage(X5,X5,X48),X93)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ohom__commute) ).

fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
    ! [X93,X48,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ! [X3,X33] : hAPP(X48,hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X3),X33)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),hAPP(X48,X3)),hAPP(X48,X33))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X93))
         => ( X93 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X48,c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X93)) = c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(c_Set_Oimage(X5,X5,X48),X93)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ohom__commute) ).

fof(fact_list__all2__nthD,axiom,
    ! [X161,X214,X212,X29,X16,X5] :
      ( c_List_Olist__all2(X5,X16,X29,X212,X214)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X161),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
       => hBOOL(hAPP(hAPP(X29,hAPP(hAPP(c_List_Onth(X5),X212),X161)),hAPP(hAPP(c_List_Onth(X16),X214),X161))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__nthD) ).

fof(fact_list__all2__nthD2,axiom,
    ! [X161,X214,X212,X29,X16,X5] :
      ( c_List_Olist__all2(X5,X16,X29,X212,X214)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X161),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)))
       => hBOOL(hAPP(hAPP(X29,hAPP(hAPP(c_List_Onth(X5),X212),X161)),hAPP(hAPP(c_List_Onth(X16),X214),X161))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__nthD2) ).

fof(fact_vimage__subsetI,axiom,
    ! [X11,X13,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),X13),hAPP(c_Set_Oimage(X5,X16,X2),X11)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X16,X2),X13)),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__subsetI) ).

fof(fact_converseD,axiom,
    ! [X34,X17,X6,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17)),hAPP(c_Relation_Oconverse(X16,X5),X34)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X5)),hAPP(hAPP(c_Product__Type_OPair(X16,X5),X17),X6)),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converseD) ).

fof(fact_converse__iff,axiom,
    ! [X34,X17,X6,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17)),hAPP(c_Relation_Oconverse(X16,X5),X34)))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X5)),hAPP(hAPP(c_Product__Type_OPair(X16,X5),X17),X6)),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__iff) ).

fof(fact_sup2I1,axiom,
    ! [X13,X16,X5,X27,X12,X11] :
      ( hBOOL(hAPP(hAPP(X11,X12),X27))
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),X11),X13),X12),X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup2I1) ).

fof(fact_sup2I2,axiom,
    ! [X11,X16,X5,X27,X12,X13] :
      ( hBOOL(hAPP(hAPP(X13,X12),X27))
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),X11),X13),X12),X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup2I2) ).

fof(fact_Int__mono,axiom,
    ! [X18,X13,X19,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X19))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),X18))
       => 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)),X11),X13)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X18))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__mono) ).

fof(fact_Diff__mono,axiom,
    ! [X13,X18,X19,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X19))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X18),X13))
       => 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)),X11),X13)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X18))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__mono) ).

fof(fact_Un__mono,axiom,
    ! [X18,X13,X19,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X19))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),X18))
       => 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)),X11),X13)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X18))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__mono) ).

fof(fact_hom__fold1__commute,axiom,
    ! [X93,X48,X5] :
      ( class_Lattices_Oab__semigroup__idem__mult(X5)
     => ( ! [X3,X33] : hAPP(X48,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X33)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(X48,X3)),hAPP(X48,X33))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X93))
         => ( X93 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X48,hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X93)) = hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(c_Set_Oimage(X5,X5,X48),X93)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hom__fold1__commute) ).

fof(fact_setsum_Oreindex,axiom,
    ! [X1,X48,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( c_Fun_Oinj__on(X5,X5,X48,X11)
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),hAPP(c_Set_Oimage(X5,X5,X48),X11)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),hAPP(c_Fun_Ocomp(X5,X16,X5,X1),X48)),X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Oreindex) ).

fof(fact_setprod_Oreindex,axiom,
    ! [X1,X48,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( c_Fun_Oinj__on(X5,X5,X48,X11)
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),hAPP(c_Set_Oimage(X5,X5,X48),X11)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),hAPP(c_Fun_Ocomp(X5,X16,X5,X1),X48)),X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Oreindex) ).

fof(fact_acc_OaccI,axiom,
    ! [X34,X12,X5] :
      ( ! [X33] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X12)),X34))
         => hBOOL(hAPP(hAPP(c_member(X5),X33),c_Wellfounded_Oacc(X5,X34))) )
     => hBOOL(hAPP(hAPP(c_member(X5),X12),c_Wellfounded_Oacc(X5,X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc_OaccI) ).

fof(fact_acc_Osimps,axiom,
    ! [X34,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Wellfounded_Oacc(X5,X34)))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X6)),X34))
         => hBOOL(hAPP(hAPP(c_member(X5),X3),c_Wellfounded_Oacc(X5,X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc_Osimps) ).

fof(fact_rtrancl__listrel1__eq__len,axiom,
    ! [X34,X27,X12,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)),X12),X27)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X34))))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X12) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__eq__len) ).

fof(fact_list__update_Osimps_I2_J,axiom,
    ! [X56,X70,X212,X12,X5] : hAPP(hAPP(c_List_Olist__update(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)),X70),X56) = c_Nat_Onat_Onat__case(tc_List_Olist(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X56),X212),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_List_Olist(X5),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X5),X12)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X5,tc_List_Olist(X5)),c_List_Olist__update(X5,X212)),X56)),X70),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update_Osimps_I2_J) ).

fof(fact_split__eta,axiom,
    ! [X2,X38,X16,X5] : hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,X38),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_prod(X5,X16)),tc_fun(X16,X38),X5),hAPP(c_COMBB(tc_prod(X5,X16),X38,X16),X2)),c_Product__Type_OPair(X5,X16))) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__eta) ).

fof(fact_aset_I7_J,axiom,
    ! [X10,X11,X18] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18))
     => ! [X3] :
          ( ! [X39] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X39),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X18)))
             => ! [X179] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X179),X11))
                 => X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X179),X39) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10),X3))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X18))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I7_J) ).

fof(fact_aset_I8_J,axiom,
    ! [X10,X11,X18] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18))
     => ! [X3] :
          ( ! [X39] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X39),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X18)))
             => ! [X179] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X179),X11))
                 => X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X179),X39) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10),X3))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X18))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I8_J) ).

fof(fact_nth__take__lemma,axiom,
    ! [X225,X221,X15,X100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X100),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X100),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X225)))
       => ( ! [X145] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X145),X100))
             => hAPP(hAPP(c_List_Onth(X15),X221),X145) = hAPP(hAPP(c_List_Onth(X15),X225),X145) )
         => hAPP(hAPP(c_List_Otake(X15),X100),X221) = hAPP(hAPP(c_List_Otake(X15),X100),X225) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__take__lemma) ).

fof(fact_rel__pow__0__E,axiom,
    ! [X36,X27,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X36)))
     => X12 = X27 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__0__E) ).

fof(fact_exI__realizer,axiom,
    ! [X5,X16,X12,X27,X29] :
      ( hBOOL(hAPP(hAPP(X29,X27),X12))
     => hBOOL(hAPP(hAPP(X29,hAPP(c_Product__Type_Osnd(X16,X5),hAPP(hAPP(c_Product__Type_OPair(X16,X5),X12),X27))),hAPP(c_Product__Type_Ofst(X16,X5),hAPP(hAPP(c_Product__Type_OPair(X16,X5),X12),X27)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exI__realizer) ).

fof(fact_comp__inj__on__iff,axiom,
    ! [X58,X38,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => ( c_Fun_Oinj__on(X16,X38,X58,hAPP(c_Set_Oimage(X5,X16,X2),X11))
      <=> c_Fun_Oinj__on(X5,X38,hAPP(c_Fun_Ocomp(X16,X38,X5,X58),X2),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__inj__on__iff) ).

fof(fact_comp__surj,axiom,
    ! [X1,X38,X2,X5,X16] :
      ( hAPP(c_Set_Oimage(X16,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => ( hAPP(c_Set_Oimage(X5,X38,X1),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X38,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(X16,X38,hAPP(c_Fun_Ocomp(X5,X38,X16,X1),X2)),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X38,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__surj) ).

fof(fact_zdiv__zmod__equality,axiom,
    ! [X100,X25,X26] : 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),X26),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26))),X100) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25),X100),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmod__equality) ).

fof(fact_setsum__reindex,axiom,
    ! [X48,X13,X2,X16,X5,X38] :
      ( class_Groups_Ocomm__monoid__add(X38)
     => ( c_Fun_Oinj__on(X5,X16,X2,X13)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X38),X48),hAPP(c_Set_Oimage(X5,X16,X2),X13)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X38),hAPP(c_Fun_Ocomp(X16,X38,X5,X48),X2)),X13) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__reindex) ).

fof(fact_setprod__reindex,axiom,
    ! [X48,X13,X2,X16,X5,X38] :
      ( class_Groups_Ocomm__monoid__mult(X38)
     => ( c_Fun_Oinj__on(X5,X16,X2,X13)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16,X38),X48),hAPP(c_Set_Oimage(X5,X16,X2),X13)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X38),hAPP(c_Fun_Ocomp(X16,X38,X5,X48),X2)),X13) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__reindex) ).

fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
    ! [X13,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) != 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)),X11),X13))),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)),X11),X13))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X11)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X13)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ounion__inter) ).

fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
    ! [X13,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) != 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)),X11),X13))),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)),X11),X13))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X11)),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X13)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ounion__inter) ).

fof(fact_lexn__length,axiom,
    ! [X76,X34,X214,X212,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)),X212),X214)),hAPP(c_List_Olexn(X5,X34),X76)))
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = X76
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X214) = X76 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexn__length) ).

fof(fact_converseI,axiom,
    ! [X34,X17,X6,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17)),X34))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X5)),hAPP(hAPP(c_Product__Type_OPair(X16,X5),X17),X6)),hAPP(c_Relation_Oconverse(X5,X16),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converseI) ).

fof(fact_def__coinduct__set,axiom,
    ! [X31,X6,X2,X5,X11] :
      ( X11 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),X2)
     => ( c_Orderings_Oorder__class_Omono(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X2)
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X31))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X31),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X31),X11))))
           => hBOOL(hAPP(hAPP(c_member(X5),X6),X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__coinduct__set) ).

fof(fact_rel__comp__distrib,axiom,
    ! [X108,X35,X36,X16,X38,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X38,X16),X36),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X38,X16),tc_HOL_Obool)),X35),X108)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X38,X16),X36),X35)),hAPP(hAPP(c_Relation_Orel__comp(X5,X38,X16),X36),X108)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__distrib) ).

fof(fact_bot__empty__eq2,axiom,
    ! [X27,X12,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),X12),X27))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X12),X27)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__empty__eq2) ).

fof(fact_transpose__transpose,axiom,
    ! [X212,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))),X212)))
     => c_List_Otranspose(X5,c_List_Otranspose(X5,X212)) = 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))),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__transpose) ).

fof(fact_Min_Ohom__commute,axiom,
    ! [X93,X48,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ! [X3,X33] : hAPP(X48,hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X3),X33)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),hAPP(X48,X3)),hAPP(X48,X33))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X93))
         => ( X93 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X48,c_Big__Operators_Olinorder__class_OMin(X5,X93)) = c_Big__Operators_Olinorder__class_OMin(X5,hAPP(c_Set_Oimage(X5,X5,X48),X93)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Ohom__commute) ).

fof(fact_Max_Ohom__commute,axiom,
    ! [X93,X48,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ! [X3,X33] : hAPP(X48,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X3),X33)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(X48,X3)),hAPP(X48,X33))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X93))
         => ( X93 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X48,c_Big__Operators_Olinorder__class_OMax(X5,X93)) = c_Big__Operators_Olinorder__class_OMax(X5,hAPP(c_Set_Oimage(X5,X5,X48),X93)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Ohom__commute) ).

fof(fact_Sup__fin_Ohom__commute,axiom,
    ! [X93,X48,X5] :
      ( class_Lattices_Olattice(X5)
     => ( ! [X3,X33] : hAPP(X48,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X3),X33)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),hAPP(X48,X3)),hAPP(X48,X33))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X93))
         => ( X93 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X48,c_Big__Operators_Olattice__class_OSup__fin(X5,X93)) = c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(c_Set_Oimage(X5,X5,X48),X93)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Ohom__commute) ).

fof(fact_Inf__fin_Ohom__commute,axiom,
    ! [X93,X48,X5] :
      ( class_Lattices_Olattice(X5)
     => ( ! [X3,X33] : hAPP(X48,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X3),X33)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),hAPP(X48,X3)),hAPP(X48,X33))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X93))
         => ( X93 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X48,c_Big__Operators_Olattice__class_OInf__fin(X5,X93)) = c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(c_Set_Oimage(X5,X5,X48),X93)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Ohom__commute) ).

fof(fact_periodic__finite__ex,axiom,
    ! [X29,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20))
     => ( ! [X3,X109] :
            ( hBOOL(hAPP(X29,X3))
          <=> hBOOL(hAPP(X29,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X109),X20)))) )
       => ( ? [X32] : hBOOL(hAPP(X29,X32))
        <=> ? [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),X20)))
              & hBOOL(hAPP(X29,X3)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_periodic__finite__ex) ).

fof(fact_listrel__Nil1,axiom,
    ! [X34,X212,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)),X212)),c_List_Olistrel(X5,X34)))
     => X212 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Nil1) ).

fof(fact_the__elem__def,axiom,
    ! [X31,X5] : c_Set_Othe__elem(X5,X31) = c_HOL_OThe(X5,hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),hAPP(c_fequal,X31)),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,
    ! [X13,X11] :
      ( c_Nat__Transfer_Onat__set(X11)
     => ( c_Nat__Transfer_Onat__set(X13)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X11),X13))
        <=> 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),X11)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X13))) ) ) ),
    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,
    ! [X13,X11] :
      ( c_Nat__Transfer_Onat__set(X11)
     => ( c_Nat__Transfer_Onat__set(X13)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X11),X13))
        <=> 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),X11)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X13))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I5_J) ).

fof(fact_union__comp__emptyL,axiom,
    ! [X13,X19,X11,X5] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X11),X19) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))
     => ( hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X13),X19) = 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)),X11),X13)),X19) = 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,
    ! [X45] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X45) = 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),X45),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_min__max_Odistrib__sup__le,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X22),X23))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),X22)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),X23)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Odistrib__sup__le) ).

fof(fact_distrib__sup__le,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Lattices_Olattice(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X22),X23))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X22)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X23)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distrib__sup__le) ).

fof(fact_min__max_Ofold__inf__le__inf,axiom,
    ! [X17,X6,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X17),X11)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X6),X17))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ofold__inf__le__inf) ).

fof(fact_fold__inf__le__inf,axiom,
    ! [X17,X6,X11,X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => 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)),X17),X11)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X6),X17))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__inf__le__inf) ).

fof(fact_set__update__subsetI,axiom,
    ! [X70,X12,X11,X212,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X212)),X11))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => 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,X212),X70),X12))),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__update__subsetI) ).

fof(fact_setsum__ub__add__nat,axiom,
    ! [X161,X2,X76,X45,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X76),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,X45,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X76),X161))) = 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,X45,X76))),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),X76),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X76),X161)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__ub__add__nat) ).

fof(fact_Times__Int__distrib1,axiom,
    ! [X19,X13,X11,X16,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X16),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X19)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X19))),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X13),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X19))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Times__Int__distrib1) ).

fof(fact_Times__Diff__distrib1,axiom,
    ! [X19,X13,X11,X16,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X16),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13)),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X19)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X19))),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X13),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X19))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Times__Diff__distrib1) ).

fof(fact_Times__Un__distrib1,axiom,
    ! [X19,X13,X11,X16,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X16),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X19)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X19))),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X13),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X19))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Times__Un__distrib1) ).

fof(fact_card__inj__on__le,axiom,
    ! [X13,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X16,X2),X11)),X13))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X13))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X11)),hAPP(c_Finite__Set_Ocard(X16),X13))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__inj__on__le) ).

fof(fact_fold__image__1,axiom,
    ! [X2,X35,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X35))
             => hAPP(X2,X3) = c_Groups_Oone__class_Oone(X16) )
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X2),c_Groups_Oone__class_Oone(X16)),X35) = c_Groups_Oone__class_Oone(X16) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__1) ).

fof(fact_list__ball__nth,axiom,
    ! [X29,X212,X5,X76] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
           => hBOOL(hAPP(X29,X3)) )
       => hBOOL(hAPP(X29,hAPP(hAPP(c_List_Onth(X5),X212),X76))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ball__nth) ).

fof(fact_sum__case__KK,axiom,
    ! [X12,X6,X38,X5,X16] : hAPP(c_Sum__Type_Osum_Osum__case(X16,X5,X38,hAPP(c_COMBK(X5,X16),X6),hAPP(c_COMBK(X5,X38),X6)),X12) = X6,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__case__KK) ).

fof(fact_listrel__Nil2,axiom,
    ! [X34,X212,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)),X212),c_List_Olist_ONil(X5))),c_List_Olistrel(X5,X34)))
     => X212 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Nil2) ).

fof(fact_INF__commute,axiom,
    ! [X2,X13,X38,X11,X16,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,X5),X11),hAPP(hAPP(c_COMBB(tc_fun(X38,X5),X5,X16),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X38,X5),X13)),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X38,X5),X13),hAPP(hAPP(c_COMBB(tc_fun(X16,X5),X5,X38),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,X5),X11)),hAPP(c_COMBC(X16,X38,X5),X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__commute) ).

fof(fact_SUP__commute,axiom,
    ! [X2,X13,X38,X11,X16,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,X5),X11),hAPP(hAPP(c_COMBB(tc_fun(X38,X5),X5,X16),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,X5),X13)),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,X5),X13),hAPP(hAPP(c_COMBB(tc_fun(X16,X5),X5,X38),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,X5),X11)),hAPP(c_COMBC(X16,X38,X5),X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__commute) ).

fof(fact_eq__equiv__class__iff,axiom,
    ! [X27,X12,X34,X11,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X11,X34)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X27),X11))
         => ( hAPP(c_Relation_OImage(X5,X5,X34),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X5,X5,X34),hAPP(hAPP(c_Set_Oinsert(X5),X27),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),X12),X27)),X34)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__equiv__class__iff) ).

fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
    ! [X2,X11,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
         => c_Nat__Transfer_Ois__nat(hAPP(X2,X3)) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Int_Oint),X2),X11) = 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)),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod2_I1_J) ).

fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
    ! [X2,X11,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
         => c_Nat__Transfer_Ois__nat(hAPP(X2,X3)) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Int_Oint),X2),X11) = 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)),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod2_I2_J) ).

fof(fact_coinduct__lemma,axiom,
    ! [X2,X31,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X31),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X31),c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X2)))))
       => ( c_Orderings_Oorder__class_Omono(X5,X5,X2)
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X31),c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X2))),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X31),c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X2))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coinduct__lemma) ).

fof(fact_listrel__eq__len,axiom,
    ! [X34,X214,X212,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)),X212),X214)),c_List_Olistrel(X5,X34)))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X214) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__eq__len) ).

fof(fact_listrel1__eq__len,axiom,
    ! [X34,X214,X212,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)),X212),X214)),c_List_Olistrel1(X5,X34)))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X214) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__eq__len) ).

fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
    ! [X10,X212,X2,X16,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(c_List_Orev(X5),hAPP(hAPP(c_List_Omap(X16,X5),X2),X212)))
       => hAPP(c_List_Ofilter(X16,hAPP(hAPP(c_COMBB(X5,tc_HOL_Obool,X16),hAPP(c_Orderings_Oord__class_Oless(X5),X10)),X2)),X212) = c_List_OtakeWhile(X16,hAPP(hAPP(c_COMBB(X5,tc_HOL_Obool,X16),hAPP(c_Orderings_Oord__class_Oless(X5),X10)),X2),X212) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__equals__takeWhile__sorted__rev) ).

fof(fact_Sigma__Union,axiom,
    ! [X13,X31,X16,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X16),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X31)),X13) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X31),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(X16,tc_HOL_Obool)),tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),c_Product__Type_OSigma(X5,X16)),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Union) ).

fof(fact_bset_I4_J,axiom,
    ! [X13,X10,X18] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X10),X13))
       => ! [X3] :
            ( ! [X39] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X39),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X18)))
               => ! [X179] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X179),X13))
                   => X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X179),X39) ) )
           => ( X3 != X10
             => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X18) != X10 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I4_J) ).

fof(fact_aset_I4_J,axiom,
    ! [X11,X10,X18] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X10),X11))
       => ! [X3] :
            ( ! [X39] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X39),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X18)))
               => ! [X179] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X179),X11))
                   => X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X179),X39) ) )
           => ( X3 != X10
             => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X18) != X10 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I4_J) ).

fof(fact_fold__def,axiom,
    ! [X11,X37,X2,X5,X16] : hAPP(hAPP(c_Finite__Set_Ofold(X16,X5,X2),X37),X11) = c_HOL_OThe(X5,c_Finite__Set_Ofold__graph(X16,X5,X2,X37,X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__def) ).

fof(fact_split__paired__All,axiom,
    ! [X16,X5,X29] :
      ( ! [X32] : hBOOL(hAPP(X29,X32))
    <=> ! [X74,X52] : hBOOL(hAPP(X29,hAPP(hAPP(c_Product__Type_OPair(X5,X16),X74),X52))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__All) ).

fof(fact_diff__card__le__card__Diff,axiom,
    ! [X11,X13,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
     => 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),X11)),hAPP(c_Finite__Set_Ocard(X5),X13))),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__card__le__card__Diff) ).

fof(fact_inj__on__Inter,axiom,
    ! [X2,X16,X5,X35] :
      ( X35 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))
     => ( ! [X75] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X75),X35))
           => c_Fun_Oinj__on(X5,X16,X2,X75) )
       => c_Fun_Oinj__on(X5,X16,X2,c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X35)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__Inter) ).

fof(fact_map__of__filter__in,axiom,
    ! [X29,X37,X30,X212,X5,X16] :
      ( hAPP(hAPP(c_Map_Omap__of(X16,X5),X212),X30) = hAPP(c_Option_Ooption_OSome(X5),X37)
     => ( hBOOL(hAPP(hAPP(X29,X30),X37))
       => hAPP(hAPP(c_Map_Omap__of(X16,X5),hAPP(c_List_Ofilter(tc_prod(X16,X5),hAPP(c_Product__Type_Oprod_Oprod__case(X16,X5,tc_HOL_Obool),X29)),X212)),X30) = hAPP(c_Option_Ooption_OSome(X5),X37) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__filter__in) ).

fof(fact_Bex__set__replicate,axiom,
    ! [X29,X6,X76,X5] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X76,X6))))
          & hBOOL(hAPP(X29,X3)) )
    <=> ( hBOOL(hAPP(X29,X6))
        & X76 != 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,
    ! [X34,X5] :
      ( c_Nitpick_Orefl_H(X5,X34)
    <=> ! [X3] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).

fof(fact_incr__mult__lemma,axiom,
    ! [X30,X29,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20))
     => ( ! [X3] :
            ( hBOOL(hAPP(X29,X3))
           => hBOOL(hAPP(X29,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X20))) )
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))
         => ! [X3] :
              ( hBOOL(hAPP(X29,X3))
             => hBOOL(hAPP(X29,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X20)))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__mult__lemma) ).

fof(fact_decr__mult__lemma,axiom,
    ! [X30,X29,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20))
     => ( ! [X3] :
            ( hBOOL(hAPP(X29,X3))
           => hBOOL(hAPP(X29,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X20))) )
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))
         => ! [X3] :
              ( hBOOL(hAPP(X29,X3))
             => hBOOL(hAPP(X29,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X20)))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decr__mult__lemma) ).

fof(fact_measures__less,axiom,
    ! [X261,X5,X27,X12,X2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X12)),hAPP(X2,X27)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_List_Omeasures(X5,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X5,tc_Nat_Onat)),X2),X261)))) ),
    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,X12,X38,X90,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__idem(X5,X16,X2,X90)
     => hAPP(c_Fun_Ocomp(X16,X16,X38,hAPP(X2,X12)),hAPP(c_Fun_Ocomp(X16,X16,X38,hAPP(X2,X12)),X1)) = hAPP(c_Fun_Ocomp(X16,X16,X38,hAPP(X2,X12)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__idem_Oidem__left__comp) ).

fof(fact_mem__splitI,axiom,
    ! [X38,X16,X17,X6,X21,X37,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X37),hAPP(hAPP(X21,X6),X17)))
     => hBOOL(hAPP(hAPP(c_member(X5),X37),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X16,X38,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Product__Type_OPair(X16,X38),X6),X17)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__splitI) ).

fof(fact_Ball__set__replicate,axiom,
    ! [X29,X6,X76,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X76,X6))))
         => hBOOL(hAPP(X29,X3)) )
    <=> ( hBOOL(hAPP(X29,X6))
        | X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ball__set__replicate) ).

fof(fact_listrel__Cons,axiom,
    ! [X212,X12,X34,X5] : hAPP(c_Relation_OImage(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Olistrel(X5,X34)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)),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,X34),hAPP(hAPP(c_Set_Oinsert(X5),X12),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,X34)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),X212),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,
    ! [X30,X67,X76,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),X76)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool),tc_Nat_Onat),X67),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X30))) = 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,X30,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X76),X30))),X67),
    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_fun__upds__append__drop,axiom,
    ! [X227,X45,X214,X16,X212,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)
     => c_Map_Omap__upds(X5,X16,X45,hAPP(hAPP(c_List_Oappend(X5),X212),X227),X214) = c_Map_Omap__upds(X5,X16,X45,X212,X214) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upds__append__drop) ).

fof(fact_fun__upds__append2__drop,axiom,
    ! [X227,X45,X214,X16,X212,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)
     => c_Map_Omap__upds(X5,X16,X45,X212,hAPP(hAPP(c_List_Oappend(X16),X214),X227)) = c_Map_Omap__upds(X5,X16,X45,X212,X214) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upds__append2__drop) ).

fof(fact_option__map__eq__Some,axiom,
    ! [X27,X83,X2,X5,X16] :
      ( hAPP(hAPP(c_Option_Omap(X16,X5),X2),X83) = hAPP(c_Option_Ooption_OSome(X5),X27)
    <=> ? [X44] :
          ( X83 = hAPP(c_Option_Ooption_OSome(X16),X44)
          & hAPP(X2,X44) = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option__map__eq__Some) ).

fof(fact_override__on__apply__in,axiom,
    ! [X1,X2,X16,X11,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
     => hAPP(c_Fun_Ooverride__on(X5,X16,X2,X1,X11),X6) = hAPP(X1,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_override__on__apply__in) ).

fof(fact_restrict__map__insert,axiom,
    ! [X11,X6,X2,X16,X5] : c_Map_Orestrict__map(X5,X16,X2,hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),c_Map_Orestrict__map(X5,X16,X2,X11)),X6),hAPP(X2,X6)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__map__insert) ).

fof(fact_lexord__append__rightI,axiom,
    ! [X34,X12,X5,X27] :
      ( ? [X52,X44] : X27 = hAPP(hAPP(c_List_Olist_OCons(X5),X52),X44)
     => 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)),X12),hAPP(hAPP(c_List_Oappend(X5),X12),X27))),c_List_Olexord(X5,X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__rightI) ).

fof(fact_list__eq__iff__zip__eq,axiom,
    ! [X5,X214,X212] :
      ( X212 = X214
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X214)
        & ! [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),X212),X214))))
           => 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,
    ! [X29,X47,X158] :
      ( 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),X158),X47)))
     => ( ! [X3,X33] :
            ( 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),X33)))
           => ( ( X33 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
               => hBOOL(hAPP(hAPP(X29,X33),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X33))) )
             => hBOOL(hAPP(hAPP(X29,X3),X33)) ) )
       => hBOOL(hAPP(hAPP(X29,X158),X47)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__gcd_Opinduct) ).

fof(fact_inj__on__strict__subset,axiom,
    ! [X11,X13,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X13)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),X13))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X16,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X16,X2),X11)),hAPP(c_Set_Oimage(X5,X16,X2),X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).

fof(fact_inj__on__image__Int,axiom,
    ! [X13,X11,X19,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X19)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X19))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),X19))
         => hAPP(c_Set_Oimage(X5,X16,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X16,X2),X11)),hAPP(c_Set_Oimage(X5,X16,X2),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__image__Int) ).

fof(fact_inj__on__image__set__diff,axiom,
    ! [X13,X11,X19,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X19)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X19))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),X19))
         => hAPP(c_Set_Oimage(X5,X16,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X16,X2),X11)),hAPP(c_Set_Oimage(X5,X16,X2),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__image__set__diff) ).

fof(fact_filter__in__sublist,axiom,
    ! [X84,X212,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X212))
     => 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,X212,X84)))),X212) = c_List_Osublist(X5,X212,X84) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__in__sublist) ).

fof(fact_surj__iff__all,axiom,
    ! [X2,X5,X16] :
      ( hAPP(c_Set_Oimage(X16,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] : hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X16,X5,c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)),X2),X3)) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__iff__all) ).

fof(fact_list__ex1__iff__raw,axiom,
    ! [X212,X29,X5] :
      ( c_List_Olist__ex1(X5,X29,X212)
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
          & hBOOL(hAPP(X29,X3))
          & ! [X33] :
              ( ( hBOOL(hAPP(hAPP(c_member(X5),X33),hAPP(c_List_Oset(X5),X212)))
                & hBOOL(hAPP(X29,X33)) )
             => X33 = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex1__iff__raw) ).

fof(fact_list__ex1__iff,axiom,
    ! [X212,X29,X5] :
      ( c_List_Olist__ex1(X5,X29,X212)
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
          & hBOOL(hAPP(X29,X3))
          & ! [X33] :
              ( ( hBOOL(hAPP(hAPP(c_member(X5),X33),hAPP(c_List_Oset(X5),X212)))
                & hBOOL(hAPP(X29,X33)) )
             => X33 = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex1__iff) ).

fof(fact_endo__inj__surj,axiom,
    ! [X2,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X5,X2),X11)),X11))
       => ( c_Fun_Oinj__on(X5,X5,X2,X11)
         => hAPP(c_Set_Oimage(X5,X5,X2),X11) = X11 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_endo__inj__surj) ).

fof(fact_map__upds__def,axiom,
    ! [X214,X212,X45,X16,X5] : c_Map_Omap__upds(X5,X16,X45,X212,X214) = c_Map_Omap__add(X5,X16,X45,hAPP(c_Map_Omap__of(X5,X16),hAPP(c_List_Orev(tc_prod(X5,X16)),hAPP(hAPP(c_List_Ozip(X5,X16),X212),X214)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__upds__def) ).

fof(fact_insort__insert__key__triv,axiom,
    ! [X212,X16,X12,X2,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X12)),hAPP(c_Set_Oimage(X16,X5,X2),hAPP(c_List_Oset(X16),X212))))
       => c_List_Olinorder__class_Oinsort__insert__key(X16,X5,X2,X12,X212) = X212 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__insert__key__triv) ).

fof(fact_set__insort__insert,axiom,
    ! [X212,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(c_List_Oset(X5),c_List_Olinorder__class_Oinsort__insert__key(X5,X5,c_COMBI(X5),X12,X212)) = hAPP(hAPP(c_Set_Oinsert(X5),X12),hAPP(c_List_Oset(X5),X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__insort__insert) ).

fof(fact_listrel1__subset__listrel,axiom,
    ! [X61,X34,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),X61))
     => ( c_Relation_Orefl__on(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X61)
       => 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,X34)),c_List_Olistrel(X5,X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__subset__listrel) ).

fof(fact_folding__image_Oeq__fold,axiom,
    ! [X1,X11,X90,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__image(X5,X16,X2,X37,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11))
       => hAPP(hAPP(X90,X1),X11) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X16,X2),X1),X37),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image_Oeq__fold) ).

fof(fact_fun__left__comm_Ofold__rec,axiom,
    ! [X37,X12,X11,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X16,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),X37),X11) = hAPP(hAPP(X2,X12),hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),X37),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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_equal__fun__def,axiom,
    ! [X1,X2,X5,X16] :
      ( ( class_HOL_Oequal(X16)
        & class_Enum_Oenum(X5) )
     => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X5,X16)),X2),X1))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),c_Enum_Oenum__class_Oenum(X5))))
           => hAPP(X2,X3) = hAPP(X1,X3) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__fun__def) ).

fof(fact_vimage__compose,axiom,
    ! [X12,X2,X1,X38,X16,X5] : hAPP(c_Set_Ovimage(X5,X16,hAPP(c_Fun_Ocomp(X38,X16,X5,X1),X2)),X12) = hAPP(c_Set_Ovimage(X5,X38,X2),hAPP(c_Set_Ovimage(X38,X16,X1),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__compose) ).

fof(fact_image__compose,axiom,
    ! [X34,X1,X2,X38,X5,X16] : hAPP(c_Set_Oimage(X16,X5,hAPP(c_Fun_Ocomp(X38,X5,X16,X2),X1)),X34) = hAPP(c_Set_Oimage(X38,X5,X2),hAPP(c_Set_Oimage(X16,X38,X1),X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__compose) ).

fof(fact_rtrancl__power,axiom,
    ! [X36,X161,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X161),c_Transitive__Closure_Ortrancl(X5,X36)))
    <=> ? [X107] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X161),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X107),X36))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__power) ).

fof(fact_scomp__unfold,axiom,
    ! [X12,X1,X2,X5,X55,X38,X16] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X16,X38,X55,X5),X2),X1),X12) = hAPP(hAPP(X1,hAPP(c_Product__Type_Ofst(X38,X55),hAPP(X2,X12))),hAPP(c_Product__Type_Osnd(X38,X55),hAPP(X2,X12))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_scomp__unfold) ).

fof(fact_equiv__class__eq__iff,axiom,
    ! [X27,X12,X34,X11,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X11,X34)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),X34))
      <=> ( hAPP(c_Relation_OImage(X5,X5,X34),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X5,X5,X34),hAPP(hAPP(c_Set_Oinsert(X5),X27),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
          & hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
          & hBOOL(hAPP(hAPP(c_member(X5),X27),X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__eq__iff) ).

fof(fact_sum__squares__gt__zero__iff,axiom,
    ! [X27,X12,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),X12),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X27),X27))))
      <=> ( X12 != c_Groups_Ozero__class_Ozero(X5)
          | X27 != 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,
    ! [X36,X5] : c_Transitive__Closure_Ortrancl(X5,X36) = 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)),X36)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__is__UN__rel__pow) ).

fof(fact_takeWhile__append2,axiom,
    ! [X214,X29,X212,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
         => hBOOL(hAPP(X29,X3)) )
     => c_List_OtakeWhile(X5,X29,hAPP(hAPP(c_List_Oappend(X5),X212),X214)) = hAPP(hAPP(c_List_Oappend(X5),X212),c_List_OtakeWhile(X5,X29,X214)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__append2) ).

fof(fact_inj__on__imageI,axiom,
    ! [X11,X2,X1,X38,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,hAPP(c_Fun_Ocomp(X38,X16,X5,X1),X2),X11)
     => c_Fun_Oinj__on(X38,X16,X1,hAPP(c_Set_Oimage(X5,X38,X2),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__imageI) ).

fof(fact_setsum__eq__Suc0__iff,axiom,
    ! [X2,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X11) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
            & hAPP(X2,X3) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            & ! [X39] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X39),X11))
               => ( X3 != X39
                 => hAPP(X2,X39) = 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,
    ! [X12,X212,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,X212)
       => c_List_Olinorder__class_Osorted(X5,c_List_Olinorder__class_Oinsort__insert__key(X5,X5,c_COMBI(X5),X12,X212)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__insort__insert) ).

fof(fact_abs__mult__less,axiom,
    ! [X41,X26,X24,X25,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),X24))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X26)),X41))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),hAPP(c_Groups_Oabs__class_Oabs(X15),X26))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X41))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__less) ).

fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
    ! [X12,X37,X11,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X16,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),X37),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(X2,X12),hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),X37),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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,
    ! [X212,X2,X16,X29,X5] : c_List_OtakeWhile(X5,X29,hAPP(hAPP(c_List_Omap(X16,X5),X2),X212)) = hAPP(hAPP(c_List_Omap(X16,X5),X2),c_List_OtakeWhile(X16,hAPP(c_Fun_Ocomp(X5,tc_HOL_Obool,X16,X29),X2),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__map) ).

fof(fact_setsum__eq__1__iff,axiom,
    ! [X2,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X11) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
            & hAPP(X2,X3) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & ! [X39] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X39),X11))
               => ( X3 != X39
                 => hAPP(X2,X39) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__eq__1__iff) ).

fof(fact_gfp__fun__UnI2,axiom,
    ! [X31,X6,X2,X5] :
      ( c_Orderings_Oorder__class_Omono(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X2)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),X2)))
       => hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X31),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),X2))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gfp__fun__UnI2) ).

fof(fact_refl__on__comp__subset,axiom,
    ! [X34,X11,X5] :
      ( c_Relation_Orefl__on(X5,X11,X34)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(c_Relation_Oconverse(X5,X5),X34)),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__comp__subset) ).

fof(fact_comp__inj__on,axiom,
    ! [X1,X38,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => ( c_Fun_Oinj__on(X16,X38,X1,hAPP(c_Set_Oimage(X5,X16,X2),X11))
       => c_Fun_Oinj__on(X5,X38,hAPP(c_Fun_Ocomp(X16,X38,X5,X1),X2),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__inj__on) ).

fof(fact_product_Osimps_I2_J,axiom,
    ! [X214,X212,X12,X16,X5] : c_Enum_Oproduct(X5,X16,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212),X214) = hAPP(hAPP(c_List_Oappend(tc_prod(X5,X16)),hAPP(hAPP(c_List_Omap(X16,tc_prod(X5,X16)),hAPP(c_Product__Type_OPair(X5,X16),X12)),X214)),c_Enum_Oproduct(X5,X16,X212,X214)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_product_Osimps_I2_J) ).

fof(fact_elem__le__sum,axiom,
    ! [X224,X76] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X76),hAPP(c_List_Oset(tc_Nat_Onat),X224)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X76),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)),X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_elem__le__sum) ).

fof(fact_rev__ImageI,axiom,
    ! [X34,X17,X16,X11,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17)),X34))
       => hBOOL(hAPP(hAPP(c_member(X16),X17),hAPP(c_Relation_OImage(X5,X16,X34),X11))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__ImageI) ).

fof(fact_Option_Omap_Ocompositionality,axiom,
    ! [X216,X1,X38,X2,X5,X16] : hAPP(hAPP(c_Option_Omap(X16,X5),X2),hAPP(hAPP(c_Option_Omap(X38,X16),X1),X216)) = hAPP(hAPP(c_Option_Omap(X38,X5),hAPP(c_Fun_Ocomp(X16,X5,X38,X2),X1)),X216),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Option_Omap_Ocompositionality) ).

fof(fact_option__map__comp,axiom,
    ! [X215,X1,X38,X2,X5,X16] : hAPP(hAPP(c_Option_Omap(X16,X5),X2),hAPP(hAPP(c_Option_Omap(X38,X16),X1),X215)) = hAPP(hAPP(c_Option_Omap(X38,X5),hAPP(c_Fun_Ocomp(X16,X5,X38,X2),X1)),X215),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option__map__comp) ).

fof(fact_List_Omap_Ocompositionality,axiom,
    ! [X213,X1,X38,X2,X5,X16] : hAPP(hAPP(c_List_Omap(X16,X5),X2),hAPP(hAPP(c_List_Omap(X38,X16),X1),X213)) = hAPP(hAPP(c_List_Omap(X38,X5),hAPP(c_Fun_Ocomp(X16,X5,X38,X2),X1)),X213),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Omap_Ocompositionality) ).

fof(fact_map__map,axiom,
    ! [X212,X1,X38,X2,X5,X16] : hAPP(hAPP(c_List_Omap(X16,X5),X2),hAPP(hAPP(c_List_Omap(X38,X16),X1),X212)) = hAPP(hAPP(c_List_Omap(X38,X5),hAPP(c_Fun_Ocomp(X16,X5,X38,X2),X1)),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__map) ).

fof(fact_take__Cons,axiom,
    ! [X212,X12,X76,X5] : hAPP(hAPP(c_List_Otake(X5),X76),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = 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),X12)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Otake(X5)),X212)),X76),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Cons) ).

fof(fact_Un__Image,axiom,
    ! [X11,X35,X36,X5,X16] : hAPP(c_Relation_OImage(X16,X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X16,X5),tc_HOL_Obool)),X36),X35)),X11) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X16,X5,X36),X11)),hAPP(c_Relation_OImage(X16,X5,X35),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Image) ).

fof(fact_iterate_Osimps,axiom,
    ! [X12,X2,X5,X16,X30] :
      ( ( X30 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Random_Oiterate(X16,X5,X30,X2),X12) = hAPP(c_Product__Type_OPair(X16,X5),X12) )
      & ( X30 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Random_Oiterate(X16,X5,X30,X2),X12) = hAPP(hAPP(c_Product__Type_Oscomp(X5,X16,X5,tc_prod(X16,X5)),hAPP(X2,X12)),c_Random_Oiterate(X16,X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X30),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,
    ! [X17,X6,X34,X11,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X11,X34)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),X34))
       => hAPP(c_Relation_OImage(X5,X5,X34),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X5,X5,X34),hAPP(hAPP(c_Set_Oinsert(X5),X17),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,
    ! [X13,X11,X17,X6,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),X13)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
        & hBOOL(hAPP(hAPP(c_member(X16),X17),hAPP(X13,X6))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__Sigma__iff) ).

fof(fact_SigmaD2,axiom,
    ! [X13,X11,X17,X6,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),X13)))
     => hBOOL(hAPP(hAPP(c_member(X16),X17),hAPP(X13,X6))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaD2) ).

fof(fact_listrel__mono,axiom,
    ! [X84,X34,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),X84))
     => 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,X34)),c_List_Olistrel(X5,X84))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__mono) ).

fof(fact_listrel1__mono,axiom,
    ! [X84,X34,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),X84))
     => 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,X34)),c_List_Olistrel1(X5,X84))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__mono) ).

fof(fact_seq__case,axiom,
    ! [X253,X1,X2,X16,X5] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X5,X16,X2,X1,X253) = hAPP(c_Option_Ooption_Ooption__case(X5,tc_prod(X16,tc_Lazy__Sequence_Olazy__sequence(X16)),X2,hAPP(c_Product__Type_Oprod_Oprod__case(X16,tc_Lazy__Sequence_Olazy__sequence(X16),X5),X1)),hAPP(c_Lazy__Sequence_Oyield(X16),X253)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_seq__case) ).

fof(fact_scomp__def,axiom,
    ! [X12,X1,X2,X5,X55,X38,X16] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X16,X38,X55,X5),X2),X1),X12) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X38,X55,X5),X1),hAPP(X2,X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_scomp__def) ).

fof(fact_scomp__apply,axiom,
    ! [X12,X1,X2,X5,X55,X38,X16] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X16,X38,X55,X5),X2),X1),X12) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X38,X55,X5),X1),hAPP(X2,X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_scomp__apply) ).

fof(fact_Un__least,axiom,
    ! [X13,X19,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X19))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),X19))
       => 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)),X11),X13)),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__least) ).

fof(fact_folding__one_Ounion__inter,axiom,
    ! [X13,X11,X90,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(X2,hAPP(X90,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13))),hAPP(X90,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13))) = hAPP(hAPP(X2,hAPP(X90,X11)),hAPP(X90,X13)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Ounion__inter) ).

fof(fact_f__the__inv__into__f,axiom,
    ! [X27,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => ( hBOOL(hAPP(hAPP(c_member(X16),X27),hAPP(c_Set_Oimage(X5,X16,X2),X11)))
       => hAPP(X2,hAPP(c_Fun_Othe__inv__into(X5,X16,X11,X2),X27)) = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_f__the__inv__into__f) ).

fof(fact_INT__extend__simps_I8_J,axiom,
    ! [X13,X11,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X16,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBC(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool))),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X16,tc_HOL_Obool),X11)),X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I8_J) ).

fof(fact_UN__extend__simps_I8_J,axiom,
    ! [X13,X11,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X16,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBC(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool))),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X16,tc_HOL_Obool),X11)),X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I8_J) ).

fof(fact_INT__simps_I8_J,axiom,
    ! [X13,X11,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X16,tc_HOL_Obool),X11)),X13) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X16,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBC(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool))),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I8_J) ).

fof(fact_UN__simps_I8_J,axiom,
    ! [X13,X11,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X16,tc_HOL_Obool),X11)),X13) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X16,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBC(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool))),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I8_J) ).

fof(fact_inj__on__def,axiom,
    ! [X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
         => ! [X39] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X39),X11))
             => ( hAPP(X2,X3) = hAPP(X2,X39)
               => X3 = X39 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__def) ).

fof(fact_rtrancl__subset,axiom,
    ! [X35,X36,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X36),X35))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X35),c_Transitive__Closure_Ortrancl(X5,X36)))
       => c_Transitive__Closure_Ortrancl(X5,X35) = c_Transitive__Closure_Ortrancl(X5,X36) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__subset) ).

fof(fact_eq__equiv__class,axiom,
    ! [X11,X17,X6,X34,X5] :
      ( hAPP(c_Relation_OImage(X5,X5,X34),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X5,X5,X34),hAPP(hAPP(c_Set_Oinsert(X5),X17),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
     => ( c_Equiv__Relations_Oequiv(X5,X11,X34)
       => ( hBOOL(hAPP(hAPP(c_member(X5),X17),X11))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),X34)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__equiv__class) ).

fof(fact_SigmaD1,axiom,
    ! [X13,X11,X17,X6,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),X13)))
     => hBOOL(hAPP(hAPP(c_member(X5),X6),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaD1) ).

fof(fact_setprod__zero__iff,axiom,
    ! [X2,X11,X5,X16] :
      ( ( class_Rings_Ocomm__semiring__1(X16)
        & class_Rings_Ono__zero__divisors(X16) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),X11) = c_Groups_Ozero__class_Ozero(X16)
        <=> ? [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
              & hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X16) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__zero__iff) ).

fof(fact_card__image__le,axiom,
    ! [X2,X16,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X16),hAPP(c_Set_Oimage(X5,X16,X2),X11))),hAPP(c_Finite__Set_Ocard(X5),X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__image__le) ).

fof(fact_INTER__UNIV__conv_I2_J,axiom,
    ! [X13,X11,X5,X16] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X11),X13) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X16),X3),X11))
         => hAPP(X13,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,
    ! [X13,X11,X5,X16] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X11),X13) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X16),X3),X11))
         => hAPP(X13,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,
    ! [X13,X11,X16,X5] :
      ( c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X11),X13)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X16),X3),X11))
         => hAPP(X13,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,
    ! [X13,X11,X16,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X11),X13)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X16),X3),X11))
         => hAPP(X13,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,
    ! [X76,X11,X2,X5] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X11) = hAPP(c_Nat_OSuc,X76)
     => ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
          & 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_Max_Ounion__inter,axiom,
    ! [X13,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) != 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)),X11),X13))),c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olinorder__class_OMax(X5,X11)),c_Big__Operators_Olinorder__class_OMax(X5,X13)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Ounion__inter) ).

fof(fact_Min_Ounion__inter,axiom,
    ! [X13,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) != 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)),X11),X13))),c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olinorder__class_OMin(X5,X11)),c_Big__Operators_Olinorder__class_OMin(X5,X13)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Ounion__inter) ).

fof(fact_Inf__fin_Ounion__inter,axiom,
    ! [X13,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) != 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)),X11),X13))),c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X11)),c_Big__Operators_Olattice__class_OInf__fin(X5,X13)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Ounion__inter) ).

fof(fact_Sup__fin_Ounion__inter,axiom,
    ! [X13,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) != 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)),X11),X13))),c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,X11)),c_Big__Operators_Olattice__class_OSup__fin(X5,X13)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_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)
          | ? [X228,X3] :
              ( X6 = hAPP(hAPP(c_List_Olist_OCons(X5),X3),X228)
              & ! [X39] :
                  ( hBOOL(hAPP(hAPP(c_member(X5),X39),hAPP(c_List_Oset(X5),X228)))
                 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X39)) )
              & c_List_Olinorder__class_Osorted(X5,X228) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted_Osimps) ).

fof(fact_type__definition_OAbs__inject,axiom,
    ! [X27,X12,X11,X177,X178,X16,X5] :
      ( c_Typedef_Otype__definition(X5,X16,X178,X177,X11)
     => ( hBOOL(hAPP(hAPP(c_member(X16),X12),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X16),X27),X11))
         => ( hAPP(X177,X12) = hAPP(X177,X27)
          <=> X12 = X27 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_OAbs__inject) ).

fof(fact_acyclicP__converse,axiom,
    ! [X34,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,X34))))
    <=> c_Wellfounded_Oacyclic(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclicP__converse) ).

fof(fact_Field__insert,axiom,
    ! [X34,X17,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),X17)),X34)) = 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),X17),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(c_Relation_OField(X5),X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__insert) ).

fof(fact_start__le__sum,axiom,
    ! [X224,X76,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X76),X224))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_start__le__sum) ).

fof(fact_pair__box_Osize_I1_J,axiom,
    ! [X17,X6,X280,X92,X16,X5] : c_Nitpick_Opair__box_Opair__box__size(X5,X16,X92,X280,c_Nitpick_Opair__box_OPairBox(X5,X16,X6,X17)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X92,X6)),hAPP(X280,X17))),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,
    ! [X30,X19,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),X19))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X19)))
       => ( ! [X191] :
              ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X191),X19))
             => hAPP(c_Finite__Set_Ocard(X5),X191) = X30 )
         => ( ! [X192] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X192),X19))
               => ! [X193] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X193),X19))
                   => ( X192 != X193
                     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X192),X193) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ) )
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),hAPP(c_Finite__Set_Ocard(tc_fun(X5,tc_HOL_Obool)),X19)) = hAPP(c_Finite__Set_Ocard(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X19)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__partition) ).

fof(fact_map__of__Cons__code_I2_J,axiom,
    ! [X222,X126,X16,X5,X100,X103] :
      ( ( X103 = X100
       => hAPP(hAPP(c_Map_Omap__of(X5,X16),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X103),X126)),X222)),X100) = hAPP(c_Option_Ooption_OSome(X16),X126) )
      & ( X103 != X100
       => hAPP(hAPP(c_Map_Omap__of(X5,X16),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X103),X126)),X222)),X100) = hAPP(hAPP(c_Map_Omap__of(X5,X16),X222),X100) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__Cons__code_I2_J) ).

fof(fact_sorted__same,axiom,
    ! [X212,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,X212))),X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__same) ).

fof(fact_inj__comp,axiom,
    ! [X1,X38,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( c_Fun_Oinj__on(X38,X5,X1,c_Orderings_Otop__class_Otop(tc_fun(X38,tc_HOL_Obool)))
       => c_Fun_Oinj__on(X38,X16,hAPP(c_Fun_Ocomp(X5,X16,X38,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X38,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__comp) ).

fof(fact_set__update__subset__insert,axiom,
    ! [X12,X70,X212,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,X212),X70),X12))),hAPP(hAPP(c_Set_Oinsert(X5),X12),hAPP(c_List_Oset(X5),X212)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__update__subset__insert) ).

fof(fact_min__max_OSup__fin_Oremove,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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),X11) = X12 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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),X11) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X12),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)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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_min__max_OInf__fin_Oremove,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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),X11) = X12 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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),X11) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X12),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)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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_transfer__nat__int__sum__prod2_I1_J,axiom,
    ! [X11,X2,X5] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X11) = 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)),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod2_I1_J) ).

fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
    ! [X11,X2,X5] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Nat_Onat),X2),X11) = 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)),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod2_I2_J) ).

fof(fact_vimage__singleton__eq,axiom,
    ! [X17,X2,X16,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Set_Ovimage(X5,X16,X2),hAPP(hAPP(c_Set_Oinsert(X16),X17),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))))))
    <=> hAPP(X2,X6) = X17 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__singleton__eq) ).

fof(fact_inj__on__imageI2,axiom,
    ! [X11,X2,X58,X38,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,hAPP(c_Fun_Ocomp(X38,X16,X5,X58),X2),X11)
     => c_Fun_Oinj__on(X5,X38,X2,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__imageI2) ).

fof(fact_finite__Diff__insert,axiom,
    ! [X13,X6,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13))))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Diff__insert) ).

fof(fact_insert__def,axiom,
    ! [X13,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),X13) = 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))),X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__def) ).

fof(fact_eq__add__iff1,axiom,
    ! [X20,X17,X21,X114,X6,X5] :
      ( class_Rings_Oring(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X114)),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X114)),X20)
      <=> 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),X17)),X114)),X21) = X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff1) ).

fof(fact_eq__add__iff2,axiom,
    ! [X20,X17,X21,X114,X6,X5] :
      ( class_Rings_Oring(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X114)),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X114)),X20)
      <=> X21 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X17),X6)),X114)),X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff2) ).

fof(fact_Image__INT__eq,axiom,
    ! [X13,X38,X11,X34,X16,X5] :
      ( c_Relation_Osingle__valued(X5,X16,hAPP(c_Relation_Oconverse(X16,X5),X34))
     => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X38,tc_HOL_Obool))
       => hAPP(c_Relation_OImage(X16,X5,X34),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X38,tc_fun(X16,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X38,tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X38),c_Relation_OImage(X16,X5,X34)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__INT__eq) ).

fof(fact_partition__filter2,axiom,
    ! [X212,X29,X5] : hAPP(c_Product__Type_Osnd(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Opartition(X5,X29,X212)) = hAPP(c_List_Ofilter(X5,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X5,c_fNot),X29)),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition__filter2) ).

fof(fact_inv__into__image__cancel,axiom,
    ! [X35,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X35),X11))
       => hAPP(c_Set_Oimage(X16,X5,c_Hilbert__Choice_Oinv__into(X5,X16,X11,X2)),hAPP(c_Set_Oimage(X5,X16,X2),X35)) = X35 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__image__cancel) ).

fof(fact_vimage__mono,axiom,
    ! [X2,X16,X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X16,X5,X2),X11)),hAPP(c_Set_Ovimage(X16,X5,X2),X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__mono) ).

fof(fact_image__mono,axiom,
    ! [X2,X16,X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X16,X2),X11)),hAPP(c_Set_Oimage(X5,X16,X2),X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__mono) ).

fof(fact_UN__equiv__class,axiom,
    ! [X6,X2,X16,X34,X11,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X11,X34)
     => ( c_Equiv__Relations_Ocongruent(X5,tc_fun(X16,tc_HOL_Obool),X34,X2)
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X34),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_OSup__fin_Oinsert__remove,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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),X12),X11)) = X12 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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),X12),X11)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X12),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)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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_min__max_OInf__fin_Oinsert__remove,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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),X12),X11)) = X12 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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),X12),X11)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X12),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)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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_comp__cong,axiom,
    ! [X85,X55,X38,X5,X16,X86,X87,X58,X12,X1,X2] :
      ( hAPP(X2,hAPP(X1,X12)) = hAPP(X58,hAPP(X87,X86))
     => hAPP(hAPP(c_Fun_Ocomp(X16,X5,X38,X2),X1),X12) = hAPP(hAPP(c_Fun_Ocomp(X55,X5,X85,X58),X87),X86) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__cong) ).

fof(fact_inv__o__cancel,axiom,
    ! [X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Fun_Ocomp(X16,X5,X5,c_Hilbert__Choice_Oinv__into(X5,X16,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_folding__one_Oremove,axiom,
    ! [X12,X11,X90,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => hAPP(X90,X11) = X12 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => hAPP(X90,X11) = hAPP(hAPP(X2,X12),hAPP(X90,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
       => 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)),X11),X13))),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X11)),hAPP(c_Finite__Set_Ocard(X5),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Ounion__inter) ).

fof(fact_card__Un__Int,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X11)),hAPP(c_Finite__Set_Ocard(X5),X13)) = 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)),X11),X13))),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Un__Int) ).

fof(fact_wf__same__fst,axiom,
    ! [X5,X36,X16,X29] :
      ( ! [X3] :
          ( hBOOL(hAPP(X29,X3))
         => c_Wellfounded_Owf(X16,hAPP(X36,X3)) )
     => c_Wellfounded_Owf(tc_prod(X5,X16),c_Recdef_Osame__fst(X5,X16,X29,X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__same__fst) ).

fof(fact_in__rel__def,axiom,
    ! [X27,X12,X36,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X5,X16,X36),X12),X27))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X12),X27)),X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__rel__def) ).

fof(fact_restrict__upd__same,axiom,
    ! [X27,X12,X45,X16,X5] : c_Map_Orestrict__map(X5,X16,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),X45),X12),hAPP(c_Option_Ooption_OSome(X16),X27)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = c_Map_Orestrict__map(X5,X16,X45,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__upd__same) ).

fof(fact_Image__closed__trancl,axiom,
    ! [X31,X34,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X34),X31)),X31))
     => hAPP(c_Relation_OImage(X5,X5,c_Transitive__Closure_Ortrancl(X5,X34)),X31) = X31 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__closed__trancl) ).

fof(fact_acc__downwards__aux,axiom,
    ! [X34,X6,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X17),X6)),c_Transitive__Closure_Ortrancl(X5,X34)))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Wellfounded_Oacc(X5,X34)))
       => hBOOL(hAPP(hAPP(c_member(X5),X17),c_Wellfounded_Oacc(X5,X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).

fof(fact_acc__downwards,axiom,
    ! [X17,X34,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Wellfounded_Oacc(X5,X34)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X17),X6)),c_Transitive__Closure_Ortrancl(X5,X34)))
       => hBOOL(hAPP(hAPP(c_member(X5),X17),c_Wellfounded_Oacc(X5,X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downwards) ).

fof(fact_ran__distinct,axiom,
    ! [X223,X16,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Omap(tc_prod(X5,X16),X5),c_Product__Type_Ofst(X5,X16)),X223)))
     => c_Map_Oran(X5,X16,hAPP(c_Map_Omap__of(X5,X16),X223)) = hAPP(c_Set_Oimage(tc_prod(X5,X16),X16,c_Product__Type_Osnd(X5,X16)),hAPP(c_List_Oset(tc_prod(X5,X16)),X223)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ran__distinct) ).

fof(fact_INT__simps_I2_J,axiom,
    ! [X13,X11,X16,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(X16,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),X11)),X13)) = c_Orderings_Otop__class_Otop(tc_fun(X16,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(X16,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),X11)),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X19),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I2_J) ).

fof(fact_INT__simps_I4_J,axiom,
    ! [X13,X11,X16,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(X16,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool)),X11)),X13)) = c_Orderings_Otop__class_Otop(tc_fun(X16,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(X16,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool)),X11)),X13)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool)),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X19),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I4_J) ).

fof(fact_UN__simps_I3_J,axiom,
    ! [X13,X11,X16,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(X16,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),X11)),X13)) = c_Orderings_Obot__class_Obot(tc_fun(X16,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(X16,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),X11)),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X19),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I3_J) ).

fof(fact_INT__extend__simps_I2_J,axiom,
    ! [X13,X11,X16,X5,X19] :
      ( ( X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X19),X13)) = X11 )
      & ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X19),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),X11)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I2_J) ).

fof(fact_INT__extend__simps_I4_J,axiom,
    ! [X13,X11,X16,X5,X19] :
      ( ( X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool)),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X19),X13)) = X11 )
      & ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool)),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X19),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool)),X11)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I4_J) ).

fof(fact_UN__extend__simps_I3_J,axiom,
    ! [X13,X11,X16,X5,X19] :
      ( ( X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X19),X13)) = X11 )
      & ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X19),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),X11)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I3_J) ).

fof(fact_folding__one_Oinsert__remove,axiom,
    ! [X12,X11,X90,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X90,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = X12 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X90,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(X2,X12),hAPP(X90,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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_Min_Oremove,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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,X11) = X12 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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,X11) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X12),c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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,X11) = X12 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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,X11) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X12),c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oremove) ).

fof(fact_Sup__fin_Oremove,axiom,
    ! [X12,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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,X11) = X12 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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,X11) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X12),c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oremove) ).

fof(fact_Inf__fin_Oremove,axiom,
    ! [X12,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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,X11) = X12 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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,X11) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X12),c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oremove) ).

fof(fact_type__definition_ORep,axiom,
    ! [X12,X11,X177,X178,X16,X5] :
      ( c_Typedef_Otype__definition(X5,X16,X178,X177,X11)
     => hBOOL(hAPP(hAPP(c_member(X16),hAPP(X178,X12)),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep) ).

fof(fact_type__definition_OAbs__inverse,axiom,
    ! [X27,X11,X177,X178,X16,X5] :
      ( c_Typedef_Otype__definition(X5,X16,X178,X177,X11)
     => ( hBOOL(hAPP(hAPP(c_member(X16),X27),X11))
       => hAPP(X178,hAPP(X177,X27)) = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_OAbs__inverse) ).

fof(fact_sorted__insort__key,axiom,
    ! [X212,X12,X2,X16,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X16,X5),X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X16,X5,X2),X12),X212)))
      <=> c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X16,X5),X2),X212)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__insort__key) ).

fof(fact_mod__induct__0,axiom,
    ! [X70,X29,X161] :
      ( ! [X145] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X145),X161))
         => ( hBOOL(hAPP(X29,X145))
           => hBOOL(hAPP(X29,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X145),X161))) ) )
     => ( hBOOL(hAPP(X29,X70))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X70),X161))
         => hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__induct__0) ).

fof(fact_zdiv__zmult1__eq,axiom,
    ! [X24,X26,X25] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X26)),X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26),X24))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),c_Divides_Odiv__class_Omod(tc_Int_Oint,X26,X24))),X24)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmult1__eq) ).

fof(fact_div__mult1__eq,axiom,
    ! [X24,X26,X25] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X26)),X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X26),X24))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X24))),X24)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult1__eq) ).

fof(fact_nat__eq__add__iff1,axiom,
    ! [X76,X45,X66,X70,X115] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X115),X70))
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X70),X66)),X45) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X115),X66)),X76)
      <=> 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),X70),X115)),X66)),X45) = X76 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).

fof(fact_nat__eq__add__iff2,axiom,
    ! [X76,X45,X66,X115,X70] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X70),X115))
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X70),X66)),X45) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X115),X66)),X76)
      <=> X45 = 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),X115),X70)),X66)),X76) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).

fof(fact_Un__Int__assoc__eq,axiom,
    ! [X19,X13,X11,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)),X11),X13)),X19) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X13),X19))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Int__assoc__eq) ).

fof(fact_INT__simps_I7_J,axiom,
    ! [X13,X11,X19,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X16),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11)),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X19),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I7_J) ).

fof(fact_UN__simps_I5_J,axiom,
    ! [X13,X11,X19,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X16),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11)),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X19),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I5_J) ).

fof(fact_UN__simps_I7_J,axiom,
    ! [X13,X11,X19,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X16),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11)),X13)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X19),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I7_J) ).

fof(fact_Int__UN__distrib,axiom,
    ! [X11,X68,X16,X13,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X68),X11)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X68),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X16),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X13)),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__UN__distrib) ).

fof(fact_UN__extend__simps_I5_J,axiom,
    ! [X13,X19,X16,X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X19),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X16),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11)),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I5_J) ).

fof(fact_UN__extend__simps_I7_J,axiom,
    ! [X13,X19,X16,X11,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X19),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X16),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11)),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I7_J) ).

fof(fact_INT__extend__simps_I7_J,axiom,
    ! [X13,X19,X16,X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X19),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X16),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11)),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I7_J) ).

fof(fact_Un__INT__distrib,axiom,
    ! [X11,X68,X16,X13,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X68),X11)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X68),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X16),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X13)),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__INT__distrib) ).

fof(fact_union__comp__emptyR,axiom,
    ! [X19,X13,X11,X5] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X11),X13) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))
     => ( hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X11),X19) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))
       => hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X11),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X13),X19)) = 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_type__definition_ORep__range,axiom,
    ! [X11,X177,X178,X16,X5] :
      ( c_Typedef_Otype__definition(X5,X16,X178,X177,X11)
     => hAPP(c_Set_Oimage(X5,X16,X178),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__range) ).

fof(fact_singleton__quotient,axiom,
    ! [X34,X12,X5] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X34) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X34),hAPP(hAPP(c_Set_Oinsert(X5),X12),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,
    ! [X37,X27,X2,X34,X16,X5] :
      ( c_Equiv__Relations_Ocongruent(X5,X16,X34,X2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X27),X37)),X34))
       => hAPP(X2,X27) = hAPP(X2,X37) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruentD) ).

fof(fact_rtrancl__subset__rtrancl,axiom,
    ! [X84,X34,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),c_Transitive__Closure_Ortrancl(X5,X84)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X34)),c_Transitive__Closure_Ortrancl(X5,X84))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__subset__rtrancl) ).

fof(fact_rel__pow__imp__rtrancl,axiom,
    ! [X36,X76,X161,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X161),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X76),X36)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X161),c_Transitive__Closure_Ortrancl(X5,X36))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__imp__rtrancl) ).

fof(fact_acc__downward,axiom,
    ! [X6,X34,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X17),c_Wellfounded_Oacc(X5,X34)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),X34))
       => hBOOL(hAPP(hAPP(c_member(X5),X6),c_Wellfounded_Oacc(X5,X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downward) ).

fof(fact_Min_Oinsert__remove,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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),X12),X11)) = X12 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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),X12),X11)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X12),c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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),X12),X11)) = X12 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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),X12),X11)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X12),c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oinsert__remove) ).

fof(fact_Sup__fin_Oinsert__remove,axiom,
    ! [X12,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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),X12),X11)) = X12 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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),X12),X11)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X12),c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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_Inf__fin_Oinsert__remove,axiom,
    ! [X12,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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),X12),X11)) = X12 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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),X12),X11)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X12),c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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_type__definition_OAbs__image,axiom,
    ! [X11,X177,X178,X16,X5] :
      ( c_Typedef_Otype__definition(X5,X16,X178,X177,X11)
     => hAPP(c_Set_Oimage(X16,X5,X177),X11) = 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,
    ! [X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,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)),X11)))
     => c_Fun_Oinj__on(tc_List_Olist(X5),tc_List_Olist(X16),hAPP(c_List_Omap(X5,X16),X2),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__mapI) ).

fof(fact_image__inv__f__f,axiom,
    ! [X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X16,X5,c_Hilbert__Choice_Oinv__into(X5,X16,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2)),hAPP(c_Set_Oimage(X5,X16,X2),X11)) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__inv__f__f) ).

fof(fact_inv__image__comp,axiom,
    ! [X31,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X16,X5,c_Hilbert__Choice_Oinv__into(X5,X16,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2)),hAPP(c_Set_Oimage(X5,X16,X2),X31)) = X31 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__image__comp) ).

fof(fact_update__zip,axiom,
    ! [X233,X102,X225,X221,X5,X15] : hAPP(hAPP(c_List_Olist__update(tc_prod(X15,X5),hAPP(hAPP(c_List_Ozip(X15,X5),X221),X225)),X102),X233) = hAPP(hAPP(c_List_Ozip(X15,X5),hAPP(hAPP(c_List_Olist__update(X15,X221),X102),hAPP(c_Product__Type_Ofst(X15,X5),X233))),hAPP(hAPP(c_List_Olist__update(X5,X225),X102),hAPP(c_Product__Type_Osnd(X15,X5),X233))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_update__zip) ).

fof(fact_finite__Collect__less__nat,axiom,
    ! [X30] : 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)),X30)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__less__nat) ).

fof(fact_finite__Collect__le__nat,axiom,
    ! [X30] : 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)),X30)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__le__nat) ).

fof(fact_O__assoc,axiom,
    ! [X108,X35,X36,X55,X16,X38,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X38,X16),hAPP(hAPP(c_Relation_Orel__comp(X5,X55,X38),X36),X35)),X108) = hAPP(hAPP(c_Relation_Orel__comp(X5,X55,X16),X36),hAPP(hAPP(c_Relation_Orel__comp(X55,X38,X16),X35),X108)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_O__assoc) ).

fof(fact_setsum_Oremove,axiom,
    ! [X1,X12,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),X11) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16),hAPP(X1,X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Oremove) ).

fof(fact_setsum__diff1_H,axiom,
    ! [X2,X6,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X11) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16),hAPP(X2,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),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_setprod_Oremove,axiom,
    ! [X1,X12,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X11) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(X1,X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Oremove) ).

fof(fact_Pow__INT__eq,axiom,
    ! [X13,X11,X16,X5] : hAPP(c_Set_OPow(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),X16),c_Set_OPow(X5)),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__INT__eq) ).

fof(fact_q__pos__lemma,axiom,
    ! [X141,X142,X143] :
      ( 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),X143),X142)),X141)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X141),X143))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X143))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X142)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).

fof(fact_UN__le__eq__Un0,axiom,
    ! [X67,X76,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),X76)),X67) = 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),X76)),X67)),hAPP(X67,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,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
     => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X11)),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13))) ),
    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,
    ! [X67,X13,X11,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),X11),X13)),X67) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X11),X67)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X13),X67)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__Un) ).

fof(fact_UN__Un,axiom,
    ! [X67,X13,X11,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),X11),X13)),X67) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X11),X67)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X13),X67)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__Un) ).

fof(fact_dom__eq__singleton__conv,axiom,
    ! [X12,X2,X16,X5] :
      ( c_Map_Odom(X5,X16,X2) = hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))
    <=> ? [X57] : X2 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),hAPP(c_COMBK(tc_Option_Ooption(X16),X5),c_Option_Ooption_ONone(X16))),X12),hAPP(c_Option_Ooption_OSome(X16),X57)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dom__eq__singleton__conv) ).

fof(fact_Compl__subset__Compl__iff,axiom,
    ! [X13,X11,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)),X11)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X13)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__subset__Compl__iff) ).

fof(fact_INT__lower,axiom,
    ! [X13,X16,X11,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X11),X13)),hAPP(X13,X6))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__lower) ).

fof(fact_rtrancl__mono,axiom,
    ! [X84,X34,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),X84))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X34)),c_Transitive__Closure_Ortrancl(X5,X84))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__mono) ).

fof(fact_vimage__INT,axiom,
    ! [X13,X11,X38,X2,X16,X5] : hAPP(c_Set_Ovimage(X5,X16,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X38,tc_fun(X16,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X38,tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X38),c_Set_Ovimage(X5,X16,X2)),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__INT) ).

fof(fact_vimage__UN,axiom,
    ! [X13,X11,X38,X2,X16,X5] : hAPP(c_Set_Ovimage(X5,X16,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,tc_fun(X16,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X38),c_Set_Ovimage(X5,X16,X2)),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__UN) ).

fof(fact_Image__UN,axiom,
    ! [X13,X11,X38,X34,X5,X16] : hAPP(c_Relation_OImage(X16,X5,X34),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,tc_fun(X16,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X38),c_Relation_OImage(X16,X5,X34)),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__UN) ).

fof(fact_image__UN,axiom,
    ! [X13,X11,X38,X2,X5,X16] : hAPP(c_Set_Oimage(X16,X5,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,tc_fun(X16,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X38),c_Set_Oimage(X16,X5,X2)),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__UN) ).

fof(fact_add__frac__eq,axiom,
    ! [X132,X14,X23,X22,X15] :
      ( class_Fields_Ofield(X15)
     => ( X22 != c_Groups_Ozero__class_Ozero(X15)
       => ( X23 != c_Groups_Ozero__class_Ozero(X15)
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X22)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X132),X23)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X132),X22))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X22),X23)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__eq) ).

fof(fact_diff__frac__eq,axiom,
    ! [X132,X14,X23,X22,X15] :
      ( class_Fields_Ofield(X15)
     => ( X22 != c_Groups_Ozero__class_Ozero(X15)
       => ( X23 != c_Groups_Ozero__class_Ozero(X15)
         => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X22)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X132),X23)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X132),X22))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X22),X23)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__frac__eq) ).

fof(fact_Compl__eq,axiom,
    ! [X11,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11) = 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)),X11))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__eq) ).

fof(fact_list__all2__lengthD,axiom,
    ! [X214,X212,X29,X16,X5] :
      ( c_List_Olist__all2(X5,X16,X29,X212,X214)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__lengthD) ).

fof(fact_Suc__mult__less__cancel1,axiom,
    ! [X76,X45,X30] :
      ( 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,X30)),X45)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),X76)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).

fof(fact_Suc__mult__le__cancel1,axiom,
    ! [X76,X45,X30] :
      ( 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,X30)),X45)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),X76)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).

fof(fact_split__pos__lemma,axiom,
    ! [X76,X29,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))
     => ( hBOOL(hAPP(hAPP(X29,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X76),X30)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X76,X30)))
      <=> ! [X145,X124] :
            ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X124))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X124),X30))
              & X76 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X145)),X124) )
           => hBOOL(hAPP(hAPP(X29,X145),X124)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__pos__lemma) ).

fof(fact_enum__all__option__def,axiom,
    ! [X29,X5] :
      ( class_Enum_Oenum(X5)
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X5)),X29))
      <=> ( hBOOL(hAPP(X29,c_Option_Ooption_ONone(X5)))
          & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X5),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X5),tc_HOL_Obool,X5),X29),c_Option_Ooption_OSome(X5)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__all__option__def) ).

fof(fact_inj__on__inv__into,axiom,
    ! [X11,X2,X16,X13,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),hAPP(c_Set_Oimage(X16,X5,X2),X11)))
     => c_Fun_Oinj__on(X5,X16,c_Hilbert__Choice_Oinv__into(X16,X5,X11,X2),X13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__inv__into) ).

fof(fact_UN__o,axiom,
    ! [X2,X1,X38,X11,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Fun_Ocomp(X38,tc_fun(X5,tc_HOL_Obool),X16,X1),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X16,X38,X2),X11)),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__o) ).

fof(fact_setsum_Oinsert__remove,axiom,
    ! [X12,X1,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16),hAPP(X1,X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Oinsert__remove) ).

fof(fact_setprod_Oinsert__remove,axiom,
    ! [X12,X1,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(X1,X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Oinsert__remove) ).

fof(fact_fun__upd__upd,axiom,
    ! [X37,X27,X12,X2,X16,X5] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),X2),X12),X27)),X12),X37) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),X2),X12),X37),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__upd) ).

fof(fact_f__inv__into__f,axiom,
    ! [X11,X2,X16,X27,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X27),hAPP(c_Set_Oimage(X16,X5,X2),X11)))
     => hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X16,X5,X11,X2),X27)) = X27 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_f__inv__into__f) ).

fof(fact_split__neg__lemma,axiom,
    ! [X76,X29,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(X29,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X76),X30)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X76,X30)))
      <=> ! [X145,X124] :
            ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),X124))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X124),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & X76 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X145)),X124) )
           => hBOOL(hAPP(hAPP(X29,X145),X124)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__neg__lemma) ).

fof(fact_zip__same__conv__map,axiom,
    ! [X212,X5] : hAPP(hAPP(c_List_Ozip(X5,X5),X212),X212) = 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))),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__same__conv__map) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
    ! [X13,X11] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X11),X13) = 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)),X11)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X13))),
    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,
    ! [X13,X11] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X11),X13) = 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)),X11)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X13))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J) ).

fof(fact_surj__iff,axiom,
    ! [X2,X5,X16] :
      ( hAPP(c_Set_Oimage(X16,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
    <=> hAPP(c_Fun_Ocomp(X16,X5,X5,X2),c_Hilbert__Choice_Oinv__into(X16,X5,c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)),X2)) = c_Fun_Oid(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__iff) ).

fof(fact_power__Suc__less,axiom,
    ! [X98,X25,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),c_Groups_Oone__class_Oone(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98))),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less) ).

fof(fact_type__definition_ORep__inject,axiom,
    ! [X27,X12,X11,X177,X178,X16,X5] :
      ( c_Typedef_Otype__definition(X5,X16,X178,X177,X11)
     => ( hAPP(X178,X12) = hAPP(X178,X27)
      <=> X12 = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).

fof(fact_finite__cartesian__productD2,axiom,
    ! [X13,X11,X16,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X13))))
     => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__cartesian__productD2) ).

fof(fact_finite__cartesian__productD1,axiom,
    ! [X13,X11,X16,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X13))))
     => ( X13 != c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__cartesian__productD1) ).

fof(fact_type__definition_ORep__inverse,axiom,
    ! [X12,X11,X177,X178,X16,X5] :
      ( c_Typedef_Otype__definition(X5,X16,X178,X177,X11)
     => hAPP(X177,hAPP(X178,X12)) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).

fof(fact_abs__triangle__ineq2,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),hAPP(c_Groups_Oabs__class_Oabs(X15),X26))),hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X25),X26)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2) ).

fof(fact_abs__triangle__ineq2__sym,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),hAPP(c_Groups_Oabs__class_Oabs(X15),X26))),hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X26),X25)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2__sym) ).

fof(fact_vimage__insert,axiom,
    ! [X13,X6,X2,X16,X5] : hAPP(c_Set_Ovimage(X5,X16,X2),hAPP(hAPP(c_Set_Oinsert(X16),X6),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X16,X2),hAPP(hAPP(c_Set_Oinsert(X16),X6),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(X5,X16,X2),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__insert) ).

fof(fact_list__all2__Nil,axiom,
    ! [X214,X29,X16,X5] :
      ( c_List_Olist__all2(X5,X16,X29,c_List_Olist_ONil(X5),X214)
    <=> X214 = c_List_Olist_ONil(X16) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__Nil) ).

fof(fact_list__all2__Nil2,axiom,
    ! [X212,X29,X16,X5] :
      ( c_List_Olist__all2(X5,X16,X29,X212,c_List_Olist_ONil(X16))
    <=> X212 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__Nil2) ).

fof(fact_DomainI,axiom,
    ! [X34,X17,X6,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17)),X34))
     => hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Relation_ODomain(X5,X16),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainI) ).

fof(fact_RangeI,axiom,
    ! [X34,X17,X6,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17)),X34))
     => hBOOL(hAPP(hAPP(c_member(X16),X17),hAPP(c_Relation_ORange(X5,X16),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeI) ).

fof(fact_set__drop__subset__set__drop,axiom,
    ! [X212,X5,X45,X76] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X76),X45))
     => 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),X45),X212))),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Odrop(X5),X76),X212)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__drop__subset__set__drop) ).

fof(fact_set__take__subset__set__take,axiom,
    ! [X212,X5,X76,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76))
     => 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),X45),X212))),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Otake(X5),X76),X212)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__take__subset__set__take) ).

fof(fact_list__all2__eq,axiom,
    ! [X5,X214,X212] :
      ( X212 = X214
    <=> c_List_Olist__all2(X5,X5,c_fequal,X212,X214) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__eq) ).

fof(fact_sorted__list__of__set__insert,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => c_List_Olinorder__class_Osorted__list__of__set(X5,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X12),c_List_Olinorder__class_Osorted__list__of__set(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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,
    ! [X26,X98,X25,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),hAPP(c_Nat_OSuc,X98))),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X26),hAPP(c_Nat_OSuc,X98))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).

fof(fact_enum__ex__option__def,axiom,
    ! [X29,X5] :
      ( class_Enum_Oenum(X5)
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X5)),X29))
      <=> ( hBOOL(hAPP(X29,c_Option_Ooption_ONone(X5)))
          | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X5),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X5),tc_HOL_Obool,X5),X29),c_Option_Ooption_OSome(X5)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__ex__option__def) ).

fof(fact_min__max_Osup__le__fold__sup,axiom,
    ! [X17,X6,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),X17)),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X17),X11))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__le__fold__sup) ).

fof(fact_sup__le__fold__sup,axiom,
    ! [X17,X6,X11,X5] :
      ( class_Lattices_Osemilattice__sup(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X6),X17)),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X17),X11))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__le__fold__sup) ).

fof(fact_Domain__mono,axiom,
    ! [X84,X34,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X34),X84))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X16),X34)),hAPP(c_Relation_ODomain(X5,X16),X84))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__mono) ).

fof(fact_inj__imp__surj__inv,axiom,
    ! [X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X16,X5,c_Hilbert__Choice_Oinv__into(X5,X16,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2)),c_Orderings_Otop__class_Otop(tc_fun(X16,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,
    ! [X26,X25,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),c_Groups_Oone__class_Oone(X15)),c_Groups_Oone__class_Oone(X15))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__half__sum) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
    ! [X13,X11] :
      ( c_Nat__Transfer_Onat__set(X11)
     => ( c_Nat__Transfer_Onat__set(X13)
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X11),X13) = 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),X11)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X13))) ) ),
    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,
    ! [X13,X11] :
      ( c_Nat__Transfer_Onat__set(X11)
     => ( c_Nat__Transfer_Onat__set(X13)
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X11),X13) = 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),X11)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J) ).

fof(fact_combine__common__factor,axiom,
    ! [X24,X26,X113,X25,X15] :
      ( class_Rings_Osemiring(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X113)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X113)),X24)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26)),X113)),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).

fof(fact_Id__on__subset__Times,axiom,
    ! [X11,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Relation_OId__on(X5,X11)),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X11),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X11)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__subset__Times) ).

fof(fact_sort__foldl__insort,axiom,
    ! [X212,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Olinorder__class_Osort__key(X5,X5,c_COMBI(X5),X212) = 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)),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sort__foldl__insort) ).

fof(fact_def__lfp__induct,axiom,
    ! [X29,X2,X11,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( X11 = c_Inductive_Ocomplete__lattice__class_Olfp(X5,X2)
       => ( c_Orderings_Oorder__class_Omono(X5,X5,X2)
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X11),X29))),X29))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X11),X29)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__lfp__induct) ).

fof(fact_Range__Collect__split,axiom,
    ! [X29,X5,X16] : hAPP(c_Relation_ORange(X16,X5),hAPP(c_Set_OCollect(tc_prod(X16,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X16,X5,tc_HOL_Obool),X29))) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X16)),hAPP(c_COMBC(X16,X5,tc_HOL_Obool),X29))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Collect__split) ).

fof(fact_equiv__type,axiom,
    ! [X34,X11,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X11,X34)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X11),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X11)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__type) ).

fof(fact_List_Omap_Ocomp,axiom,
    ! [X1,X2,X5,X16,X38] : hAPP(c_Fun_Ocomp(tc_List_Olist(X38),tc_List_Olist(X16),tc_List_Olist(X5),hAPP(c_List_Omap(X38,X16),X2)),hAPP(c_List_Omap(X5,X38),X1)) = hAPP(c_List_Omap(X5,X16),hAPP(c_Fun_Ocomp(X38,X16,X5,X2),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Omap_Ocomp) ).

fof(fact_map__comp__map,axiom,
    ! [X1,X2,X5,X16,X38] : hAPP(c_Fun_Ocomp(tc_List_Olist(X38),tc_List_Olist(X16),tc_List_Olist(X5),hAPP(c_List_Omap(X38,X16),X2)),hAPP(c_List_Omap(X5,X38),X1)) = hAPP(c_List_Omap(X5,X16),hAPP(c_Fun_Ocomp(X38,X16,X5,X2),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__comp__map) ).

fof(fact_Option_Omap_Ocomp,axiom,
    ! [X1,X2,X5,X16,X38] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(X38),tc_Option_Ooption(X16),tc_Option_Ooption(X5),hAPP(c_Option_Omap(X38,X16),X2)),hAPP(c_Option_Omap(X5,X38),X1)) = hAPP(c_Option_Omap(X5,X16),hAPP(c_Fun_Ocomp(X38,X16,X5,X2),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Option_Omap_Ocomp) ).

fof(fact_refl__onD1,axiom,
    ! [X27,X12,X34,X11,X5] :
      ( c_Relation_Orefl__on(X5,X11,X34)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),X34))
       => hBOOL(hAPP(hAPP(c_member(X5),X12),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD1) ).

fof(fact_refl__onD2,axiom,
    ! [X27,X12,X34,X11,X5] :
      ( c_Relation_Orefl__on(X5,X11,X34)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),X34))
       => hBOOL(hAPP(hAPP(c_member(X5),X27),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD2) ).

fof(fact_listrel_ONil,axiom,
    ! [X34,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,X34))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel_ONil) ).

fof(fact_Int__Union2,axiom,
    ! [X11,X13,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),X13)),X11) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X13),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))),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Union2) ).

fof(fact_Id__on__iff,axiom,
    ! [X11,X27,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_Relation_OId__on(X5,X11)))
    <=> ( X12 = X27
        & hBOOL(hAPP(hAPP(c_member(X5),X12),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__iff) ).

fof(fact_finite__Plus__iff,axiom,
    ! [X13,X11,X16,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X5,X16)),c_Sum__Type_OPlus(X5,X16,X11,X13)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus__iff) ).

fof(fact_finite__PlusD_I1_J,axiom,
    ! [X13,X11,X16,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X5,X16)),c_Sum__Type_OPlus(X5,X16,X11,X13)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__PlusD_I1_J) ).

fof(fact_finite__PlusD_I2_J,axiom,
    ! [X13,X11,X16,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X5,X16)),c_Sum__Type_OPlus(X5,X16,X11,X13)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J) ).

fof(fact_SigmaI,axiom,
    ! [X13,X17,X16,X11,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
     => ( hBOOL(hAPP(hAPP(c_member(X16),X17),hAPP(X13,X6)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaI) ).

fof(fact_foldl__assoc,axiom,
    ! [X227,X27,X12,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),X12),X27)),X227) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X12),hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),X27),X227)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__assoc) ).

fof(fact_rel__pow__0__I,axiom,
    ! [X36,X12,X5] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X12)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X36))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__0__I) ).

fof(fact_quotient__disj,axiom,
    ! [X42,X31,X34,X11,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X11,X34)
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X31),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X11),X34)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X42),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X11),X34)))
         => ( X31 = X42
            | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X31),X42) = 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,
    ! [X212,X5,X97] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
     => 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))),X212)),hAPP(c_Code__Numeral_Oof__nat,X97)) = hAPP(hAPP(c_List_Onth(X5),X212),X97) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pick__same) ).

fof(fact_subset__card__intvl__is__intvl,axiom,
    ! [X30,X11] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X11),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X11)))))
     => X11 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__card__intvl__is__intvl) ).

fof(fact_ord_OgreaterThanLessThan__iff,axiom,
    ! [X66,X97,X96,X70,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X70),c_SetInterval_Oord_OgreaterThanLessThan(X5,X96,X97,X66)))
    <=> ( hBOOL(hAPP(hAPP(X96,X97),X70))
        & hBOOL(hAPP(hAPP(X96,X70),X66)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).

fof(fact_ord_OatLeastAtMost__iff,axiom,
    ! [X66,X97,X95,X70,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X70),c_SetInterval_Oord_OatLeastAtMost(X5,X95,X97,X66)))
    <=> ( hBOOL(hAPP(hAPP(X95,X97),X70))
        & hBOOL(hAPP(hAPP(X95,X70),X66)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).

fof(fact_set__Cons__sing__Nil,axiom,
    ! [X11,X5] : c_List_Oset__Cons(X5,X11,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))),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__Cons__sing__Nil) ).

fof(fact_INT__insert__distrib,axiom,
    ! [X13,X6,X16,X11,X66,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X66),X11))
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_Set_Oinsert(X16),X6)),X13)) = hAPP(hAPP(c_Set_Oinsert(X16),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X11),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__insert__distrib) ).

fof(fact_UN__insert__distrib,axiom,
    ! [X13,X6,X16,X11,X66,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X66),X11))
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_Set_Oinsert(X16),X6)),X13)) = hAPP(hAPP(c_Set_Oinsert(X16),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X11),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__insert__distrib) ).

fof(fact_finite__conv__nat__seg__image,axiom,
    ! [X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
    <=> ? [X107,X43] : X11 = hAPP(c_Set_Oimage(tc_Nat_Onat,X5,X43),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)),X107))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__conv__nat__seg__image) ).

fof(fact_nat__seg__image__imp__finite,axiom,
    ! [X76,X2,X5,X11] :
      ( X11 = 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)),X76)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__seg__image__imp__finite) ).

fof(fact_take__hd__drop,axiom,
    ! [X221,X15,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
     => hAPP(hAPP(c_List_Oappend(X15),hAPP(hAPP(c_List_Otake(X15),X98),X221)),hAPP(hAPP(c_List_Olist_OCons(X15),hAPP(c_List_Ohd(X15),hAPP(hAPP(c_List_Odrop(X15),X98),X221))),c_List_Olist_ONil(X15))) = hAPP(hAPP(c_List_Otake(X15),hAPP(c_Nat_OSuc,X98)),X221) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__hd__drop) ).

fof(fact_Diff__insert2,axiom,
    ! [X13,X6,X11,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13)) = 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)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__insert2) ).

fof(fact_listrel__rtrancl__refl,axiom,
    ! [X34,X212,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)),X212),X212)),c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X34)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__refl) ).

fof(fact_Inter__subset,axiom,
    ! [X13,X11,X5] :
      ( ! [X195] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X195),X11))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X195),X13)) )
     => ( X11 != 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),X11)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__subset) ).

fof(fact_zmod__zmult2__eq,axiom,
    ! [X26,X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X24)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26),X24))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zmult2__eq) ).

fof(fact_Int__greatest,axiom,
    ! [X13,X11,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X11))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X13))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__greatest) ).

fof(fact_max__Suc2,axiom,
    ! [X76,X45] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X45),hAPP(c_Nat_OSuc,X76)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X76),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)),X76)),X45),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__Suc2) ).

fof(fact_rel__pow__add,axiom,
    ! [X36,X76,X45,X5] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X76)),X36) = hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X45),X36)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X76),X36)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__add) ).

fof(fact_Union__mono,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X11),X13))
     => 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),X11)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__mono) ).

fof(fact_Inter__anti__mono,axiom,
    ! [X11,X13,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X13),X11))
     => 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),X11)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__anti__mono) ).

fof(fact_abs__triangle__ineq,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),hAPP(c_Groups_Oabs__class_Oabs(X15),X26)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq) ).

fof(fact_abs__triangle__ineq4,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X25),X26))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),hAPP(c_Groups_Oabs__class_Oabs(X15),X26)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq4) ).

fof(fact_min__Suc2,axiom,
    ! [X76,X45] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X45),hAPP(c_Nat_OSuc,X76)) = 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)),X76)),X45),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__Suc2) ).

fof(fact_card_Oremove,axiom,
    ! [X12,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hAPP(c_Finite__Set_Ocard(X5),X11) = 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)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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,
    ! [X22,X225,X14,X102,X221,X5,X15] : hAPP(hAPP(c_List_Ozip(X15,X5),hAPP(hAPP(c_List_Olist__update(X15,X221),X102),X14)),hAPP(hAPP(c_List_Olist__update(X5,X225),X102),X22)) = hAPP(hAPP(c_List_Olist__update(tc_prod(X15,X5),hAPP(hAPP(c_List_Ozip(X15,X5),X221),X225)),X102),hAPP(hAPP(c_Product__Type_OPair(X15,X5),X14),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__update) ).

fof(fact_image__Int,axiom,
    ! [X13,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X5,X16,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X16,X2),X11)),hAPP(c_Set_Oimage(X5,X16,X2),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Int) ).

fof(fact_image__set__diff,axiom,
    ! [X13,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X5,X16,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X16,X2),X11)),hAPP(c_Set_Oimage(X5,X16,X2),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__set__diff) ).

fof(fact_the__inv__into__onto,axiom,
    ! [X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => hAPP(c_Set_Oimage(X16,X5,c_Fun_Othe__inv__into(X5,X16,X11,X2)),hAPP(c_Set_Oimage(X5,X16,X2),X11)) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__onto) ).

fof(fact_pair__box_Orecs,axiom,
    ! [X17,X6,X89,X5,X38,X16] : c_Nitpick_Opair__box_Opair__box__rec(X16,X38,X5,X89,c_Nitpick_Opair__box_OPairBox(X16,X38,X6,X17)) = hAPP(hAPP(X89,X6),X17),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Orecs) ).

fof(fact_pair__box_Osimps_I2_J,axiom,
    ! [X17,X6,X89,X5,X38,X16] : c_Nitpick_Opair__box_Opair__box__case(X16,X38,X5,X89,c_Nitpick_Opair__box_OPairBox(X16,X38,X6,X17)) = hAPP(hAPP(X89,X6),X17),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Osimps_I2_J) ).

fof(fact_zip__takeWhile__fst,axiom,
    ! [X214,X212,X29,X16,X5] : hAPP(hAPP(c_List_Ozip(X5,X16),c_List_OtakeWhile(X5,X29,X212)),X214) = c_List_OtakeWhile(tc_prod(X5,X16),hAPP(c_Fun_Ocomp(X5,tc_HOL_Obool,tc_prod(X5,X16),X29),c_Product__Type_Ofst(X5,X16)),hAPP(hAPP(c_List_Ozip(X5,X16),X212),X214)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__takeWhile__fst) ).

fof(fact_zmult__zless__mono2__lemma,axiom,
    ! [X100,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X102),X101))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X100))
       => 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),X100)),X102)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X100)),X101))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2__lemma) ).

fof(fact_Diff__Int2,axiom,
    ! [X13,X19,X11,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)),X11),X19)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X13),X19)) = 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)),X11),X19)),X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Int2) ).

fof(fact_Diff__Int__distrib2,axiom,
    ! [X19,X13,X11,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)),X11),X13)),X19) = 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)),X11),X19)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X13),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Int__distrib2) ).

fof(fact_Int__Un__distrib2,axiom,
    ! [X11,X19,X13,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)),X13),X19)),X11) = 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)),X13),X11)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Un__distrib2) ).

fof(fact_Un__Diff,axiom,
    ! [X19,X13,X11,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)),X11),X13)),X19) = 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)),X11),X19)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X13),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Diff) ).

fof(fact_Un__Int__distrib2,axiom,
    ! [X11,X19,X13,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)),X13),X19)),X11) = 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)),X13),X11)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X19),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Int__distrib2) ).

fof(fact_aset_I3_J,axiom,
    ! [X11,X10,X18] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10),c_Groups_Oone__class_Oone(tc_Int_Oint))),X11))
       => ( ! [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),X18)))
             => ! [X39] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X39),X11))
                 => X10 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X39),X3) ) )
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10),X18) = X10 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I3_J) ).

fof(fact_bset_I3_J,axiom,
    ! [X13,X10,X18] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10),c_Groups_Oone__class_Oone(tc_Int_Oint))),X13))
       => ( ! [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),X18)))
             => ! [X39] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X39),X13))
                 => X10 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X39),X3) ) )
         => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10),X18) = X10 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I3_J) ).

fof(fact_take__add,axiom,
    ! [X221,X15,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X101)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
     => hAPP(hAPP(c_List_Otake(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X101)),X221) = hAPP(hAPP(c_List_Oappend(X15),hAPP(hAPP(c_List_Otake(X15),X102),X221)),hAPP(hAPP(c_List_Otake(X15),X101),hAPP(hAPP(c_List_Odrop(X15),X102),X221))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__add) ).

fof(fact_card_Ounion__inter__neutral,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
       => ( ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
           => 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)),X11),X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X11)),hAPP(c_Finite__Set_Ocard(X5),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Ounion__inter__neutral) ).

fof(fact_inj__on__map__add__dom,axiom,
    ! [X208,X45,X16,X5] :
      ( c_Fun_Oinj__on(X5,tc_Option_Ooption(X16),c_Map_Omap__add(X5,X16,X45,X208),c_Map_Odom(X5,X16,X208))
    <=> c_Fun_Oinj__on(X5,tc_Option_Ooption(X16),X208,c_Map_Odom(X5,X16,X208)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__map__add__dom) ).

fof(fact_card__Suc__Diff1,axiom,
    ! [X12,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(X5),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Suc__Diff1) ).

fof(fact_min__max_Omono__sup,axiom,
    ! [X13,X11,X2,X5,X16] :
      ( ( class_Lattices_Osemilattice__sup(X16)
        & class_Orderings_Olinorder(X5) )
     => ( c_Orderings_Oorder__class_Omono(X5,X16,X2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X16),hAPP(X2,X11)),hAPP(X2,X13))),hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X11),X13)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Omono__sup) ).

fof(fact_mono__sup,axiom,
    ! [X13,X11,X2,X5,X16] :
      ( ( class_Lattices_Osemilattice__sup(X16)
        & class_Lattices_Osemilattice__sup(X5) )
     => ( c_Orderings_Oorder__class_Omono(X5,X16,X2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X16),hAPP(X2,X11)),hAPP(X2,X13))),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X11),X13)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mono__sup) ).

fof(fact_folding_Ocommute__comp_H_H,axiom,
    ! [X13,X11,X90,X2,X16,X5] :
      ( c_Finite__Set_Ofolding(X5,X16,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => hAPP(c_Fun_Ocomp(X16,X16,X16,hAPP(X90,X13)),hAPP(X90,X11)) = hAPP(c_Fun_Ocomp(X16,X16,X16,hAPP(X90,X11)),hAPP(X90,X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ocommute__comp_H_H) ).

fof(fact_takeWhile__not__last,axiom,
    ! [X5,X212] :
      ( X212 != c_List_Olist_ONil(X5)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),X212))
       => 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,X212))),X212) = c_List_Obutlast(X5,X212) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__not__last) ).

fof(fact_Compl__INT,axiom,
    ! [X13,X11,X16,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X16),c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool))),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__INT) ).

fof(fact_Compl__UN,axiom,
    ! [X13,X11,X16,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X16),c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool))),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__UN) ).

fof(fact_fold1Set__sing,axiom,
    ! [X17,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)))),X17))
    <=> X6 = X17 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1Set__sing) ).

fof(fact_folding_Ounion,axiom,
    ! [X13,X11,X90,X2,X16,X5] :
      ( c_Finite__Set_Ofolding(X5,X16,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X90,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(c_Fun_Ocomp(X16,X16,X16,hAPP(X90,X11)),hAPP(X90,X13)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ounion) ).

fof(fact_split__div_H,axiom,
    ! [X76,X45,X29] :
      ( hBOOL(hAPP(X29,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X45),X76)))
    <=> ( ( X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        | ? [X150] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X76),X150)),X45))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X76),hAPP(c_Nat_OSuc,X150))))
            & hBOOL(hAPP(X29,X150)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__div_H) ).

fof(fact_card_Oinsert__remove,axiom,
    ! [X12,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = 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)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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,
    ! [X20,X21,X55,X17,X6,X5,X16,X38] :
      ( hAPP(c_Fun_Ocomp(X38,X16,X5,X6),X17) = hAPP(c_Fun_Ocomp(X55,X16,X5,X21),X20)
     => ! [X57] : hAPP(X6,hAPP(X17,X57)) = hAPP(X21,hAPP(X20,X57)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__elim) ).

fof(fact_o__eq__dest,axiom,
    ! [X56,X20,X21,X55,X17,X6,X5,X16,X38] :
      ( hAPP(c_Fun_Ocomp(X38,X16,X5,X6),X17) = hAPP(c_Fun_Ocomp(X55,X16,X5,X21),X20)
     => hAPP(X6,hAPP(X17,X56)) = hAPP(X21,hAPP(X20,X56)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest) ).

fof(fact_insort__left__comm,axiom,
    ! [X212,X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X12),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X27),X212)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X27),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X12),X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__left__comm) ).

fof(fact_o__eq__id__dest,axiom,
    ! [X56,X21,X17,X6,X5,X16,X38] :
      ( hAPP(c_Fun_Ocomp(X38,X16,X5,X6),X17) = hAPP(c_Fun_Ocomp(X16,X16,X5,c_Fun_Oid(X16)),X21)
     => hAPP(X6,hAPP(X17,X56)) = hAPP(X21,X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__id__dest) ).

fof(fact_distinct__sort,axiom,
    ! [X212,X2,X5,X16] :
      ( class_Orderings_Olinorder(X16)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),c_List_Olinorder__class_Osort__key(X5,X16,X2,X212)))
      <=> hBOOL(hAPP(c_List_Odistinct(X5),X212)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__sort) ).

fof(fact_equiv__class__self,axiom,
    ! [X6,X34,X11,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X11,X34)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Relation_OImage(X5,X5,X34),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,
    ! [X11,X6,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_member(X16),hAPP(X2,X6)),hAPP(c_Set_Oimage(X5,X16,X2),X11)))
      <=> hBOOL(hAPP(hAPP(c_member(X5),X6),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).

fof(fact_INF__subset,axiom,
    ! [X2,X13,X11,X5,X16] :
      ( class_Complete__Lattice_Ocomplete__lattice(X16)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X16),X13),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X16),X11),X2))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__subset) ).

fof(fact_SUP__subset,axiom,
    ! [X2,X13,X11,X5,X16] :
      ( class_Complete__Lattice_Ocomplete__lattice(X16)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X16),X11),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X16),X13),X2))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__subset) ).

fof(fact_UN__simps_I1_J,axiom,
    ! [X13,X6,X16,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(X16,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_Set_Oinsert(X16),X6)),X13)) = c_Orderings_Obot__class_Obot(tc_fun(X16,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(X16,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_Set_Oinsert(X16),X6)),X13)) = hAPP(hAPP(c_Set_Oinsert(X16),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X19),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I1_J) ).

fof(fact_UN__extend__simps_I1_J,axiom,
    ! [X13,X6,X16,X5,X19] :
      ( ( X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Set_Oinsert(X16),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X19),X13)) = hAPP(hAPP(c_Set_Oinsert(X16),X6),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))) )
      & ( X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Set_Oinsert(X16),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X19),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_Set_Oinsert(X16),X6)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I1_J) ).

fof(fact_setsum__right__distrib,axiom,
    ! [X11,X2,X16,X34,X5] :
      ( class_Rings_Osemiring__0(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X34),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),X2),X11)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),hAPP(hAPP(c_COMBB(X5,X5,X16),hAPP(c_Groups_Otimes__class_Otimes(X5),X34)),X2)),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__right__distrib) ).

fof(fact_mlex__less,axiom,
    ! [X36,X5,X27,X12,X2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X12)),hAPP(X2,X27)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_Wellfounded_Omlex__prod(X5,X2,X36))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__less) ).

fof(fact_range__composition,axiom,
    ! [X1,X2,X38,X5,X16] : hAPP(c_Set_Oimage(X16,X5,hAPP(hAPP(c_COMBB(X38,X5,X16),X2),X1)),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X38,X5,X2),hAPP(c_Set_Oimage(X16,X38,X1),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__composition) ).

fof(fact_hb__flat_Osimps_I2_J,axiom,
    ! [X276,X253,X5] : c_Lazy__Sequence_Ohb__flat(X5,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5))),X253,X276)) = c_Lazy__Sequence_Oappend(tc_Option_Ooption(X5),hAPP(c_Option_Ooption_Ooption__case(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5)),tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5)),c_Lazy__Sequence_Ohit__bound(X5),c_COMBI(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5)))),X253),c_Lazy__Sequence_Ohb__flat(X5,X276)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hb__flat_Osimps_I2_J) ).

fof(fact_min__max_Omono__inf,axiom,
    ! [X13,X11,X2,X5,X16] :
      ( ( class_Lattices_Osemilattice__inf(X16)
        & class_Orderings_Olinorder(X5) )
     => ( c_Orderings_Oorder__class_Omono(X5,X16,X2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X11),X13))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16),hAPP(X2,X11)),hAPP(X2,X13)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Omono__inf) ).

fof(fact_mono__inf,axiom,
    ! [X13,X11,X2,X5,X16] :
      ( ( class_Lattices_Osemilattice__inf(X16)
        & class_Lattices_Osemilattice__inf(X5) )
     => ( c_Orderings_Oorder__class_Omono(X5,X16,X2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X11),X13))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16),hAPP(X2,X11)),hAPP(X2,X13)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mono__inf) ).

fof(fact_sorted__nth__monoI,axiom,
    ! [X221,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( ! [X145,X124] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X145),X124))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X124),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_List_Onth(X15),X221),X145)),hAPP(hAPP(c_List_Onth(X15),X221),X124))) ) )
       => c_List_Olinorder__class_Osorted(X15,X221) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__nth__monoI) ).

fof(fact_sorted__equals__nth__mono,axiom,
    ! [X212,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,X212)
      <=> ! [X124] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X124),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
           => ! [X145] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X145),X124))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_List_Onth(X5),X212),X145)),hAPP(hAPP(c_List_Onth(X5),X212),X124))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__equals__nth__mono) ).

fof(fact_INT__D,axiom,
    ! [X6,X13,X11,X16,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X11),X13)))
     => ( hBOOL(hAPP(hAPP(c_member(X16),X6),X11))
       => hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(X13,X6))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__D) ).

fof(fact_foldl__absorb0,axiom,
    ! [X227,X12,X5] :
      ( class_Groups_Omonoid__add(X5)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X12),hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X227)) = hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),X12),X227) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__absorb0) ).

fof(fact_list__update__swap,axiom,
    ! [X231,X14,X221,X15,X232,X102] :
      ( X102 != X232
     => hAPP(hAPP(c_List_Olist__update(X15,hAPP(hAPP(c_List_Olist__update(X15,X221),X102),X14)),X232),X231) = hAPP(hAPP(c_List_Olist__update(X15,hAPP(hAPP(c_List_Olist__update(X15,X221),X232),X231)),X102),X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__swap) ).

fof(fact_rel__pow__commute,axiom,
    ! [X76,X36,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X36),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X76),X36)) = hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X76),X36)),X36),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__commute) ).

fof(fact_card__insert,axiom,
    ! [X12,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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,
    ! [X24,X25,X26,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X24),X25)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X24),X26))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono) ).

fof(fact_divide__left__mono,axiom,
    ! [X24,X25,X26,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X24),X25)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X24),X26))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__left__mono) ).

fof(fact_mono__Field,axiom,
    ! [X84,X34,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),X84))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OField(X5),X34)),hAPP(c_Relation_OField(X5),X84))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mono__Field) ).

fof(fact_folding_Ocommute__comp_H,axiom,
    ! [X12,X11,X90,X2,X16,X5] :
      ( c_Finite__Set_Ofolding(X5,X16,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(c_Fun_Ocomp(X16,X16,X16,hAPP(X2,X12)),hAPP(X90,X11)) = hAPP(c_Fun_Ocomp(X16,X16,X16,hAPP(X90,X11)),hAPP(X2,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ocommute__comp_H) ).

fof(fact_INT__simps_I5_J,axiom,
    ! [X13,X6,X19,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X16),hAPP(c_Set_Oinsert(X5),X6)),X13)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X19),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I5_J) ).

fof(fact_INT__extend__simps_I5_J,axiom,
    ! [X13,X19,X16,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X19),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X19),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X16),hAPP(c_Set_Oinsert(X5),X6)),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I5_J) ).

fof(fact_left__add__mult__distrib,axiom,
    ! [X100,X101,X120,X102] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X102),X120)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X120)),X100)) = 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),X102),X101)),X120)),X100),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).

fof(fact_zip__takeWhile__snd,axiom,
    ! [X214,X29,X212,X16,X5] : hAPP(hAPP(c_List_Ozip(X5,X16),X212),c_List_OtakeWhile(X16,X29,X214)) = c_List_OtakeWhile(tc_prod(X5,X16),hAPP(c_Fun_Ocomp(X16,tc_HOL_Obool,tc_prod(X5,X16),X29),c_Product__Type_Osnd(X5,X16)),hAPP(hAPP(c_List_Ozip(X5,X16),X212),X214)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__takeWhile__snd) ).

fof(fact_option__map__o__empty,axiom,
    ! [X12,X2,X38,X5,X16] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(X16),tc_Option_Ooption(X5),X38,hAPP(c_Option_Omap(X16,X5),X2)),hAPP(c_COMBK(tc_Option_Ooption(X16),X38),c_Option_Ooption_ONone(X16))),X12) = c_Option_Ooption_ONone(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option__map__o__empty) ).

fof(fact_inj__fun,axiom,
    ! [X38,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => c_Fun_Oinj__on(X5,tc_fun(X38,X16),hAPP(hAPP(c_COMBB(X16,tc_fun(X38,X16),X5),c_COMBK(X16,X38)),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,
    ! [X13,X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X13),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,
    ! [X13,X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X13),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,
    ! [X24,X26,X25,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X24),c_Groups_Ozero__class_Ozero(X15)))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X24),X25)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X24),X26))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono__neg) ).

fof(fact_divide__left__mono__neg,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Fields_Olinordered__field__inverse__zero(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X24),c_Groups_Ozero__class_Ozero(X15)))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X24),X25)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X24),X26))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__left__mono__neg) ).

fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
    ! [X2,X12,X5,X16,X70] :
      ( ( X70 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Opos__decr__bind(X16,X5,X12,X2),X70) = c_Lazy__Sequence_Oempty(X5) )
      & ( X70 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Opos__decr__bind(X16,X5,X12,X2),X70) = hAPP(c_Lazy__Sequence_Obind(X16,X5,hAPP(X12,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X70),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(X16,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5)),X2),X70)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__decr__bind__def) ).

fof(fact_nth__zip,axiom,
    ! [X225,X5,X221,X15,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X225)))
       => hAPP(hAPP(c_List_Onth(tc_prod(X15,X5)),hAPP(hAPP(c_List_Ozip(X15,X5),X221),X225)),X102) = hAPP(hAPP(c_Product__Type_OPair(X15,X5),hAPP(hAPP(c_List_Onth(X15),X221),X102)),hAPP(hAPP(c_List_Onth(X5),X225),X102)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__zip) ).

fof(fact_mod__mult2__eq,axiom,
    ! [X24,X26,X25] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X24)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X25),X26),X24))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25,X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult2__eq) ).

fof(fact_list__update__length,axiom,
    ! [X22,X225,X14,X221,X15] : hAPP(hAPP(c_List_Olist__update(X15,hAPP(hAPP(c_List_Oappend(X15),X221),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X225))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),X22) = hAPP(hAPP(c_List_Oappend(X15),X221),hAPP(hAPP(c_List_Olist_OCons(X15),X22),X225)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__length) ).

fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
    ! [X34,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,X34))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X34)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__rtrancl__subset__rtrancl__listrel1) ).

fof(fact_rtrancl__Un__rtrancl,axiom,
    ! [X35,X36,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,X36)),c_Transitive__Closure_Ortrancl(X5,X35))) = c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X36),X35)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__Un__rtrancl) ).

fof(fact_zip__map__fst__snd,axiom,
    ! [X227,X16,X5] : hAPP(hAPP(c_List_Ozip(X5,X16),hAPP(hAPP(c_List_Omap(tc_prod(X5,X16),X5),c_Product__Type_Ofst(X5,X16)),X227)),hAPP(hAPP(c_List_Omap(tc_prod(X5,X16),X16),c_Product__Type_Osnd(X5,X16)),X227)) = X227,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__map__fst__snd) ).

fof(fact_setprod__reindex__cong,axiom,
    ! [X48,X1,X13,X11,X2,X16,X5,X38] :
      ( class_Groups_Ocomm__monoid__mult(X38)
     => ( c_Fun_Oinj__on(X5,X16,X2,X11)
       => ( X13 = hAPP(c_Set_Oimage(X5,X16,X2),X11)
         => ( X1 = hAPP(c_Fun_Ocomp(X16,X38,X5,X48),X2)
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16,X38),X48),X13) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X38),X1),X11) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__reindex__cong) ).

fof(fact_sum__squares__ge__zero,axiom,
    ! [X22,X14,X15] :
      ( class_Rings_Olinordered__ring(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X22),X22)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).

fof(fact_pred__nat__trancl__eq__le,axiom,
    ! [X76,X45] :
      ( 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),X45),X76)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__nat__trancl__eq__le) ).

fof(fact_psubset__imp__ex__mem,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => ? [X52] : hBOOL(hAPP(hAPP(c_member(X5),X52),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X13),X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__imp__ex__mem) ).

fof(fact_folding_Ocommute__comp,axiom,
    ! [X12,X27,X90,X2,X16,X5] :
      ( c_Finite__Set_Ofolding(X5,X16,X2,X90)
     => hAPP(c_Fun_Ocomp(X16,X16,X16,hAPP(X2,X27)),hAPP(X2,X12)) = hAPP(c_Fun_Ocomp(X16,X16,X16,hAPP(X2,X12)),hAPP(X2,X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ocommute__comp) ).

fof(fact_Sigma__Int__distrib1,axiom,
    ! [X19,X69,X68,X16,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X16),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X68),X69)),X19) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X68),X19)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X69),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Int__distrib1) ).

fof(fact_Sigma__Diff__distrib1,axiom,
    ! [X19,X69,X68,X16,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X16),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X68),X69)),X19) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X68),X19)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X69),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Diff__distrib1) ).

fof(fact_Sigma__Un__distrib1,axiom,
    ! [X19,X69,X68,X16,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X16),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X68),X69)),X19) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X68),X19)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X69),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Un__distrib1) ).

fof(fact_in__set__butlast__appendI,axiom,
    ! [X214,X212,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),c_List_Obutlast(X5,X212))))
        | hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),c_List_Obutlast(X5,X214)))) )
     => hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),c_List_Obutlast(X5,hAPP(hAPP(c_List_Oappend(X5),X212),X214))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__butlast__appendI) ).

fof(fact_acc__subset,axiom,
    ! [X156,X157,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X157),X156))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Wellfounded_Oacc(X5,X156)),c_Wellfounded_Oacc(X5,X157))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__subset) ).

fof(fact_insort__key__left__comm,axiom,
    ! [X212,X16,X27,X12,X2,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hAPP(X2,X12) != hAPP(X2,X27)
       => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X16,X5,X2),X27),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X16,X5,X2),X12),X212)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X16,X5,X2),X12),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X16,X5,X2),X27),X212)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__key__left__comm) ).

fof(fact_surj__f__inv__f,axiom,
    ! [X27,X2,X5,X16] :
      ( hAPP(c_Set_Oimage(X16,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X16,X5,c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)),X2),X27)) = X27 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__f__inv__f) ).

fof(fact_divmod__int__rel__div__mod,axiom,
    ! [X25,X26] :
      ( X26 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X25,X26),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__div__mod) ).

fof(fact_INT__extend__simps_I10_J,axiom,
    ! [X2,X13,X38,X11,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBB(X38,tc_fun(X5,tc_HOL_Obool),X16),X13),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X38,tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X16,X38,X2),X11)),X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I10_J) ).

fof(fact_UN__extend__simps_I10_J,axiom,
    ! [X2,X13,X38,X11,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBB(X38,tc_fun(X5,tc_HOL_Obool),X16),X13),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X16,X38,X2),X11)),X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I10_J) ).

fof(fact_INT__simps_I10_J,axiom,
    ! [X13,X11,X2,X38,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X38,X16,X2),X11)),X13) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X38,tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBB(X16,tc_fun(X5,tc_HOL_Obool),X38),X13),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I10_J) ).

fof(fact_UN__simps_I10_J,axiom,
    ! [X13,X11,X2,X38,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X38,X16,X2),X11)),X13) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBB(X16,tc_fun(X5,tc_HOL_Obool),X38),X13),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I10_J) ).

fof(fact_divmod__nat__rel,axiom,
    ! [X98,X99] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X99,X98),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),X98)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel) ).

fof(fact_Compl__anti__mono,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => 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)),X13)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__anti__mono) ).

fof(fact_finite__surj__inj,axiom,
    ! [X2,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Set_Oimage(X5,X5,X2),X11)))
       => c_Fun_Oinj__on(X5,X5,X2,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__surj__inj) ).

fof(fact_Compl__Times__UNIV1,axiom,
    ! [X11,X16,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X11))) = hAPP(hAPP(c_Product__Type_OSigma(X5,X16),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X16,tc_HOL_Obool)),X11))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__Times__UNIV1) ).

fof(fact_Compl__Times__UNIV2,axiom,
    ! [X11,X16,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(X5,X16),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11)),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__Times__UNIV2) ).

fof(fact_Cons__acc__listrel1I,axiom,
    ! [X212,X34,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),c_Wellfounded_Oacc(X5,X34)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X212),c_Wellfounded_Oacc(tc_List_Olist(X5),c_List_Olistrel1(X5,X34))))
       => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)),c_Wellfounded_Oacc(tc_List_Olist(X5),c_List_Olistrel1(X5,X34)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__acc__listrel1I) ).

fof(fact_neg__divide__less__eq,axiom,
    ! [X6,X17,X21,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( 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),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X17),X21)),X6))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21)),X17)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__less__eq) ).

fof(fact_neg__divide__le__eq,axiom,
    ! [X6,X17,X21,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),c_Groups_Ozero__class_Ozero(X5)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X17),X21)),X6))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21)),X17)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__le__eq) ).

fof(fact_accp__subset,axiom,
    ! [X156,X157,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X157),X156))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Wellfounded_Oaccp(X5,X156)),c_Wellfounded_Oaccp(X5,X157))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__subset) ).

fof(fact_folding__idem_Osubset__comp__idem,axiom,
    ! [X13,X11,X90,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__idem(X5,X16,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),X11))
         => hAPP(c_Fun_Ocomp(X16,X16,X16,hAPP(X90,X11)),hAPP(X90,X13)) = hAPP(X90,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__idem_Osubset__comp__idem) ).

fof(fact_insort__insert__triv,axiom,
    ! [X212,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => c_List_Olinorder__class_Oinsort__insert__key(X5,X5,c_COMBI(X5),X12,X212) = X212 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__insert__triv) ).

fof(fact_split__div__lemma,axiom,
    ! [X45,X149,X76] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X76))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X76),X149)),X45))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X76),hAPP(c_Nat_OSuc,X149)))) )
      <=> X149 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X45),X76) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__div__lemma) ).

fof(fact_setsum__diff,axiom,
    ! [X2,X13,X11,X5,X16] :
      ( class_Groups_Oab__group__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),X11))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__diff) ).

fof(fact_id__take__nth__drop,axiom,
    ! [X221,X15,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
     => X221 = hAPP(hAPP(c_List_Oappend(X15),hAPP(hAPP(c_List_Otake(X15),X102),X221)),hAPP(hAPP(c_List_Olist_OCons(X15),hAPP(hAPP(c_List_Onth(X15),X221),X102)),hAPP(hAPP(c_List_Odrop(X15),hAPP(c_Nat_OSuc,X102)),X221))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__take__nth__drop) ).

fof(fact_map__of__is__SomeD,axiom,
    ! [X27,X12,X210,X5,X16] :
      ( hAPP(hAPP(c_Map_Omap__of(X16,X5),X210),X12) = hAPP(c_Option_Ooption_OSome(X5),X27)
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X5)),hAPP(hAPP(c_Product__Type_OPair(X16,X5),X12),X27)),hAPP(c_List_Oset(tc_prod(X16,X5)),X210))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__is__SomeD) ).

fof(fact_map__of__SomeD,axiom,
    ! [X27,X30,X212,X5,X16] :
      ( hAPP(hAPP(c_Map_Omap__of(X16,X5),X212),X30) = hAPP(c_Option_Ooption_OSome(X5),X27)
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X5)),hAPP(hAPP(c_Product__Type_OPair(X16,X5),X30),X27)),hAPP(c_List_Oset(tc_prod(X16,X5)),X212))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__SomeD) ).

fof(fact_less__than__iff,axiom,
    ! [X27,X12] :
      ( 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),X12),X27)),c_Wellfounded_Oless__than))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__than__iff) ).

fof(fact_image__image,axiom,
    ! [X11,X1,X38,X2,X5,X16] : hAPP(c_Set_Oimage(X16,X5,X2),hAPP(c_Set_Oimage(X38,X16,X1),X11)) = hAPP(c_Set_Oimage(X38,X5,hAPP(hAPP(c_COMBB(X16,X5,X38),X2),X1)),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__image) ).

fof(fact_inj__on__map__eq__map,axiom,
    ! [X214,X212,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X212)),hAPP(c_List_Oset(X5),X214)))
     => ( hAPP(hAPP(c_List_Omap(X5,X16),X2),X212) = hAPP(hAPP(c_List_Omap(X5,X16),X2),X214)
      <=> X212 = X214 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__map__eq__map) ).

fof(fact_map__inj__on,axiom,
    ! [X214,X212,X2,X5,X16] :
      ( hAPP(hAPP(c_List_Omap(X16,X5),X2),X212) = hAPP(hAPP(c_List_Omap(X16,X5),X2),X214)
     => ( c_Fun_Oinj__on(X16,X5,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),hAPP(c_List_Oset(X16),X212)),hAPP(c_List_Oset(X16),X214)))
       => X212 = X214 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__inj__on) ).

fof(fact_zdiff__int__split,axiom,
    ! [X27,X12,X29] :
      ( hBOOL(hAPP(X29,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X27))))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X27),X12))
         => hBOOL(hAPP(X29,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X12)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X27)))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X27))
         => hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__int__split) ).

fof(fact_listsp__infI,axiom,
    ! [X13,X97,X11,X5] :
      ( hBOOL(hAPP(c_List_Olistsp(X5,X11),X97))
     => ( hBOOL(hAPP(c_List_Olistsp(X5,X13),X97))
       => hBOOL(hAPP(c_List_Olistsp(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)),X97)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__infI) ).

fof(fact_map__add__assoc,axiom,
    ! [X205,X202,X203,X16,X5] : c_Map_Omap__add(X5,X16,X203,c_Map_Omap__add(X5,X16,X202,X205)) = c_Map_Omap__add(X5,X16,c_Map_Omap__add(X5,X16,X203,X202),X205),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__assoc) ).

fof(fact_Image__Int__eq,axiom,
    ! [X13,X11,X36,X16,X5] :
      ( c_Relation_Osingle__valued(X5,X16,hAPP(c_Relation_Oconverse(X16,X5),X36))
     => hAPP(c_Relation_OImage(X16,X5,X36),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X16,X5,X36),X11)),hAPP(c_Relation_OImage(X16,X5,X36),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Int__eq) ).

fof(fact_frac__less2,axiom,
    ! [X23,X132,X22,X14,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X132))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X132),X23))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X23)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X22),X132))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__less2) ).

fof(fact_frac__less,axiom,
    ! [X23,X132,X22,X14,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X132))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X132),X23))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X23)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X22),X132))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__less) ).

fof(fact_mult__strict__mono,axiom,
    ! [X41,X24,X26,X25,X15] :
      ( class_Rings_Olinordered__semiring__strict(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X24),X41))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X26))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X41))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono) ).

fof(fact_mult__strict__mono_H,axiom,
    ! [X41,X24,X26,X25,X15] :
      ( class_Rings_Olinordered__semiring__strict(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X24),X41))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X41))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).

fof(fact_mult__le__less__imp__less,axiom,
    ! [X41,X24,X26,X25,X15] :
      ( class_Rings_Olinordered__semiring__strict(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X24),X41))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X41))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).

fof(fact_mult__less__le__imp__less,axiom,
    ! [X41,X24,X26,X25,X15] :
      ( class_Rings_Olinordered__semiring__strict(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X24),X41))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X41))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).

fof(fact_frac__le,axiom,
    ! [X23,X132,X22,X14,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X132))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X132),X23))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X23)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X22),X132))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__le) ).

fof(fact_mult__mono_H,axiom,
    ! [X41,X24,X26,X25,X15] :
      ( class_Rings_Oordered__semiring(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X24),X41))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X41))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).

fof(fact_mult__mono,axiom,
    ! [X41,X24,X26,X25,X15] :
      ( class_Rings_Oordered__semiring(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X24),X41))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X26))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X41))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).

fof(fact_setsum__diff1__ring,axiom,
    ! [X2,X6,X11,X5,X16] :
      ( class_Rings_Oring(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),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(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X11)),hAPP(X2,X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__diff1__ring) ).

fof(fact_geometric__sum,axiom,
    ! [X76,X12,X5] :
      ( class_Fields_Ofield(X5)
     => ( X12 != 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),X12)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X76)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),X76)),c_Groups_Oone__class_Oone(X5))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X12),c_Groups_Oone__class_Oone(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_geometric__sum) ).

fof(fact_listsum__abs,axiom,
    ! [X212,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),X212))),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X5,X5),c_Groups_Oabs__class_Oabs(X5)),X212)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__abs) ).

fof(fact_coinduct,axiom,
    ! [X31,X2,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( c_Orderings_Oorder__class_Omono(X5,X5,X2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X31),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X31),c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X2)))))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X31),c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X2))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coinduct) ).

fof(fact_image__add__atLeastLessThan,axiom,
    ! [X115,X70,X30] : 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)),X30)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X70),X115)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X70),X30)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X115),X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__add__atLeastLessThan) ).

fof(fact_setsum__add__nat__ivl,axiom,
    ! [X2,X161,X76,X45,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X76),X161))
         => 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,X45),X76))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X76),X161))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45),X161)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__add__nat__ivl) ).

fof(fact_setsum__diff__nat__ivl,axiom,
    ! [X2,X161,X76,X45,X5] :
      ( class_Groups_Oab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X76),X161))
         => 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,X45),X161))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45),X76))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X76),X161)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__diff__nat__ivl) ).

fof(fact_mult__right__less__imp__less,axiom,
    ! [X26,X24,X25,X15] :
      ( class_Rings_Olinordered__semiring(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X24)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).

fof(fact_mult__less__imp__less__right,axiom,
    ! [X26,X24,X25,X15] :
      ( class_Rings_Olinordered__semiring__strict(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X24)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).

fof(fact_power__less__imp__less__base,axiom,
    ! [X26,X98,X25,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X26),X98)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).

fof(fact_mult__left__less__imp__less,axiom,
    ! [X26,X25,X24,X15] :
      ( class_Rings_Olinordered__semiring(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X26)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).

fof(fact_mult__less__imp__less__left,axiom,
    ! [X26,X25,X24,X15] :
      ( class_Rings_Olinordered__semiring__strict(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X26)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).

fof(fact_mult__less__cancel__left__pos,axiom,
    ! [X17,X6,X21,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X17)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X17)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).

fof(fact_mult__right__le__imp__le,axiom,
    ! [X26,X24,X25,X15] :
      ( class_Rings_Olinordered__semiring__strict(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X24)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).

fof(fact_mult__left__le__imp__le,axiom,
    ! [X26,X25,X24,X15] :
      ( class_Rings_Olinordered__semiring__strict(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X26)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).

fof(fact_mult__le__cancel__left__pos,axiom,
    ! [X17,X6,X21,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X21))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X17)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X17)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).

fof(fact_setsum__diff__nat,axiom,
    ! [X2,X11,X13,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),X11))
       => 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)),X11),X13)) = 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),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__diff__nat) ).

fof(fact_fold1__strict__below__iff,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != 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)),X11)),X12))
          <=> ? [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X3),X12)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__strict__below__iff) ).

fof(fact_fold1__below__iff,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != 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)),X11)),X12))
          <=> ? [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X12)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__below__iff) ).

fof(fact_INF1__D,axiom,
    ! [X6,X17,X13,X11,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X11),X13),X17))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => hBOOL(hAPP(hAPP(X13,X6),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF1__D) ).

fof(fact_power__less__imp__less__exp,axiom,
    ! [X98,X99,X25,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Oone__class_Oone(X15)),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X99)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).

fof(fact_power__strict__increasing__iff,axiom,
    ! [X27,X12,X17,X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Oone__class_Oone(X5)),X17))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X17),X12)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X17),X27)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X27)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).

fof(fact_power__increasing__iff,axiom,
    ! [X27,X12,X17,X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Oone__class_Oone(X5)),X17))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X17),X12)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X17),X27)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12),X27)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing__iff) ).

fof(fact_power__le__imp__le__exp,axiom,
    ! [X98,X99,X25,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Oone__class_Oone(X15)),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X99)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X98)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).

fof(fact_select,axiom,
    ! [X84,X5,X212] :
      ( X212 != 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,X212),X84))),hAPP(c_List_Oset(X5),X212))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_select) ).

fof(fact_card__cartesian__product__singleton,axiom,
    ! [X11,X12,X16,X5] : hAPP(c_Finite__Set_Ocard(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X11))) = hAPP(c_Finite__Set_Ocard(X16),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__cartesian__product__singleton) ).

fof(fact_splitD,axiom,
    ! [X17,X6,X2,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_HOL_Obool),X2),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17)))
     => hBOOL(hAPP(hAPP(X2,X6),X17)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splitD) ).

fof(fact_swap__inj__on,axiom,
    ! [X11,X16,X5] : c_Fun_Oinj__on(tc_prod(X5,X16),tc_prod(X16,X5),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_prod(X16,X5)),hAPP(c_COMBC(X16,X5,tc_prod(X16,X5)),c_Product__Type_OPair(X16,X5))),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_swap__inj__on) ).

fof(fact_setprod__pos__nat,axiom,
    ! [X2,X35,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X35))
           => 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),X35))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__pos__nat) ).

fof(fact_setprod__pos__nat__iff,axiom,
    ! [X2,X35,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
     => ( 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),X35)))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X35))
           => 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,
    ! [X76,X45,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,X45),hAPP(c_Nat_OSuc,X76))) = 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,X45,X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__shift__bounds__cl__Suc__ivl) ).

fof(fact_mult__less__cancel__left__neg,axiom,
    ! [X17,X6,X21,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X17)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).

fof(fact_mult__le__cancel__left__neg,axiom,
    ! [X17,X6,X21,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),c_Groups_Ozero__class_Ozero(X5)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X17)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).

fof(fact_empty__upd__none,axiom,
    ! [X59,X12,X5,X16] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X16,tc_Option_Ooption(X5)),hAPP(c_COMBK(tc_Option_Ooption(X5),X16),c_Option_Ooption_ONone(X5))),X12),c_Option_Ooption_ONone(X5)),X59) = c_Option_Ooption_ONone(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__upd__none) ).

fof(fact_Int__lower1,axiom,
    ! [X13,X11,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)),X11),X13)),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__lower1) ).

fof(fact_Int__lower2,axiom,
    ! [X13,X11,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)),X11),X13)),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__lower2) ).

fof(fact_Diff__subset,axiom,
    ! [X13,X11,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)),X11),X13)),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__subset) ).

fof(fact_listsum__map__remove1,axiom,
    ! [X2,X212,X12,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => hAPP(c_List_Omonoid__add__class_Olistsum(X16),hAPP(hAPP(c_List_Omap(X5,X16),X2),X212)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16),hAPP(X2,X12)),hAPP(c_List_Omonoid__add__class_Olistsum(X16),hAPP(hAPP(c_List_Omap(X5,X16),X2),c_List_Oremove1(X5,X12,X212)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__map__remove1) ).

fof(fact_Diff__Int__distrib,axiom,
    ! [X13,X11,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)),X11),X13)) = 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),X11)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X19),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Int__distrib) ).

fof(fact_Int__Un__distrib,axiom,
    ! [X19,X13,X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X13),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)),X11),X13)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Un__distrib) ).

fof(fact_Diff__Int,axiom,
    ! [X19,X13,X11,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X13),X19)) = 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)),X11),X13)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Int) ).

fof(fact_Diff__Un,axiom,
    ! [X19,X13,X11,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X13),X19)) = 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)),X11),X13)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Un) ).

fof(fact_Un__Int__distrib,axiom,
    ! [X19,X13,X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X13),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)),X11),X13)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Int__distrib) ).

fof(fact_finite__range__map__of,axiom,
    ! [X210,X16,X5] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X5)),hAPP(c_Set_Oimage(X16,tc_Option_Ooption(X5),hAPP(c_Map_Omap__of(X16,X5),X210)),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__range__map__of) ).

fof(fact_prod_Orecs,axiom,
    ! [X17,X6,X89,X5,X38,X16] : c_Product__Type_Oprod_Oprod__rec(X16,X38,X5,X89,hAPP(hAPP(c_Product__Type_OPair(X16,X38),X6),X17)) = hAPP(hAPP(X89,X6),X17),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod_Orecs) ).

fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
    ! [X76,X45,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,X45)),hAPP(c_Nat_OSuc,X76))) = 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,X45),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__shift__bounds__Suc__ivl) ).

fof(fact_image__add__atLeastAtMost,axiom,
    ! [X115,X70,X30] : 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)),X30)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X70,X115)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X70),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X115),X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__add__atLeastAtMost) ).

fof(fact_Int__Collect,axiom,
    ! [X29,X11,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Set_OCollect(X5),X29))))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
        & hBOOL(hAPP(X29,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Collect) ).

fof(fact_atLeastLessThan__subset__iff,axiom,
    ! [X20,X21,X17,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),X17)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X21),X20)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),X6))
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),X20)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__subset__iff) ).

fof(fact_folding__idem_Ounion__idem,axiom,
    ! [X13,X11,X90,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__idem(X5,X16,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => hAPP(X90,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(c_Fun_Ocomp(X16,X16,X16,hAPP(X90,X11)),hAPP(X90,X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__idem_Ounion__idem) ).

fof(fact_wf__Un,axiom,
    ! [X84,X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => ( c_Wellfounded_Owf(X5,X84)
       => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X5),X34)),hAPP(c_Relation_ORange(X5,X5),X84)) = 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)),X34),X84)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__Un) ).

fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
    ! [X212,X27,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X16,X2)
     => hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),X27),hAPP(c_List_Oset(X5),X212)) = hAPP(c_List_Ofoldl(X16,X5,hAPP(c_COMBC(X5,X16,X16),X2),X27),c_List_Oremdups(X5,X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__set__remdups) ).

fof(fact_converse__meet,axiom,
    ! [X84,X34,X5,X16] : c_Predicate_Oconversep(X16,X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_fun(X5,tc_HOL_Obool))),X34),X84)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),c_Predicate_Oconversep(X16,X5,X34)),c_Predicate_Oconversep(X16,X5,X84)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__meet) ).

fof(fact_converse__join,axiom,
    ! [X84,X34,X5,X16] : c_Predicate_Oconversep(X16,X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_fun(X5,tc_HOL_Obool))),X34),X84)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),c_Predicate_Oconversep(X16,X5,X34)),c_Predicate_Oconversep(X16,X5,X84)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__join) ).

fof(fact_less__diff__iff,axiom,
    ! [X76,X45,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30),X45))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30),X76))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X45),X30)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X76),X30)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__iff) ).

fof(fact_le__diff__iff,axiom,
    ! [X76,X45,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30),X45))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30),X76))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X45),X30)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X76),X30)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__iff) ).

fof(fact_mult__less__cancel__left__disj,axiom,
    ! [X17,X6,X21,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X17)))
      <=> ( ( 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),X17)) )
          | ( 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),X17),X6)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).

fof(fact_mult__less__cancel__right__disj,axiom,
    ! [X17,X21,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),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X21)))
      <=> ( ( 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),X17)) )
          | ( 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),X17),X6)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).

fof(fact_insert__subset,axiom,
    ! [X13,X11,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)),X13))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X12),X13))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__subset) ).

fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
    ! [X2,X11,X5] :
      ( ( class_Groups_Ocomm__monoid__add(X5)
        & class_Groups_Ocomm__monoid__mult(X5) )
     => ( c_Nat__Transfer_Onat__set(X11)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X2),X11) = 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),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod_I1_J) ).

fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
    ! [X2,X11,X5] :
      ( ( class_Groups_Ocomm__monoid__add(X5)
        & class_Groups_Ocomm__monoid__mult(X5) )
     => ( c_Nat__Transfer_Onat__set(X11)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X2),X11) = 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),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod_I2_J) ).

fof(fact_setsum__Un__disjoint,axiom,
    ! [X1,X13,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),X13)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__Un__disjoint) ).

fof(fact_setprod__Un__disjoint,axiom,
    ! [X1,X13,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X13)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__Un__disjoint) ).

fof(fact_setprod_Ounion__disjoint,axiom,
    ! [X1,X13,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X13)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Ounion__disjoint) ).

fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
    ! [X11,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),X11) = 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)),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod_I1_J) ).

fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
    ! [X11,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),X11) = 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)),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod_I2_J) ).

fof(fact_listrel__subset__rtrancl__listrel1,axiom,
    ! [X34,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,X34)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X34)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__subset__rtrancl__listrel1) ).

fof(fact_image__add__int__atLeastLessThan,axiom,
    ! [X66,X97] : 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)),X97)),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),X66),X97))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X97),X66),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__add__int__atLeastLessThan) ).

fof(fact_drop__append,axiom,
    ! [X225,X221,X98,X15] : hAPP(hAPP(c_List_Odrop(X15),X98),hAPP(hAPP(c_List_Oappend(X15),X221),X225)) = hAPP(hAPP(c_List_Oappend(X15),hAPP(hAPP(c_List_Odrop(X15),X98),X221)),hAPP(hAPP(c_List_Odrop(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221))),X225)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__append) ).

fof(fact_take__append,axiom,
    ! [X225,X221,X98,X15] : hAPP(hAPP(c_List_Otake(X15),X98),hAPP(hAPP(c_List_Oappend(X15),X221),X225)) = hAPP(hAPP(c_List_Oappend(X15),hAPP(hAPP(c_List_Otake(X15),X98),X221)),hAPP(hAPP(c_List_Otake(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221))),X225)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__append) ).

fof(fact_set__remove1__subset,axiom,
    ! [X212,X12,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,X12,X212))),hAPP(c_List_Oset(X5),X212))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__remove1__subset) ).

fof(fact_set__sublist__subset,axiom,
    ! [X68,X212,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,X212,X68))),hAPP(c_List_Oset(X5),X212))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__sublist__subset) ).

fof(fact_inj__on__the__inv__into,axiom,
    ! [X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => c_Fun_Oinj__on(X16,X5,c_Fun_Othe__inv__into(X5,X16,X11,X2),hAPP(c_Set_Oimage(X5,X16,X2),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__the__inv__into) ).

fof(fact_Domain__Collect__split,axiom,
    ! [X29,X16,X5] : hAPP(c_Relation_ODomain(X5,X16),hAPP(c_Set_OCollect(tc_prod(X5,X16)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_HOL_Obool),X29))) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X16)),X29)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Collect__split) ).

fof(fact_fun__left__comm__idem_Ofold__set,axiom,
    ! [X212,X27,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm__idem(X5,X16,X2)
     => hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),X27),hAPP(c_List_Oset(X5),X212)) = hAPP(c_List_Ofoldl(X16,X5,hAPP(c_COMBC(X5,X16,X16),X2),X27),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__set) ).

fof(fact_setsum__negf,axiom,
    ! [X11,X2,X16,X5] :
      ( class_Groups_Oab__group__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),hAPP(hAPP(c_COMBB(X5,X5,X16),c_Groups_Ouminus__class_Ouminus(X5)),X2)),X11) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),X2),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__negf) ).

fof(fact_abs__setprod,axiom,
    ! [X11,X2,X16,X5] :
      ( class_Fields_Olinordered__field(X5)
     => hAPP(c_Groups_Oabs__class_Oabs(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16,X5),X2),X11)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16,X5),hAPP(hAPP(c_COMBB(X5,X5,X16),c_Groups_Oabs__class_Oabs(X5)),X2)),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__setprod) ).

fof(fact_all__set__conv__all__nth,axiom,
    ! [X29,X212,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
         => hBOOL(hAPP(X29,X3)) )
    <=> ! [X145] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X145),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
         => hBOOL(hAPP(X29,hAPP(hAPP(c_List_Onth(X5),X212),X145))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__set__conv__all__nth) ).

fof(fact_insert__mono,axiom,
    ! [X6,X18,X19,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),X18))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X19)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X18))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__mono) ).

fof(fact_lazy__sequence_Osimps_I5_J,axiom,
    ! [X268,X6,X88,X89,X16,X5] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X5,X16,X89,X88,c_Lazy__Sequence_Olazy__sequence_OInsert(X16,X6,X268)) = hAPP(hAPP(X88,X6),X268),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Osimps_I5_J) ).

fof(fact_sorted__append,axiom,
    ! [X214,X212,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Oappend(X5),X212),X214))
      <=> ( c_List_Olinorder__class_Osorted(X5,X212)
          & c_List_Olinorder__class_Osorted(X5,X214)
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
             => ! [X39] :
                  ( hBOOL(hAPP(hAPP(c_member(X5),X39),hAPP(c_List_Oset(X5),X214)))
                 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X39)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__append) ).

fof(fact_power__less__power__Suc,axiom,
    ! [X98,X25,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Oone__class_Oone(X15)),X25))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).

fof(fact_double__diff,axiom,
    ! [X19,X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),X19))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X13),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X19),X11)) = X11 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__diff) ).

fof(fact_Pow__mono,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => 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),X11)),hAPP(c_Set_OPow(X5),X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__mono) ).

fof(fact_K__record__comp,axiom,
    ! [X12,X2,X21,X38,X5,X16] : hAPP(hAPP(c_Fun_Ocomp(X16,X5,X38,hAPP(c_COMBK(X5,X16),X21)),X2),X12) = X21,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_K__record__comp) ).

fof(fact_set__drop__subset,axiom,
    ! [X212,X76,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),X76),X212))),hAPP(c_List_Oset(X5),X212))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__drop__subset) ).

fof(fact_set__take__subset,axiom,
    ! [X212,X76,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),X76),X212))),hAPP(c_List_Oset(X5),X212))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__take__subset) ).

fof(fact_pos__less__divide__eq,axiom,
    ! [X17,X6,X21,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( 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),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X17),X21)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21)),X17)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__less__divide__eq) ).

fof(fact_pos__divide__less__eq,axiom,
    ! [X6,X17,X21,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( 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),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X17),X21)),X6))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__less__eq) ).

fof(fact_mult__imp__less__div__pos,axiom,
    ! [X14,X23,X22,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X22))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X23),X22)),X14))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X23),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X22))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__less__div__pos) ).

fof(fact_pos__le__divide__eq,axiom,
    ! [X17,X6,X21,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X21))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X17),X21)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21)),X17)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__le__divide__eq) ).

fof(fact_pos__divide__le__eq,axiom,
    ! [X6,X17,X21,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X21))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X17),X21)),X6))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__le__eq) ).

fof(fact_mult__imp__le__div__pos,axiom,
    ! [X14,X23,X22,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X22))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X23),X22)),X14))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X23),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X22))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__le__div__pos) ).

fof(fact_takeWhile__nth,axiom,
    ! [X212,X29,X5,X115] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X115),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X29,X212))))
     => hAPP(hAPP(c_List_Onth(X5),c_List_OtakeWhile(X5,X29,X212)),X115) = hAPP(hAPP(c_List_Onth(X5),X212),X115) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__nth) ).

fof(fact_of__nat__setprod,axiom,
    ! [X11,X2,X16,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(X16,tc_Nat_Onat),X2),X11)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,X16),c_Nat_Osemiring__1__class_Oof__nat(X5)),X2)),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__setprod) ).

fof(fact_of__int__setprod,axiom,
    ! [X11,X2,X16,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(X16,tc_Int_Oint),X2),X11)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16,X5),hAPP(hAPP(c_COMBB(tc_Int_Oint,X5,X16),c_Int_Oring__1__class_Oof__int(X5)),X2)),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__setprod) ).

fof(fact_converse__Int,axiom,
    ! [X84,X34,X5,X16] : hAPP(c_Relation_Oconverse(X16,X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X16,X5),tc_HOL_Obool)),X34),X84)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X16,X5),X34)),hAPP(c_Relation_Oconverse(X16,X5),X84)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__Int) ).

fof(fact_converse__Un,axiom,
    ! [X84,X34,X5,X16] : hAPP(c_Relation_Oconverse(X16,X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X16,X5),tc_HOL_Obool)),X34),X84)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X16,X5),X34)),hAPP(c_Relation_Oconverse(X16,X5),X84)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__Un) ).

fof(fact_length__takeWhile__le,axiom,
    ! [X212,X29,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,X29,X212))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__takeWhile__le) ).

fof(fact_funpow__add,axiom,
    ! [X2,X76,X45,X5] : hAPP(hAPP(c_Nat_Ocompow(X5,X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X76)),X2) = hAPP(c_Fun_Ocomp(X5,X5,X5,hAPP(hAPP(c_Nat_Ocompow(X5,X5),X45),X2)),hAPP(hAPP(c_Nat_Ocompow(X5,X5),X76),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow__add) ).

fof(fact_of__nat__setsum,axiom,
    ! [X11,X2,X16,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(X16,tc_Nat_Onat),X2),X11)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,X16),c_Nat_Osemiring__1__class_Oof__nat(X5)),X2)),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__setsum) ).

fof(fact_of__int__setsum,axiom,
    ! [X11,X2,X16,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(X16,tc_Int_Oint),X2),X11)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),hAPP(hAPP(c_COMBB(tc_Int_Oint,X5,X16),c_Int_Oring__1__class_Oof__int(X5)),X2)),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__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,
    ! [X13,X16,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X13))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X13)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__cartesian__product) ).

fof(fact_card__psubset,axiom,
    ! [X11,X13,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X11)),hAPP(c_Finite__Set_Ocard(X5),X13)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__psubset) ).

fof(fact_finite__surj,axiom,
    ! [X2,X13,X16,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),X13),hAPP(c_Set_Oimage(X5,X16,X2),X11)))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__surj) ).

fof(fact_all__n__lists__def,axiom,
    ! [X76,X29,X5] :
      ( class_Enum_Oenum(X5)
     => ( c_Enum_Oall__n__lists(X5,X29,X76)
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X3),hAPP(c_List_Oset(tc_List_Olist(X5)),c_Enum_On__lists(X5,X76,c_Enum_Oenum__class_Oenum(X5)))))
           => hBOOL(hAPP(X29,X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__n__lists__def) ).

fof(fact_inj__on__Int,axiom,
    ! [X13,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => ( c_Fun_Oinj__on(X5,X16,X2,X13)
       => c_Fun_Oinj__on(X5,X16,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__Int) ).

fof(fact_nth__drop,axiom,
    ! [X221,X15,X102,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X102)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
     => hAPP(hAPP(c_List_Onth(X15),hAPP(hAPP(c_List_Odrop(X15),X98),X221)),X102) = hAPP(hAPP(c_List_Onth(X15),X221),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X102)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__drop) ).

fof(fact_sorted__rev__nth__mono,axiom,
    ! [X101,X102,X221,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( c_List_Olinorder__class_Osorted(X15,hAPP(c_List_Orev(X15),X221))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X101))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X101),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_List_Onth(X15),X221),X101)),hAPP(hAPP(c_List_Onth(X15),X221),X102))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__rev__nth__mono) ).

fof(fact_zip__append,axiom,
    ! [X240,X225,X241,X5,X221,X15] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X241)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X225) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X240)
       => hAPP(hAPP(c_List_Ozip(X15,X5),hAPP(hAPP(c_List_Oappend(X15),X221),X225)),hAPP(hAPP(c_List_Oappend(X5),X241),X240)) = hAPP(hAPP(c_List_Oappend(tc_prod(X15,X5)),hAPP(hAPP(c_List_Ozip(X15,X5),X221),X241)),hAPP(hAPP(c_List_Ozip(X15,X5),X225),X240)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__append) ).

fof(fact_ex__n__lists__def,axiom,
    ! [X76,X29,X5] :
      ( class_Enum_Oenum(X5)
     => ( c_Enum_Oex__n__lists(X5,X29,X76)
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X3),hAPP(c_List_Oset(tc_List_Olist(X5)),c_Enum_On__lists(X5,X76,c_Enum_Oenum__class_Oenum(X5)))))
            & hBOOL(hAPP(X29,X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__n__lists__def) ).

fof(fact_list__size__map,axiom,
    ! [X212,X1,X16,X2,X5] : c_List_Olist_Olist__size(X5,X2,hAPP(hAPP(c_List_Omap(X16,X5),X1),X212)) = c_List_Olist_Olist__size(X16,hAPP(c_Fun_Ocomp(X5,tc_Nat_Onat,X16,X2),X1),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__size__map) ).

fof(fact_refl__onD,axiom,
    ! [X6,X34,X11,X5] :
      ( c_Relation_Orefl__on(X5,X11,X34)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X6)),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD) ).

fof(fact_UN__upper,axiom,
    ! [X13,X16,X11,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool)),hAPP(X13,X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X11),X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__upper) ).

fof(fact_take__Cons__number__of,axiom,
    ! [X221,X14,X15,X126] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(X15),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = c_List_Olist_ONil(X15) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(X15),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = hAPP(hAPP(c_List_Olist_OCons(X15),X14),hAPP(hAPP(c_List_Otake(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X221)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Cons__number__of) ).

fof(fact_predicate2D,axiom,
    ! [X27,X12,X28,X29,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),X29),X28))
     => ( hBOOL(hAPP(hAPP(X29,X12),X27))
       => hBOOL(hAPP(hAPP(X28,X12),X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate2D) ).

fof(fact_rev__predicate2D,axiom,
    ! [X28,X16,X5,X27,X12,X29] :
      ( hBOOL(hAPP(hAPP(X29,X12),X27))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),X29),X28))
       => hBOOL(hAPP(hAPP(X28,X12),X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate2D) ).

fof(fact_fold1__antimono,axiom,
    ! [X13,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( X11 != 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)),X11),X13))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X13)),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X11))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__antimono) ).

fof(fact_Un__iff,axiom,
    ! [X13,X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
        | hBOOL(hAPP(hAPP(c_member(X5),X21),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__iff) ).

fof(fact_field__le__epsilon,axiom,
    ! [X22,X14,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( ! [X279] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X279))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X22),X279))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__le__epsilon) ).

fof(fact_restrict__restrict,axiom,
    ! [X13,X11,X45,X16,X5] : c_Map_Orestrict__map(X5,X16,c_Map_Orestrict__map(X5,X16,X45,X11),X13) = c_Map_Orestrict__map(X5,X16,X45,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__restrict) ).

fof(fact_foldl__Cons,axiom,
    ! [X212,X12,X6,X2,X16,X5] : hAPP(c_List_Ofoldl(X5,X16,X2,X6),hAPP(hAPP(c_List_Olist_OCons(X16),X12),X212)) = hAPP(c_List_Ofoldl(X5,X16,X2,hAPP(hAPP(X2,X6),X12)),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__Cons) ).

fof(fact_length__transpose__sorted,axiom,
    ! [X212,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))),X212)))
     => ( ( X212 = 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,X212)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( X212 != 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,X212)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),X212),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,
    ! [X98,X26,X25,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
         => ( 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(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X26),X98))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__mono) ).

fof(fact_power__strict__decreasing,axiom,
    ! [X25,X130,X98,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X130))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),c_Groups_Oone__class_Oone(X15)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X130)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).

fof(fact_power__decreasing,axiom,
    ! [X25,X130,X98,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X130))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),c_Groups_Oone__class_Oone(X15)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X130)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__decreasing) ).

fof(fact_mono__iff__le__Suc,axiom,
    ! [X2,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,X5,X2)
      <=> ! [X107] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X2,X107)),hAPP(X2,hAPP(c_Nat_OSuc,X107)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mono__iff__le__Suc) ).

fof(fact_vimage__Int,axiom,
    ! [X13,X11,X2,X16,X5] : hAPP(c_Set_Ovimage(X5,X16,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X16,X2),X11)),hAPP(c_Set_Ovimage(X5,X16,X2),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Int) ).

fof(fact_vimage__Diff,axiom,
    ! [X13,X11,X2,X16,X5] : hAPP(c_Set_Ovimage(X5,X16,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X16,X2),X11)),hAPP(c_Set_Ovimage(X5,X16,X2),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Diff) ).

fof(fact_vimage__Un,axiom,
    ! [X13,X11,X2,X16,X5] : hAPP(c_Set_Ovimage(X5,X16,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X16,X2),X11)),hAPP(c_Set_Ovimage(X5,X16,X2),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Un) ).

fof(fact_Image__Un,axiom,
    ! [X13,X11,X36,X5,X16] : hAPP(c_Relation_OImage(X16,X5,X36),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X16,X5,X36),X11)),hAPP(c_Relation_OImage(X16,X5,X36),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Un) ).

fof(fact_image__Un,axiom,
    ! [X13,X11,X2,X5,X16] : hAPP(c_Set_Oimage(X16,X5,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X16,X5,X2),X11)),hAPP(c_Set_Oimage(X16,X5,X2),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Un) ).

fof(fact_append__in__lists__conv,axiom,
    ! [X11,X214,X212,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X212),X214)),c_List_Olists(X5,X11)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X212),c_List_Olists(X5,X11)))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X214),c_List_Olists(X5,X11))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__in__lists__conv) ).

fof(fact_Powp__mono,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X5,X11)),c_Predicate_OPowp(X5,X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Powp__mono) ).

fof(fact_map__add__comm,axiom,
    ! [X202,X203,X16,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Map_Odom(X5,X16,X203)),c_Map_Odom(X5,X16,X202)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
     => c_Map_Omap__add(X5,X16,X203,X202) = c_Map_Omap__add(X5,X16,X202,X203) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__comm) ).

fof(fact_distinct__product,axiom,
    ! [X225,X5,X221,X15] :
      ( hBOOL(hAPP(c_List_Odistinct(X15),X221))
     => ( hBOOL(hAPP(c_List_Odistinct(X5),X225))
       => hBOOL(hAPP(c_List_Odistinct(tc_prod(X15,X5)),c_Enum_Oproduct(X15,X5,X221,X225))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__product) ).

fof(fact_finite__Plus,axiom,
    ! [X13,X16,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X13))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X5,X16)),c_Sum__Type_OPlus(X5,X16,X11,X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus) ).

fof(fact_Id__on__eqI,axiom,
    ! [X11,X5,X17,X6] :
      ( X6 = X17
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X17)),c_Relation_OId__on(X5,X11))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__eqI) ).

fof(fact_Rep__Integ__induct,axiom,
    ! [X29,X27] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X27),c_Int_OInteg))
     => ( ! [X3] : hBOOL(hAPP(X29,hAPP(c_Int_ORep__Integ,X3)))
       => hBOOL(hAPP(X29,X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__induct) ).

fof(fact_list__update__append1,axiom,
    ! [X14,X225,X221,X15,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
     => hAPP(hAPP(c_List_Olist__update(X15,hAPP(hAPP(c_List_Oappend(X15),X221),X225)),X102),X14) = hAPP(hAPP(c_List_Oappend(X15),hAPP(hAPP(c_List_Olist__update(X15,X221),X102),X14)),X225) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__append1) ).

fof(fact_nat__power__less__imp__less,axiom,
    ! [X98,X99,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X102))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X102),X99)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X102),X98)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).

fof(fact_nat__mult__less__cancel1,axiom,
    ! [X76,X45,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X45)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X76)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).

fof(fact_mult__le__cancel2,axiom,
    ! [X76,X30,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X76),X30)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).

fof(fact_nat__mult__le__cancel1,axiom,
    ! [X76,X45,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X45)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X76)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).

fof(fact_mult__le__cancel1,axiom,
    ! [X76,X45,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X45)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X76)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).

fof(fact_wfE__pf,axiom,
    ! [X11,X36,X5] :
      ( c_Wellfounded_Owf(X5,X36)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Relation_OImage(X5,X5,X36),X11)))
       => X11 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfE__pf) ).

fof(fact_int__setsum,axiom,
    ! [X11,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),X11)) = 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)),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__setsum) ).

fof(fact_int__setprod,axiom,
    ! [X11,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),X11)) = 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)),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__setprod) ).

fof(fact_override__on__emptyset,axiom,
    ! [X1,X2,X16,X5] : c_Fun_Ooverride__on(X5,X16,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,
    ! [X27,X12,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X16,X2)
     => hAPP(c_Fun_Ocomp(X16,X16,X16,hAPP(X2,X12)),hAPP(X2,X27)) = hAPP(c_Fun_Ocomp(X16,X16,X16,hAPP(X2,X27)),hAPP(X2,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__comp__comm) ).

fof(fact_option_Orecs_I2_J,axiom,
    ! [X6,X88,X89,X16,X5] : c_Option_Ooption_Ooption__rec(X5,X16,X89,X88,hAPP(c_Option_Ooption_OSome(X16),X6)) = hAPP(X88,X6),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option_Orecs_I2_J) ).

fof(fact_map__of_Osimps_I2_J,axiom,
    ! [X211,X161,X16,X5] : hAPP(c_Map_Omap__of(X5,X16),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X5,X16)),X161),X211)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),hAPP(c_Map_Omap__of(X5,X16),X211)),hAPP(c_Product__Type_Ofst(X5,X16),X161)),hAPP(c_Option_Ooption_OSome(X16),hAPP(c_Product__Type_Osnd(X5,X16),X161))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of_Osimps_I2_J) ).

fof(fact_set__update__memI,axiom,
    ! [X12,X212,X5,X76] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
     => hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist__update(X5,X212),X76),X12)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__update__memI) ).

fof(fact_UN__I,axiom,
    ! [X13,X17,X16,X11,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
     => ( hBOOL(hAPP(hAPP(c_member(X16),X17),hAPP(X13,X6)))
       => hBOOL(hAPP(hAPP(c_member(X16),X17),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X11),X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__I) ).

fof(fact_unique__quotient,axiom,
    ! [X141,X142,X123,X128,X26,X25] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X25,X26),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X128),X123)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X25,X26),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X142),X141)))
       => ( X26 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => X128 = X142 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient) ).

fof(fact_unique__remainder,axiom,
    ! [X141,X142,X123,X128,X26,X25] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X25,X26),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X128),X123)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X25,X26),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X142),X141)))
       => ( X26 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => X123 = X141 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__remainder) ).

fof(fact_finite__imageD,axiom,
    ! [X11,X2,X16,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_Oimage(X16,X5,X2),X11)))
     => ( c_Fun_Oinj__on(X16,X5,X2,X11)
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageD) ).

fof(fact_single__valued__subset,axiom,
    ! [X84,X34,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X34),X84))
     => ( c_Relation_Osingle__valued(X5,X16,X84)
       => c_Relation_Osingle__valued(X5,X16,X34) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__subset) ).

fof(fact_add__less__cancel__right,axiom,
    ! [X17,X21,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),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X17),X21)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).

fof(fact_add__less__imp__less__right,axiom,
    ! [X26,X24,X25,X15] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X26),X24)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).

fof(fact_add__less__cancel__left,axiom,
    ! [X17,X6,X21,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),X21),X6)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X17)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).

fof(fact_add__less__imp__less__left,axiom,
    ! [X26,X25,X24,X15] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X24),X25)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X24),X26)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).

fof(fact_add__le__imp__le__right,axiom,
    ! [X26,X24,X25,X15] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X26),X24)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).

fof(fact_add__le__cancel__right,axiom,
    ! [X17,X21,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),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X17),X21)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).

fof(fact_add__le__imp__le__left,axiom,
    ! [X26,X25,X24,X15] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X24),X25)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X24),X26)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).

fof(fact_add__le__cancel__left,axiom,
    ! [X17,X6,X21,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),X21),X6)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X17)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).

fof(fact_sorted__nth__mono,axiom,
    ! [X101,X102,X221,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( c_List_Olinorder__class_Osorted(X15,X221)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X101))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X101),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_List_Onth(X15),X221),X102)),hAPP(hAPP(c_List_Onth(X15),X221),X101))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__nth__mono) ).

fof(fact_relpow_Osimps_I2_J,axiom,
    ! [X36,X76,X5] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X76)),X36) = hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X76),X36)),X36),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_relpow_Osimps_I2_J) ).

fof(fact_add__divide__eq__iff,axiom,
    ! [X22,X14,X23,X15] :
      ( class_Fields_Ofield(X15)
     => ( X23 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X14),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X22),X23)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X23),X14)),X22)),X23) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).

fof(fact_diff__divide__eq__iff,axiom,
    ! [X22,X14,X23,X15] :
      ( class_Fields_Ofield(X15)
     => ( X23 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X14),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X22),X23)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X23),X14)),X22)),X23) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__divide__eq__iff) ).

fof(fact_filter__insort,axiom,
    ! [X12,X29,X212,X2,X16,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X16,X5),X2),X212))
       => ( hBOOL(hAPP(X29,X12))
         => hAPP(c_List_Ofilter(X16,X29),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X16,X5,X2),X12),X212)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X16,X5,X2),X12),hAPP(c_List_Ofilter(X16,X29),X212)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__insort) ).

fof(fact_subset__singletonD,axiom,
    ! [X12,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))
     => ( X11 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        | X11 = hAPP(hAPP(c_Set_Oinsert(X5),X12),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,
    ! [X13,X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
         => hBOOL(hAPP(hAPP(c_member(X5),X21),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffE) ).

fof(fact_folding__idem_Oin__comp__idem,axiom,
    ! [X12,X11,X90,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__idem(X5,X16,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(c_Fun_Ocomp(X16,X16,X16,hAPP(X90,X11)),hAPP(X2,X12)) = hAPP(X90,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__idem_Oin__comp__idem) ).

fof(fact_take__Suc__conv__app__nth,axiom,
    ! [X221,X15,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
     => hAPP(hAPP(c_List_Otake(X15),hAPP(c_Nat_OSuc,X102)),X221) = hAPP(hAPP(c_List_Oappend(X15),hAPP(hAPP(c_List_Otake(X15),X102),X221)),hAPP(hAPP(c_List_Olist_OCons(X15),hAPP(hAPP(c_List_Onth(X15),X221),X102)),c_List_Olist_ONil(X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Suc__conv__app__nth) ).

fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
    ! [X13,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
           => ( X13 != 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)),X11),X13) = 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)),X11),X13)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X11)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X13)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ounion__disjoint) ).

fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
    ! [X13,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
           => ( X13 != 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)),X11),X13) = 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)),X11),X13)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X11)),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X13)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ounion__disjoint) ).

fof(fact_comp__funpow,axiom,
    ! [X2,X76,X16,X5] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(X5,X16),tc_fun(X5,X16)),X76),c_Fun_Ocomp(X16,X16,X5,X2)) = c_Fun_Ocomp(X16,X16,X5,hAPP(hAPP(c_Nat_Ocompow(X16,X16),X76),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__funpow) ).

fof(fact_New__DSequence_Opos__bind__def,axiom,
    ! [X70,X2,X12,X5,X16] : hAPP(c_New__DSequence_Opos__bind(X16,X5,X12,X2),X70) = hAPP(c_Lazy__Sequence_Obind(X16,X5,hAPP(X12,X70)),hAPP(hAPP(c_COMBC(X16,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5)),X2),X70)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__bind__def) ).

fof(fact_inj__on__Un__image__eq__iff,axiom,
    ! [X13,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => ( hAPP(c_Set_Oimage(X5,X16,X2),X11) = hAPP(c_Set_Oimage(X5,X16,X2),X13)
      <=> X11 = X13 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__Un__image__eq__iff) ).

fof(fact_mult__imp__div__pos__less,axiom,
    ! [X23,X14,X22,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X22))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X23),X22)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X22)),X23)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__less) ).

fof(fact_mult__imp__div__pos__le,axiom,
    ! [X23,X14,X22,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X22))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X23),X22)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X22)),X23)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__le) ).

fof(fact_refl__on__Int,axiom,
    ! [X84,X13,X34,X11,X5] :
      ( c_Relation_Orefl__on(X5,X11,X34)
     => ( c_Relation_Orefl__on(X5,X13,X84)
       => c_Relation_Orefl__on(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),X84)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__Int) ).

fof(fact_refl__on__Un,axiom,
    ! [X84,X13,X34,X11,X5] :
      ( c_Relation_Orefl__on(X5,X11,X34)
     => ( c_Relation_Orefl__on(X5,X13,X84)
       => c_Relation_Orefl__on(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),X84)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__Un) ).

fof(fact_map__upds__Nil1,axiom,
    ! [X234,X45,X16,X5] : c_Map_Omap__upds(X5,X16,X45,c_List_Olist_ONil(X5),X234) = X45,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__upds__Nil1) ).

fof(fact_lazy__sequence_Osimps_I4_J,axiom,
    ! [X88,X89,X16,X5] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X5,X16,X89,X88,c_Lazy__Sequence_Olazy__sequence_OEmpty(X16)) = X89,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Osimps_I4_J) ).

fof(fact_map__upds__Nil2,axiom,
    ! [X235,X45,X16,X5] : c_Map_Omap__upds(X5,X16,X45,X235,c_List_Olist_ONil(X16)) = X45,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__upds__Nil2) ).

fof(fact_option_Orecs_I1_J,axiom,
    ! [X88,X89,X16,X5] : c_Option_Ooption_Ooption__rec(X5,X16,X89,X88,c_Option_Ooption_ONone(X16)) = X89,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option_Orecs_I1_J) ).

fof(fact_surj__imp__inj__inv,axiom,
    ! [X2,X5,X16] :
      ( hAPP(c_Set_Oimage(X16,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => c_Fun_Oinj__on(X5,X16,c_Hilbert__Choice_Oinv__into(X16,X5,c_Orderings_Otop__class_Otop(tc_fun(X16,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_Domain__insert,axiom,
    ! [X34,X17,X6,X16,X5] : hAPP(c_Relation_ODomain(X5,X16),hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17)),X34)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(c_Relation_ODomain(X5,X16),X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__insert) ).

fof(fact_Range__insert,axiom,
    ! [X34,X17,X6,X5,X16] : hAPP(c_Relation_ORange(X16,X5),hAPP(hAPP(c_Set_Oinsert(tc_prod(X16,X5)),hAPP(hAPP(c_Product__Type_OPair(X16,X5),X6),X17)),X34)) = hAPP(hAPP(c_Set_Oinsert(X5),X17),hAPP(c_Relation_ORange(X16,X5),X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__insert) ).

fof(fact_psubset__trans,axiom,
    ! [X19,X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X13),X19))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__trans) ).

fof(fact_subset__psubset__trans,axiom,
    ! [X19,X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X13),X19))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).

fof(fact_psubset__subset__trans,axiom,
    ! [X19,X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),X19))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).

fof(fact_subset__trans,axiom,
    ! [X19,X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),X19))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__trans) ).

fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
    ! [X11,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X12),X11))
    <=> hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X12)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I2_J) ).

fof(fact_Pair__scomp,axiom,
    ! [X2,X12,X16,X38,X5] : hAPP(hAPP(c_Product__Type_Oscomp(X5,X38,X5,X16),hAPP(c_Product__Type_OPair(X38,X5),X12)),X2) = hAPP(X2,X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__scomp) ).

fof(fact_mod__div__equality,axiom,
    ! [X26,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),X25),X26)),X26)),c_Divides_Odiv__class_Omod(X15,X25,X26)) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__div__equality) ).

fof(fact_mod__div__decomp,axiom,
    ! [X26,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => X25 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),X25),X26)),X26)),c_Divides_Odiv__class_Omod(X15,X25,X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__div__decomp) ).

fof(fact_sorted__sort__key,axiom,
    ! [X212,X2,X16,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X16,X5),X2),c_List_Olinorder__class_Osort__key(X16,X5,X2,X212))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__sort__key) ).

fof(fact_UN__singleton,axiom,
    ! [X11,X5] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X5,tc_HOL_Obool)),X11),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)))) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__singleton) ).

fof(fact_upd__conv__take__nth__drop,axiom,
    ! [X25,X221,X15,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
     => hAPP(hAPP(c_List_Olist__update(X15,X221),X102),X25) = hAPP(hAPP(c_List_Oappend(X15),hAPP(hAPP(c_List_Otake(X15),X102),X221)),hAPP(hAPP(c_List_Olist_OCons(X15),X25),hAPP(hAPP(c_List_Odrop(X15),hAPP(c_Nat_OSuc,X102)),X221))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upd__conv__take__nth__drop) ).

fof(fact_distinct__set__sublists,axiom,
    ! [X212,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X212))
     => 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,X212)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__set__sublists) ).

fof(fact_Pow__insert,axiom,
    ! [X11,X6,X5] : hAPP(c_Set_OPow(X5),hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X5),X11)),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),X11))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__insert) ).

fof(fact_finite__vimageD,axiom,
    ! [X90,X48,X16,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_Ovimage(X5,X16,X48),X90)))
     => ( hAPP(c_Set_Oimage(X5,X16,X48),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X90)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__vimageD) ).

fof(fact_Cons__in__lists__iff,axiom,
    ! [X11,X212,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)),c_List_Olists(X5,X11)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X212),c_List_Olists(X5,X11))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__in__lists__iff) ).

fof(fact_range,axiom,
    ! [X105,X100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X100))
     => 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(X100),X105))),X100)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range) ).

fof(fact_Int__iff,axiom,
    ! [X13,X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
        & hBOOL(hAPP(hAPP(c_member(X5),X21),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__iff) ).

fof(fact_IntD1,axiom,
    ! [X13,X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
     => hBOOL(hAPP(hAPP(c_member(X5),X21),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntD1) ).

fof(fact_DiffD1,axiom,
    ! [X13,X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
     => hBOOL(hAPP(hAPP(c_member(X5),X21),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffD1) ).

fof(fact_IntD2,axiom,
    ! [X13,X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
     => hBOOL(hAPP(hAPP(c_member(X5),X21),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntD2) ).

fof(fact_Diff__insert,axiom,
    ! [X13,X6,X11,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13)) = 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)),X11),X13)),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,
    ! [X13,X11,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
           => ( X13 != 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)),X11),X13) = 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)),X11),X13)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X11)),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X13)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__Un) ).

fof(fact_folding__idem_Oinsert__idem,axiom,
    ! [X12,X11,X90,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__idem(X5,X16,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(X90,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(c_Fun_Ocomp(X16,X16,X16,hAPP(X90,X11)),hAPP(X2,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__idem_Oinsert__idem) ).

fof(fact_scomp__Pair,axiom,
    ! [X12,X38,X16,X5] : hAPP(hAPP(c_Product__Type_Oscomp(X5,X16,X38,tc_prod(X16,X38)),X12),c_Product__Type_OPair(X16,X38)) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_scomp__Pair) ).

fof(fact_Pow__def,axiom,
    ! [X11,X5] : hAPP(c_Set_OPow(X5),X11) = 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))),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__def) ).

fof(fact_rev__foldl__cons,axiom,
    ! [X212,X5] : hAPP(c_List_Orev(X5),X212) = 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)),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__foldl__cons) ).

fof(fact_gauss__sum,axiom,
    ! [X76,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),X76))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X76)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X76)),c_Groups_Oone__class_Oone(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gauss__sum) ).

fof(fact_length__n__lists__elem,axiom,
    ! [X212,X76,X214,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X214),hAPP(c_List_Oset(tc_List_Olist(X5)),c_Enum_On__lists(X5,X76,X212))))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X214) = X76 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__n__lists__elem) ).

fof(fact_acyclic__subset,axiom,
    ! [X34,X84,X5] :
      ( c_Wellfounded_Oacyclic(X5,X84)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),X84))
       => c_Wellfounded_Oacyclic(X5,X34) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__subset) ).

fof(fact_wf__subset,axiom,
    ! [X161,X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X161),X34))
       => c_Wellfounded_Owf(X5,X161) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__subset) ).

fof(fact_in__set__remove1,axiom,
    ! [X212,X5,X17,X6] :
      ( X6 != X17
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_List_Oset(X5),c_List_Oremove1(X5,X17,X212))))
      <=> hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_List_Oset(X5),X212))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__remove1) ).

fof(fact_Int__assoc,axiom,
    ! [X19,X13,X11,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)),X11),X13)),X19) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X13),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__assoc) ).

fof(fact_Int__Diff,axiom,
    ! [X19,X13,X11,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)),X11),X13)),X19) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X13),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Diff) ).

fof(fact_Un__assoc,axiom,
    ! [X19,X13,X11,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)),X11),X13)),X19) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X13),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__assoc) ).

fof(fact_le__add__diff,axiom,
    ! [X99,X98,X100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X100),X98))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X99)),X100))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff) ).

fof(fact_set__takeWhileD,axiom,
    ! [X212,X29,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),c_List_OtakeWhile(X5,X29,X212))))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
        & hBOOL(hAPP(X29,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__takeWhileD) ).

fof(fact_in__set__sublistD,axiom,
    ! [X68,X212,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),c_List_Osublist(X5,X212,X68))))
     => hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__sublistD) ).

fof(fact_filter__is__subset,axiom,
    ! [X212,X29,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,X29),X212))),hAPP(c_List_Oset(X5),X212))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__is__subset) ).

fof(fact_crossproduct__noteq,axiom,
    ! [X20,X21,X17,X6,X5] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
     => ( ( X6 != X17
          & X21 != X20 )
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X20)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X20)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).

fof(fact_crossproduct__eq,axiom,
    ! [X37,X12,X27,X112,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),X112),X27)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X37)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X112),X37)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X27))
      <=> ( X112 = X12
          | X27 = X37 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__eq) ).

fof(fact_reflp__def,axiom,
    ! [X34,X5] :
      ( c_Predicate_Oreflp(X5,X34)
    <=> 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),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reflp__def) ).

fof(fact_le__diff__conv2,axiom,
    ! [X70,X115,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30),X115))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X70),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X115),X30)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X70),X30)),X115)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv2) ).

fof(fact_map__of__zip__enum__is__Some,axiom,
    ! [X14,X225,X5,X15] :
      ( class_Enum_Oenum(X15)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X225) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),c_Enum_Oenum__class_Oenum(X15))
       => ? [X33] : hAPP(hAPP(c_Map_Omap__of(X15,X5),hAPP(hAPP(c_List_Ozip(X15,X5),c_Enum_Oenum__class_Oenum(X15)),X225)),X14) = hAPP(c_Option_Ooption_OSome(X5),X33) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__zip__enum__is__Some) ).

fof(fact_THE__default__def,axiom,
    ! [X20,X5,X29] :
      ( ( ? [X3] :
            ( hBOOL(hAPP(X29,X3))
            & ! [X33] :
                ( hBOOL(hAPP(X29,X33))
               => X33 = X3 ) )
       => c_FunDef_OTHE__default(X5,X20,X29) = c_HOL_OThe(X5,X29) )
      & ( ~ ? [X3] :
              ( hBOOL(hAPP(X29,X3))
              & ! [X33] :
                  ( hBOOL(hAPP(X29,X33))
                 => X33 = X3 ) )
       => c_FunDef_OTHE__default(X5,X20,X29) = X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_THE__default__def) ).

fof(fact_vimageD,axiom,
    ! [X11,X2,X16,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Set_Ovimage(X5,X16,X2),X11)))
     => hBOOL(hAPP(hAPP(c_member(X16),hAPP(X2,X6)),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageD) ).

fof(fact_vimage__eq,axiom,
    ! [X13,X2,X16,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Set_Ovimage(X5,X16,X2),X13)))
    <=> hBOOL(hAPP(hAPP(c_member(X16),hAPP(X2,X6)),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__eq) ).

fof(fact_subsetI,axiom,
    ! [X13,X11,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
         => hBOOL(hAPP(hAPP(c_member(X5),X3),X13)) )
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subsetI) ).

fof(fact_drop__Cons,axiom,
    ! [X212,X12,X76,X5] : hAPP(hAPP(c_List_Odrop(X5),X76),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = c_Nat_Onat_Onat__case(tc_List_Olist(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Odrop(X5)),X212),X76),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__Cons) ).

fof(fact_mult__right__le__one__le,axiom,
    ! [X22,X14,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X22))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),c_Groups_Oone__class_Oone(X15)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),X22)),X14)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).

fof(fact_mult__left__le__one__le,axiom,
    ! [X22,X14,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X22))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),c_Groups_Oone__class_Oone(X15)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X22),X14)),X14)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).

fof(fact_Union__disjoint,axiom,
    ! [X11,X19,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),X19)),X11) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X3),X19))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X3),X11) = 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,
    ! [X26,X143,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X143))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X143),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X143))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2) ).

fof(fact_Domain__Un__eq,axiom,
    ! [X13,X11,X16,X5] : hAPP(c_Relation_ODomain(X5,X16),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X16),X11)),hAPP(c_Relation_ODomain(X5,X16),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Un__eq) ).

fof(fact_Range__Un__eq,axiom,
    ! [X13,X11,X5,X16] : hAPP(c_Relation_ORange(X16,X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X16,X5),tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ORange(X16,X5),X11)),hAPP(c_Relation_ORange(X16,X5),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Un__eq) ).

fof(fact_map__update,axiom,
    ! [X27,X30,X212,X2,X5,X16] : hAPP(hAPP(c_List_Omap(X16,X5),X2),hAPP(hAPP(c_List_Olist__update(X16,X212),X30),X27)) = hAPP(hAPP(c_List_Olist__update(X5,hAPP(hAPP(c_List_Omap(X16,X5),X2),X212)),X30),hAPP(X2,X27)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__update) ).

fof(fact_def__coinduct,axiom,
    ! [X31,X2,X11,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( X11 = c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X2)
       => ( c_Orderings_Oorder__class_Omono(X5,X5,X2)
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X31),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X31),X11))))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X31),X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__coinduct) ).

fof(fact_map__add__def,axiom,
    ! [X12,X202,X203,X5,X16] : hAPP(c_Map_Omap__add(X16,X5,X203,X202),X12) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X5),X5,hAPP(X203,X12),c_Option_Ooption_OSome(X5)),hAPP(X202,X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__def) ).

fof(fact_set__ConsD,axiom,
    ! [X212,X12,X27,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X27),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212))))
     => ( X27 = X12
        | hBOOL(hAPP(hAPP(c_member(X5),X27),hAPP(c_List_Oset(X5),X212))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__ConsD) ).

fof(fact_code__numeral__decr,axiom,
    ! [X100] :
      ( X100 != 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,X100)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,X100))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral__decr) ).

fof(fact_in__set__dropD,axiom,
    ! [X212,X76,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Odrop(X5),X76),X212))))
     => hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__dropD) ).

fof(fact_in__set__takeD,axiom,
    ! [X212,X76,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Otake(X5),X76),X212))))
     => hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__takeD) ).

fof(fact_dom__fun__upd,axiom,
    ! [X12,X2,X16,X5,X27] :
      ( ( X27 = c_Option_Ooption_ONone(X5)
       => c_Map_Odom(X16,X5,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X16,tc_Option_Ooption(X5)),X2),X12),X27)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool)),c_Map_Odom(X16,X5,X2)),hAPP(hAPP(c_Set_Oinsert(X16),X12),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)))) )
      & ( X27 != c_Option_Ooption_ONone(X5)
       => c_Map_Odom(X16,X5,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X16,tc_Option_Ooption(X5)),X2),X12),X27)) = hAPP(hAPP(c_Set_Oinsert(X16),X12),c_Map_Odom(X16,X5,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dom__fun__upd) ).

fof(fact_power__Suc__less__one,axiom,
    ! [X98,X25,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),c_Groups_Oone__class_Oone(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),hAPP(c_Nat_OSuc,X98))),c_Groups_Oone__class_Oone(X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).

fof(fact_zdiv__mono2__neg,axiom,
    ! [X26,X143,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),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)),X143))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X143),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X143)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg) ).

fof(fact_Id__onE,axiom,
    ! [X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X21),c_Relation_OId__on(X5,X11)))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
           => X21 != 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,
    ! [X12,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Hilbert__Choice_Oinv__into(X5,X16,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),hAPP(X2,X12)) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__f__f) ).

fof(fact_the__inv__f__f,axiom,
    ! [X12,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Fun_Othe__inv__into(X5,X16,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),hAPP(X2,X12)) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__f__f) ).

fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
    ! [X37,X12,X11,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X16,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(X2,X12),hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),X37),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),hAPP(hAPP(X2,X12),X37)),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__fun__comm) ).

fof(fact_inv__f__eq,axiom,
    ! [X27,X12,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hAPP(X2,X12) = X27
       => hAPP(c_Hilbert__Choice_Oinv__into(X5,X16,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),X27) = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__f__eq) ).

fof(fact_wfP__subset,axiom,
    ! [X161,X34,X5] :
      ( c_Wellfounded_OwfP(X5,X34)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X161),X34))
       => c_Wellfounded_OwfP(X5,X161) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__subset) ).

fof(fact_pred__equals__eq,axiom,
    ! [X35,X36,X5] :
      ( hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X36) = hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X35)
    <=> X36 = X35 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq) ).

fof(fact_mult__less__cancel1,axiom,
    ! [X76,X45,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X45)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X76)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).

fof(fact_mult__less__cancel2,axiom,
    ! [X76,X30,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X76),X30)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).

fof(fact_sort__key__simps_I2_J,axiom,
    ! [X212,X12,X2,X5,X16] :
      ( class_Orderings_Olinorder(X16)
     => c_List_Olinorder__class_Osort__key(X5,X16,X2,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X16,X2),X12),c_List_Olinorder__class_Osort__key(X5,X16,X2,X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sort__key__simps_I2_J) ).

fof(fact_hb__map_Osimps_I2_J,axiom,
    ! [X253,X12,X2,X5,X16] : c_Lazy__Sequence_Ohb__map(X16,X5,X2,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X16),X12,X253)) = c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X5),hAPP(hAPP(c_Option_Omap(X16,X5),X2),X12),c_Lazy__Sequence_Ohb__map(X16,X5,X2,X253)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hb__map_Osimps_I2_J) ).

fof(fact_divide__strict__right__mono,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),X24)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X26),X24))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono) ).

fof(fact_mult__strict__right__mono,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Rings_Olinordered__semiring__strict(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X24))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).

fof(fact_mult__strict__left__mono,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Rings_Olinordered__semiring__strict(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X26))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).

fof(fact_comm__mult__strict__left__mono,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Rings_Olinordered__comm__semiring__strict(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X26))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).

fof(fact_divide__right__mono,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Fields_Olinordered__field__inverse__zero(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),X24)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X26),X24))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__right__mono) ).

fof(fact_power__mono,axiom,
    ! [X98,X26,X25,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X26),X98))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mono) ).

fof(fact_mult__right__mono,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Rings_Oordered__semiring(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X24))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono) ).

fof(fact_comm__mult__left__mono,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Rings_Oordered__comm__semiring(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X26))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).

fof(fact_mult__left__mono,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Rings_Oordered__semiring(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X26))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).

fof(fact_zip__Cons__Cons,axiom,
    ! [X225,X22,X221,X14,X5,X15] : hAPP(hAPP(c_List_Ozip(X15,X5),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)),hAPP(hAPP(c_List_Olist_OCons(X5),X22),X225)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(X15,X5)),hAPP(hAPP(c_Product__Type_OPair(X15,X5),X14),X22)),hAPP(hAPP(c_List_Ozip(X15,X5),X221),X225)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__Cons__Cons) ).

fof(fact_divide__less__0__iff,axiom,
    ! [X17,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),X17)),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),X17),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)),X17)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__0__iff) ).

fof(fact_divide__le__0__iff,axiom,
    ! [X17,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),X17)),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),X17),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)),X17)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__0__iff) ).

fof(fact_mult__le__0__iff,axiom,
    ! [X17,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),X17)),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),X17),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)),X17)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).

fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
    ! [X11,X12] :
      ( c_Nat__Transfer_Ois__nat(X12)
     => ( c_Nat__Transfer_Onat__set(X11)
       => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X12),X11))
        <=> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X12)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X11))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I2_J) ).

fof(fact_Max__eqI,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ! [X33] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X33),X11))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X33),X12)) )
         => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
           => c_Big__Operators_Olinorder__class_OMax(X5,X11) = X12 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max__eqI) ).

fof(fact_list__all__length,axiom,
    ! [X212,X29,X5] :
      ( c_List_Olist__all(X5,X29,X212)
    <=> ! [X107] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
         => hBOOL(hAPP(X29,hAPP(hAPP(c_List_Onth(X5),X212),X107))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__length) ).

fof(fact_mod__pos__neg__1__number__of,axiom,
    ! [X132] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)),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),X132)) = 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),X132))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__neg__1__number__of) ).

fof(fact_subset__inj__on,axiom,
    ! [X11,X13,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X13)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
       => c_Fun_Oinj__on(X5,X16,X2,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__inj__on) ).

fof(fact_length__filter__le,axiom,
    ! [X212,X29,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,X29),X212))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__filter__le) ).

fof(fact_rtrancl_Ortrancl__refl,axiom,
    ! [X34,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,X34))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).

fof(fact_nat__add__left__cancel__less,axiom,
    ! [X76,X45,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X45)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X76)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).

fof(fact_nat__add__left__cancel__le,axiom,
    ! [X76,X45,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X45)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X76)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).

fof(fact_inv__into__f__f,axiom,
    ! [X12,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hAPP(c_Hilbert__Choice_Oinv__into(X5,X16,X11,X2),hAPP(X2,X12)) = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__f__f) ).

fof(fact_the__inv__into__f__f,axiom,
    ! [X12,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hAPP(c_Fun_Othe__inv__into(X5,X16,X11,X2),hAPP(X2,X12)) = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__f__f) ).

fof(fact_div__pos__neg__1__number__of,axiom,
    ! [X132] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)),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),X132)) = 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),X132))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__neg__1__number__of) ).

fof(fact_inv__into__f__eq,axiom,
    ! [X27,X12,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => ( hAPP(X2,X12) = X27
         => hAPP(c_Hilbert__Choice_Oinv__into(X5,X16,X11,X2),X27) = X12 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__f__eq) ).

fof(fact_the__inv__into__f__eq,axiom,
    ! [X27,X12,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => ( hAPP(X2,X12) = X27
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(c_Fun_Othe__inv__into(X5,X16,X11,X2),X27) = X12 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__f__eq) ).

fof(fact_finite__INT,axiom,
    ! [X11,X16,X68,X5] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X68))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(X16),hAPP(X11,X3))) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X16),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X68),X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__INT) ).

fof(fact_power__strict__increasing,axiom,
    ! [X25,X130,X98,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X130))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Oone__class_Oone(X15)),X25))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X130))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing) ).

fof(fact_power__increasing,axiom,
    ! [X25,X130,X98,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X130))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Oone__class_Oone(X15)),X25))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X130))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing) ).

fof(fact_divide__strict__right__mono__neg,axiom,
    ! [X24,X25,X26,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X24),c_Groups_Ozero__class_Ozero(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),X24)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X26),X24))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono__neg) ).

fof(fact_mult__strict__right__mono__neg,axiom,
    ! [X24,X25,X26,X15] :
      ( class_Rings_Olinordered__ring__strict(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X24),c_Groups_Ozero__class_Ozero(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X24))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).

fof(fact_mult__strict__left__mono__neg,axiom,
    ! [X24,X25,X26,X15] :
      ( class_Rings_Olinordered__ring__strict(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X24),c_Groups_Ozero__class_Ozero(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X26))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).

fof(fact_divide__right__mono__neg,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Fields_Olinordered__field__inverse__zero(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X24),c_Groups_Ozero__class_Ozero(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X26),X24)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),X24))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__right__mono__neg) ).

fof(fact_mult__right__mono__neg,axiom,
    ! [X24,X25,X26,X15] :
      ( class_Rings_Oordered__ring(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X24),c_Groups_Ozero__class_Ozero(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X24))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).

fof(fact_mult__left__mono__neg,axiom,
    ! [X24,X25,X26,X15] :
      ( class_Rings_Oordered__ring(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X24),c_Groups_Ozero__class_Ozero(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X26))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).

fof(fact_card__Diff__singleton,axiom,
    ! [X12,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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),X11)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff__singleton) ).

fof(fact_finite__Diff2,axiom,
    ! [X11,X13,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Diff2) ).

fof(fact_listsum__update__nat,axiom,
    ! [X98,X230,X100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X100),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X230)))
     => hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X230),X100),X98)) = 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),X230)),X98)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X230),X100)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__update__nat) ).

fof(fact_o__def,axiom,
    ! [X12,X1,X2,X38,X5,X16] : hAPP(hAPP(c_Fun_Ocomp(X16,X5,X38,X2),X1),X12) = hAPP(X2,hAPP(X1,X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__def) ).

fof(fact_o__apply,axiom,
    ! [X12,X1,X2,X38,X5,X16] : hAPP(hAPP(c_Fun_Ocomp(X16,X5,X38,X2),X1),X12) = hAPP(X2,hAPP(X1,X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__apply) ).

fof(fact_add__strict__mono,axiom,
    ! [X41,X24,X26,X25,X15] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X24),X41))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X26),X41))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).

fof(fact_add__le__less__mono,axiom,
    ! [X41,X24,X26,X25,X15] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X24),X41))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X26),X41))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).

fof(fact_add__less__le__mono,axiom,
    ! [X41,X24,X26,X25,X15] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X24),X41))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X26),X41))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).

fof(fact_min__max_Osup__mono,axiom,
    ! [X41,X26,X24,X25,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X24))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),X41))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X25),X26)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X24),X41))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__mono) ).

fof(fact_min__max_Oinf__mono,axiom,
    ! [X41,X26,X24,X25,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X24))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),X41))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X25),X26)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X24),X41))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__mono) ).

fof(fact_add__mono,axiom,
    ! [X41,X24,X26,X25,X15] :
      ( class_Groups_Oordered__ab__semigroup__add(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X24),X41))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X26),X41))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).

fof(fact_inf__mono,axiom,
    ! [X41,X26,X24,X25,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X24))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),X41))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X25),X26)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X24),X41))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__mono) ).

fof(fact_sup__mono,axiom,
    ! [X41,X26,X24,X25,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X24))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),X41))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X25),X26)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X24),X41))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__mono) ).

fof(fact_right__distrib__number__of,axiom,
    ! [X24,X26,X126,X5] :
      ( ( class_Int_Onumber(X5)
        & class_Rings_Osemiring(X5) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X26),X24)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)),X26)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__distrib__number__of) ).

fof(fact_right__diff__distrib__number__of,axiom,
    ! [X24,X26,X126,X5] :
      ( ( class_Int_Onumber(X5)
        & class_Rings_Oring(X5) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X26),X24)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)),X26)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__diff__distrib__number__of) ).

fof(fact_min__max_Ofold__sup__insert,axiom,
    ! [X6,X17,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X17),hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X17),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ofold__sup__insert) ).

fof(fact_min__max_Ofold__inf__insert,axiom,
    ! [X6,X17,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X17),hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X6),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X17),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ofold__inf__insert) ).

fof(fact_fold__inf__insert,axiom,
    ! [X6,X17,X11,X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X17),hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = 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)),X17),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__inf__insert) ).

fof(fact_fold__sup__insert,axiom,
    ! [X6,X17,X11,X5] :
      ( class_Lattices_Osemilattice__sup(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X17),hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = 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)),X17),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__sup__insert) ).

fof(fact_finite__vimageI,axiom,
    ! [X48,X16,X90,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X90))
     => ( c_Fun_Oinj__on(X16,X5,X48,c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X16),hAPP(c_Set_Ovimage(X16,X5,X48),X90))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__vimageI) ).

fof(fact_INF__leI,axiom,
    ! [X67,X11,X70,X5,X16] :
      ( class_Complete__Lattice_Ocomplete__lattice(X16)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X70),X11))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X16),X11),X67)),hAPP(X67,X70))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__leI) ).

fof(fact_add__number__of__diff2,axiom,
    ! [X132,X24,X126,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X126)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X24),hAPP(c_Int_Onumber__class_Onumber__of(X15),X132))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X126),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X132)))),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__diff2) ).

fof(fact_less__eq__nat_Osimps_I2_J,axiom,
    ! [X76,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X45)),X76))
    <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).

fof(fact_SUP1__I,axiom,
    ! [X16,X17,X13,X11,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
     => ( hBOOL(hAPP(hAPP(X13,X6),X17))
       => hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X11),X13),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP1__I) ).

fof(fact_Sup__le__iff,axiom,
    ! [X17,X11,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Complete__Lattice_OSup__class_OSup(X5,X11)),X17))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X17)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__le__iff) ).

fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
    ! [X12,X37,X11,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm__idem(X5,X16,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),X37),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(X2,X12),hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),X37),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem) ).

fof(fact_sum__eq__0__conv,axiom,
    ! [X224,X45] :
      ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X224) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X45 = 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),X224)))
           => 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,
    ! [X99,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X98))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X99))
       => 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),X99),X98))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__mult) ).

fof(fact_one__le__mult__iff,axiom,
    ! [X76,X45] :
      ( 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),X45),X76)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X45))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X76)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).

fof(fact_mod__mult__self4,axiom,
    ! [X99,X98,X100] : 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),X100),X98)),X99)),X98) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X99),X98),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self4) ).

fof(fact_Union__Un__distrib,axiom,
    ! [X13,X11,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)),X11),X13)) = 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),X11)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__Un__distrib) ).

fof(fact_Inter__Un__distrib,axiom,
    ! [X13,X11,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)),X11),X13)) = 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),X11)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__Un__distrib) ).

fof(fact_split__mod,axiom,
    ! [X30,X76,X29] :
      ( hBOOL(hAPP(X29,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X76,X30)))
    <=> ( ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hBOOL(hAPP(X29,X76)) )
        & ( X30 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => ! [X145,X124] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X124),X30))
             => ( X76 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X145)),X124)
               => hBOOL(hAPP(X29,X124)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mod) ).

fof(fact_in__lists__conv__set,axiom,
    ! [X11,X212,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X212),c_List_Olists(X5,X11)))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
         => hBOOL(hAPP(hAPP(c_member(X5),X3),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__lists__conv__set) ).

fof(fact_list_Osize_I2_J,axiom,
    ! [X213,X6,X92,X5] : c_List_Olist_Olist__size(X5,X92,hAPP(hAPP(c_List_Olist_OCons(X5),X6),X213)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X92,X6)),c_List_Olist_Olist__size(X5,X92,X213))),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_restrict__complement__singleton__eq,axiom,
    ! [X12,X2,X16,X5] : c_Map_Orestrict__map(X5,X16,X2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),X2),X12),c_Option_Ooption_ONone(X16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__complement__singleton__eq) ).

fof(fact_select__weight__cons__zero,axiom,
    ! [X212,X12,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)),X12)),X212)) = c_Random_Oselect__weight(X5,X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_select__weight__cons__zero) ).

fof(fact_transpose_Opsimps_I2_J,axiom,
    ! [X256,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)),X256)))
     => c_List_Otranspose(X5,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X256)) = c_List_Otranspose(X5,X256) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose_Opsimps_I2_J) ).

fof(fact_disjoint__eq__subset__Compl,axiom,
    ! [X13,X11,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) = 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)),X11),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_disjoint__eq__subset__Compl) ).

fof(fact_card__seteq,axiom,
    ! [X11,X13,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X13)),hAPP(c_Finite__Set_Ocard(X5),X11)))
         => X11 = X13 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__seteq) ).

fof(fact_Inter__lower,axiom,
    ! [X11,X13,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X13),X11))
     => 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),X11)),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__lower) ).

fof(fact_converse__rel__comp,axiom,
    ! [X84,X34,X38,X5,X16] : hAPP(c_Relation_Oconverse(X16,X5),hAPP(hAPP(c_Relation_Orel__comp(X16,X38,X5),X34),X84)) = hAPP(hAPP(c_Relation_Orel__comp(X5,X38,X16),hAPP(c_Relation_Oconverse(X38,X5),X84)),hAPP(c_Relation_Oconverse(X16,X38),X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rel__comp) ).

fof(fact_min__less__iff__disj,axiom,
    ! [X37,X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X12),X27)),X37))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X12),X37))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X27),X37)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__less__iff__disj) ).

fof(fact_min__le__iff__disj,axiom,
    ! [X37,X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X12),X27)),X37))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X37))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X27),X37)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__le__iff__disj) ).

fof(fact_split__div,axiom,
    ! [X30,X76,X29] :
      ( hBOOL(hAPP(X29,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X76),X30)))
    <=> ( ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        & ( X30 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => ! [X145,X124] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X124),X30))
             => ( X76 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X145)),X124)
               => hBOOL(hAPP(X29,X145)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__div) ).

fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
    ! [X13,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X13 != 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)),X13),X11))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X13)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X11)) = c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X11) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Osubset__idem) ).

fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
    ! [X13,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X13 != 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)),X13),X11))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X13)),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X11)) = c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X11) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Osubset__idem) ).

fof(fact_map__add__dom__app__simps_I1_J,axiom,
    ! [X206,X207,X16,X45,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X45),c_Map_Odom(X5,X16,X207)))
     => hAPP(c_Map_Omap__add(X5,X16,X206,X207),X45) = hAPP(X207,X45) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__dom__app__simps_I1_J) ).

fof(fact_subset__Pow__Union,axiom,
    ! [X11,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X11),hAPP(c_Set_OPow(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X11)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__Pow__Union) ).

fof(fact_IntI,axiom,
    ! [X13,X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X21),X13))
       => hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntI) ).

fof(fact_dom__map__add,axiom,
    ! [X76,X45,X16,X5] : c_Map_Odom(X5,X16,c_Map_Omap__add(X5,X16,X45,X76)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_Map_Odom(X5,X16,X76)),c_Map_Odom(X5,X16,X45)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dom__map__add) ).

fof(fact_conjI__realizer,axiom,
    ! [X16,X5,X149,X28,X161,X29] :
      ( hBOOL(hAPP(X29,X161))
     => ( hBOOL(hAPP(X28,X149))
       => ( hBOOL(hAPP(X29,hAPP(c_Product__Type_Ofst(X5,X16),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X161),X149))))
          & hBOOL(hAPP(X28,hAPP(c_Product__Type_Osnd(X5,X16),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X161),X149)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conjI__realizer) ).

fof(fact_INFI__apply,axiom,
    ! [X12,X2,X11,X38,X16,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X38,X5)),X11),X2),X12) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,X5),X11),hAPP(hAPP(c_COMBC(X16,X38,X5),X2),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INFI__apply) ).

fof(fact_SUPR__apply,axiom,
    ! [X12,X2,X11,X38,X16,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X38,X5)),X11),X2),X12) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,X5),X11),hAPP(hAPP(c_COMBC(X16,X38,X5),X2),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUPR__apply) ).

fof(fact_finite__Un,axiom,
    ! [X4,X90,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X90),X4)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X90))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Un) ).

fof(fact_Un__Diff__Int,axiom,
    ! [X13,X11,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)),X11),X13)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Diff__Int) ).

fof(fact_listsp__mono,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),c_List_Olistsp(X5,X11)),c_List_Olistsp(X5,X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__mono) ).

fof(fact_lists__mono,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),c_List_Olists(X5,X11)),c_List_Olists(X5,X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__mono) ).

fof(fact_neg__less__divide__eq,axiom,
    ! [X17,X6,X21,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( 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),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X17),X21)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__divide__eq) ).

fof(fact_neg__le__divide__eq,axiom,
    ! [X17,X6,X21,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),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),X17),X21)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__divide__eq) ).

fof(fact_wfP__def,axiom,
    ! [X34,X5] :
      ( c_Wellfounded_OwfP(X5,X34)
    <=> c_Wellfounded_Owf(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__def) ).

fof(fact_pos__imp__zdiv__neg__iff,axiom,
    ! [X6,X17] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6),X17)),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,
    ! [X13,X11,X16,X19,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),X19))
     => ( hAPP(hAPP(c_Product__Type_OSigma(X16,X5),X11),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X16),X19)) = hAPP(hAPP(c_Product__Type_OSigma(X16,X5),X13),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X16),X19))
      <=> X11 = X13 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Times__eq__cancel2) ).

fof(fact_mod__pos__neg__trivial,axiom,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25),X26)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25),X26) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__neg__trivial) ).

fof(fact_wfI__pf,axiom,
    ! [X36,X5] :
      ( ! [X75] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X75),hAPP(c_Relation_OImage(X5,X5,X36),X75)))
         => X75 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) )
     => c_Wellfounded_Owf(X5,X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfI__pf) ).

fof(fact_prod__caseI,axiom,
    ! [X16,X5,X17,X6,X89] :
      ( hBOOL(hAPP(hAPP(X89,X6),X17))
     => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_HOL_Obool),X89),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod__caseI) ).

fof(fact_splitI,axiom,
    ! [X16,X5,X17,X6,X2] :
      ( hBOOL(hAPP(hAPP(X2,X6),X17))
     => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_HOL_Obool),X2),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splitI) ).

fof(fact_neg__imp__zdiv__neg__iff,axiom,
    ! [X6,X17] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17),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),X17)),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,
    ! [X30,X115,X70] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X70),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X115),X30)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X70),X30)),X115)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__conv) ).

fof(fact_le__diff__conv,axiom,
    ! [X70,X30,X115] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X115),X30)),X70))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X115),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X70),X30))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv) ).

fof(fact_card__Diff__subset,axiom,
    ! [X11,X13,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),X11))
       => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X11)),hAPP(c_Finite__Set_Ocard(X5),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff__subset) ).

fof(fact_folding__idem_Oidem__comp,axiom,
    ! [X12,X90,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__idem(X5,X16,X2,X90)
     => hAPP(c_Fun_Ocomp(X16,X16,X16,hAPP(X2,X12)),hAPP(X2,X12)) = hAPP(X2,X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__idem_Oidem__comp) ).

fof(fact_Field__Un,axiom,
    ! [X84,X34,X5] : hAPP(c_Relation_OField(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),X84)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OField(X5),X34)),hAPP(c_Relation_OField(X5),X84)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__Un) ).

fof(fact_product__list__set,axiom,
    ! [X214,X212,X16,X5] : hAPP(c_List_Oset(tc_prod(X5,X16)),c_Enum_Oproduct(X5,X16,X212,X214)) = hAPP(hAPP(c_Product__Type_OSigma(X5,X16),hAPP(c_List_Oset(X5),X212)),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),hAPP(c_List_Oset(X16),X214))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_product__list__set) ).

fof(fact_zip__eq__conv,axiom,
    ! [X227,X214,X16,X212,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)
     => ( hAPP(hAPP(c_List_Ozip(X5,X16),X212),X214) = X227
      <=> ( hAPP(hAPP(c_List_Omap(tc_prod(X5,X16),X5),c_Product__Type_Ofst(X5,X16)),X227) = X212
          & hAPP(hAPP(c_List_Omap(tc_prod(X5,X16),X16),c_Product__Type_Osnd(X5,X16)),X227) = X214 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__eq__conv) ).

fof(fact_map__upd__Some__unfold,axiom,
    ! [X27,X12,X17,X6,X45,X5,X16] :
      ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X16,tc_Option_Ooption(X5)),X45),X6),hAPP(c_Option_Ooption_OSome(X5),X17)),X12) = hAPP(c_Option_Ooption_OSome(X5),X27)
    <=> ( ( X12 = X6
          & X17 = X27 )
        | ( X12 != X6
          & hAPP(X45,X12) = hAPP(c_Option_Ooption_OSome(X5),X27) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__upd__Some__unfold) ).

fof(fact_inf1D1,axiom,
    ! [X12,X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13),X12))
     => hBOOL(hAPP(X11,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1D1) ).

fof(fact_inf1D2,axiom,
    ! [X12,X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13),X12))
     => hBOOL(hAPP(X13,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1D2) ).

fof(fact_listrelp_OCons,axiom,
    ! [X214,X212,X5,X27,X12,X34] :
      ( hBOOL(hAPP(hAPP(X34,X12),X27))
     => ( c_List_Olistrelp(X5,X34,X212,X214)
       => c_List_Olistrelp(X5,X34,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212),hAPP(hAPP(c_List_Olist_OCons(X5),X27),X214)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_OCons) ).

fof(fact_listrelp_Oequations_I2_J,axiom,
    ! [X50,X46,X51,X47,X34,X5] :
      ( c_List_Olistrelp(X5,X34,hAPP(hAPP(c_List_Olist_OCons(X5),X47),X51),hAPP(hAPP(c_List_Olist_OCons(X5),X46),X50))
    <=> ( hBOOL(hAPP(hAPP(X34,X47),X46))
        & c_List_Olistrelp(X5,X34,X51,X50) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_Oequations_I2_J) ).

fof(fact_map__of__zip__inject,axiom,
    ! [X227,X212,X16,X214,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X214) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X212)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X227) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X212)
       => ( hBOOL(hAPP(c_List_Odistinct(X16),X212))
         => ( hAPP(c_Map_Omap__of(X16,X5),hAPP(hAPP(c_List_Ozip(X16,X5),X212),X214)) = hAPP(c_Map_Omap__of(X16,X5),hAPP(hAPP(c_List_Ozip(X16,X5),X212),X227))
           => X214 = X227 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__zip__inject) ).

fof(fact_Rep__Integ__cases,axiom,
    ! [X27] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X27),c_Int_OInteg))
     => ~ ! [X3] : X27 != hAPP(c_Int_ORep__Integ,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__cases) ).

fof(fact_InterI,axiom,
    ! [X11,X19,X5] :
      ( ! [X195] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X195),X19))
         => hBOOL(hAPP(hAPP(c_member(X5),X11),X195)) )
     => hBOOL(hAPP(hAPP(c_member(X5),X11),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X19))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_InterI) ).

fof(fact_lists_Osimps,axiom,
    ! [X11,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X6),c_List_Olists(X5,X11)))
    <=> ( X6 = c_List_Olist_ONil(X5)
        | ? [X74,X254] :
            ( X6 = hAPP(hAPP(c_List_Olist_OCons(X5),X74),X254)
            & hBOOL(hAPP(hAPP(c_member(X5),X74),X11))
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X254),c_List_Olists(X5,X11))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists_Osimps) ).

fof(fact_in__set__replicate,axiom,
    ! [X27,X76,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X76,X27))))
    <=> ( X12 = X27
        & X76 != 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,
    ! [X13,X11,X90,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
           => ( X13 != 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)),X11),X13) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
               => hAPP(X90,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(X2,hAPP(X90,X11)),hAPP(X90,X13)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Ounion__disjoint) ).

fof(fact_mod__add__eq,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26),X24) = c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),c_Divides_Odiv__class_Omod(X15,X25,X24)),c_Divides_Odiv__class_Omod(X15,X26,X24)),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__eq) ).

fof(fact_mod__mult__eq,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26),X24) = c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),c_Divides_Odiv__class_Omod(X15,X25,X24)),c_Divides_Odiv__class_Omod(X15,X26,X24)),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__eq) ).

fof(fact_mod__diff__eq,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Divides_Oring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X25),X26),X24) = c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),c_Divides_Odiv__class_Omod(X15,X25,X24)),c_Divides_Odiv__class_Omod(X15,X26,X24)),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__eq) ).

fof(fact_power__gt1__lemma,axiom,
    ! [X98,X25,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Oone__class_Oone(X15)),X25))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Oone__class_Oone(X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)))) ) ),
    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,
    ! [X30,X93] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X93))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30),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)),X30),X93) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__diff__nat) ).

fof(fact_InterD,axiom,
    ! [X31,X19,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X11),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X19)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X31),X19))
       => hBOOL(hAPP(hAPP(c_member(X5),X11),X31)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_InterD) ).

fof(fact_InterE,axiom,
    ! [X31,X19,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X11),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X19)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X31),X19))
       => hBOOL(hAPP(hAPP(c_member(X5),X11),X31)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_InterE) ).

fof(fact_weak__coinduct,axiom,
    ! [X2,X31,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X31))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X31),hAPP(X2,X31)))
       => hBOOL(hAPP(hAPP(c_member(X5),X6),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),X2))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_weak__coinduct) ).

fof(fact_div__pos__neg__trivial,axiom,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25),X26)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26) = 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,
    ! [X16,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,X16)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,X16),tc_HOL_Obool))))
     => ( hAPP(c_Finite__Set_Ocard(X16),c_Orderings_Otop__class_Otop(tc_fun(X16,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_OSup__fin_Ounion__idem,axiom,
    ! [X13,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
           => ( X13 != 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)),X11),X13)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X11)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X13)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ounion__idem) ).

fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
    ! [X13,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
           => ( X13 != 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)),X11),X13)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X11)),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X13)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ounion__idem) ).

fof(fact_zmult__zless__mono2,axiom,
    ! [X100,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X102),X101))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X100))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X100),X102)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X100),X101))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).

fof(fact_mult__less__mono1,axiom,
    ! [X100,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X101))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X100))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X102),X100)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X100))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).

fof(fact_mult__less__mono2,axiom,
    ! [X100,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X101))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X100))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),X102)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),X101))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).

fof(fact_zdiv__mono1,axiom,
    ! [X26,X81,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25),X81))
     => ( 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__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X81),X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono1) ).

fof(fact_div__le__mono2,axiom,
    ! [X100,X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X99))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X98))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X100),X98)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X100),X99))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__mono2) ).

fof(fact_inj__map,axiom,
    ! [X2,X16,X5] :
      ( c_Fun_Oinj__on(tc_List_Olist(X5),tc_List_Olist(X16),hAPP(c_List_Omap(X5,X16),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)))
    <=> c_Fun_Oinj__on(X5,X16,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,X16,X5] :
      ( c_Fun_Oinj__on(tc_List_Olist(X5),tc_List_Olist(X16),hAPP(c_List_Omap(X5,X16),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)))
     => c_Fun_Oinj__on(X5,X16,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,
    ! [X17,X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X17),X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insertI2) ).

fof(fact_replicate__app__Cons__same,axiom,
    ! [X221,X14,X98,X15] : hAPP(hAPP(c_List_Oappend(X15),c_List_Oreplicate(X15,X98,X14)),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = hAPP(hAPP(c_List_Olist_OCons(X15),X14),hAPP(hAPP(c_List_Oappend(X15),c_List_Oreplicate(X15,X98,X14)),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__app__Cons__same) ).

fof(fact_INT__insert,axiom,
    ! [X13,X11,X6,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X16),X6),X11)),X13) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(X13,X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X11),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__insert) ).

fof(fact_UN__insert,axiom,
    ! [X13,X11,X6,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X16),X6),X11)),X13) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(X13,X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X11),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__insert) ).

fof(fact_strict__below__fold1__iff,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X12),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X11)))
          <=> ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X12),X3)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_strict__below__fold1__iff) ).

fof(fact_min__max_Obelow__fold1__iff,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X11)))
          <=> ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X3)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Obelow__fold1__iff) ).

fof(fact_below__fold1__iff,axiom,
    ! [X12,X11,X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),hAPP(c_Finite__Set_Ofold1(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X11)))
          <=> ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X3)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_below__fold1__iff) ).

fof(fact_maps__simps_I1_J,axiom,
    ! [X212,X12,X2,X5,X16] : c_List_Omaps(X16,X5,X2,hAPP(hAPP(c_List_Olist_OCons(X16),X12),X212)) = hAPP(hAPP(c_List_Oappend(X5),hAPP(X2,X12)),c_List_Omaps(X16,X5,X2,X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_maps__simps_I1_J) ).

fof(fact_less__iff__diff__less__0,axiom,
    ! [X17,X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X17))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X17)),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,
    ! [X17,X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X17))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X17)),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,
    ! [X26,X81,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25),X81))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),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),X81),X26)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono1__neg) ).

fof(fact_nth__mem,axiom,
    ! [X212,X5,X76] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_List_Onth(X5),X212),X76)),hAPP(c_List_Oset(X5),X212))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__mem) ).

fof(fact_n__less__n__mult__m,axiom,
    ! [X99,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X98))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X99))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X99))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).

fof(fact_n__less__m__mult__n,axiom,
    ! [X99,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X98))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X99))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),X98))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).

fof(fact_card_Oeq__fold__g,axiom,
    ! [X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => hAPP(c_Finite__Set_Ocard(X5),X11) = 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)),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oeq__fold__g) ).

fof(fact_divide__add__eq__iff,axiom,
    ! [X22,X14,X23,X15] :
      ( class_Fields_Ofield(X15)
     => ( X23 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X23)),X22) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X23),X22))),X23) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).

fof(fact_add__frac__num,axiom,
    ! [X23,X14,X22,X15] :
      ( class_Fields_Ofield__inverse__zero(X15)
     => ( X22 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X22)),X23) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X23),X22))),X22) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__num) ).

fof(fact_divide__diff__eq__iff,axiom,
    ! [X22,X14,X23,X15] :
      ( class_Fields_Ofield(X15)
     => ( X23 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X23)),X22) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X23),X22))),X23) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__diff__eq__iff) ).

fof(fact_in__set__conv__nth,axiom,
    ! [X212,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
    <=> ? [X145] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X145),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
          & hAPP(hAPP(c_List_Onth(X5),X212),X145) = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__conv__nth) ).

fof(fact_zadd__zless__mono,axiom,
    ! [X23,X139,X132,X140] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X140),X132))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X139),X23))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X140),X139)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X132),X23))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).

fof(fact_add__less__mono,axiom,
    ! [X103,X100,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X101))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X100),X103))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X100)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),X103))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).

fof(fact_diff__less__mono,axiom,
    ! [X24,X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X26))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X24)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26),X24))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono) ).

fof(fact_diff__less__mono2,axiom,
    ! [X103,X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X103))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X103),X98)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X103),X99))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).

fof(fact_add__le__mono,axiom,
    ! [X103,X100,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X101))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X100),X103))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X100)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),X103))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).

fof(fact_mult__le__mono,axiom,
    ! [X103,X100,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X101))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X100),X103))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X102),X100)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X103))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
    ! [X116,X117,X118,X119,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X119),X118)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X117),X116)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X117),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X119),X118)),X116)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).

fof(fact_lessThan__strict__subset__iff,axiom,
    ! [X76,X45,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),X45)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X76)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X45),X76)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__strict__subset__iff) ).

fof(fact_atMost__subset__iff,axiom,
    ! [X27,X12,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),X12)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X27)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__subset__iff) ).

fof(fact_lessThan__subset__iff,axiom,
    ! [X27,X12,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),X12)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X27)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__subset__iff) ).

fof(fact_atLeast__subset__iff,axiom,
    ! [X27,X12,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),X12)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X27)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X27),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast__subset__iff) ).

fof(fact_greaterThan__subset__iff,axiom,
    ! [X27,X12,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),X12)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X27)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X27),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThan__subset__iff) ).

fof(fact_divide__neg__pos,axiom,
    ! [X22,X14,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),c_Groups_Ozero__class_Ozero(X15)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X22))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X22)),c_Groups_Ozero__class_Ozero(X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__pos) ).

fof(fact_divide__pos__neg,axiom,
    ! [X22,X14,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),c_Groups_Ozero__class_Ozero(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X22)),c_Groups_Ozero__class_Ozero(X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__neg) ).

fof(fact_mult__neg__pos,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Olinordered__semiring__strict(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),c_Groups_Ozero__class_Ozero(X15)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26)),c_Groups_Ozero__class_Ozero(X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__pos) ).

fof(fact_mult__pos__neg,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Olinordered__semiring__strict(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),c_Groups_Ozero__class_Ozero(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26)),c_Groups_Ozero__class_Ozero(X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg) ).

fof(fact_mult__pos__neg2,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Olinordered__semiring__strict(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),c_Groups_Ozero__class_Ozero(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X25)),c_Groups_Ozero__class_Ozero(X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).

fof(fact_divide__nonneg__neg,axiom,
    ! [X22,X14,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),c_Groups_Ozero__class_Ozero(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X22)),c_Groups_Ozero__class_Ozero(X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonneg__neg) ).

fof(fact_divide__nonpos__pos,axiom,
    ! [X22,X14,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),c_Groups_Ozero__class_Ozero(X15)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X22))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X22)),c_Groups_Ozero__class_Ozero(X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonpos__pos) ).

fof(fact_split__mult__neg__le,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Oordered__cancel__semiring(X15)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),c_Groups_Ozero__class_Ozero(X15))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),c_Groups_Ozero__class_Ozero(X15)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X26)) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26)),c_Groups_Ozero__class_Ozero(X15))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).

fof(fact_mult__nonpos__nonneg,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Oordered__cancel__semiring(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),c_Groups_Ozero__class_Ozero(X15)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26)),c_Groups_Ozero__class_Ozero(X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).

fof(fact_mult__nonneg__nonpos,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Oordered__cancel__semiring(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),c_Groups_Ozero__class_Ozero(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26)),c_Groups_Ozero__class_Ozero(X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).

fof(fact_mult__nonneg__nonpos2,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Oordered__cancel__semiring(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),c_Groups_Ozero__class_Ozero(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X25)),c_Groups_Ozero__class_Ozero(X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).

fof(fact_set__subset__Cons,axiom,
    ! [X12,X212,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X212)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__subset__Cons) ).

fof(fact_transpose__map__map,axiom,
    ! [X212,X2,X16,X5] : c_List_Otranspose(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X16),tc_List_Olist(X5)),hAPP(c_List_Omap(X16,X5),X2)),X212)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X16),tc_List_Olist(X5)),hAPP(c_List_Omap(X16,X5),X2)),c_List_Otranspose(X16,X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__map__map) ).

fof(fact_max__less__iff__conj,axiom,
    ! [X37,X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X12),X27)),X37))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X12),X37))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X27),X37)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__less__iff__conj) ).

fof(fact_le__sup__iff,axiom,
    ! [X37,X27,X12,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),X12),X27)),X37))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X37))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X27),X37)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__sup__iff) ).

fof(fact_min__max_Ole__sup__iff,axiom,
    ! [X37,X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X12),X27)),X37))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X37))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X27),X37)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__sup__iff) ).

fof(fact_nth__eq__iff__index__eq,axiom,
    ! [X115,X70,X212,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X212))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X70),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X115),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
         => ( hAPP(hAPP(c_List_Onth(X5),X212),X70) = hAPP(hAPP(c_List_Onth(X5),X212),X115)
          <=> X70 = X115 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__eq__iff__index__eq) ).

fof(fact_distinct__conv__nth,axiom,
    ! [X212,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X212))
    <=> ! [X145] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X145),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
         => ! [X124] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X124),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
             => ( X145 != X124
               => hAPP(hAPP(c_List_Onth(X5),X212),X145) != hAPP(hAPP(c_List_Onth(X5),X212),X124) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__conv__nth) ).

fof(fact_distinct__map,axiom,
    ! [X212,X2,X16,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Omap(X16,X5),X2),X212)))
    <=> ( hBOOL(hAPP(c_List_Odistinct(X16),X212))
        & c_Fun_Oinj__on(X16,X5,X2,hAPP(c_List_Oset(X16),X212)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__map) ).

fof(fact_min__max_OInf__le__Sup,axiom,
    ! [X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != 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),X11)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X11))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__le__Sup) ).

fof(fact_inj__on__diff,axiom,
    ! [X13,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => c_Fun_Oinj__on(X5,X16,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__diff) ).

fof(fact_lazy__sequence_Osize_I2_J,axiom,
    ! [X268,X6,X92,X5] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X5,X92),c_Lazy__Sequence_Olazy__sequence_OInsert(X5,X6,X268)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X92,X6)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X5,X92),X268))),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,
    ! [X12,X37,X11,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm__idem(X5,X16,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),X37),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),hAPP(hAPP(X2,X12),X37)),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem2) ).

fof(fact_insert__Diff,axiom,
    ! [X11,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
     => hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff) ).

fof(fact_finite__Plus__UNIV__iff,axiom,
    ! [X16,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X5,X16)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X5,X16),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(X16),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff) ).

fof(fact_finite__Prod__UNIV,axiom,
    ! [X16,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(X16),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X16)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).

fof(fact_setsum__head__Suc,axiom,
    ! [X2,X76,X45,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X45,X76)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(X2,X45)),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,X45),X76))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__head__Suc) ).

fof(fact_vimageI2,axiom,
    ! [X16,X11,X6,X2,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X6)),X11))
     => hBOOL(hAPP(hAPP(c_member(X16),X6),hAPP(c_Set_Ovimage(X16,X5,X2),X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageI2) ).

fof(fact_sorted__insort,axiom,
    ! [X212,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X12),X212))
      <=> c_List_Olinorder__class_Osorted(X5,X212) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__insort) ).

fof(fact_setsum__head__upt__Suc,axiom,
    ! [X2,X76,X45,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45),X76)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(X2,X45)),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,X45)),X76))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__head__upt__Suc) ).

fof(fact_set__eq__subset,axiom,
    ! [X5,X13,X11] :
      ( X11 = X13
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__eq__subset) ).

fof(fact_equalityI,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),X11))
       => X11 = X13 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityI) ).

fof(fact_rev__nth,axiom,
    ! [X221,X15,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
     => hAPP(hAPP(c_List_Onth(X15),hAPP(c_List_Orev(X15),X221)),X98) = hAPP(hAPP(c_List_Onth(X15),X221),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),hAPP(c_Nat_OSuc,X98))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__nth) ).

fof(fact_INT__absorb,axiom,
    ! [X11,X16,X68,X30,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X30),X68))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),hAPP(X11,X30)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X68),X11)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X68),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__absorb) ).

fof(fact_UN__absorb,axiom,
    ! [X11,X16,X68,X30,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X30),X68))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool)),hAPP(X11,X30)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X68),X11)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X68),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__absorb) ).

fof(fact_list__update__overwrite,axiom,
    ! [X22,X14,X102,X221,X15] : hAPP(hAPP(c_List_Olist__update(X15,hAPP(hAPP(c_List_Olist__update(X15,X221),X102),X14)),X102),X22) = hAPP(hAPP(c_List_Olist__update(X15,X221),X102),X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__overwrite) ).

fof(fact_negative__zless,axiom,
    ! [X99,X98] : 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,X98)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X99))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zless) ).

fof(fact_add__neg__neg,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Oordered__comm__monoid__add(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),c_Groups_Ozero__class_Ozero(X15)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),c_Groups_Ozero__class_Ozero(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26)),c_Groups_Ozero__class_Ozero(X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).

fof(fact_add__nonpos__neg,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Oordered__comm__monoid__add(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),c_Groups_Ozero__class_Ozero(X15)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),c_Groups_Ozero__class_Ozero(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26)),c_Groups_Ozero__class_Ozero(X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).

fof(fact_add__neg__nonpos,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Oordered__comm__monoid__add(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),c_Groups_Ozero__class_Ozero(X15)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),c_Groups_Ozero__class_Ozero(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26)),c_Groups_Ozero__class_Ozero(X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).

fof(fact_Nats__add,axiom,
    ! [X17,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),X17),c_Nat_Osemiring__1__class_ONats(X5)))
         => hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X17)),c_Nat_Osemiring__1__class_ONats(X5))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nats__add) ).

fof(fact_Ints__add,axiom,
    ! [X17,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),X17),c_Int_Oring__1__class_OInts(X5)))
         => hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X17)),c_Int_Oring__1__class_OInts(X5))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__add) ).

fof(fact_Nats__mult,axiom,
    ! [X17,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),X17),c_Nat_Osemiring__1__class_ONats(X5)))
         => hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X17)),c_Nat_Osemiring__1__class_ONats(X5))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nats__mult) ).

fof(fact_Ints__mult,axiom,
    ! [X17,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),X17),c_Int_Oring__1__class_OInts(X5)))
         => hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X17)),c_Int_Oring__1__class_OInts(X5))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__mult) ).

fof(fact_Ints__diff,axiom,
    ! [X17,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),X17),c_Int_Oring__1__class_OInts(X5)))
         => hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X17)),c_Int_Oring__1__class_OInts(X5))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__diff) ).

fof(fact_add__nonpos__nonpos,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Oordered__comm__monoid__add(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),c_Groups_Ozero__class_Ozero(X15)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),c_Groups_Ozero__class_Ozero(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26)),c_Groups_Ozero__class_Ozero(X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).

fof(fact_list__size__conv__listsum,axiom,
    ! [X212,X2,X5] : c_List_Olist_Olist__size(X5,X2,X212) = 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),X212))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__size__conv__listsum) ).

fof(fact_dom__restrict,axiom,
    ! [X11,X45,X16,X5] : c_Map_Odom(X5,X16,c_Map_Orestrict__map(X5,X16,X45,X11)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Map_Odom(X5,X16,X45)),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dom__restrict) ).

fof(fact_Collect__mono,axiom,
    ! [X5,X28,X29] :
      ( ! [X3] :
          ( hBOOL(hAPP(X29,X3))
         => hBOOL(hAPP(X28,X3)) )
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X29)),hAPP(c_Set_OCollect(X5),X28))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__mono) ).

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,
    ! [X212,X34,X16,X5] :
      ( class_Rings_Osemiring__1(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X16,X5),hAPP(c_COMBK(X5,X16),X34)),X212)) = 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(X16)),X212))),X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__triv) ).

fof(fact_power__minus,axiom,
    ! [X98,X25,X15] :
      ( class_Rings_Oring__1(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)),X98) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),c_Groups_Oone__class_Oone(X15))),X98)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus) ).

fof(fact_rangeI,axiom,
    ! [X16,X12,X2,X5] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X12)),hAPP(c_Set_Oimage(X16,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rangeI) ).

fof(fact_left__distrib__number__of,axiom,
    ! [X126,X26,X25,X5] :
      ( ( class_Int_Onumber(X5)
        & class_Rings_Osemiring(X5) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X25),X26)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X26),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__distrib__number__of) ).

fof(fact_left__diff__distrib__number__of,axiom,
    ! [X126,X26,X25,X5] :
      ( ( class_Int_Onumber(X5)
        & class_Rings_Oring(X5) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X25),X26)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X26),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__diff__distrib__number__of) ).

fof(fact_map__add__Some__iff,axiom,
    ! [X12,X30,X76,X45,X5,X16] :
      ( hAPP(c_Map_Omap__add(X16,X5,X45,X76),X30) = hAPP(c_Option_Ooption_OSome(X5),X12)
    <=> ( hAPP(X76,X30) = hAPP(c_Option_Ooption_OSome(X5),X12)
        | ( hAPP(X76,X30) = c_Option_Ooption_ONone(X5)
          & hAPP(X45,X30) = hAPP(c_Option_Ooption_OSome(X5),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__Some__iff) ).

fof(fact_map__add__SomeD,axiom,
    ! [X12,X30,X76,X45,X5,X16] :
      ( hAPP(c_Map_Omap__add(X16,X5,X45,X76),X30) = hAPP(c_Option_Ooption_OSome(X5),X12)
     => ( hAPP(X76,X30) = hAPP(c_Option_Ooption_OSome(X5),X12)
        | ( hAPP(X76,X30) = c_Option_Ooption_ONone(X5)
          & hAPP(X45,X30) = hAPP(c_Option_Ooption_OSome(X5),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__SomeD) ).

fof(fact_Min_Ounion__disjoint,axiom,
    ! [X13,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
           => ( X13 != 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)),X11),X13) = 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)),X11),X13)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olinorder__class_OMin(X5,X11)),c_Big__Operators_Olinorder__class_OMin(X5,X13)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Ounion__disjoint) ).

fof(fact_Max_Ounion__disjoint,axiom,
    ! [X13,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
           => ( X13 != 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)),X11),X13) = 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)),X11),X13)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olinorder__class_OMax(X5,X11)),c_Big__Operators_Olinorder__class_OMax(X5,X13)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Ounion__disjoint) ).

fof(fact_Sup__fin_Ounion__disjoint,axiom,
    ! [X13,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
           => ( X13 != 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)),X11),X13) = 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)),X11),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,X11)),c_Big__Operators_Olattice__class_OSup__fin(X5,X13)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Ounion__disjoint) ).

fof(fact_Inf__fin_Ounion__disjoint,axiom,
    ! [X13,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
           => ( X13 != 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)),X11),X13) = 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)),X11),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X11)),c_Big__Operators_Olattice__class_OInf__fin(X5,X13)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Ounion__disjoint) ).

fof(fact_add__strict__right__mono,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X26),X24))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).

fof(fact_add__strict__left__mono,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X24),X25)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X24),X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).

fof(fact_add__right__mono,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Groups_Oordered__ab__semigroup__add(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X26),X24))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).

fof(fact_add__left__mono,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Groups_Oordered__ab__semigroup__add(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X24),X25)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X24),X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).

fof(fact_fold1__Un2,axiom,
    ! [X13,X11,X5] :
      ( class_Lattices_Oab__semigroup__idem__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
           => ( X13 != 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)),X11),X13)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X11)),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X13)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__Un2) ).

fof(fact_rev__drop,axiom,
    ! [X221,X102,X15] : hAPP(c_List_Orev(X15),hAPP(hAPP(c_List_Odrop(X15),X102),X221)) = hAPP(hAPP(c_List_Otake(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),X102)),hAPP(c_List_Orev(X15),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__drop) ).

fof(fact_rev__take,axiom,
    ! [X221,X102,X15] : hAPP(c_List_Orev(X15),hAPP(hAPP(c_List_Otake(X15),X102),X221)) = hAPP(hAPP(c_List_Odrop(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),X102)),hAPP(c_List_Orev(X15),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__take) ).

fof(fact_ivl__disj__un_I5_J,axiom,
    ! [X66,X97,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X97),X66))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X97),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X97,X66)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X97,X66) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I5_J) ).

fof(fact_subset__Compl__self__eq,axiom,
    ! [X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11)))
    <=> X11 = 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_map__upd__eqD1,axiom,
    ! [X27,X76,X12,X6,X45,X16,X5] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),X45),X6),hAPP(c_Option_Ooption_OSome(X16),X12)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),X76),X6),hAPP(c_Option_Ooption_OSome(X16),X27))
     => X12 = X27 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__upd__eqD1) ).

fof(fact_pdivmod__def,axiom,
    ! [X103,X100] : c_Divides_Opdivmod(X100,X103) = 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),X100)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X103))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X100),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X103))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__def) ).

fof(fact_Union__upper,axiom,
    ! [X11,X13,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X13),X11))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__upper) ).

fof(fact_fold__image__def,axiom,
    ! [X1,X2,X16,X5] : hAPP(c_Finite__Set_Ofold__image(X5,X16,X2),X1) = c_Finite__Set_Ofold(X16,X5,hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X16),X2),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__def) ).

fof(fact_max__Suc1,axiom,
    ! [X45,X76] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X76)),X45) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X76),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),X76)),X45),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__Suc1) ).

fof(fact_Field__Union,axiom,
    ! [X36,X5] : hAPP(c_Relation_OField(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),X36)) = 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)),X36)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__Union) ).

fof(fact_Diff__partition,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X13),X11)) = X13 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__partition) ).

fof(fact_inj__mapI,axiom,
    ! [X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => c_Fun_Oinj__on(tc_List_Olist(X5),tc_List_Olist(X16),hAPP(c_List_Omap(X5,X16),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,
    ! [X13,X11,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)),X11),X13)) = 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)),X11)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__Int) ).

fof(fact_Compl__Un,axiom,
    ! [X13,X11,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)),X11),X13)) = 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)),X11)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__Un) ).

fof(fact_conversep__iff,axiom,
    ! [X17,X6,X34,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5,X16,X34),X6),X17))
    <=> hBOOL(hAPP(hAPP(X34,X17),X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__iff) ).

fof(fact_conversep_Oequations,axiom,
    ! [X47,X46,X34,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5,X16,X34),X46),X47))
    <=> hBOOL(hAPP(hAPP(X34,X47),X46)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep_Oequations) ).

fof(fact_conversepD,axiom,
    ! [X17,X6,X34,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5,X16,X34),X6),X17))
     => hBOOL(hAPP(hAPP(X34,X17),X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversepD) ).

fof(fact_vimage__code,axiom,
    ! [X12,X11,X2,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_Set_Ovimage(X5,X16,X2),X11),X12))
    <=> hBOOL(hAPP(X11,hAPP(X2,X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__code) ).

fof(fact_Inf__less__iff,axiom,
    ! [X6,X35,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,X35)),X6))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X35))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X3),X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__less__iff) ).

fof(fact_add__number__of__left,axiom,
    ! [X23,X132,X126,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X126)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X132)),X23)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X126),X132))),X23) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__left) ).

fof(fact_add__number__of__diff1,axiom,
    ! [X24,X132,X126,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X126)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X132)),X24)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X126),X132))),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__diff1) ).

fof(fact_mult__number__of__left,axiom,
    ! [X23,X132,X126,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X126)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X132)),X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X126),X132))),X23) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__number__of__left) ).

fof(fact_Option_Omap__def,axiom,
    ! [X2,X16,X5] : hAPP(c_Option_Omap(X5,X16),X2) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(X16),X5,c_Option_Ooption_ONone(X16),hAPP(hAPP(c_COMBB(X16,tc_Option_Ooption(X16),X5),c_Option_Ooption_OSome(X16)),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Option_Omap__def) ).

fof(fact_ivl__disj__un_I3_J,axiom,
    ! [X66,X97,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X97),X66))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X97),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X97,X66)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X97),X66) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I3_J) ).

fof(fact_nth__map,axiom,
    ! [X2,X16,X212,X5,X76] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
     => hAPP(hAPP(c_List_Onth(X16),hAPP(hAPP(c_List_Omap(X5,X16),X2),X212)),X76) = hAPP(X2,hAPP(hAPP(c_List_Onth(X5),X212),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__map) ).

fof(fact_nat__gcd_Opsimps,axiom,
    ! [X27,X12] :
      ( 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),X12),X27)))
     => ( ( X27 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Nitpick_Onat__gcd(X12,X27) = X12 )
        & ( X27 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Nitpick_Onat__gcd(X12,X27) = c_Nitpick_Onat__gcd(X27,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,X27)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__gcd_Opsimps) ).

fof(fact_UnionI,axiom,
    ! [X11,X19,X31,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X31),X19))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X11),X31))
       => hBOOL(hAPP(hAPP(c_member(X5),X11),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X19))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UnionI) ).

fof(fact_zero__less__mult__pos2,axiom,
    ! [X25,X26,X15] :
      ( class_Rings_Olinordered__semiring__strict(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X25)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).

fof(fact_zero__less__mult__pos,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Olinordered__semiring__strict(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).

fof(fact_in__set__conv__decomp,axiom,
    ! [X212,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
    <=> ? [X229,X260] : X212 = hAPP(hAPP(c_List_Oappend(X5),X229),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X260)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__conv__decomp) ).

fof(fact_card__Un__disjoint,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
       => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) = 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)),X11),X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X11)),hAPP(c_Finite__Set_Ocard(X5),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Un__disjoint) ).

fof(fact_min__Suc1,axiom,
    ! [X45,X76] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X76)),X45) = 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),X76)),X45),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__Suc1) ).

fof(fact_sorted__list__of__set__remove,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => c_List_Olinorder__class_Osorted__list__of__set(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = c_List_Oremove1(X5,X12,c_List_Olinorder__class_Osorted__list__of__set(X5,X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__list__of__set__remove) ).

fof(fact_finite__fun__UNIVD2,axiom,
    ! [X16,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,X16)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,X16),tc_HOL_Obool))))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X16),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).

fof(fact_filter__sort,axiom,
    ! [X212,X2,X29,X5,X16] :
      ( class_Orderings_Olinorder(X16)
     => hAPP(c_List_Ofilter(X5,X29),c_List_Olinorder__class_Osort__key(X5,X16,X2,X212)) = c_List_Olinorder__class_Osort__key(X5,X16,X2,hAPP(c_List_Ofilter(X5,X29),X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__sort) ).

fof(fact_PowD,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Set_OPow(X5),X13)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PowD) ).

fof(fact_Pow__iff,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Set_OPow(X5),X13)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__iff) ).

fof(fact_zero__less__zpower__abs__iff,axiom,
    ! [X76,X12] :
      ( 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),X12)),X76)))
    <=> ( X12 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X76 = 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,
    ! [X66,X45,X97,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X97),X45))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X45),X66))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X97,X45)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X45,X66)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X97,X66) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I22_J) ).

fof(fact_ivl__disj__un_I20_J,axiom,
    ! [X66,X45,X97,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X97),X45))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X45),X66))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X97,X45)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X45,X66)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X97,X66) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I20_J) ).

fof(fact_ivl__disj__un_I16_J,axiom,
    ! [X66,X45,X97,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X97),X45))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X45),X66))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X97,X45)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X45,X66)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X97,X66) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I16_J) ).

fof(fact_ivl__disj__un_I19_J,axiom,
    ! [X66,X45,X97,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X97),X45))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X45),X66))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X97,X45)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X45,X66)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X97,X66) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I19_J) ).

fof(fact_Un__upper1,axiom,
    ! [X13,X11,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__upper1) ).

fof(fact_Un__upper2,axiom,
    ! [X11,X13,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__upper2) ).

fof(fact_r__into__rtrancl,axiom,
    ! [X34,X161,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X161),X34))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X161),c_Transitive__Closure_Ortrancl(X5,X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).

fof(fact_card__Plus,axiom,
    ! [X13,X16,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X13))
       => hAPP(c_Finite__Set_Ocard(tc_sum(X5,X16)),c_Sum__Type_OPlus(X5,X16,X11,X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X11)),hAPP(c_Finite__Set_Ocard(X16),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Plus) ).

fof(fact_card__Plus__conv__if,axiom,
    ! [X13,X16,X11,X5] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X13)) )
       => hAPP(c_Finite__Set_Ocard(tc_sum(X5,X16)),c_Sum__Type_OPlus(X5,X16,X11,X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X11)),hAPP(c_Finite__Set_Ocard(X16),X13)) )
      & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
            & hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X13)) )
       => hAPP(c_Finite__Set_Ocard(tc_sum(X5,X16)),c_Sum__Type_OPlus(X5,X16,X11,X13)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Plus__conv__if) ).

fof(fact_map__of__eq__dom,axiom,
    ! [X214,X212,X16,X5] :
      ( hAPP(c_Map_Omap__of(X5,X16),X212) = hAPP(c_Map_Omap__of(X5,X16),X214)
     => hAPP(c_Set_Oimage(tc_prod(X5,X16),X5,c_Product__Type_Ofst(X5,X16)),hAPP(c_List_Oset(tc_prod(X5,X16)),X212)) = hAPP(c_Set_Oimage(tc_prod(X5,X16),X5,c_Product__Type_Ofst(X5,X16)),hAPP(c_List_Oset(tc_prod(X5,X16)),X214)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__eq__dom) ).

fof(fact_min__max_Ole__supI,axiom,
    ! [X26,X14,X25,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),X14))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X25),X26)),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__supI) ).

fof(fact_min__max_Osup__least,axiom,
    ! [X23,X14,X22,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X23),X14))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X22),X23)),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__least) ).

fof(fact_le__supI,axiom,
    ! [X26,X14,X25,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),X14))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X25),X26)),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__supI) ).

fof(fact_sup__least,axiom,
    ! [X23,X14,X22,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X23),X14))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X22),X23)),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__least) ).

fof(fact_Int__left__commute,axiom,
    ! [X19,X13,X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X13),X19)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__commute) ).

fof(fact_Un__left__commute,axiom,
    ! [X19,X13,X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X13),X19)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__left__commute) ).

fof(fact_Diff__idemp,axiom,
    ! [X13,X11,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)),X11),X13)),X13) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__idemp) ).

fof(fact_Un__Diff__cancel2,axiom,
    ! [X11,X13,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)),X13),X11)),X11) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X13),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Diff__cancel2) ).

fof(fact_imageI,axiom,
    ! [X2,X16,X11,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
     => hBOOL(hAPP(hAPP(c_member(X16),hAPP(X2,X12)),hAPP(c_Set_Oimage(X5,X16,X2),X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_imageI) ).

fof(fact_hoare__derivs_Oinsert,axiom,
    ! [X7,X10,X4,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),X10),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
     => ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X7)
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),X10),X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hoare__derivs_Oinsert) ).

fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
    ! [X1,X38,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X16,X2)
     => c_Finite__Set_Ofun__left__comm(X38,X16,hAPP(hAPP(c_COMBB(X5,tc_fun(X16,X16),X38),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,X38,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm__idem(X5,X16,X2)
     => c_Finite__Set_Ofun__left__comm__idem(X38,X16,hAPP(hAPP(c_COMBB(X5,tc_fun(X16,X16),X38),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,
    ! [X13,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)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13)),X19) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X13),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__left__if1) ).

fof(fact_inj__image__eq__iff,axiom,
    ! [X13,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hAPP(c_Set_Oimage(X5,X16,X2),X11) = hAPP(c_Set_Oimage(X5,X16,X2),X13)
      <=> X11 = X13 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).

fof(fact_o__eq__dest__lhs,axiom,
    ! [X56,X21,X17,X6,X5,X16,X38] :
      ( hAPP(c_Fun_Ocomp(X38,X16,X5,X6),X17) = X21
     => hAPP(X6,hAPP(X17,X56)) = hAPP(X21,X56) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).

fof(fact_negative__zless__0,axiom,
    ! [X98] : 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,X98)))),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,
    ! [X221,X15,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
     => hAPP(hAPP(c_List_Olist_OCons(X15),hAPP(hAPP(c_List_Onth(X15),X221),X102)),hAPP(hAPP(c_List_Odrop(X15),hAPP(c_Nat_OSuc,X102)),X221)) = hAPP(hAPP(c_List_Odrop(X15),X102),X221) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__drop_H) ).

fof(fact_image__vimage__eq,axiom,
    ! [X11,X2,X5,X16] : hAPP(c_Set_Oimage(X16,X5,X2),hAPP(c_Set_Ovimage(X16,X5,X2),X11)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Set_Oimage(X16,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__vimage__eq) ).

fof(fact_add1__zle__eq,axiom,
    ! [X37,X112] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X112),c_Groups_Oone__class_Oone(tc_Int_Oint))),X37))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X112),X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).

fof(fact_ivl__disj__un_I18_J,axiom,
    ! [X66,X45,X97,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X97),X45))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X45),X66))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X97,X45)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X45,X66)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X97),X66) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I18_J) ).

fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
    ! [X11] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X11))
    <=> 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)),X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I1_J) ).

fof(fact_psubset__card__mono,axiom,
    ! [X11,X13,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),X13))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X11)),hAPP(c_Finite__Set_Ocard(X5),X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__card__mono) ).

fof(fact_card__mono,axiom,
    ! [X11,X13,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X11)),hAPP(c_Finite__Set_Ocard(X5),X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__mono) ).

fof(fact_dom__minus,axiom,
    ! [X11,X16,X5,X12,X2] :
      ( hAPP(X2,X12) = c_Option_Ooption_ONone(X5)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool)),c_Map_Odom(X16,X5,X2)),hAPP(hAPP(c_Set_Oinsert(X16),X12),X11)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16,tc_HOL_Obool)),c_Map_Odom(X16,X5,X2)),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dom__minus) ).

fof(fact_UnI1,axiom,
    ! [X13,X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
     => hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UnI1) ).

fof(fact_UnI2,axiom,
    ! [X11,X13,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),X13))
     => hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13))) ),
    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,
    ! [X17,X6,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Oabs__class_Oabs(X5),X6)),X17))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X17))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)),X17)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__less__iff) ).

fof(fact_abs__leI,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__leI) ).

fof(fact_abs__le__iff,axiom,
    ! [X17,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)),X17))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X17))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)),X17)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__iff) ).

fof(fact_lists__accI,axiom,
    ! [X34,X212,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X212),c_Wellfounded_Oacc(tc_List_Olist(X5),c_List_Olistrel1(X5,X34))))
     => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X212),c_List_Olists(X5,c_Wellfounded_Oacc(X5,X34)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__accI) ).

fof(fact_inj__vimage__image__eq,axiom,
    ! [X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Set_Ovimage(X5,X16,X2),hAPP(c_Set_Oimage(X5,X16,X2),X11)) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__vimage__image__eq) ).

fof(fact_ivl__disj__un_I15_J,axiom,
    ! [X66,X45,X97,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X97),X45))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X45),X66))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X97,X45)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X45),X66)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X97,X66) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I15_J) ).

fof(fact_div__mult__self2,axiom,
    ! [X24,X25,X26,X15] :
      ( class_Divides_Osemiring__div(X15)
     => ( X26 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X24))),X26) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X24),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),X25),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self2) ).

fof(fact_div__mult__self1,axiom,
    ! [X24,X25,X26,X15] :
      ( class_Divides_Osemiring__div(X15)
     => ( X26 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X26))),X26) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X24),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),X25),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self1) ).

fof(fact_add__num__frac,axiom,
    ! [X14,X23,X22,X15] :
      ( class_Fields_Ofield__inverse__zero(X15)
     => ( X22 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X23),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X22)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X23),X22))),X22) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__num__frac) ).

fof(fact_setsum__reindex__id,axiom,
    ! [X13,X2,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( c_Fun_Oinj__on(X5,X16,X2,X13)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X13) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X16),c_Fun_Oid(X16)),hAPP(c_Set_Oimage(X5,X16,X2),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__reindex__id) ).

fof(fact_setprod__reindex__id,axiom,
    ! [X13,X2,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( c_Fun_Oinj__on(X5,X16,X2,X13)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),X13) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16,X16),c_Fun_Oid(X16)),hAPP(c_Set_Oimage(X5,X16,X2),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__reindex__id) ).

fof(fact_wf__comp__self,axiom,
    ! [X36,X5] :
      ( c_Wellfounded_Owf(X5,X36)
    <=> c_Wellfounded_Owf(X5,hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X36),X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__comp__self) ).

fof(fact_less__by__empty,axiom,
    ! [X13,X5,X11] :
      ( X11 = 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)),X11),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__by__empty) ).

fof(fact_distinct__append,axiom,
    ! [X214,X212,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Oappend(X5),X212),X214)))
    <=> ( hBOOL(hAPP(c_List_Odistinct(X5),X212))
        & hBOOL(hAPP(c_List_Odistinct(X5),X214))
        & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X212)),hAPP(c_List_Oset(X5),X214)) = 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_OSup__fin__set__fold,axiom,
    ! [X212,X12,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),X12),X212))) = hAPP(c_List_Ofoldl(X5,X5,c_Orderings_Oord__class_Omax(X5),X12),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin__set__fold) ).

fof(fact_min__max_OInf__fin__set__fold,axiom,
    ! [X212,X12,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),X12),X212))) = hAPP(c_List_Ofoldl(X5,X5,c_Orderings_Oord__class_Omin(X5),X12),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin__set__fold) ).

fof(fact_setsum__head,axiom,
    ! [X29,X76,X45,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X29),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X45,X76)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(X29,X45)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X29),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X45,X76))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__head) ).

fof(fact_funpow_Osimps_I2_J,axiom,
    ! [X2,X76,X5] : hAPP(hAPP(c_Nat_Ocompow(X5,X5),hAPP(c_Nat_OSuc,X76)),X2) = hAPP(c_Fun_Ocomp(X5,X5,X5,X2),hAPP(hAPP(c_Nat_Ocompow(X5,X5),X76),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow_Osimps_I2_J) ).

fof(fact_list__size__estimation,axiom,
    ! [X2,X27,X212,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27),hAPP(X2,X12)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27),c_List_Olist_Olist__size(X5,X2,X212))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__size__estimation) ).

fof(fact_list__size__estimation_H,axiom,
    ! [X2,X27,X212,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X27),hAPP(X2,X12)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X27),c_List_Olist_Olist__size(X5,X2,X212))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__size__estimation_H) ).

fof(fact_elem__le__listsum__nat,axiom,
    ! [X230,X100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X100),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X230)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X230),X100)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X230))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_elem__le__listsum__nat) ).

fof(fact_le__div__geq,axiom,
    ! [X99,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__eq(tc_Nat_Onat),X98),X99))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),X98) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98)),X98)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__div__geq) ).

fof(fact_lists__accD,axiom,
    ! [X34,X212,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X212),c_List_Olists(X5,c_Wellfounded_Oacc(X5,X34))))
     => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X212),c_Wellfounded_Oacc(tc_List_Olist(X5),c_List_Olistrel1(X5,X34)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__accD) ).

fof(fact_semiring__1__class_Oof__nat__code,axiom,
    ! [X76,X5] :
      ( class_Rings_Osemiring__1(X5)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X76) = 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)),X76,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,
    ! [X14,X225,X221,X15] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X225)))
     => X221 != hAPP(hAPP(c_List_Olist_OCons(X15),X14),X225) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_impossible__Cons) ).

fof(fact_PowI,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Set_OPow(X5),X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PowI) ).

fof(fact_power_Opower_Opower__Suc,axiom,
    ! [X76,X6,X136,X137,X5] : hAPP(hAPP(c_Power_Opower_Opower(X5,X137,X136),X6),hAPP(c_Nat_OSuc,X76)) = hAPP(hAPP(X136,X6),hAPP(hAPP(c_Power_Opower_Opower(X5,X137,X136),X6),X76)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).

fof(fact_map__add__None,axiom,
    ! [X30,X76,X45,X5,X16] :
      ( hAPP(c_Map_Omap__add(X16,X5,X45,X76),X30) = c_Option_Ooption_ONone(X5)
    <=> ( hAPP(X76,X30) = c_Option_Ooption_ONone(X5)
        & hAPP(X45,X30) = c_Option_Ooption_ONone(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__None) ).

fof(fact_Min__antimono,axiom,
    ! [X93,X67,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X67),X93))
       => ( X67 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X93))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Big__Operators_Olinorder__class_OMin(X5,X93)),c_Big__Operators_Olinorder__class_OMin(X5,X67))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min__antimono) ).

fof(fact_Max__mono,axiom,
    ! [X93,X67,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X67),X93))
       => ( X67 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X93))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Big__Operators_Olinorder__class_OMax(X5,X67)),c_Big__Operators_Olinorder__class_OMax(X5,X93))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max__mono) ).

fof(fact_less__bin__lemma,axiom,
    ! [X97,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),X97))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X30),X97)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__bin__lemma) ).

fof(fact_singleton__iff,axiom,
    ! [X6,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))
    <=> X17 = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__iff) ).

fof(fact_singletonE,axiom,
    ! [X6,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))
     => X17 = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singletonE) ).

fof(fact_range__eqI,axiom,
    ! [X16,X5,X12,X2,X17] :
      ( X17 = hAPP(X2,X12)
     => hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(c_Set_Oimage(X16,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__eqI) ).

fof(fact_snd__image__times,axiom,
    ! [X13,X16,X5,X11] :
      ( ( X11 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(X5,X16),X16,c_Product__Type_Osnd(X5,X16)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X13))) = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)) )
      & ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(X5,X16),X16,c_Product__Type_Osnd(X5,X16)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X13))) = X13 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__image__times) ).

fof(fact_fst__image__times,axiom,
    ! [X11,X16,X5,X13] :
      ( ( X13 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(X16,X5),X16,c_Product__Type_Ofst(X16,X5)),hAPP(hAPP(c_Product__Type_OSigma(X16,X5),X11),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X16),X13))) = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)) )
      & ( X13 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(X16,X5),X16,c_Product__Type_Ofst(X16,X5)),hAPP(hAPP(c_Product__Type_OSigma(X16,X5),X11),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X16),X13))) = X11 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__image__times) ).

fof(fact_doubleton__eq__iff,axiom,
    ! [X20,X21,X17,X6,X5] :
      ( hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X17),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X5),X21),hAPP(hAPP(c_Set_Oinsert(X5),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
    <=> ( ( X6 = X21
          & X17 = X20 )
        | ( X6 = X20
          & X17 = X21 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_doubleton__eq__iff) ).

fof(fact_nth__list__update,axiom,
    ! [X14,X101,X221,X15,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
     => ( ( X102 = X101
         => hAPP(hAPP(c_List_Onth(X15),hAPP(hAPP(c_List_Olist__update(X15,X221),X102),X14)),X101) = X14 )
        & ( X102 != X101
         => hAPP(hAPP(c_List_Onth(X15),hAPP(hAPP(c_List_Olist__update(X15,X221),X102),X14)),X101) = hAPP(hAPP(c_List_Onth(X15),X221),X101) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__list__update) ).

fof(fact_add__lessD1,axiom,
    ! [X100,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X101)),X100))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X100)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).

fof(fact_add__leD1,axiom,
    ! [X98,X100,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X100)),X98))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).

fof(fact_add__leD2,axiom,
    ! [X98,X100,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X100)),X98))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X100),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).

fof(fact_diff__Suc__less,axiom,
    ! [X102,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_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),hAPP(c_Nat_OSuc,X102))),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__less) ).

fof(fact_ran__map__upd,axiom,
    ! [X17,X16,X5,X6,X45] :
      ( hAPP(X45,X6) = c_Option_Ooption_ONone(X5)
     => c_Map_Oran(X16,X5,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X16,tc_Option_Ooption(X5)),X45),X6),hAPP(c_Option_Ooption_OSome(X5),X17))) = hAPP(hAPP(c_Set_Oinsert(X5),X17),c_Map_Oran(X16,X5,X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ran__map__upd) ).

fof(fact_ivl__disj__un_I21_J,axiom,
    ! [X66,X45,X97,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X97),X45))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X45),X66))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X97),X45)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X45,X66)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X97,X66) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I21_J) ).

fof(fact_atLeastLessThan__add__Un,axiom,
    ! [X30,X115,X70] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X70),X115))
     => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X70),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X115),X30)) = 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,X70),X115)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X115),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X115),X30))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__add__Un) ).

fof(fact_insert__Diff__single,axiom,
    ! [X11,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),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),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff__single) ).

fof(fact_card__insert__le,axiom,
    ! [X12,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X11)),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__le) ).

fof(fact_zadd__int__left,axiom,
    ! [X23,X98,X99] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X99)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X98)),X23)) = 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),X99),X98))),X23),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__int__left) ).

fof(fact_less__Sup__iff,axiom,
    ! [X35,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,X35)))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X35))
            & 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,
    ! [X11] :
      ( c_Nat__Transfer_Onat__set(X11)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X11))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X11))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I1_J) ).

fof(fact_transfer__nat__int__relations_I2_J,axiom,
    ! [X27,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X27))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X12)),hAPP(c_Int_Onat,X27)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),X27)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I2_J) ).

fof(fact_transfer__nat__int__relations_I3_J,axiom,
    ! [X27,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X27))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X12)),hAPP(c_Int_Onat,X27)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12),X27)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I3_J) ).

fof(fact_ivl__disj__un_I4_J,axiom,
    ! [X66,X97,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X97),X66))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X97,X66)),hAPP(hAPP(c_Set_Oinsert(X5),X66),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X97,X66) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I4_J) ).

fof(fact_Min__eqI,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ! [X33] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X33),X11))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X33)) )
         => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
           => c_Big__Operators_Olinorder__class_OMin(X5,X11) = X12 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min__eqI) ).

fof(fact_map__append,axiom,
    ! [X214,X212,X2,X5,X16] : hAPP(hAPP(c_List_Omap(X16,X5),X2),hAPP(hAPP(c_List_Oappend(X16),X212),X214)) = hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(c_List_Omap(X16,X5),X2),X212)),hAPP(hAPP(c_List_Omap(X16,X5),X2),X214)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__append) ).

fof(fact_finite__Union,axiom,
    ! [X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),X11))
     => ( ! [X194] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X194),X11))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X194)) )
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X11))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Union) ).

fof(fact_int__div__less__self,axiom,
    ! [X100,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X100))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14),X100)),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__div__less__self) ).

fof(fact_div__less__dividend,axiom,
    ! [X99,X98] :
      ( 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(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X99))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),X98)),X99)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__less__dividend) ).

fof(fact_diff__less,axiom,
    ! [X99,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),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X99))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98)),X99)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less) ).

fof(fact_insert__inter__insert,axiom,
    ! [X13,X11,X6,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__inter__insert) ).

fof(fact_div__neg__pos__less0,axiom,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),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)),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26)),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,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),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),X25),X26)),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,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25),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)),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nonpos__pos__le0) ).

fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
    ! [X26,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),c_Divides_Odiv__class_Omod(X15,X25,X26)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),X25),X26)),X26)) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__div__class_Omod__div__equality_H) ).

fof(fact_zero__less__divide__iff,axiom,
    ! [X17,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),X17)))
      <=> ( ( 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)),X17)) )
          | ( 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),X17),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,
    ! [X17,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),X17)))
      <=> ( ( 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)),X17)) )
          | ( 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),X17),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,
    ! [X17,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),X17)))
      <=> ( ( 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)),X17)) )
          | ( 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),X17),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,
    ! [X115,X70,X29] :
      ( c_List_Oall__interval__int(X29,X70,X115)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X70,X115)))
         => hBOOL(hAPP(X29,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__interval__int__def) ).

fof(fact_zadd__strict__right__mono,axiom,
    ! [X100,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X102),X101))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X102),X100)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X101),X100))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).

fof(fact_add__less__mono1,axiom,
    ! [X100,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X101))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X100)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),X100))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).

fof(fact_zadd__left__mono,axiom,
    ! [X100,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X102),X101))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X100),X102)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X100),X101))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).

fof(fact_div__le__mono,axiom,
    ! [X100,X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X98))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),X100)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X98),X100))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__mono) ).

fof(fact_add__le__mono1,axiom,
    ! [X100,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X101))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X100)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),X100))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).

fof(fact_mult__le__mono1,axiom,
    ! [X100,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X101))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X102),X100)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X100))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono1) ).

fof(fact_mult__le__mono2,axiom,
    ! [X100,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X101))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),X102)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),X101))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono2) ).

fof(fact_diff__le__mono,axiom,
    ! [X103,X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X98))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X103)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),X103))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono) ).

fof(fact_diff__le__mono2,axiom,
    ! [X103,X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X98))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X103),X98)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X103),X99))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono2) ).

fof(fact_Min__fin__set__fold,axiom,
    ! [X212,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212))) = hAPP(c_List_Ofoldl(X5,X5,c_Orderings_Oord__class_Omin(X5),X12),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min__fin__set__fold) ).

fof(fact_Max__fin__set__fold,axiom,
    ! [X212,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212))) = hAPP(c_List_Ofoldl(X5,X5,c_Orderings_Oord__class_Omax(X5),X12),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max__fin__set__fold) ).

fof(fact_Sup__fin__set__fold,axiom,
    ! [X212,X12,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),X12),X212))) = hAPP(c_List_Ofoldl(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5),X12),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin__set__fold) ).

fof(fact_Inf__fin__set__fold,axiom,
    ! [X212,X12,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),X12),X212))) = hAPP(c_List_Ofoldl(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5),X12),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin__set__fold) ).

fof(fact_diff__Suc__diff__eq2,axiom,
    ! [X99,X101,X100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X100),X101))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X101),X100))),X99) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X101)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),X99)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).

fof(fact_mod__div__equality2,axiom,
    ! [X25,X26,X15] :
      ( class_Divides_Osemiring__div(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),X25),X26))),c_Divides_Odiv__class_Omod(X15,X25,X26)) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__div__equality2) ).

fof(fact_list__update__code_I3_J,axiom,
    ! [X22,X102,X221,X14,X15] : hAPP(hAPP(c_List_Olist__update(X15,hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)),hAPP(c_Nat_OSuc,X102)),X22) = hAPP(hAPP(c_List_Olist_OCons(X15),X14),hAPP(hAPP(c_List_Olist__update(X15,X221),X102),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__code_I3_J) ).

fof(fact_pair__box_Oinject,axiom,
    ! [X138,X82,X17,X6,X16,X5] :
      ( c_Nitpick_Opair__box_OPairBox(X5,X16,X6,X17) = c_Nitpick_Opair__box_OPairBox(X5,X16,X82,X138)
    <=> ( X6 = X82
        & X17 = X138 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Oinject) ).

fof(fact_vimageI,axiom,
    ! [X16,X13,X5,X17,X6,X2] :
      ( hAPP(X2,X6) = X17
     => ( hBOOL(hAPP(hAPP(c_member(X5),X17),X13))
       => hBOOL(hAPP(hAPP(c_member(X16),X6),hAPP(c_Set_Ovimage(X16,X5,X2),X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageI) ).

fof(fact_image__eqI,axiom,
    ! [X5,X11,X16,X12,X2,X17] :
      ( X17 = hAPP(X2,X12)
     => ( hBOOL(hAPP(hAPP(c_member(X16),X12),X11))
       => hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(c_Set_Oimage(X16,X5,X2),X11))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eqI) ).

fof(fact_rev__image__eqI,axiom,
    ! [X16,X2,X17,X11,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
     => ( X17 = hAPP(X2,X12)
       => hBOOL(hAPP(hAPP(c_member(X16),X17),hAPP(c_Set_Oimage(X5,X16,X2),X11))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__image__eqI) ).

fof(fact_inj__on__iff,axiom,
    ! [X27,X12,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X27),X11))
         => ( hAPP(X2,X12) = hAPP(X2,X27)
          <=> X12 = X27 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff) ).

fof(fact_inj__onD,axiom,
    ! [X27,X12,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => ( hAPP(X2,X12) = hAPP(X2,X27)
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( hBOOL(hAPP(hAPP(c_member(X5),X27),X11))
           => X12 = X27 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__onD) ).

fof(fact_inj__on__contraD,axiom,
    ! [X27,X12,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => ( X12 != X27
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( hBOOL(hAPP(hAPP(c_member(X5),X27),X11))
           => hAPP(X2,X12) != hAPP(X2,X27) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__contraD) ).

fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
    ! [X17,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),X17)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17),X6))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).

fof(fact_list__ex__length,axiom,
    ! [X212,X29,X5] :
      ( c_List_Olist__ex(X5,X29,X212)
    <=> ? [X107] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
          & hBOOL(hAPP(X29,hAPP(hAPP(c_List_Onth(X5),X212),X107))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__length) ).

fof(fact_folding__one__idem_Osubset__idem,axiom,
    ! [X13,X11,X90,X2,X5] :
      ( c_Finite__Set_Ofolding__one__idem(X5,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X13 != 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)),X13),X11))
           => hAPP(hAPP(X2,hAPP(X90,X13)),hAPP(X90,X11)) = hAPP(X90,X11) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Osubset__idem) ).

fof(fact_comp__equivI,axiom,
    ! [X11,X34,X5] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(c_Relation_Oconverse(X5,X5),X34)),X34) = X34
     => ( hAPP(c_Relation_ODomain(X5,X5),X34) = X11
       => c_Equiv__Relations_Oequiv(X5,X11,X34) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__equivI) ).

fof(fact_zip__replicate,axiom,
    ! [X22,X101,X14,X102,X5,X15] : hAPP(hAPP(c_List_Ozip(X15,X5),c_List_Oreplicate(X15,X102,X14)),c_List_Oreplicate(X5,X101,X22)) = c_List_Oreplicate(tc_prod(X15,X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X102),X101),hAPP(hAPP(c_Product__Type_OPair(X15,X5),X14),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__replicate) ).

fof(fact_le__funD,axiom,
    ! [X12,X1,X2,X5,X16] :
      ( class_Orderings_Oord(X16)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X16)),X2),X1))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(X2,X12)),hAPP(X1,X12))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).

fof(fact_le__funE,axiom,
    ! [X12,X1,X2,X5,X16] :
      ( class_Orderings_Oord(X16)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X16)),X2),X1))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(X2,X12)),hAPP(X1,X12))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).

fof(fact_inj__map__eq__map,axiom,
    ! [X214,X212,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hAPP(hAPP(c_List_Omap(X5,X16),X2),X212) = hAPP(hAPP(c_List_Omap(X5,X16),X2),X214)
      <=> X212 = X214 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__map__eq__map) ).

fof(fact_map__injective,axiom,
    ! [X214,X212,X2,X5,X16] :
      ( hAPP(hAPP(c_List_Omap(X16,X5),X2),X212) = hAPP(hAPP(c_List_Omap(X16,X5),X2),X214)
     => ( c_Fun_Oinj__on(X16,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)))
       => X212 = X214 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__injective) ).

fof(fact_nth__list__update__eq,axiom,
    ! [X14,X221,X15,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
     => hAPP(hAPP(c_List_Onth(X15),hAPP(hAPP(c_List_Olist__update(X15,X221),X102),X14)),X102) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__list__update__eq) ).

fof(fact_setsum__atMost__Suc,axiom,
    ! [X76,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,X76))) = 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),X76))),hAPP(X2,hAPP(c_Nat_OSuc,X76))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__atMost__Suc) ).

fof(fact_ivl__disj__un_I17_J,axiom,
    ! [X66,X45,X97,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X97),X45))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X45),X66))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X97),X45)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X45),X66)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X97),X66) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I17_J) ).

fof(fact_butlast__conv__take,axiom,
    ! [X221,X15] : c_List_Obutlast(X15,X221) = hAPP(hAPP(c_List_Otake(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X221),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__conv__take) ).

fof(fact_min__max_Ofold1__belowI,axiom,
    ! [X6,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X11)),X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ofold1__belowI) ).

fof(fact_fold1__belowI,axiom,
    ! [X6,X11,X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X11)),X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__belowI) ).

fof(fact_sorted_OCons,axiom,
    ! [X12,X212,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X3)) )
       => ( c_List_Olinorder__class_Osorted(X5,X212)
         => c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted_OCons) ).

fof(fact_sorted_Oequations_I2_J,axiom,
    ! [X47,X46,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X46),X47))
      <=> ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X47)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X46),X3)) )
          & c_List_Olinorder__class_Osorted(X5,X47) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted_Oequations_I2_J) ).

fof(fact_sorted__Cons,axiom,
    ! [X212,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212))
      <=> ( c_List_Olinorder__class_Osorted(X5,X212)
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X3)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__Cons) ).

fof(fact_int__power__div__base,axiom,
    ! [X100,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X99))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X100))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X100),X99)),X100) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X100),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),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,
    ! [X22,X14,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X22))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X22))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__pos) ).

fof(fact_add__pos__pos,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Oordered__comm__monoid__add(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).

fof(fact_add__nonneg__pos,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Oordered__comm__monoid__add(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).

fof(fact_add__pos__nonneg,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Oordered__comm__monoid__add(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).

fof(fact_mult__pos__pos,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Olinordered__semiring__strict(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).

fof(fact_less__1__mult,axiom,
    ! [X98,X99,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Oone__class_Oone(X15)),X99))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Oone__class_Oone(X15)),X98))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Oone__class_Oone(X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X99),X98))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).

fof(fact_divide__nonneg__pos,axiom,
    ! [X22,X14,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X22))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X22))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonneg__pos) ).

fof(fact_add__nonneg__nonneg,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Oordered__comm__monoid__add(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).

fof(fact_mult__nonneg__nonneg,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Oordered__cancel__semiring(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).

fof(fact_split__mult__pos__le,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Oordered__ring(X15)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X26)) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),c_Groups_Ozero__class_Ozero(X15)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),c_Groups_Ozero__class_Ozero(X15))) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).

fof(fact_eq__card__imp__inj__on,axiom,
    ! [X2,X16,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hAPP(c_Finite__Set_Ocard(X16),hAPP(c_Set_Oimage(X5,X16,X2),X11)) = hAPP(c_Finite__Set_Ocard(X5),X11)
       => c_Fun_Oinj__on(X5,X16,X2,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).

fof(fact_inj__on__iff__eq__card,axiom,
    ! [X2,X16,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( c_Fun_Oinj__on(X5,X16,X2,X11)
      <=> hAPP(c_Finite__Set_Ocard(X16),hAPP(c_Set_Oimage(X5,X16,X2),X11)) = hAPP(c_Finite__Set_Ocard(X5),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).

fof(fact_Compl__Diff__eq,axiom,
    ! [X13,X11,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)),X11),X13)) = 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)),X11)),X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__Diff__eq) ).

fof(fact_power__eq__imp__eq__base,axiom,
    ! [X26,X98,X25,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98) = hAPP(hAPP(c_Power_Opower__class_Opower(X15),X26),X98)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X26))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X98))
             => X25 = X26 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).

fof(fact_card__cartesian__product,axiom,
    ! [X13,X11,X16,X5] : hAPP(c_Finite__Set_Ocard(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X13))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X11)),hAPP(c_Finite__Set_Ocard(X16),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__cartesian__product) ).

fof(fact_map__of__append,axiom,
    ! [X214,X212,X16,X5] : hAPP(c_Map_Omap__of(X5,X16),hAPP(hAPP(c_List_Oappend(tc_prod(X5,X16)),X212),X214)) = c_Map_Omap__add(X5,X16,hAPP(c_Map_Omap__of(X5,X16),X214),hAPP(c_Map_Omap__of(X5,X16),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__append) ).

fof(fact_Int__insert__right__if1,axiom,
    ! [X13,X11,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__right__if1) ).

fof(fact_list__eq__iff__nth__eq,axiom,
    ! [X5,X214,X212] :
      ( X212 = X214
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X214)
        & ! [X145] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X145),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
           => hAPP(hAPP(c_List_Onth(X5),X212),X145) = hAPP(hAPP(c_List_Onth(X5),X214),X145) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__eq__iff__nth__eq) ).

fof(fact_folding_Oeq__fold,axiom,
    ! [X84,X11,X90,X2,X16,X5] :
      ( c_Finite__Set_Ofolding(X5,X16,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(X90,X11),X84) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),X84),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Oeq__fold) ).

fof(fact_weaken,axiom,
    ! [X7,X8,X4,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X8)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)),X7),X8))
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_weaken) ).

fof(fact_le__SUPI,axiom,
    ! [X67,X11,X70,X5,X16] :
      ( class_Complete__Lattice_Ocomplete__lattice(X16)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X70),X11))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(X67,X70)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X16),X11),X67))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SUPI) ).

fof(fact_zmod__simps_I1_J,axiom,
    ! [X26,X24,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),c_Divides_Odiv__class_Omod(X15,X25,X24)),X26),X24) = c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I1_J) ).

fof(fact_zmod__simps_I4_J,axiom,
    ! [X26,X24,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),c_Divides_Odiv__class_Omod(X15,X25,X24)),X26),X24) = c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I4_J) ).

fof(fact_mod__add__left__eq,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26),X24) = c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),c_Divides_Odiv__class_Omod(X15,X25,X24)),X26),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__left__eq) ).

fof(fact_mod__mult__left__eq,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26),X24) = c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),c_Divides_Odiv__class_Omod(X15,X25,X24)),X26),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__left__eq) ).

fof(fact_mod__diff__left__eq,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Divides_Oring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X25),X26),X24) = c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),c_Divides_Odiv__class_Omod(X15,X25,X24)),X26),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__left__eq) ).

fof(fact_subset__iff__psubset__eq,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),X13))
        | X11 = X13 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).

fof(fact_psubset__eq,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),X13))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
        & X11 != X13 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__eq) ).

fof(fact_finite__UnI,axiom,
    ! [X4,X90,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X90))
     => ( 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)),X90),X4))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UnI) ).

fof(fact_Pow__Int__eq,axiom,
    ! [X13,X11,X5] : hAPP(c_Set_OPow(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X5),X11)),hAPP(c_Set_OPow(X5),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__Int__eq) ).

fof(fact_finite__maxlen,axiom,
    ! [X67,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X5)),X67))
     => ? [X107] :
        ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X3),X67))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X3)),X107)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__maxlen) ).

fof(fact_setsum_Oeq__fold,axiom,
    ! [X1,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),X11) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Oplus__class_Oplus(X16)),X1),c_Groups_Ozero__class_Ozero(X16)),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Oeq__fold) ).

fof(fact_setprod_Oeq__fold,axiom,
    ! [X1,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X11) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X1),c_Groups_Oone__class_Oone(X16)),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Oeq__fold) ).

fof(fact_psubset__imp__subset,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).

fof(fact_append__replicate__commute,axiom,
    ! [X100,X14,X98,X15] : hAPP(hAPP(c_List_Oappend(X15),c_List_Oreplicate(X15,X98,X14)),c_List_Oreplicate(X15,X100,X14)) = hAPP(hAPP(c_List_Oappend(X15),c_List_Oreplicate(X15,X100,X14)),c_List_Oreplicate(X15,X98,X14)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__replicate__commute) ).

fof(fact_mod__pos__neg,axiom,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26) = 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),X25),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__neg) ).

fof(fact_ex__nat__less,axiom,
    ! [X29,X76] :
      ( ? [X94] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X94),X76))
          & hBOOL(hAPP(X29,X94)) )
    <=> ? [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),X76)))
          & hBOOL(hAPP(X29,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__nat__less) ).

fof(fact_restrict__map__empty,axiom,
    ! [X12,X18,X5,X16] : hAPP(c_Map_Orestrict__map(X16,X5,hAPP(c_COMBK(tc_Option_Ooption(X5),X16),c_Option_Ooption_ONone(X5)),X18),X12) = c_Option_Ooption_ONone(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__map__empty) ).

fof(fact_drop__Cons__number__of,axiom,
    ! [X221,X14,X15,X126] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(X15),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(X15),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = hAPP(hAPP(c_List_Odrop(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X221) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__Cons__number__of) ).

fof(fact_Abs__Integ__induct,axiom,
    ! [X12,X29] :
      ( ! [X33] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X33),c_Int_OInteg))
         => hBOOL(hAPP(X29,hAPP(c_Int_OAbs__Integ,X33))) )
     => hBOOL(hAPP(X29,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Abs__Integ__induct) ).

fof(fact_wf__Int1,axiom,
    ! [X61,X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X34),X61)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__Int1) ).

fof(fact_wf__Int2,axiom,
    ! [X61,X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X61),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__Int2) ).

fof(fact_div__pos__neg,axiom,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26) = 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),X25),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__neg) ).

fof(fact_fold1__set,axiom,
    ! [X212,X5] :
      ( class_Lattices_Oab__semigroup__idem__mult(X5)
     => ( X212 != c_List_Olist_ONil(X5)
       => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(c_List_Oset(X5),X212)) = hAPP(c_List_Ofoldl(X5,X5,c_Groups_Otimes__class_Otimes(X5),hAPP(c_List_Ohd(X5),X212)),hAPP(c_List_Otl(X5),X212)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__set) ).

fof(fact_drop__zip,axiom,
    ! [X225,X221,X98,X5,X15] : hAPP(hAPP(c_List_Odrop(tc_prod(X15,X5)),X98),hAPP(hAPP(c_List_Ozip(X15,X5),X221),X225)) = hAPP(hAPP(c_List_Ozip(X15,X5),hAPP(hAPP(c_List_Odrop(X15),X98),X221)),hAPP(hAPP(c_List_Odrop(X5),X98),X225)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__zip) ).

fof(fact_take__zip,axiom,
    ! [X225,X221,X98,X5,X15] : hAPP(hAPP(c_List_Otake(tc_prod(X15,X5)),X98),hAPP(hAPP(c_List_Ozip(X15,X5),X221),X225)) = hAPP(hAPP(c_List_Ozip(X15,X5),hAPP(hAPP(c_List_Otake(X15),X98),X221)),hAPP(hAPP(c_List_Otake(X5),X98),X225)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__zip) ).

fof(fact_ivl__disj__un_I6_J,axiom,
    ! [X66,X97,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X97),X66))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X97),X66)),hAPP(hAPP(c_Set_Oinsert(X5),X66),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X97,X66) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I6_J) ).

fof(fact_mod__neg__neg,axiom,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26) = 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),X25),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__neg__neg) ).

fof(fact_single__valued__rel__comp,axiom,
    ! [X84,X38,X34,X16,X5] :
      ( c_Relation_Osingle__valued(X5,X16,X34)
     => ( c_Relation_Osingle__valued(X16,X38,X84)
       => c_Relation_Osingle__valued(X5,X38,hAPP(hAPP(c_Relation_Orel__comp(X5,X16,X38),X34),X84)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__rel__comp) ).

fof(fact_sorted__transpose,axiom,
    ! [X212,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,X212)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__transpose) ).

fof(fact_Int__atLeastLessThan,axiom,
    ! [X20,X21,X17,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),X17)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X21),X20)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),X21)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X17),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__atLeastLessThan) ).

fof(fact_Int__atLeastAtMost,axiom,
    ! [X20,X21,X17,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,X17)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X21,X20)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),X21),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X17),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__atLeastAtMost) ).

fof(fact_Int__greaterThanAtMost,axiom,
    ! [X20,X21,X17,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,X17)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X21,X20)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),X21),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X17),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__greaterThanAtMost) ).

fof(fact_Int__greaterThanLessThan,axiom,
    ! [X20,X21,X17,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,X17)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X21,X20)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),X21),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X17),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__greaterThanLessThan) ).

fof(fact_set__rev__mp,axiom,
    ! [X13,X11,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
       => hBOOL(hAPP(hAPP(c_member(X5),X12),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rev__mp) ).

fof(fact_psubsetD,axiom,
    ! [X21,X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
       => hBOOL(hAPP(hAPP(c_member(X5),X21),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubsetD) ).

fof(fact_in__mono,axiom,
    ! [X12,X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hBOOL(hAPP(hAPP(c_member(X5),X12),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mono) ).

fof(fact_set__mp,axiom,
    ! [X12,X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hBOOL(hAPP(hAPP(c_member(X5),X12),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__mp) ).

fof(fact_subsetD,axiom,
    ! [X21,X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
       => hBOOL(hAPP(hAPP(c_member(X5),X21),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subsetD) ).

fof(fact_nth__append__length,axiom,
    ! [X225,X14,X221,X15] : hAPP(hAPP(c_List_Onth(X15),hAPP(hAPP(c_List_Oappend(X15),X221),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X225))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)) = X14,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__append__length) ).

fof(fact_div__neg__neg,axiom,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26) = 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),X25),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__neg__neg) ).

fof(fact_inj__on__add__nat,axiom,
    ! [X93,X30] : 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)),X30),X93),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__add__nat) ).

fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
    ! [X6,X17] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17))
     => ( 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),X17)))
      <=> 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,
    ! [X132,X23,X22,X14,X15] :
      ( class_Fields_Ofield__inverse__zero(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X22)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X23),X132)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X22),X132)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
    ! [X41,X24,X26,X25,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X24),X41)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X26),X41)) ),
    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_I13_J,axiom,
    ! [X116,X117,X118,X119,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X119),X118)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X117),X116)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X119),X117)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X118),X116)) ),
    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_I14_J,axiom,
    ! [X116,X117,X118,X119,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X119),X118)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X117),X116)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X119),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X118),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X117),X116))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).

fof(fact_sorted__map__remove1,axiom,
    ! [X12,X212,X2,X16,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X16,X5),X2),X212))
       => c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X16,X5),X2),c_List_Oremove1(X16,X12,X212))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__map__remove1) ).

fof(fact_Domain__Union,axiom,
    ! [X35,X16,X5] : hAPP(c_Relation_ODomain(X5,X16),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),X35)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X5,X16),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X35),c_Relation_ODomain(X5,X16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Union) ).

fof(fact_Range__Union,axiom,
    ! [X35,X5,X16] : hAPP(c_Relation_ORange(X16,X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X16,X5),tc_HOL_Obool),X35)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X16,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X35),c_Relation_ORange(X16,X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Union) ).

fof(fact_all__nat__less,axiom,
    ! [X29,X76] :
      ( ! [X94] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X94),X76))
         => hBOOL(hAPP(X29,X94)) )
    <=> ! [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),X76)))
         => hBOOL(hAPP(X29,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nat__less) ).

fof(fact_Ints__power,axiom,
    ! [X76,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),X76)),c_Int_Oring__1__class_OInts(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__power) ).

fof(fact_Collect__mem__eq,axiom,
    ! [X11,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X11)) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__mem__eq) ).

fof(fact_nat__one__le__power,axiom,
    ! [X98,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X102))
     => 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),X102),X98))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__one__le__power) ).

fof(fact_one__less__power,axiom,
    ! [X98,X25,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Oone__class_Oone(X15)),X25))
       => ( 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(X15),c_Groups_Oone__class_Oone(X15)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__power) ).

fof(fact_divide__neg__neg,axiom,
    ! [X22,X14,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),c_Groups_Ozero__class_Ozero(X15)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),c_Groups_Ozero__class_Ozero(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X22))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__neg) ).

fof(fact_mult__neg__neg,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Olinordered__ring__strict(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),c_Groups_Ozero__class_Ozero(X15)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),c_Groups_Ozero__class_Ozero(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).

fof(fact_divide__nonpos__neg,axiom,
    ! [X22,X14,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),c_Groups_Ozero__class_Ozero(X15)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),c_Groups_Ozero__class_Ozero(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X22))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonpos__neg) ).

fof(fact_mult__nonpos__nonpos,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Oordered__ring(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),c_Groups_Ozero__class_Ozero(X15)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),c_Groups_Ozero__class_Ozero(X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).

fof(fact_setsum__lessThan__Suc,axiom,
    ! [X76,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,X76))) = 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),X76))),hAPP(X2,X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__lessThan__Suc) ).

fof(fact_posDivAlg__div__mod,axiom,
    ! [X103,X100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X100))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X103))
       => c_Divides_OposDivAlg(X100,X103) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X100),X103)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X100,X103)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg__div__mod) ).

fof(fact_pos__imp__zdiv__pos__iff,axiom,
    ! [X70,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))
     => ( 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),X70),X30)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),X70)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).

fof(fact_lex__def,axiom,
    ! [X34,X5] : c_List_Olex(X5,X34) = 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,X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lex__def) ).

fof(fact_less__max__iff__disj,axiom,
    ! [X27,X12,X37,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X37),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X12),X27)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X37),X12))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X37),X27)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__max__iff__disj) ).

fof(fact_le__max__iff__disj,axiom,
    ! [X27,X12,X37,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X37),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X12),X27)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X37),X12))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X37),X27)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__max__iff__disj) ).

fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
    ! [X6,X17] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17),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),X17)))
      <=> 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,X212] :
      ( X212 != 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))),X212)) = c_Random_Oselect(X5,X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_select__weigth__select) ).

fof(fact_finite__Inter,axiom,
    ! [X67,X5] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X3),X67))
          & 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),X67))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Inter) ).

fof(fact_abs__eq__mult,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Oordered__ring__abs(X15)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),c_Groups_Ozero__class_Ozero(X15))) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X26))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),c_Groups_Ozero__class_Ozero(X15))) ) )
       => hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),hAPP(c_Groups_Oabs__class_Oabs(X15),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__mult) ).

fof(fact_butlast__take,axiom,
    ! [X221,X15,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
     => c_List_Obutlast(X15,hAPP(hAPP(c_List_Otake(X15),X98),X221)) = hAPP(hAPP(c_List_Otake(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X221) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__take) ).

fof(fact_single__Diff__lessThan,axiom,
    ! [X30,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X30),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X30)) = hAPP(hAPP(c_Set_Oinsert(X5),X30),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,
    ! [X13,X11,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
         => ! [X39] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X39),X13))
             => X3 != X39 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_disjoint__iff__not__equal) ).

fof(fact_insort__remove1,axiom,
    ! [X212,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_List_Oset(X5),X212)))
       => ( c_List_Olinorder__class_Osorted(X5,X212)
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X6),c_List_Oremove1(X5,X6,X212)) = X212 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__remove1) ).

fof(fact_negDivAlg__div__mod,axiom,
    ! [X103,X100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X100),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)),X103))
       => c_Divides_OnegDivAlg(X100,X103) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X100),X103)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X100,X103)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg__div__mod) ).

fof(fact_Max_Osubset__idem,axiom,
    ! [X13,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X13 != 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)),X13),X11))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olinorder__class_OMax(X5,X13)),c_Big__Operators_Olinorder__class_OMax(X5,X11)) = c_Big__Operators_Olinorder__class_OMax(X5,X11) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Osubset__idem) ).

fof(fact_Min_Osubset__idem,axiom,
    ! [X13,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X13 != 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)),X13),X11))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olinorder__class_OMin(X5,X13)),c_Big__Operators_Olinorder__class_OMin(X5,X11)) = c_Big__Operators_Olinorder__class_OMin(X5,X11) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Osubset__idem) ).

fof(fact_Inf__fin_Osubset__idem,axiom,
    ! [X13,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X13 != 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)),X13),X11))
           => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X13)),c_Big__Operators_Olattice__class_OInf__fin(X5,X11)) = c_Big__Operators_Olattice__class_OInf__fin(X5,X11) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Osubset__idem) ).

fof(fact_Sup__fin_Osubset__idem,axiom,
    ! [X13,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X13 != 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)),X13),X11))
           => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,X13)),c_Big__Operators_Olattice__class_OSup__fin(X5,X11)) = c_Big__Operators_Olattice__class_OSup__fin(X5,X11) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Osubset__idem) ).

fof(fact_zpower__zmod,axiom,
    ! [X22,X99,X14] : 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,X14,X99)),X22),X99) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14),X22),X99),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zmod) ).

fof(fact_zdiff__zmod__left,axiom,
    ! [X22,X99,X14] : 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,X14,X99)),X22),X99) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X14),X22),X99),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmod__left) ).

fof(fact_le__Inf__iff,axiom,
    ! [X11,X17,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),c_Complete__Lattice_OInf__class_OInf(X5,X11)))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Inf__iff) ).

fof(fact_take__Cons_H,axiom,
    ! [X221,X14,X15,X98] :
      ( ( X98 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(X15),X98),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = c_List_Olist_ONil(X15) )
      & ( X98 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(X15),X98),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = hAPP(hAPP(c_List_Olist_OCons(X15),X14),hAPP(hAPP(c_List_Otake(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X221)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Cons_H) ).

fof(fact_inf1I,axiom,
    ! [X5,X13,X12,X11] :
      ( hBOOL(hAPP(X11,X12))
     => ( hBOOL(hAPP(X13,X12))
       => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1I) ).

fof(fact_list__ex__iff,axiom,
    ! [X212,X29,X5] :
      ( c_List_Olist__ex(X5,X29,X212)
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
          & hBOOL(hAPP(X29,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__iff) ).

fof(fact_Rep__Integ,axiom,
    ! [X12] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X12)),c_Int_OInteg)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ) ).

fof(fact_folding__one__idem_Ounion__idem,axiom,
    ! [X13,X11,X90,X2,X5] :
      ( c_Finite__Set_Ofolding__one__idem(X5,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
           => ( X13 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => hAPP(X90,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(X2,hAPP(X90,X11)),hAPP(X90,X13)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Ounion__idem) ).

fof(fact_in__listsp__conv__set,axiom,
    ! [X212,X11,X5] :
      ( hBOOL(hAPP(c_List_Olistsp(X5,X11),X212))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
         => hBOOL(hAPP(X11,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__listsp__conv__set) ).

fof(fact_add__strict__increasing2,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Groups_Oordered__comm__monoid__add(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),X24))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X24))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).

fof(fact_add__strict__increasing,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Groups_Oordered__comm__monoid__add(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),X24))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X24))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).

fof(fact_pos__add__strict,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),X24))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X24))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).

fof(fact_add__increasing,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Groups_Oordered__comm__monoid__add(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),X24))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X24))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).

fof(fact_add__increasing2,axiom,
    ! [X25,X26,X24,X15] :
      ( class_Groups_Oordered__comm__monoid__add(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X24))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),X25))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X24))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).

fof(fact_zmod__zdiv__equality,axiom,
    ! [X26,X25] : X25 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zdiv__equality) ).

fof(fact_min__max_Oless__infI1,axiom,
    ! [X26,X14,X25,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X14))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X25),X26)),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oless__infI1) ).

fof(fact_min__max_Oless__infI2,axiom,
    ! [X25,X14,X26,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),X14))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X25),X26)),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oless__infI2) ).

fof(fact_less__infI1,axiom,
    ! [X26,X14,X25,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X14))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X25),X26)),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__infI1) ).

fof(fact_less__infI2,axiom,
    ! [X25,X14,X26,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),X14))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X25),X26)),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__infI2) ).

fof(fact_min__max_Ole__infI1,axiom,
    ! [X26,X14,X25,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X14))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X25),X26)),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__infI1) ).

fof(fact_min__max_Ole__infI2,axiom,
    ! [X25,X14,X26,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),X14))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X25),X26)),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__infI2) ).

fof(fact_le__infI1,axiom,
    ! [X26,X14,X25,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X14))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X25),X26)),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI1) ).

fof(fact_le__infI2,axiom,
    ! [X25,X14,X26,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),X14))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X25),X26)),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI2) ).

fof(fact_listrel__Nil,axiom,
    ! [X34,X5] : hAPP(c_Relation_OImage(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Olistrel(X5,X34)),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_setsum__eq__0__iff,axiom,
    ! [X2,X90,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X90))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X90) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X90))
           => 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_setprod__eq__1__iff,axiom,
    ! [X2,X90,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X90))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Nat_Onat),X2),X90) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X90))
           => 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_restrict__in,axiom,
    ! [X45,X16,X11,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
     => hAPP(c_Map_Orestrict__map(X5,X16,X45,X11),X12) = hAPP(X45,X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__in) ).

fof(fact_nat__diff__split,axiom,
    ! [X17,X6,X29] :
      ( hBOOL(hAPP(X29,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6),X17)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X17))
         => hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        & ! [X125] :
            ( X6 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X125)
           => hBOOL(hAPP(X29,X125)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split) ).

fof(fact_finite__compl,axiom,
    ! [X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11)))
      <=> 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,
    ! [X168,X56] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X56),X168))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X168)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X56),X168)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__number__of) ).

fof(fact_Un__insert__left,axiom,
    ! [X19,X13,X6,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13)),X19) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X13),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__insert__left) ).

fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
    ! [X12,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm__idem(X5,X16,X2)
     => hAPP(c_Fun_Ocomp(X16,X16,X16,hAPP(X2,X12)),hAPP(X2,X12)) = hAPP(X2,X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__comp__idem) ).

fof(fact_dom__map__of__zip,axiom,
    ! [X214,X16,X212,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),X212))
       => c_Map_Odom(X5,X16,hAPP(c_Map_Omap__of(X5,X16),hAPP(hAPP(c_List_Ozip(X5,X16),X212),X214))) = hAPP(c_List_Oset(X5),X212) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dom__map__of__zip) ).

fof(fact_divmod__int__rel__mod,axiom,
    ! [X123,X128,X26,X25] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X25,X26),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X128),X123)))
     => ( X26 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26) = X123 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__mod) ).

fof(fact_snd__def,axiom,
    ! [X161,X5,X16] : hAPP(c_Product__Type_Osnd(X16,X5),X161) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X16,X5,X5),hAPP(c_COMBK(tc_fun(X5,X5),X16),c_COMBI(X5))),X161),
    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,X90,X5] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X90))
        | 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)),X90),X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Int) ).

fof(fact_finite__Diff,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Diff) ).

fof(fact_sorted__many,axiom,
    ! [X242,X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22))
       => ( c_List_Olinorder__class_Osorted(X15,hAPP(hAPP(c_List_Olist_OCons(X15),X22),X242))
         => c_List_Olinorder__class_Osorted(X15,hAPP(hAPP(c_List_Olist_OCons(X15),X14),hAPP(hAPP(c_List_Olist_OCons(X15),X22),X242))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__many) ).

fof(fact_sorted__many__eq,axiom,
    ! [X227,X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X12),hAPP(hAPP(c_List_Olist_OCons(X5),X27),X227)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27))
          & c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X27),X227)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__many__eq) ).

fof(fact_mod__eq,axiom,
    ! [X123,X128,X98,X99] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X99,X98),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X128),X123)))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98) = X123 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__eq) ).

fof(fact_pos__mod__conj,axiom,
    ! [X25,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__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26)),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__mod__conj) ).

fof(fact_pos__mod__bound,axiom,
    ! [X25,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),c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26)),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__mod__bound) ).

fof(fact_mod__less__divisor,axiom,
    ! [X99,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),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98)),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less__divisor) ).

fof(fact_zmod__le__nonneg__dividend,axiom,
    ! [X100,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X99))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X99,X100)),X99)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__le__nonneg__dividend) ).

fof(fact_mod__le__divisor,axiom,
    ! [X99,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__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98)),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__le__divisor) ).

fof(fact_length__remdups__leq,axiom,
    ! [X221,X15] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),c_List_Oremdups(X15,X221))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__remdups__leq) ).

fof(fact_card__length,axiom,
    ! [X212,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(c_List_Oset(X5),X212))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__length) ).

fof(fact_image__Pow__surj,axiom,
    ! [X13,X11,X2,X5,X16] :
      ( hAPP(c_Set_Oimage(X16,X5,X2),X11) = X13
     => hAPP(c_Set_Oimage(tc_fun(X16,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),c_Set_Oimage(X16,X5,X2)),hAPP(c_Set_OPow(X16),X11)) = hAPP(c_Set_OPow(X5),X13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Pow__surj) ).

fof(fact_surj__image__vimage__eq,axiom,
    ! [X11,X2,X5,X16] :
      ( hAPP(c_Set_Oimage(X16,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => hAPP(c_Set_Oimage(X16,X5,X2),hAPP(c_Set_Ovimage(X16,X5,X2),X11)) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__image__vimage__eq) ).

fof(fact_divmod__int__rel__div,axiom,
    ! [X123,X128,X26,X25] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X25,X26),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X128),X123)))
     => ( X26 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26) = X128 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__div) ).

fof(fact_minus__less__iff,axiom,
    ! [X17,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)),X17))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X17)),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__less__iff) ).

fof(fact_abs__le__D2,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D2) ).

fof(fact_minus__le__iff,axiom,
    ! [X17,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)),X17))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X17)),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__iff) ).

fof(fact_neg__mod__conj,axiom,
    ! [X25,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),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,X25,X26)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__mod__conj) ).

fof(fact_neg__mod__sign,axiom,
    ! [X25,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),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,X25,X26)),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,
    ! [X29,X2,X16,X5] : hAPP(c_Set_Ovimage(X5,X16,X2),hAPP(c_Set_OCollect(X16),X29)) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(X16,tc_HOL_Obool,X5),X29),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Collect__eq) ).

fof(fact_div__eq,axiom,
    ! [X123,X128,X98,X99] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X99,X98),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X128),X123)))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),X98) = X128 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__eq) ).

fof(fact_card__image,axiom,
    ! [X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => hAPP(c_Finite__Set_Ocard(X16),hAPP(c_Set_Oimage(X5,X16,X2),X11)) = hAPP(c_Finite__Set_Ocard(X5),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__image) ).

fof(fact_take__drop,axiom,
    ! [X221,X99,X98,X15] : hAPP(hAPP(c_List_Otake(X15),X98),hAPP(hAPP(c_List_Odrop(X15),X99),X221)) = hAPP(hAPP(c_List_Odrop(X15),X99),hAPP(hAPP(c_List_Otake(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X99)),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__drop) ).

fof(fact_sorted__filter,axiom,
    ! [X29,X212,X2,X16,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X16,X5),X2),X212))
       => c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X16,X5),X2),hAPP(c_List_Ofilter(X16,X29),X212))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__filter) ).

fof(fact_nat__mod__eq__lemma,axiom,
    ! [X22,X98,X14] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X14,X98) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22,X98)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14))
       => ? [X150] : X14 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X150)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mod__eq__lemma) ).

fof(fact_takeWhile__eq__all__conv,axiom,
    ! [X212,X29,X5] :
      ( c_List_OtakeWhile(X5,X29,X212) = X212
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
         => hBOOL(hAPP(X29,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,
    ! [X29,X212,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
         => hBOOL(hAPP(X29,X3)) )
    <=> c_List_Olist__all(X5,X29,X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ball__set__list__all) ).

fof(fact_list__all__iff__raw,axiom,
    ! [X212,X29,X5] :
      ( c_List_Olist__all(X5,X29,X212)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
         => hBOOL(hAPP(X29,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__iff__raw) ).

fof(fact_list__all__iff,axiom,
    ! [X212,X29,X5] :
      ( c_List_Olist__all(X5,X29,X212)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
         => hBOOL(hAPP(X29,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__iff) ).

fof(fact_add__gr__0,axiom,
    ! [X76,X45] :
      ( 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),X45),X76)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X45))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X76)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).

fof(fact_asm,axiom,
    ! [X4,X7,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)),X7),X4))
     => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_asm) ).

fof(fact_mod__add__cong,axiom,
    ! [X143,X26,X81,X24,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => ( c_Divides_Odiv__class_Omod(X15,X25,X24) = c_Divides_Odiv__class_Omod(X15,X81,X24)
       => ( c_Divides_Odiv__class_Omod(X15,X26,X24) = c_Divides_Odiv__class_Omod(X15,X143,X24)
         => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26),X24) = c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X81),X143),X24) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__cong) ).

fof(fact_mod__mult__cong,axiom,
    ! [X143,X26,X81,X24,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => ( c_Divides_Odiv__class_Omod(X15,X25,X24) = c_Divides_Odiv__class_Omod(X15,X81,X24)
       => ( c_Divides_Odiv__class_Omod(X15,X26,X24) = c_Divides_Odiv__class_Omod(X15,X143,X24)
         => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26),X24) = c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X81),X143),X24) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__cong) ).

fof(fact_mod__diff__cong,axiom,
    ! [X143,X26,X81,X24,X25,X15] :
      ( class_Divides_Oring__div(X15)
     => ( c_Divides_Odiv__class_Omod(X15,X25,X24) = c_Divides_Odiv__class_Omod(X15,X81,X24)
       => ( c_Divides_Odiv__class_Omod(X15,X26,X24) = c_Divides_Odiv__class_Omod(X15,X143,X24)
         => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X25),X26),X24) = c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X81),X143),X24) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__cong) ).

fof(fact_power__diff,axiom,
    ! [X99,X98,X25,X15] :
      ( class_Fields_Ofield(X15)
     => ( X25 != c_Groups_Ozero__class_Ozero(X15)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X99))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X99)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__diff) ).

fof(fact_divmod__int__rel__neg,axiom,
    ! [X159,X26,X25] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26)),X159))
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X25,X26),hAPP(c_Divides_OnegateSnd,X159))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__neg) ).

fof(fact_insert__Diff1,axiom,
    ! [X11,X13,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),X13))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)),X13) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff1) ).

fof(fact_dom__const,axiom,
    ! [X2,X16,X5] : c_Map_Odom(X5,X16,hAPP(hAPP(c_COMBB(X16,tc_Option_Ooption(X16),X5),c_Option_Ooption_OSome(X16)),X2)) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dom__const) ).

fof(fact_Nat_Odiff__diff__eq,axiom,
    ! [X98,X99,X100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X100),X99))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X100),X98))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X100)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),X100)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).

fof(fact_takeWhile__eq__take,axiom,
    ! [X212,X29,X5] : c_List_OtakeWhile(X5,X29,X212) = hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X29,X212))),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__eq__take) ).

fof(fact_ex__nat__less__eq,axiom,
    ! [X29,X76] :
      ( ? [X94] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X94),X76))
          & hBOOL(hAPP(X29,X94)) )
    <=> ? [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)),X76)))
          & hBOOL(hAPP(X29,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__nat__less__eq) ).

fof(fact_Suc__diff__diff,axiom,
    ! [X100,X98,X99] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X99)),X98)),hAPP(c_Nat_OSuc,X100)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98)),X100),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).

fof(fact_power__inject__base,axiom,
    ! [X26,X98,X25,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),hAPP(c_Nat_OSuc,X98)) = hAPP(hAPP(c_Power_Opower__class_Opower(X15),X26),hAPP(c_Nat_OSuc,X98))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X26))
           => X25 = X26 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__base) ).

fof(fact_int__zle__neg,axiom,
    ! [X45,X76] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X76)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X45))))
    <=> ( X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & X45 = 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,
    ! [X27,X12,X37,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X37),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X12),X27)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X37),X12))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X37),X27)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__less__iff__conj) ).

fof(fact_min__max_Ole__inf__iff,axiom,
    ! [X37,X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X27),X37)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X37)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__inf__iff) ).

fof(fact_min__max_Ole__infI,axiom,
    ! [X26,X25,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X25),X26))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__infI) ).

fof(fact_min__max_Oinf__greatest,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X23))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X22),X23))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__greatest) ).

fof(fact_le__inf__iff,axiom,
    ! [X37,X27,X12,X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X27),X37)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X37)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__inf__iff) ).

fof(fact_le__infI,axiom,
    ! [X26,X25,X14,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X25),X26))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI) ).

fof(fact_inf__greatest,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X23))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X22),X23))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__greatest) ).

fof(fact_self__quotient__aux2,axiom,
    ! [X128,X123,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
     => ( X25 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X123),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X128))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X123))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X128),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,
    ! [X212,X29,X5] :
      ( hAPP(c_List_Ofilter(X5,X29),X212) = X212
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
         => hBOOL(hAPP(X29,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__id__conv) ).

fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
    ! [X22,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))
       => 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,X14,X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I2_J) ).

fof(fact_nth__append__length__plus,axiom,
    ! [X98,X225,X221,X15] : hAPP(hAPP(c_List_Onth(X15),hAPP(hAPP(c_List_Oappend(X15),X221),X225)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),X98)) = hAPP(hAPP(c_List_Onth(X15),X225),X98),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__append__length__plus) ).

fof(fact_list_Osimps_I5_J,axiom,
    ! [X213,X6,X88,X89,X16,X5] : hAPP(c_List_Olist_Olist__case(X5,X16,X89,X88),hAPP(hAPP(c_List_Olist_OCons(X16),X6),X213)) = hAPP(hAPP(X88,X6),X213),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I5_J) ).

fof(fact_sup1I1,axiom,
    ! [X13,X5,X12,X11] :
      ( hBOOL(hAPP(X11,X12))
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup1I1) ).

fof(fact_sup1I2,axiom,
    ! [X11,X5,X12,X13] :
      ( hBOOL(hAPP(X13,X12))
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup1I2) ).

fof(fact_zero__le__power__abs,axiom,
    ! [X98,X25,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),X98))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power__abs) ).

fof(fact_diff__Suc__diff__eq1,axiom,
    ! [X99,X101,X100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X100),X101))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X101),X100))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X100)),hAPP(c_Nat_OSuc,X101)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).

fof(fact_subset__empty,axiom,
    ! [X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
    <=> X11 = 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,
    ! [X34,X5] :
      ( c_Wellfounded_OwfP(X5,X34)
     => c_Wellfounded_Oacyclic(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__acyclicP) ).

fof(fact_rel__comp__empty1,axiom,
    ! [X36,X16,X38,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X38,X16),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X38),tc_HOL_Obool))),X36) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__empty1) ).

fof(fact_zdiv__zminus1__eq__if,axiom,
    ! [X25,X26] :
      ( X26 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26) = 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),X25)),X26) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26)) )
        & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26) != 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),X25)),X26) = 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),X25),X26))),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,X17,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X17)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).

fof(fact_compl__le__compl__iff,axiom,
    ! [X27,X12,X5] :
      ( class_Lattices_Oboolean__algebra(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X12)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X27)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X27),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).

fof(fact_neg__le__iff__le,axiom,
    ! [X6,X17,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),X17)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).

fof(fact_all__nat__less__eq,axiom,
    ! [X29,X76] :
      ( ! [X94] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X94),X76))
         => hBOOL(hAPP(X29,X94)) )
    <=> ! [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)),X76)))
         => hBOOL(hAPP(X29,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nat__less__eq) ).

fof(fact_power__gt1,axiom,
    ! [X98,X25,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Oone__class_Oone(X15)),X25))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Oone__class_Oone(X15)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),hAPP(c_Nat_OSuc,X98)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1) ).

fof(fact_self__quotient__aux1,axiom,
    ! [X128,X123,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
     => ( X25 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X123),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X128))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),X25))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X128)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).

fof(fact_conversep_Ointros,axiom,
    ! [X16,X5,X17,X6,X34] :
      ( hBOOL(hAPP(hAPP(X34,X6),X17))
     => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5,X16,X34),X17),X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep_Ointros) ).

fof(fact_less__number__of,axiom,
    ! [X27,X12,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),X12)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X27)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of) ).

fof(fact_le__number__of,axiom,
    ! [X27,X12,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),X12)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X27)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12),X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__number__of) ).

fof(fact_list__update__beyond,axiom,
    ! [X14,X102,X221,X15] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),X102))
     => hAPP(hAPP(c_List_Olist__update(X15,X221),X102),X14) = X221 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__beyond) ).

fof(fact_le__cube,axiom,
    ! [X99] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),X99)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).

fof(fact_in__set__butlastD,axiom,
    ! [X212,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),c_List_Obutlast(X5,X212))))
     => hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__butlastD) ).

fof(fact_insert__image,axiom,
    ! [X2,X16,X11,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
     => hAPP(hAPP(c_Set_Oinsert(X16),hAPP(X2,X12)),hAPP(c_Set_Oimage(X5,X16,X2),X11)) = hAPP(c_Set_Oimage(X5,X16,X2),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__image) ).

fof(fact_self__quotient,axiom,
    ! [X123,X128,X25] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X25,X25),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X128),X123)))
     => ( X25 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => X128 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient) ).

fof(fact_self__remainder,axiom,
    ! [X123,X128,X25] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X25,X25),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X128),X123)))
     => ( X25 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => X123 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__remainder) ).

fof(fact_wf__exp,axiom,
    ! [X36,X76,X5] :
      ( c_Wellfounded_Owf(X5,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X76),X36))
     => c_Wellfounded_Owf(X5,X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__exp) ).

fof(fact_of__int__less__iff,axiom,
    ! [X37,X112,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),X112)),hAPP(c_Int_Oring__1__class_Oof__int(X5),X37)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X112),X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__less__iff) ).

fof(fact_of__nat__less__iff,axiom,
    ! [X76,X45,X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X45)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X76)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__iff) ).

fof(fact_of__nat__less__imp__less,axiom,
    ! [X98,X99,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),X99)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),X98)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__imp__less) ).

fof(fact_of__int__le__iff,axiom,
    ! [X37,X112,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),X112)),hAPP(c_Int_Oring__1__class_Oof__int(X5),X37)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X112),X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__le__iff) ).

fof(fact_of__nat__le__iff,axiom,
    ! [X76,X45,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),X45)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X76)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__le__iff) ).

fof(fact_nonzero__power__divide,axiom,
    ! [X98,X25,X26,X15] :
      ( class_Fields_Ofield(X15)
     => ( X26 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),X26)),X98) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X26),X98)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__power__divide) ).

fof(fact_zless__imp__add1__zle,axiom,
    ! [X23,X132] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X132),X23))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X132),c_Groups_Oone__class_Oone(tc_Int_Oint))),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).

fof(fact_Min__Un,axiom,
    ! [X13,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
           => ( X13 != 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)),X11),X13)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olinorder__class_OMin(X5,X11)),c_Big__Operators_Olinorder__class_OMin(X5,X13)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min__Un) ).

fof(fact_Max__Un,axiom,
    ! [X13,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
           => ( X13 != 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)),X11),X13)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olinorder__class_OMax(X5,X11)),c_Big__Operators_Olinorder__class_OMax(X5,X13)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max__Un) ).

fof(fact_Sup__fin_Ounion__idem,axiom,
    ! [X13,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
           => ( X13 != 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)),X11),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,X11)),c_Big__Operators_Olattice__class_OSup__fin(X5,X13)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Ounion__idem) ).

fof(fact_Inf__fin_Ounion__idem,axiom,
    ! [X13,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
           => ( X13 != 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)),X11),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X11)),c_Big__Operators_Olattice__class_OInf__fin(X5,X13)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Ounion__idem) ).

fof(fact_splice_Osimps_I3_J,axiom,
    ! [X225,X22,X221,X14,X15] : c_List_Osplice(X15,hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221),hAPP(hAPP(c_List_Olist_OCons(X15),X22),X225)) = hAPP(hAPP(c_List_Olist_OCons(X15),X14),hAPP(hAPP(c_List_Olist_OCons(X15),X22),c_List_Osplice(X15,X221,X225))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I3_J) ).

fof(fact_code__numeral_Oof__nat__inject,axiom,
    ! [X27,X12] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X12),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X27),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
       => ( hAPP(c_Code__Numeral_Oof__nat,X12) = hAPP(c_Code__Numeral_Oof__nat,X27)
        <=> X12 = X27 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Oof__nat__inject) ).

fof(fact_nat__mono__iff,axiom,
    ! [X112,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X112)),hAPP(c_Int_Onat,X37)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X112),X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mono__iff) ).

fof(fact_nat__less__eq__zless,axiom,
    ! [X37,X112] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X112))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X112)),hAPP(c_Int_Onat,X37)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X112),X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__eq__zless) ).

fof(fact_nat__le__eq__zle,axiom,
    ! [X37,X112] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X112))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37)) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X112)),hAPP(c_Int_Onat,X37)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X112),X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__eq__zle) ).

fof(fact_funpow__swap1,axiom,
    ! [X12,X76,X5,X2] : hAPP(X2,hAPP(hAPP(hAPP(c_Nat_Ocompow(X5,X5),X76),X2),X12)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(X5,X5),X76),X2),hAPP(X2,X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow__swap1) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
    ! [X26,X99,X25,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X99)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X99)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26)),X99) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).

fof(fact_min__max_Osup__inf__distrib2,axiom,
    ! [X14,X23,X22,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X22),X23)),X14) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X22),X14)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X23),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__inf__distrib2) ).

fof(fact_min__max_Oinf__sup__distrib2,axiom,
    ! [X14,X23,X22,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X22),X23)),X14) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X22),X14)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X23),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__sup__distrib2) ).

fof(fact_add__divide__distrib,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Rings_Odivision__ring(X15)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26)),X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),X24)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X26),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__distrib) ).

fof(fact_diff__divide__distrib,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Rings_Odivision__ring(X15)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X25),X26)),X24) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),X24)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X26),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__divide__distrib) ).

fof(fact_power__divide,axiom,
    ! [X98,X26,X25,X15] :
      ( class_Fields_Ofield__inverse__zero(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),X26)),X98) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X26),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__divide) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
    ! [X128,X22,X14,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),X22)),X128) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),X128)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X22),X128)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).

fof(fact_power__mult__distrib,axiom,
    ! [X98,X26,X25,X15] :
      ( class_Groups_Ocomm__monoid__mult(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26)),X98) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X26),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult__distrib) ).

fof(fact_max__add__distrib__left,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),X22)),X23) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X14),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X22),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__add__distrib__left) ).

fof(fact_min__add__distrib__left,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),X22)),X23) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X14),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X22),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__add__distrib__left) ).

fof(fact_comm__semiring__class_Odistrib,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Rings_Ocomm__semiring(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26)),X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26)),X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).

fof(fact_inf__sup__distrib2,axiom,
    ! [X14,X23,X22,X15] :
      ( class_Lattices_Odistrib__lattice(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X22),X23)),X14) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X22),X14)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X23),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__distrib2) ).

fof(fact_max__diff__distrib__left,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Groups_Oordered__ab__group__add(X15)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),X22)),X23) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X14),X23)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X22),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__diff__distrib__left) ).

fof(fact_min__diff__distrib__left,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Groups_Oordered__ab__group__add(X15)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),X22)),X23) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X14),X23)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X22),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__diff__distrib__left) ).

fof(fact_sup__inf__distrib2,axiom,
    ! [X14,X23,X22,X15] :
      ( class_Lattices_Odistrib__lattice(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X22),X23)),X14) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X22),X14)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X23),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__inf__distrib2) ).

fof(fact_set__insort,axiom,
    ! [X212,X12,X2,X5,X16] :
      ( class_Orderings_Olinorder(X16)
     => hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X16,X2),X12),X212)) = hAPP(hAPP(c_Set_Oinsert(X5),X12),hAPP(c_List_Oset(X5),X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__insort) ).

fof(fact_nat__0__less__mult__iff,axiom,
    ! [X76,X45] :
      ( 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),X45),X76)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X45))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X76)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).

fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
    ! [X22,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))
       => 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),X14),X22))) ) ),
    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_I1_J,axiom,
    ! [X22,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))
       => 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),X14),X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
    ! [X22,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))
       => 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),X14),X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).

fof(fact_ivl__disj__un_I1_J,axiom,
    ! [X97,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),X97),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X97)) = hAPP(c_SetInterval_Oord__class_OatLeast(X5),X97) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I1_J) ).

fof(fact_finite__converse,axiom,
    ! [X34,X16,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X16)),hAPP(c_Relation_Oconverse(X16,X5),X34)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X16,X5)),X34)) ),
    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,
    ! [X12,X212,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X212))
     => hAPP(c_List_Oset(X5),c_List_Oremove1(X5,X12,X212)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X212)),hAPP(hAPP(c_Set_Oinsert(X5),X12),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,
    ! [X13,X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X13),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Union) ).

fof(fact_Un__Inter,axiom,
    ! [X13,X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X13)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X13),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Inter) ).

fof(fact_strict__mono__less,axiom,
    ! [X27,X12,X2,X5,X16] :
      ( ( class_Orderings_Oorder(X16)
        & class_Orderings_Olinorder(X5) )
     => ( c_Orderings_Oorder__class_Ostrict__mono(X5,X16,X2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16),hAPP(X2,X12)),hAPP(X2,X27)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X12),X27)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_strict__mono__less) ).

fof(fact_strict__mono__less__eq,axiom,
    ! [X27,X12,X2,X5,X16] :
      ( ( class_Orderings_Oorder(X16)
        & class_Orderings_Olinorder(X5) )
     => ( c_Orderings_Oorder__class_Ostrict__mono(X5,X16,X2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(X2,X12)),hAPP(X2,X27)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_strict__mono__less__eq) ).

fof(fact_length__insort,axiom,
    ! [X212,X12,X2,X5,X16] :
      ( class_Orderings_Olinorder(X16)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X16,X2),X12),X212)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__insort) ).

fof(fact_nat__less__iff,axiom,
    ! [X45,X112] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X112))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X112)),X45))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X112),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X45))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__iff) ).

fof(fact_remove1__insort,axiom,
    ! [X212,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Oremove1(X5,X12,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X12),X212)) = X212 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__insort) ).

fof(fact_Powp__def,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(c_Predicate_OPowp(X5,X11),X13))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X13))
         => hBOOL(hAPP(X11,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Powp__def) ).

fof(fact_restrict__map__to__empty,axiom,
    ! [X12,X45,X5,X16] : hAPP(c_Map_Orestrict__map(X16,X5,X45,c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))),X12) = c_Option_Ooption_ONone(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__map__to__empty) ).

fof(fact_eq__number__of__eq,axiom,
    ! [X27,X12,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X12) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X27)
      <=> c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X27)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__eq) ).

fof(fact_append__eq__conv__conj,axiom,
    ! [X227,X214,X212,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X212),X214) = X227
    <=> ( X212 = hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)),X227)
        & X214 = hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)),X227) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__conv__conj) ).

fof(fact_zdiv__zminus2__eq__if,axiom,
    ! [X25,X26] :
      ( X26 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26)) )
        & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26)) = 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),X25),X26))),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,
    ! [X11,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),X11) = 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)))),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__is__Un) ).

fof(fact_less__imp__diff__less,axiom,
    ! [X98,X100,X101] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X101),X100))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X101),X98)),X100)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).

fof(fact_diff__add__assoc2,axiom,
    ! [X102,X101,X100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X100),X101))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),X102)),X100) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X101),X100)),X102) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).

fof(fact_add__diff__assoc2,axiom,
    ! [X102,X101,X100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X100),X101))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X101),X100)),X102) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),X102)),X100) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).

fof(fact_Int__absorb2,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb2) ).

fof(fact_Int__absorb1,axiom,
    ! [X11,X13,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),X11))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) = X13 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb1) ).

fof(fact_subset__Un__eq,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
    <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13) = X13 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__Un__eq) ).

fof(fact_Un__absorb1,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13) = X13 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__absorb1) ).

fof(fact_Un__absorb2,axiom,
    ! [X11,X13,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),X11))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__absorb2) ).

fof(fact_Collect__neg__eq,axiom,
    ! [X29,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X29)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X29)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).

fof(fact_drop__eq__Nil,axiom,
    ! [X212,X76,X5] :
      ( hAPP(hAPP(c_List_Odrop(X5),X76),X212) = 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)),X212)),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__eq__Nil) ).

fof(fact_drop__all,axiom,
    ! [X98,X221,X15] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),X98))
     => hAPP(hAPP(c_List_Odrop(X15),X98),X221) = c_List_Olist_ONil(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__all) ).

fof(fact_insert__iff,axiom,
    ! [X11,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X17),X11)))
    <=> ( X6 = X17
        | hBOOL(hAPP(hAPP(c_member(X5),X6),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__iff) ).

fof(fact_insertE,axiom,
    ! [X11,X17,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X17),X11)))
     => ( X6 != X17
       => hBOOL(hAPP(hAPP(c_member(X5),X6),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertE) ).

fof(fact_take__all,axiom,
    ! [X98,X221,X15] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),X98))
     => hAPP(hAPP(c_List_Otake(X15),X98),X221) = X221 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__all) ).

fof(fact_ivl__diff,axiom,
    ! [X45,X76,X70,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X70),X76))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X70),X45)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X70),X76)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X76),X45) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__diff) ).

fof(fact_accp_Osimps,axiom,
    ! [X6,X34,X5] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X34),X6))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(X34,X3),X6))
         => hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X34),X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Osimps) ).

fof(fact_accp_Oequations,axiom,
    ! [X6,X34,X5] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X34),X6))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(X34,X3),X6))
         => hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X34),X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Oequations) ).

fof(fact_Times__empty,axiom,
    ! [X13,X11,X16,X5] :
      ( hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X13)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X16),tc_HOL_Obool))
    <=> ( X11 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        | X13 = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Times__empty) ).

fof(fact_ivl__disj__un_I13_J,axiom,
    ! [X66,X97,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X97),X66))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X97,X66)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X66)) = hAPP(c_SetInterval_Oord__class_OatLeast(X5),X97) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I13_J) ).

fof(fact_ivl__disj__un_I11_J,axiom,
    ! [X66,X97,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X97),X66))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X97,X66)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X66)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X97) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I11_J) ).

fof(fact_ivl__disj__un_I12_J,axiom,
    ! [X66,X97,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X97),X66))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X97,X66)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X66)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X97) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I12_J) ).

fof(fact_Sup__set__fold,axiom,
    ! [X212,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OSup__class_OSup(X5,hAPP(c_List_Oset(X5),X212)) = hAPP(c_List_Ofoldl(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5),c_Orderings_Obot__class_Obot(X5)),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__set__fold) ).

fof(fact_Inf__set__fold,axiom,
    ! [X212,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OInf__class_OInf(X5,hAPP(c_List_Oset(X5),X212)) = hAPP(c_List_Ofoldl(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Orderings_Otop__class_Otop(X5)),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__set__fold) ).

fof(fact_card__atLeastAtMost__int,axiom,
    ! [X66,X97] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X97,X66)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X66),X97)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atLeastAtMost__int) ).

fof(fact_finite__imageI,axiom,
    ! [X48,X16,X90,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X90))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X16),hAPP(c_Set_Oimage(X5,X16,X48),X90))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageI) ).

fof(fact_Sup__binary,axiom,
    ! [X17,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),X17),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X6),X17) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__binary) ).

fof(fact_Inf__binary,axiom,
    ! [X17,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),X17),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X6),X17) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__binary) ).

fof(fact_ord_OlessThan__iff,axiom,
    ! [X30,X96,X70,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X70),c_SetInterval_Oord_OlessThan(X5,X96,X30)))
    <=> hBOOL(hAPP(hAPP(X96,X70),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OlessThan__iff) ).

fof(fact_ord_OatMost__iff,axiom,
    ! [X30,X95,X70,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X70),c_SetInterval_Oord_OatMost(X5,X95,X30)))
    <=> hBOOL(hAPP(hAPP(X95,X70),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatMost__iff) ).

fof(fact_ord_OgreaterThan__iff,axiom,
    ! [X30,X96,X70,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X70),c_SetInterval_Oord_OgreaterThan(X5,X96,X30)))
    <=> hBOOL(hAPP(hAPP(X96,X30),X70)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThan__iff) ).

fof(fact_ord_OatLeast__iff,axiom,
    ! [X30,X95,X70,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X70),c_SetInterval_Oord_OatLeast(X5,X95,X30)))
    <=> hBOOL(hAPP(hAPP(X95,X30),X70)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeast__iff) ).

fof(fact_partition__set,axiom,
    ! [X258,X259,X212,X29,X5] :
      ( c_List_Opartition(X5,X29,X212) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X259),X258)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X259)),hAPP(c_List_Oset(X5),X258)) = hAPP(c_List_Oset(X5),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition__set) ).

fof(fact_nth__Cons__number__of,axiom,
    ! [X221,X14,X15,X126] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(X15),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = X14 )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(X15),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = hAPP(hAPP(c_List_Onth(X15),X221),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),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,
    ! [X34,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X34),c_Transitive__Closure_Ortrancl(X5,X34)) = hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),c_Transitive__Closure_Ortrancl(X5,X34)),X34),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__comp__rtrancl__eq) ).

fof(help_c__COMBS__1,axiom,
    ! [X36,X28,X29,X5,X38,X16] : hAPP(hAPP(hAPP(c_COMBS(X16,X38,X5),X29),X28),X36) = hAPP(hAPP(X29,X36),hAPP(X28,X36)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBS__1) ).

fof(fact_abs__minus__le__zero,axiom,
    ! [X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25))),c_Groups_Ozero__class_Ozero(X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__le__zero) ).

fof(fact_Un__insert__right,axiom,
    ! [X13,X6,X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__insert__right) ).

fof(fact_sum__squares__eq__zero__iff,axiom,
    ! [X27,X12,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X27),X27)) = c_Groups_Ozero__class_Ozero(X5)
      <=> ( X12 = c_Groups_Ozero__class_Ozero(X5)
          & X27 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).

fof(fact_map__add__find__right,axiom,
    ! [X45,X16,X204,X5,X30,X76] :
      ( hAPP(X76,X30) = hAPP(c_Option_Ooption_OSome(X5),X204)
     => hAPP(c_Map_Omap__add(X16,X5,X45,X76),X30) = hAPP(c_Option_Ooption_OSome(X5),X204) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__find__right) ).

fof(fact_union__fold__insert,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13) = hAPP(hAPP(c_Finite__Set_Ofold(X5,tc_fun(X5,tc_HOL_Obool),c_Set_Oinsert(X5)),X13),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_union__fold__insert) ).

fof(fact_eq__special_I3_J,axiom,
    ! [X12,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X12) = 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),X12),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,
    ! [X27,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X27)
      <=> 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),X27)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__special_I1_J) ).

fof(fact_wf__lex__prod,axiom,
    ! [X182,X16,X183,X5] :
      ( c_Wellfounded_Owf(X5,X183)
     => ( c_Wellfounded_Owf(X16,X182)
       => c_Wellfounded_Owf(tc_prod(X5,X16),c_Wellfounded_Olex__prod(X5,X16,X183,X182)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__lex__prod) ).

fof(fact_distinct__zipI1,axiom,
    ! [X225,X5,X221,X15] :
      ( hBOOL(hAPP(c_List_Odistinct(X15),X221))
     => hBOOL(hAPP(c_List_Odistinct(tc_prod(X15,X5)),hAPP(hAPP(c_List_Ozip(X15,X5),X221),X225))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__zipI1) ).

fof(fact_distinct__zipI2,axiom,
    ! [X221,X5,X225,X15] :
      ( hBOOL(hAPP(c_List_Odistinct(X15),X225))
     => hBOOL(hAPP(c_List_Odistinct(tc_prod(X5,X15)),hAPP(hAPP(c_List_Ozip(X5,X15),X221),X225))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__zipI2) ).

fof(fact_vimage__Union,axiom,
    ! [X11,X2,X16,X5] : hAPP(c_Set_Ovimage(X5,X16,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X16,tc_HOL_Obool),X11)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X16,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X11),c_Set_Ovimage(X5,X16,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Union) ).

fof(fact_image__Union,axiom,
    ! [X35,X2,X5,X16] : hAPP(c_Set_Oimage(X16,X5,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X16,tc_HOL_Obool),X35)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X16,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X35),c_Set_Oimage(X16,X5,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Union) ).

fof(fact_Least__equality,axiom,
    ! [X12,X29,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(X29,X12))
       => ( ! [X33] :
              ( hBOOL(hAPP(X29,X33))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X33)) )
         => c_Orderings_Oord__class_OLeast(X5,X29) = X12 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Least__equality) ).

fof(fact_Pow__bottom,axiom,
    ! [X13,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),X13))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__bottom) ).

fof(fact_listsum__0,axiom,
    ! [X212,X16,X5] :
      ( class_Groups_Omonoid__add(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X16,X5),hAPP(c_COMBK(X5,X16),c_Groups_Ozero__class_Ozero(X5))),X212)) = c_Groups_Ozero__class_Ozero(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__0) ).

fof(fact_Int__left__absorb,axiom,
    ! [X13,X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__absorb) ).

fof(fact_Un__Diff__cancel,axiom,
    ! [X13,X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X13),X11)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Diff__cancel) ).

fof(fact_Un__left__absorb,axiom,
    ! [X13,X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__left__absorb) ).

fof(fact_rotate1__length01,axiom,
    ! [X221,X15] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
     => hAPP(c_List_Orotate1(X15),X221) = X221 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__length01) ).

fof(fact_fold__image__empty,axiom,
    ! [X37,X1,X2,X16,X5] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X16,X2),X1),X37),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))) = X37,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__empty) ).

fof(fact_mult__eq__if,axiom,
    ! [X98,X99] :
      ( ( X99 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),X98) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X99 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),X98) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X98)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__if) ).

fof(fact_listsp__inf__eq,axiom,
    ! [X13,X11,X5] : c_List_Olistsp(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),c_List_Olistsp(X5,X11)),c_List_Olistsp(X5,X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__inf__eq) ).

fof(fact_RangeP_Oequations,axiom,
    ! [X46,X34,X16,X5] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(X5,X16,X34),X46))
    <=> ? [X74] : hBOOL(hAPP(hAPP(X34,X74),X46)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).

fof(fact_nat__mult__distrib__neg,axiom,
    ! [X139,X23] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X139)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X139))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__distrib__neg) ).

fof(fact_finite__dom__map__of,axiom,
    ! [X97,X16,X5] : hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Map_Odom(X5,X16,hAPP(c_Map_Omap__of(X5,X16),X97)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__dom__map__of) ).

fof(fact_pair__box_Osize_I2_J,axiom,
    ! [X26,X25,X5,X15] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X15,X5)),c_Nitpick_Opair__box_OPairBox(X15,X5,X25,X26)) = 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,
    ! [X14,X221,X15,X100] :
      ( ( X100 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
       => c_List_Obutlast(X15,hAPP(hAPP(c_List_Olist__update(X15,X221),X100),X14)) = c_List_Obutlast(X15,X221) )
      & ( X100 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
       => c_List_Obutlast(X15,hAPP(hAPP(c_List_Olist__update(X15,X221),X100),X14)) = hAPP(hAPP(c_List_Olist__update(X15,c_List_Obutlast(X15,X221)),X100),X14) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__list__update) ).

fof(fact_image__insert,axiom,
    ! [X13,X6,X2,X5,X16] : hAPP(c_Set_Oimage(X16,X5,X2),hAPP(hAPP(c_Set_Oinsert(X16),X6),X13)) = hAPP(hAPP(c_Set_Oinsert(X5),hAPP(X2,X6)),hAPP(c_Set_Oimage(X16,X5,X2),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__insert) ).

fof(fact_finite__subset,axiom,
    ! [X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__subset) ).

fof(fact_rev__finite__subset,axiom,
    ! [X11,X13,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X13))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)) ) ),
    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,
    ! [X212,X2,X5,X16] :
      ( class_Orderings_Olinorder(X16)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Olinorder__class_Osort__key(X5,X16,X2,X212)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__sort) ).

fof(fact_lfp__lemma2,axiom,
    ! [X2,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( c_Orderings_Oorder__class_Omono(X5,X5,X2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Olfp(X5,X2))),c_Inductive_Ocomplete__lattice__class_Olfp(X5,X2))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lfp__lemma2) ).

fof(fact_gfp__lemma3,axiom,
    ! [X2,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( c_Orderings_Oorder__class_Omono(X5,X5,X2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X2))),c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X2))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gfp__lemma3) ).

fof(fact_zip__rev,axiom,
    ! [X225,X5,X221,X15] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X225)
     => hAPP(hAPP(c_List_Ozip(X15,X5),hAPP(c_List_Orev(X15),X221)),hAPP(c_List_Orev(X5),X225)) = hAPP(c_List_Orev(tc_prod(X15,X5)),hAPP(hAPP(c_List_Ozip(X15,X5),X221),X225)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__rev) ).

fof(fact_nat__zero__less__power__iff,axiom,
    ! [X76,X12] :
      ( 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),X12),X76)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12))
        | X76 = 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,
    ! [X21,X17,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,X17)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X21)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),X21),X17) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__atLeastAtMostL2) ).

fof(fact_Int__atLeastAtMostL1,axiom,
    ! [X20,X17,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,X17)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X20)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X17),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__atLeastAtMostL1) ).

fof(fact_list__update__code_I2_J,axiom,
    ! [X22,X221,X14,X15] : hAPP(hAPP(c_List_Olist__update(X15,hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22) = hAPP(hAPP(c_List_Olist_OCons(X15),X22),X221),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__code_I2_J) ).

fof(help_c__COMBC__1,axiom,
    ! [X36,X28,X29,X5,X38,X16] : hAPP(hAPP(hAPP(c_COMBC(X16,X38,X5),X29),X28),X36) = hAPP(hAPP(X29,X36),X28),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBC__1) ).

fof(help_c__COMBB__1,axiom,
    ! [X36,X28,X29,X38,X5,X16] : hAPP(hAPP(hAPP(c_COMBB(X16,X5,X38),X29),X28),X36) = hAPP(X29,hAPP(X28,X36)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).

fof(fact_option_Osimps_I5_J,axiom,
    ! [X6,X88,X89,X16,X5] : hAPP(c_Option_Ooption_Ooption__case(X5,X16,X89,X88),hAPP(c_Option_Ooption_OSome(X16),X6)) = hAPP(X88,X6),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option_Osimps_I5_J) ).

fof(fact_vimage__Compl,axiom,
    ! [X11,X2,X16,X5] : hAPP(c_Set_Ovimage(X5,X16,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X16,tc_HOL_Obool)),X11)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X16,X2),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Compl) ).

fof(fact_mod__mult__self3,axiom,
    ! [X99,X98,X100] : 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),X100),X98)),X99),X98) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self3) ).

fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
    ! [X22,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X14)),hAPP(c_Int_Onat,X22)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
    ! [X22,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X14)),hAPP(c_Int_Onat,X22)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X14),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
    ! [X22,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X14)),hAPP(c_Int_Onat,X22)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J) ).

fof(fact_nat__add__distrib,axiom,
    ! [X139,X23] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X139))
       => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23),X139)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X23)),hAPP(c_Int_Onat,X139)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__distrib) ).

fof(fact_length__zip,axiom,
    ! [X225,X221,X5,X15] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X15,X5))),hAPP(hAPP(c_List_Ozip(X15,X5),X221),X225)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X225)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__zip) ).

fof(fact_Union__image__eq,axiom,
    ! [X11,X13,X16,X5] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X16,tc_fun(X5,tc_HOL_Obool),X13),X11)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X11),X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__image__eq) ).

fof(fact_Inter__image__eq,axiom,
    ! [X11,X13,X16,X5] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X16,tc_fun(X5,tc_HOL_Obool),X13),X11)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X11),X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__image__eq) ).

fof(fact_INTER__eq__Inter__image,axiom,
    ! [X13,X11,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X11),X13) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X16,tc_fun(X5,tc_HOL_Obool),X13),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INTER__eq__Inter__image) ).

fof(fact_UNION__eq__Union__image,axiom,
    ! [X13,X11,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X11),X13) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X16,tc_fun(X5,tc_HOL_Obool),X13),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNION__eq__Union__image) ).

fof(fact_of__nat__aux_Osimps_I2_J,axiom,
    ! [X70,X76,X171,X5] :
      ( class_Rings_Osemiring__1(X5)
     => c_Nat_Osemiring__1__class_Oof__nat__aux(X5,X171,hAPP(c_Nat_OSuc,X76),X70) = c_Nat_Osemiring__1__class_Oof__nat__aux(X5,X171,X76,hAPP(X171,X70)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I2_J) ).

fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
    ! [X22,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X14),hAPP(c_Int_Onat,X22)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X14,X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I2_J) ).

fof(fact_nat__mod__distrib,axiom,
    ! [X22,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))
       => hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X14,X22)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X14),hAPP(c_Int_Onat,X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mod__distrib) ).

fof(fact_zmod__zdiv__equality_H,axiom,
    ! [X98,X99] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X99,X98) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X99),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X99),X98)),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zdiv__equality_H) ).

fof(fact_Divides_Omod__div__equality_H,axiom,
    ! [X98,X99] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),X98)),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Omod__div__equality_H) ).

fof(fact_zero__less__power,axiom,
    ! [X98,X25,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).

fof(fact_zero__le__power,axiom,
    ! [X98,X25,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power) ).

fof(fact_one__le__power,axiom,
    ! [X98,X25,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Oone__class_Oone(X15)),X25))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Oone__class_Oone(X15)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__power) ).

fof(fact_lfp__lowerbound,axiom,
    ! [X11,X2,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X2,X11)),X11))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Inductive_Ocomplete__lattice__class_Olfp(X5,X2)),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lfp__lowerbound) ).

fof(fact_image__constant,axiom,
    ! [X21,X16,X11,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
     => hAPP(c_Set_Oimage(X5,X16,hAPP(c_COMBK(X16,X5),X21)),X11) = hAPP(hAPP(c_Set_Oinsert(X16),X21),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__constant) ).

fof(fact_zless__nat__conj,axiom,
    ! [X37,X112] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X112)),hAPP(c_Int_Onat,X37)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X112),X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__nat__conj) ).

fof(fact_UNIV__Times__UNIV,axiom,
    ! [X16,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X16),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__Times__UNIV) ).

fof(fact_zless__add1__eq,axiom,
    ! [X37,X112] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X112),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X37),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X112),X37))
        | X112 = X37 ) ),
    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,
    ! [X214,X212,X11,X5] :
      ( hBOOL(hAPP(c_List_Olistsp(X5,X11),hAPP(hAPP(c_List_Oappend(X5),X212),X214)))
    <=> ( hBOOL(hAPP(c_List_Olistsp(X5,X11),X212))
        & hBOOL(hAPP(c_List_Olistsp(X5,X11),X214)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__in__listsp__conv) ).

fof(fact_funpow__mult,axiom,
    ! [X2,X45,X76,X5] : hAPP(hAPP(c_Nat_Ocompow(X5,X5),X76),hAPP(hAPP(c_Nat_Ocompow(X5,X5),X45),X2)) = hAPP(hAPP(c_Nat_Ocompow(X5,X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X76)),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow__mult) ).

fof(fact_eq__number__of__int__code,axiom,
    ! [X97,X30] :
      ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X97)))
    <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X30),X97)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__int__code) ).

fof(fact_less__number__of__int__code,axiom,
    ! [X97,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X97)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),X97)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of__int__code) ).

fof(fact_transfer__int__nat__relations_I2_J,axiom,
    ! [X27,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X12)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X27)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I2_J) ).

fof(fact_zless__int,axiom,
    ! [X76,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X45)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X76)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__int) ).

fof(fact_less__eq__number__of__int__code,axiom,
    ! [X97,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X97)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),X97)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__number__of__int__code) ).

fof(fact_transfer__int__nat__relations_I3_J,axiom,
    ! [X27,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X12)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X27)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12),X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I3_J) ).

fof(fact_zle__int,axiom,
    ! [X76,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X45)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X76)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__int) ).

fof(fact_zero__less__diff,axiom,
    ! [X45,X76] :
      ( 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),X76),X45)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__diff) ).

fof(fact_zle__diff1__eq,axiom,
    ! [X37,X112] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X112),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X37),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X112),X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).

fof(fact_zle__add1__eq__le,axiom,
    ! [X37,X112] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X112),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X37),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X112),X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).

fof(fact_minus__number__of__mult,axiom,
    ! [X23,X132,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X132))),X23) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X132))),X23) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__number__of__mult) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
    ! [X99,X25,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X99)),X99) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),c_Groups_Oone__class_Oone(X15))),X99) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).

fof(fact_list__update__same__conv,axiom,
    ! [X12,X212,X5,X70] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X70),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
     => ( hAPP(hAPP(c_List_Olist__update(X5,X212),X70),X12) = X212
      <=> hAPP(hAPP(c_List_Onth(X5),X212),X70) = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__same__conv) ).

fof(fact_negative__zle,axiom,
    ! [X99,X98] : 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),X98))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X99))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zle) ).

fof(fact_zero__le__zpower__abs,axiom,
    ! [X98,X14] : 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),X14)),X98))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__zpower__abs) ).

fof(fact_min__diff,axiom,
    ! [X98,X102,X99] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X102)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),X102)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X99),X98)),X102),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__diff) ).

fof(fact_zadd__zmult__distrib,axiom,
    ! [X132,X133,X134] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X134),X133)),X132) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X134),X132)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X133),X132)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).

fof(fact_zdiff__zmult__distrib,axiom,
    ! [X132,X133,X134] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X134),X133)),X132) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X134),X132)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X133),X132)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).

fof(fact_add__mult__distrib,axiom,
    ! [X100,X98,X99] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X98)),X100) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),X100)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X100)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).

fof(fact_diff__mult__distrib,axiom,
    ! [X100,X98,X99] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98)),X100) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),X100)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X100)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).

fof(fact_nth_Osimps,axiom,
    ! [X76,X212,X12,X5] : hAPP(hAPP(c_List_Onth(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)),X76) = c_Nat_Onat_Onat__case(X5,X12,hAPP(c_List_Onth(X5),X212),X76),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth_Osimps) ).

fof(fact_replicate__length__filter,axiom,
    ! [X212,X12,X5] : c_List_Oreplicate(X5,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,hAPP(c_fequal,X12)),X212)),X12) = hAPP(c_List_Ofilter(X5,hAPP(c_fequal,X12)),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__length__filter) ).

fof(fact_Plus__eq__empty__conv,axiom,
    ! [X13,X11,X16,X5] :
      ( c_Sum__Type_OPlus(X5,X16,X11,X13) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X5,X16),tc_HOL_Obool))
    <=> ( X11 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        & X13 = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Plus__eq__empty__conv) ).

fof(fact_set__sort,axiom,
    ! [X212,X2,X5,X16] :
      ( class_Orderings_Olinorder(X16)
     => hAPP(c_List_Oset(X5),c_List_Olinorder__class_Osort__key(X5,X16,X2,X212)) = hAPP(c_List_Oset(X5),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__sort) ).

fof(fact_replicate__append__same,axiom,
    ! [X14,X102,X15] : hAPP(hAPP(c_List_Oappend(X15),c_List_Oreplicate(X15,X102,X14)),hAPP(hAPP(c_List_Olist_OCons(X15),X14),c_List_Olist_ONil(X15))) = hAPP(hAPP(c_List_Olist_OCons(X15),X14),c_List_Oreplicate(X15,X102,X14)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__append__same) ).

fof(fact_Union__insert,axiom,
    ! [X13,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),X13)) = 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),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__insert) ).

fof(fact_Inter__insert,axiom,
    ! [X13,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),X13)) = 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),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__insert) ).

fof(fact_wf__no__loop,axiom,
    ! [X36,X5] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X36),X36) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))
     => c_Wellfounded_Owf(X5,X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__no__loop) ).

fof(fact_add__eq__if,axiom,
    ! [X98,X99] :
      ( ( X99 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X98) = X98 )
      & ( X99 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X98) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X98)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__if) ).

fof(fact_map__upd__nonempty,axiom,
    ! [X12,X30,X10,X16,X5] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),X10),X30),hAPP(c_Option_Ooption_OSome(X16),X12)) != hAPP(c_COMBK(tc_Option_Ooption(X16),X5),c_Option_Ooption_ONone(X16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__upd__nonempty) ).

fof(fact_setsum__constant,axiom,
    ! [X11,X27,X16,X5] :
      ( class_Rings_Osemiring__1(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),hAPP(c_COMBK(X5,X16),X27)),X11) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),hAPP(c_Finite__Set_Ocard(X16),X11))),X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__constant) ).

fof(fact_of__int__less__0__iff,axiom,
    ! [X37,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),X37)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),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,
    ! [X37,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),X37)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X37),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,
    ! [X24,X26,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),c_Divides_Odiv__class_Omod(X15,X26,X24)),X24) = c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I2_J) ).

fof(fact_mod__add__right__eq,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26),X24) = c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),c_Divides_Odiv__class_Omod(X15,X26,X24)),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__right__eq) ).

fof(fact_mod__mult__right__eq,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26),X24) = c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),c_Divides_Odiv__class_Omod(X15,X26,X24)),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__right__eq) ).

fof(fact_mod__diff__right__eq,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Divides_Oring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X25),X26),X24) = c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X25),c_Divides_Odiv__class_Omod(X15,X26,X24)),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__right__eq) ).

fof(fact_predicate1D,axiom,
    ! [X12,X28,X29,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X29),X28))
     => ( hBOOL(hAPP(X29,X12))
       => hBOOL(hAPP(X28,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate1D) ).

fof(fact_rev__predicate1D,axiom,
    ! [X28,X5,X12,X29] :
      ( hBOOL(hAPP(X29,X12))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X29),X28))
       => hBOOL(hAPP(X28,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate1D) ).

fof(fact_nat__diff__distrib,axiom,
    ! [X23,X139] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X139))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X139),X23))
       => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23),X139)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X23)),hAPP(c_Int_Onat,X139)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__distrib) ).

fof(fact_listsp_Oequations_I2_J,axiom,
    ! [X46,X47,X11,X5] :
      ( hBOOL(hAPP(c_List_Olistsp(X5,X11),hAPP(hAPP(c_List_Olist_OCons(X5),X47),X46)))
    <=> ( hBOOL(hAPP(X11,X47))
        & hBOOL(hAPP(c_List_Olistsp(X5,X11),X46)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_Oequations_I2_J) ).

fof(fact_ivl__disj__un_I14_J,axiom,
    ! [X66,X97,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X97),X66))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X97),X66)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X66)) = hAPP(c_SetInterval_Oord__class_OatLeast(X5),X97) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I14_J) ).

fof(fact_less__special_I3_J,axiom,
    ! [X12,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),X12)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),c_Int_OPls)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I3_J) ).

fof(fact_le__special_I3_J,axiom,
    ! [X12,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),X12)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12),c_Int_OPls)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I3_J) ).

fof(fact_domIff,axiom,
    ! [X45,X16,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Map_Odom(X5,X16,X45)))
    <=> hAPP(X45,X6) != c_Option_Ooption_ONone(X16) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_domIff) ).

fof(fact_map__fst__zip,axiom,
    ! [X214,X16,X212,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)
     => hAPP(hAPP(c_List_Omap(tc_prod(X5,X16),X5),c_Product__Type_Ofst(X5,X16)),hAPP(hAPP(c_List_Ozip(X5,X16),X212),X214)) = X212 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__fst__zip) ).

fof(fact_map__snd__zip,axiom,
    ! [X214,X16,X212,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)
     => hAPP(hAPP(c_List_Omap(tc_prod(X5,X16),X16),c_Product__Type_Osnd(X5,X16)),hAPP(hAPP(c_List_Ozip(X5,X16),X212),X214)) = X214 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__snd__zip) ).

fof(fact_div__add__self1,axiom,
    ! [X25,X26,X15] :
      ( class_Divides_Osemiring__div(X15)
     => ( X26 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X26),X25)),X26) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),X25),X26)),c_Groups_Oone__class_Oone(X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add__self1) ).

fof(fact_div__add__self2,axiom,
    ! [X25,X26,X15] :
      ( class_Divides_Osemiring__div(X15)
     => ( X26 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26)),X26) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),X25),X26)),c_Groups_Oone__class_Oone(X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add__self2) ).

fof(fact_mod__mult__mult2,axiom,
    ! [X26,X24,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),c_Divides_Odiv__class_Omod(X15,X25,X26)),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__mult2) ).

fof(fact_nat__abs__mult__distrib,axiom,
    ! [X23,X132] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X132),X23))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X132))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__abs__mult__distrib) ).

fof(fact_strict__monoD,axiom,
    ! [X27,X12,X2,X5,X16] :
      ( ( class_Orderings_Oorder(X16)
        & class_Orderings_Oorder(X5) )
     => ( c_Orderings_Oorder__class_Ostrict__mono(X5,X16,X2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X12),X27))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16),hAPP(X2,X12)),hAPP(X2,X27))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_strict__monoD) ).

fof(fact_monoD,axiom,
    ! [X27,X12,X2,X5,X16] :
      ( ( class_Orderings_Oorder(X16)
        & class_Orderings_Oorder(X5) )
     => ( c_Orderings_Oorder__class_Omono(X5,X16,X2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16),hAPP(X2,X12)),hAPP(X2,X27))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monoD) ).

fof(fact_nat__mult__div__cancel1,axiom,
    ! [X98,X99,X100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X100))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),X99)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),X98)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),X98) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__div__cancel1) ).

fof(fact_zdiv__zmult2__eq,axiom,
    ! [X26,X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X24)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26)),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmult2__eq) ).

fof(fact_split__beta,axiom,
    ! [X37,X29,X5,X38,X16] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X16,X38,X5),X29),X37) = hAPP(hAPP(X29,hAPP(c_Product__Type_Ofst(X16,X38),X37)),hAPP(c_Product__Type_Osnd(X16,X38),X37)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__beta) ).

fof(fact_prod__case__beta,axiom,
    ! [X161,X2,X5,X38,X16] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X16,X38,X5),X2),X161) = hAPP(hAPP(X2,hAPP(c_Product__Type_Ofst(X16,X38),X161)),hAPP(c_Product__Type_Osnd(X16,X38),X161)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod__case__beta) ).

fof(fact_split__def,axiom,
    ! [X161,X21,X5,X38,X16] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X16,X38,X5),X21),X161) = hAPP(hAPP(X21,hAPP(c_Product__Type_Ofst(X16,X38),X161)),hAPP(c_Product__Type_Osnd(X16,X38),X161)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__def) ).

fof(fact_sorted__sort,axiom,
    ! [X212,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Olinorder__class_Osorted(X5,c_List_Olinorder__class_Osort__key(X5,X5,c_COMBI(X5),X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__sort) ).

fof(fact_append1__eq__conv,axiom,
    ! [X27,X214,X12,X212,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X212),hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Olist_ONil(X5))) = hAPP(hAPP(c_List_Oappend(X5),X214),hAPP(hAPP(c_List_Olist_OCons(X5),X27),c_List_Olist_ONil(X5)))
    <=> ( X212 = X214
        & X12 = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append1__eq__conv) ).

fof(fact_hd__drop__conv__nth,axiom,
    ! [X98,X15,X221] :
      ( X221 != c_List_Olist_ONil(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
       => hAPP(c_List_Ohd(X15),hAPP(hAPP(c_List_Odrop(X15),X98),X221)) = hAPP(hAPP(c_List_Onth(X15),X221),X98) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__drop__conv__nth) ).

fof(fact_abs__add__abs,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),hAPP(c_Groups_Oabs__class_Oabs(X15),X26))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),hAPP(c_Groups_Oabs__class_Oabs(X15),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__abs) ).

fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
    ! [X6,X11,X90,X2,X5] :
      ( c_Finite__Set_Ofolding__one__idem(X5,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(X90,hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,X2),X6),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oeq__fold__idem_H) ).

fof(fact_min__max_Oinf__le1,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),X22)),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__le1) ).

fof(fact_min__max_Oinf__le2,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),X22)),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__le2) ).

fof(fact_inf__le1,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X22)),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le1) ).

fof(fact_inf__sup__ord_I1_J,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Olattice(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X22)),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I1_J) ).

fof(fact_inf__le2,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X22)),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le2) ).

fof(fact_inf__sup__ord_I2_J,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Olattice(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X22)),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I2_J) ).

fof(fact_expand__Suc,axiom,
    ! [X126] :
      ( 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),X126)))
     => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),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,
    ! [X66,X97,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X97),X66))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X97)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X97,X66)) = hAPP(c_SetInterval_Oord__class_OatMost(X5),X66) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I9_J) ).

fof(fact_ivl__disj__un_I7_J,axiom,
    ! [X66,X97,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X97),X66))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X97)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X97,X66)) = hAPP(c_SetInterval_Oord__class_OlessThan(X5),X66) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I7_J) ).

fof(fact_ivl__disj__un_I10_J,axiom,
    ! [X66,X97,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X97),X66))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X97)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X97,X66)) = hAPP(c_SetInterval_Oord__class_OatMost(X5),X66) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I10_J) ).

fof(fact_abs__le__D1,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D1) ).

fof(fact_min__max_Osup__inf__distrib1,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X22),X23)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),X22)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__inf__distrib1) ).

fof(fact_min__max_Oinf__sup__distrib1,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X22),X23)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),X22)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),X23)) ),
    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,
    ! [X23,X22,X14,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X22),X23)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),X22)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).

fof(fact_inf__sup__distrib1,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Lattices_Odistrib__lattice(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X22),X23)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X22)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__distrib1) ).

fof(fact_sup__inf__distrib1,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Lattices_Odistrib__lattice(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X22),X23)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X22)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__inf__distrib1) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26)),X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X24)),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
    ! [X117,X118,X119,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X119),X118)),X117) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X119),X117)),X118) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).

fof(fact_UNIV__option__conv,axiom,
    ! [X5] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X5),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(X5)),c_Option_Ooption_ONone(X5)),hAPP(c_Set_Oimage(X5,tc_Option_Ooption(X5),c_Option_Ooption_OSome(X5)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__option__conv) ).

fof(fact_id__o,axiom,
    ! [X1,X5,X16] : hAPP(c_Fun_Ocomp(X16,X16,X5,c_Fun_Oid(X16)),X1) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__o) ).

fof(fact_length__pos__if__in__set,axiom,
    ! [X212,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => 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)),X212))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__pos__if__in__set) ).

fof(fact_single__valued__rel__pow,axiom,
    ! [X76,X36,X5] :
      ( c_Relation_Osingle__valued(X5,X5,X36)
     => c_Relation_Osingle__valued(X5,X5,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X76),X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__rel__pow) ).

fof(fact_Random__Sequence_Osingle__def,axiom,
    ! [X263,X264,X12,X5] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(X5),X12),X264),X263) = 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),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Random__Sequence_Osingle__def) ).

fof(fact_DomainP_Oequations,axiom,
    ! [X47,X34,X16,X5] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(X5,X16,X34),X47))
    <=> ? [X32] : hBOOL(hAPP(hAPP(X34,X47),X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Oequations) ).

fof(fact_inj__eq,axiom,
    ! [X27,X12,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hAPP(X2,X12) = hAPP(X2,X27)
      <=> X12 = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__eq) ).

fof(fact_injD,axiom,
    ! [X27,X12,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hAPP(X2,X12) = hAPP(X2,X27)
       => X12 = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_injD) ).

fof(fact_replicate__add,axiom,
    ! [X14,X99,X98,X15] : c_List_Oreplicate(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X99),X14) = hAPP(hAPP(c_List_Oappend(X15),c_List_Oreplicate(X15,X98,X14)),c_List_Oreplicate(X15,X99,X14)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__add) ).

fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
    ! [X6,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X6),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold__idem_H) ).

fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
    ! [X6,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X6),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold__idem_H) ).

fof(fact_foldl__Nil,axiom,
    ! [X6,X2,X16,X5] : hAPP(c_List_Ofoldl(X5,X16,X2,X6),c_List_Olist_ONil(X16)) = X6,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__Nil) ).

fof(fact_list_Osimps_I4_J,axiom,
    ! [X88,X89,X16,X5] : hAPP(c_List_Olist_Olist__case(X5,X16,X89,X88),c_List_Olist_ONil(X16)) = X89,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I4_J) ).

fof(fact_option_Osimps_I4_J,axiom,
    ! [X88,X89,X16,X5] : hAPP(c_Option_Ooption_Ooption__case(X5,X16,X89,X88),c_Option_Ooption_ONone(X16)) = X89,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option_Osimps_I4_J) ).

fof(fact_o__id,axiom,
    ! [X2,X16,X5] : hAPP(c_Fun_Ocomp(X5,X16,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,
    ! [X27,X12,X5] :
      ( class_Groups_Oordered__comm__monoid__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X12))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X27))
         => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X12),X27) = c_Groups_Ozero__class_Ozero(X5)
          <=> ( X12 = c_Groups_Ozero__class_Ozero(X5)
              & X27 = 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,
    ! [X102,X101,X100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X100),X101))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X101)),X100) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X101),X100)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc) ).

fof(fact_add__diff__assoc,axiom,
    ! [X102,X101,X100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X100),X101))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X101),X100)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X101)),X100) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc) ).

fof(fact_diff__diff__right,axiom,
    ! [X102,X101,X100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X100),X101))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X102),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X101),X100)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X100)),X101) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__right) ).

fof(fact_compl__mono,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Oboolean__algebra(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X22)),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X14))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__mono) ).

fof(fact_le__imp__neg__le,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Oordered__ab__group__add(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X26)),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).

fof(fact_one__less__nat__eq,axiom,
    ! [X37] :
      ( 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,X37)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__nat__eq) ).

fof(fact_mod__less__eq__dividend,axiom,
    ! [X98,X99] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98)),X99)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less__eq__dividend) ).

fof(fact_greaterThan__Suc,axiom,
    ! [X30] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X30)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),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,
    ! [X128,X129,X14,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),X129)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),X128)) = hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X129),X128)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).

fof(fact_power__add,axiom,
    ! [X98,X99,X25,X15] :
      ( class_Groups_Omonoid__mult(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X98)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X99)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__add) ).

fof(fact_fold1__eq__fold__idem,axiom,
    ! [X6,X11,X5] :
      ( class_Lattices_Oab__semigroup__idem__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Groups_Otimes__class_Otimes(X5)),X6),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__eq__fold__idem) ).

fof(fact_add__scale__eq__noteq,axiom,
    ! [X41,X24,X26,X25,X123,X15] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X15)
     => ( X123 != c_Groups_Ozero__class_Ozero(X15)
       => ( ( X25 = X26
            & X24 != X41 )
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X123),X24)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X123),X41)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).

fof(fact_some__eq__trivial,axiom,
    ! [X12,X5] : c_Hilbert__Choice_OEps(X5,hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X12)) = X12,
    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,
    ! [X98,X99] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98)),hAPP(c_Nat_OSuc,X99))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__Suc) ).

fof(fact_less__add__Suc1,axiom,
    ! [X99,X102] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X99)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).

fof(fact_less__add__Suc2,axiom,
    ! [X99,X102] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X102)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).

fof(fact_dom__map__of__conv__image__fst,axiom,
    ! [X210,X16,X5] : c_Map_Odom(X5,X16,hAPP(c_Map_Omap__of(X5,X16),X210)) = hAPP(c_Set_Oimage(tc_prod(X5,X16),X5,c_Product__Type_Ofst(X5,X16)),hAPP(c_List_Oset(tc_prod(X5,X16)),X210)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dom__map__of__conv__image__fst) ).

fof(fact_ivl__disj__int_I16_J,axiom,
    ! [X66,X45,X97,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,X97,X45)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X45,X66)) = 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,
    ! [X66,X45,X97,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,X97,X45)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X45,X66)) = 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,
    ! [X66,X45,X97,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,X97,X45)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X45,X66)) = 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,
    ! [X66,X45,X97,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,X97,X45)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X45,X66)) = 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,
    ! [X66,X45,X97,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,X97,X45)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X45,X66)) = 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,
    ! [X11,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))),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__subsetI) ).

fof(fact_equiv__comp__eq,axiom,
    ! [X34,X11,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X11,X34)
     => hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(c_Relation_Oconverse(X5,X5),X34)),X34) = X34 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__comp__eq) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
    ! [X22,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X14,X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).

fof(fact_subset__insertI,axiom,
    ! [X6,X13,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insertI) ).

fof(fact_zmod__simps_I3_J,axiom,
    ! [X24,X26,X25] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),c_Divides_Odiv__class_Omod(tc_Int_Oint,X26,X24)),X24) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X26),X24),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I3_J) ).

fof(fact_zdiff__zmod__right,axiom,
    ! [X99,X22,X14] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X14),c_Divides_Odiv__class_Omod(tc_Int_Oint,X22,X99)),X99) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X14),X22),X99),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmod__right) ).

fof(fact_zmod__zmult1__eq,axiom,
    ! [X24,X26,X25] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X26),X24) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),c_Divides_Odiv__class_Omod(tc_Int_Oint,X26,X24)),X24),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zmult1__eq) ).

fof(fact_ivl__disj__un_I8_J,axiom,
    ! [X66,X97,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X97),X66))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X97)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X97),X66)) = hAPP(c_SetInterval_Oord__class_OlessThan(X5),X66) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I8_J) ).

fof(fact_atLeastAtMostSuc__conv,axiom,
    ! [X76,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),hAPP(c_Nat_OSuc,X76)))
     => c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X45,hAPP(c_Nat_OSuc,X76)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X76)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X45,X76)) ),
    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,
    ! [X98,X99,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),X99)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),X98))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__of__nat__less) ).

fof(fact_Int__atLeastAtMostR2,axiom,
    ! [X20,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_OatLeast(X5),X6)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X21,X20)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),X21),X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__atLeastAtMostR2) ).

fof(fact_Int__atLeastAtMostR1,axiom,
    ! [X20,X21,X17,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),X17)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X21,X20)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X21,hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X17),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__atLeastAtMostR1) ).

fof(fact_zless__nat__eq__int__zless,axiom,
    ! [X37,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),hAPP(c_Int_Onat,X37)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X45)),X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__nat__eq__int__zless) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
    ! [X22,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X14)),hAPP(c_Int_Onat,X22)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X14,X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J) ).

fof(fact_drop__take,axiom,
    ! [X221,X99,X98,X15] : hAPP(hAPP(c_List_Odrop(X15),X98),hAPP(hAPP(c_List_Otake(X15),X99),X221)) = hAPP(hAPP(c_List_Otake(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98)),hAPP(hAPP(c_List_Odrop(X15),X98),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__take) ).

fof(fact_rel__comp__empty2,axiom,
    ! [X36,X16,X38,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X38,X16),X36),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X38,X16),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__empty2) ).

fof(fact_mod__pos__pos__1__number__of,axiom,
    ! [X132] :
      ( 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),X132)))
     => 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),X132)) = 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),X132))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__pos__1__number__of) ).

fof(fact_mod__mult__distrib,axiom,
    ! [X100,X98,X99] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98)),X100) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),X100),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X100)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__distrib) ).

fof(fact_min__max_Oless__supI1,axiom,
    ! [X26,X25,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X25))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X25),X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oless__supI1) ).

fof(fact_min__max_Oless__supI2,axiom,
    ! [X25,X26,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X25),X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oless__supI2) ).

fof(fact_less__supI1,axiom,
    ! [X26,X25,X14,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X25))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X25),X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__supI1) ).

fof(fact_less__supI2,axiom,
    ! [X25,X26,X14,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X25),X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__supI2) ).

fof(fact_min__max_Ole__supI1,axiom,
    ! [X26,X25,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X25))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X25),X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__supI1) ).

fof(fact_min__max_Ole__supI2,axiom,
    ! [X25,X26,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X25),X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__supI2) ).

fof(fact_le__supI1,axiom,
    ! [X26,X25,X14,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X25))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X25),X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__supI1) ).

fof(fact_le__supI2,axiom,
    ! [X25,X26,X14,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X25),X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__supI2) ).

fof(fact_negative__zle__0,axiom,
    ! [X98] : 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),X98))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zle__0) ).

fof(fact_transpose__empty,axiom,
    ! [X212,X5] :
      ( c_List_Otranspose(X5,X212) = 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)),X212)))
         => 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,
    ! [X30,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))),X30)) = 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)),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__shift__lb__Suc0__0__upt) ).

fof(fact_UN__empty2,axiom,
    ! [X11,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X16),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,
    ! [X100,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X101))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X101),X100))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X102)),X100)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).

fof(fact_div__pos__pos__1__number__of,axiom,
    ! [X132] :
      ( 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),X132)))
     => 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),X132)) = 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),X132))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__pos__1__number__of) ).

fof(fact_pos__mod__sign,axiom,
    ! [X25,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__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__mod__sign) ).

fof(fact_greaterThanLessThan__upto,axiom,
    ! [X115,X70] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X70,X115) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X70),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X115),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,
    ! [X212,X12,X2,X5,X16] : hAPP(hAPP(c_List_Omap(X16,X5),X2),hAPP(hAPP(c_List_Olist_OCons(X16),X12),X212)) = hAPP(hAPP(c_List_Olist_OCons(X5),hAPP(X2,X12)),hAPP(hAPP(c_List_Omap(X16,X5),X2),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map_Osimps_I2_J) ).

fof(fact_power__one__over,axiom,
    ! [X98,X25,X15] :
      ( class_Fields_Ofield__inverse__zero(X15)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),c_Groups_Oone__class_Oone(X15)),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)) = hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),c_Groups_Oone__class_Oone(X15)),X25)),X98) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__over) ).

fof(fact_le__imp__0__less,axiom,
    ! [X23] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))
     => 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)),X23))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__0__less) ).

fof(fact_insertI2,axiom,
    ! [X17,X13,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X13))
     => hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X17),X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI2) ).

fof(fact_less__minus__iff,axiom,
    ! [X17,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),X17)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),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,
    ! [X17,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),X17)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),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,
    ! [X14,X100,X15,X221] :
      ( X221 != c_List_Olist_ONil(X15)
     => ( ( X100 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
         => c_List_Olast(X15,hAPP(hAPP(c_List_Olist__update(X15,X221),X100),X14)) = X14 )
        & ( X100 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
         => c_List_Olast(X15,hAPP(hAPP(c_List_Olist__update(X15,X221),X100),X14)) = c_List_Olast(X15,X221) ) ) ),
    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,
    ! [X221,X15,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
     => hAPP(hAPP(c_List_Otake(X15),X98),c_List_Obutlast(X15,X221)) = hAPP(hAPP(c_List_Otake(X15),X98),X221) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__butlast) ).

fof(fact_last__drop,axiom,
    ! [X221,X15,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
     => c_List_Olast(X15,hAPP(hAPP(c_List_Odrop(X15),X98),X221)) = c_List_Olast(X15,X221) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__drop) ).

fof(fact_split__conv,axiom,
    ! [X17,X6,X2,X5,X38,X16] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X16,X38,X5),X2),hAPP(hAPP(c_Product__Type_OPair(X16,X38),X6),X17)) = hAPP(hAPP(X2,X6),X17),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__conv) ).

fof(fact_prod_Osimps_I2_J,axiom,
    ! [X17,X6,X89,X5,X38,X16] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X16,X38,X5),X89),hAPP(hAPP(c_Product__Type_OPair(X16,X38),X6),X17)) = hAPP(hAPP(X89,X6),X17),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod_Osimps_I2_J) ).

fof(fact_min__max_OSup__fin_Oin__idem,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X12),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X11)) = c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oin__idem) ).

fof(fact_min__max_OInf__fin_Oin__idem,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X12),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X11)) = c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oin__idem) ).

fof(fact_atLeastLessThan__eq__iff,axiom,
    ! [X20,X21,X17,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X17))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),X20))
         => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X17) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X21),X20)
          <=> ( X6 = X21
              & X17 = X20 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__eq__iff) ).

fof(fact_atLeastLessThan__inj_I1_J,axiom,
    ! [X20,X21,X17,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X17) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X21),X20)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X17))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),X20))
           => X6 = X21 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).

fof(fact_atLeastLessThan__inj_I2_J,axiom,
    ! [X20,X21,X17,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X17) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X21),X20)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X17))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),X20))
           => X17 = X20 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).

fof(fact_posDivAlg__correct,axiom,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X25,X26),c_Divides_OposDivAlg(X25,X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg__correct) ).

fof(fact_nth__list__update__neq,axiom,
    ! [X14,X221,X15,X101,X102] :
      ( X102 != X101
     => hAPP(hAPP(c_List_Onth(X15),hAPP(hAPP(c_List_Olist__update(X15,X221),X102),X14)),X101) = hAPP(hAPP(c_List_Onth(X15),X221),X101) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__list__update__neq) ).

fof(fact_ivl__disj__int_I9_J,axiom,
    ! [X66,X45,X97,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,X97,X45)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X45),X66)) = 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,X36,X16,X5] : hAPP(c_Relation_Oconverse(X5,X5),hAPP(hAPP(c_Relation_Oinv__image(X16,X5),X36),X2)) = hAPP(hAPP(c_Relation_Oinv__image(X16,X5),hAPP(c_Relation_Oconverse(X16,X16),X36)),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__inv__image) ).

fof(fact_Min_Oeq__fold__idem_H,axiom,
    ! [X6,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X6),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oeq__fold__idem_H) ).

fof(fact_Max_Oeq__fold__idem_H,axiom,
    ! [X6,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X6),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oeq__fold__idem_H) ).

fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
    ! [X6,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X6),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oeq__fold__idem_H) ).

fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
    ! [X6,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X6),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oeq__fold__idem_H) ).

fof(fact_log_Osimps,axiom,
    ! [X102,X26] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X26),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X102),X26)) )
       => c_Random_Olog(X26,X102) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
      & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X26),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X102),X26)) )
       => c_Random_Olog(X26,X102) = 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(X26,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X102),X26))) ) ),
    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,
    ! [X12,X5] :
      ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),X12))
    <=> hBOOL(hAPP(hAPP(c_member(X5),X12),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,
    ! [X14,X22,X15] :
      ( class_Fields_Olinordered__field__inverse__zero(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X22))
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X14)),X22) = hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__div__pos) ).

fof(fact_abs__mult__pos,axiom,
    ! [X22,X14,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X14))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X22)),X14) = hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X22),X14)) ) ),
    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,
    ! [X30,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)),X30)) = 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),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__shift__lb__Suc0__0) ).

fof(fact_inf__fun__def,axiom,
    ! [X12,X1,X2,X16,X5] :
      ( class_Lattices_Olattice(X5)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,X5)),X2),X1),X12) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),hAPP(X2,X12)),hAPP(X1,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__fun__def) ).

fof(fact_inf__apply,axiom,
    ! [X12,X1,X2,X16,X5] :
      ( class_Lattices_Olattice(X5)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,X5)),X2),X1),X12) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),hAPP(X2,X12)),hAPP(X1,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__apply) ).

fof(fact_fun__diff__def,axiom,
    ! [X12,X13,X11,X16,X5] :
      ( class_Groups_Ominus(X5)
     => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16,X5)),X11),X13),X12) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(X11,X12)),hAPP(X13,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__diff__def) ).

fof(fact_minus__apply,axiom,
    ! [X12,X13,X11,X16,X5] :
      ( class_Groups_Ominus(X5)
     => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16,X5)),X11),X13),X12) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(X11,X12)),hAPP(X13,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__apply) ).

fof(fact_sup__apply,axiom,
    ! [X12,X1,X2,X16,X5] :
      ( class_Lattices_Olattice(X5)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,X5)),X2),X1),X12) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),hAPP(X2,X12)),hAPP(X1,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__apply) ).

fof(fact_sup__fun__def,axiom,
    ! [X12,X1,X2,X16,X5] :
      ( class_Lattices_Olattice(X5)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,X5)),X2),X1),X12) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),hAPP(X2,X12)),hAPP(X1,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__fun__def) ).

fof(fact_negDivAlg__correct,axiom,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),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)),X26))
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X25,X26),c_Divides_OnegDivAlg(X25,X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg__correct) ).

fof(fact_neg__mod__bound,axiom,
    ! [X25,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__mod__bound) ).

fof(fact_folding_Oempty,axiom,
    ! [X90,X2,X16,X5] :
      ( c_Finite__Set_Ofolding(X5,X16,X2,X90)
     => hAPP(X90,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Fun_Oid(X16) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Oempty) ).

fof(fact_lfp__lemma3,axiom,
    ! [X2,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( c_Orderings_Oorder__class_Omono(X5,X5,X2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Inductive_Ocomplete__lattice__class_Olfp(X5,X2)),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Olfp(X5,X2)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lfp__lemma3) ).

fof(fact_gfp__lemma2,axiom,
    ! [X2,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( c_Orderings_Oorder__class_Omono(X5,X5,X2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X2)),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X2)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gfp__lemma2) ).

fof(fact_less__code__numeral__def,axiom,
    ! [X45,X76] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X76),X45))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X76)),hAPP(c_Code__Numeral_Onat__of,X45))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__code__numeral__def) ).

fof(fact_less__code__numeral__code,axiom,
    ! [X45,X76] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X76)),hAPP(c_Code__Numeral_Oof__nat,X45)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__code__numeral__code) ).

fof(fact_Suc__less__SucD,axiom,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X99)),hAPP(c_Nat_OSuc,X98)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).

fof(fact_Suc__less__eq,axiom,
    ! [X76,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X45)),hAPP(c_Nat_OSuc,X76)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).

fof(fact_less__eq__code__numeral__def,axiom,
    ! [X45,X76] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X76),X45))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X76)),hAPP(c_Code__Numeral_Onat__of,X45))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__code__numeral__def) ).

fof(fact_less__eq__code__numeral__code,axiom,
    ! [X45,X76] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X76)),hAPP(c_Code__Numeral_Oof__nat,X45)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X76),X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__code__numeral__code) ).

fof(fact_Suc__le__mono,axiom,
    ! [X45,X76] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X76)),hAPP(c_Nat_OSuc,X45)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X76),X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).

fof(fact_nth__take,axiom,
    ! [X221,X15,X98,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X98))
     => hAPP(hAPP(c_List_Onth(X15),hAPP(hAPP(c_List_Otake(X15),X98),X221)),X102) = hAPP(hAPP(c_List_Onth(X15),X221),X102) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__take) ).

fof(fact_Diff__disjoint,axiom,
    ! [X13,X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X13),X11)) = 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,
    ! [X214,X27,X212,X5] :
      ( hAPP(c_List_Orev(X5),X212) = hAPP(hAPP(c_List_Olist_OCons(X5),X27),X214)
    <=> X212 = hAPP(hAPP(c_List_Oappend(X5),hAPP(c_List_Orev(X5),X214)),hAPP(hAPP(c_List_Olist_OCons(X5),X27),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,
    ! [X98,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
     => 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),X14),X98))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).

fof(fact_div__le__dividend,axiom,
    ! [X98,X99] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),X98)),X99)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__dividend) ).

fof(fact_diff__le__self,axiom,
    ! [X98,X99] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98)),X99)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__self) ).

fof(fact__01,axiom,
    ! [X270,X14,X15] : hAPP(c_Lazy__Sequence_Oyield(X15),c_Lazy__Sequence_Olazy__sequence_OInsert(X15,X14,X270)) = hAPP(c_Option_Ooption_OSome(tc_prod(X15,tc_Lazy__Sequence_Olazy__sequence(X15))),hAPP(hAPP(c_Product__Type_OPair(X15,tc_Lazy__Sequence_Olazy__sequence(X15)),X14),X270)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__01) ).

fof(fact_ivl__disj__un_I2_J,axiom,
    ! [X66,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),X66)),hAPP(hAPP(c_Set_Oinsert(X5),X66),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(X5),X66) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I2_J) ).

fof(fact_Min__le,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Big__Operators_Olinorder__class_OMin(X5,X11)),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min__le) ).

fof(fact_zpower__zadd__distrib,axiom,
    ! [X23,X22,X14] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14),X22)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14),X23)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).

fof(fact_zadd__zmult__distrib2,axiom,
    ! [X133,X134,X132] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X132),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X134),X133)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X132),X134)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X132),X133)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).

fof(fact_zdiff__zmult__distrib2,axiom,
    ! [X133,X134,X132] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X132),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X134),X133)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X132),X134)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X132),X133)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).

fof(fact_add__mult__distrib2,axiom,
    ! [X98,X99,X100] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X98)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),X99)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).

fof(fact_diff__mult__distrib2,axiom,
    ! [X98,X99,X100] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),X99)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).

fof(fact_diff__commute,axiom,
    ! [X100,X101,X102] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X102),X101)),X100) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X102),X100)),X101),
    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_order__less__trans,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Orderings_Opreorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),X23))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X23)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).

fof(fact_order__le__less__trans,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Orderings_Opreorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),X23))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X23)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).

fof(fact_order__less__le__trans,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Orderings_Opreorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X23))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X23)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).

fof(fact_xt1_I10_J,axiom,
    ! [X23,X14,X22,X15] :
      ( class_Orderings_Oorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X23),X22))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X23),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).

fof(fact_xt1_I8_J,axiom,
    ! [X23,X14,X22,X15] :
      ( class_Orderings_Oorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X23),X22))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X23),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).

fof(fact_xt1_I7_J,axiom,
    ! [X23,X14,X22,X15] :
      ( class_Orderings_Oorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X23),X22))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X23),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).

fof(fact_order__trans,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Orderings_Opreorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X23))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X23)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).

fof(fact_xt1_I6_J,axiom,
    ! [X23,X14,X22,X15] :
      ( class_Orderings_Oorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X23),X22))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X23),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).

fof(fact_divmod__int__rel__0,axiom,
    ! [X26] :
      ( X26 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X26),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,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X25,X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__pos) ).

fof(fact_diff__eq__diff__less,axiom,
    ! [X20,X21,X17,X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X17) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X21),X20)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X17))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),X20)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).

fof(fact_diff__eq__diff__less__eq,axiom,
    ! [X20,X21,X17,X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X17) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X21),X20)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X17))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),X20)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).

fof(fact_eq__diff__iff,axiom,
    ! [X76,X45,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30),X45))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30),X76))
       => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X45),X30) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X76),X30)
        <=> X45 = X76 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__diff__iff) ).

fof(fact_Sigma__empty2,axiom,
    ! [X11,X16,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X16),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,
    ! [X212,X2,X16,X5] : c_List_Oremdups(X5,hAPP(hAPP(c_List_Omap(X16,X5),X2),c_List_Oremdups(X16,X212))) = c_List_Oremdups(X5,hAPP(hAPP(c_List_Omap(X16,X5),X2),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__map__remdups) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
    ! [X25,X99,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X99),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X99)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),c_Groups_Oone__class_Oone(X15))),X99) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).

fof(fact_div__pos__pos,axiom,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X25,X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__pos) ).

fof(fact_ivl__disj__int_I15_J,axiom,
    ! [X66,X45,X97,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,X97),X45)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X45,X66)) = 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,
    ! [X37,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),X37)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__0__less__iff) ).

fof(fact_of__nat__0__less__iff,axiom,
    ! [X76,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),X76)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X76)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__0__less__iff) ).

fof(fact_of__int__0__le__iff,axiom,
    ! [X37,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),X37)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__0__le__iff) ).

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,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),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)),X26))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X25,X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__neg__pos) ).

fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != 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),X12),X11)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X12),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oinsert__idem) ).

fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != 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),X12),X11)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X12),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oinsert__idem) ).

fof(fact_of__nat__diff,axiom,
    ! [X99,X98,X15] :
      ( class_Rings_Oring__1(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X99))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),X99)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),X98)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__diff) ).

fof(fact_div__neg__pos,axiom,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),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)),X26))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X25,X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__neg__pos) ).

fof(fact_finite__insert,axiom,
    ! [X11,X6,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__insert) ).

fof(fact_inf__Inf__fold__inf,axiom,
    ! [X13,X11,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X13),c_Complete__Lattice_OInf__class_OInf(X5,X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X13),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Inf__fold__inf) ).

fof(fact_sup__Sup__fold__sup,axiom,
    ! [X13,X11,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X13),c_Complete__Lattice_OSup__class_OSup(X5,X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X13),X11) ) ),
    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,
    ! [X11,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)),X11)),X11) = 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,
    ! [X11,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)),X11)),X11) = 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,
    ! [X16,X5] : c_Sum__Type_OPlus(X5,X16,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X5,X16),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV) ).

fof(fact_ivl__disj__int_I7_J,axiom,
    ! [X66,X97,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,X97,X66)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X66)) = 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,
    ! [X66,X97,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,X97,X66)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X66)) = 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,
    ! [X66,X97,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,X97,X66)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X66)) = 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,
    ! [X27,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),X27)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I1_J) ).

fof(fact_le__special_I1_J,axiom,
    ! [X27,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),X27)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I1_J) ).

fof(fact_finite__Domain,axiom,
    ! [X34,X16,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X16)),X34))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Relation_ODomain(X5,X16),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Domain) ).

fof(fact_finite__Range,axiom,
    ! [X34,X16,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X16)),X34))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X16),hAPP(c_Relation_ORange(X5,X16),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Range) ).

fof(fact_fold1Set__nonempty,axiom,
    ! [X12,X11,X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,X11),X12))
     => X11 != 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,
    ! [X22,X14] : hAPP(hAPP(c_Nitpick_Oint__gcd,X14),X22) = 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),X14)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X22)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Oint__gcd__def) ).

fof(fact_drop__map,axiom,
    ! [X212,X2,X16,X76,X5] : hAPP(hAPP(c_List_Odrop(X5),X76),hAPP(hAPP(c_List_Omap(X16,X5),X2),X212)) = hAPP(hAPP(c_List_Omap(X16,X5),X2),hAPP(hAPP(c_List_Odrop(X16),X76),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__map) ).

fof(fact_take__map,axiom,
    ! [X212,X2,X16,X76,X5] : hAPP(hAPP(c_List_Otake(X5),X76),hAPP(hAPP(c_List_Omap(X16,X5),X2),X212)) = hAPP(hAPP(c_List_Omap(X16,X5),X2),hAPP(hAPP(c_List_Otake(X16),X76),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__map) ).

fof(fact_filter__append,axiom,
    ! [X214,X212,X29,X5] : hAPP(c_List_Ofilter(X5,X29),hAPP(hAPP(c_List_Oappend(X5),X212),X214)) = hAPP(hAPP(c_List_Oappend(X5),hAPP(c_List_Ofilter(X5,X29),X212)),hAPP(c_List_Ofilter(X5,X29),X214)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__append) ).

fof(fact_wf__acc__iff,axiom,
    ! [X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
    <=> ! [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),c_Wellfounded_Oacc(X5,X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__acc__iff) ).

fof(fact_minus__Min__eq__Max,axiom,
    ! [X35,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
       => ( X35 != 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,X35)) = c_Big__Operators_Olinorder__class_OMax(X5,hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),X35)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Min__eq__Max) ).

fof(fact_minus__Max__eq__Min,axiom,
    ! [X35,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
       => ( X35 != 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,X35)) = c_Big__Operators_Olinorder__class_OMin(X5,hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),X35)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Max__eq__Min) ).

fof(fact_finite__UnionD,axiom,
    ! [X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X11)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UnionD) ).

fof(fact_Suc__times__mod__eq,axiom,
    ! [X99,X100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X100))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),X99)),X100) = 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_mod__mult__mult1,axiom,
    ! [X26,X25,X24,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X26)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),c_Divides_Odiv__class_Omod(X15,X25,X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__mult1) ).

fof(fact_INT__constant,axiom,
    ! [X21,X16,X5,X11] :
      ( ( X11 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X11),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X21)) = c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)) )
      & ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X11),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X21)) = X21 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__constant) ).

fof(fact_UN__constant,axiom,
    ! [X21,X16,X5,X11] :
      ( ( X11 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X11),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X21)) = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)) )
      & ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_HOL_Obool)),X11),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X5),X21)) = X21 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__constant) ).

fof(fact_Random__Sequence_Oempty__def,axiom,
    ! [X263,X264,X5] : c_Random__Sequence_Oempty(X5,X264,X263) = 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,
    ! [X26,X25,X24,X15] :
      ( class_Divides_Osemiring__div(X15)
     => ( ( X24 = c_Groups_Ozero__class_Ozero(X15)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X26)) = c_Groups_Ozero__class_Ozero(X15) )
        & ( X24 != c_Groups_Ozero__class_Ozero(X15)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X26)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),X25),X26) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__mult1__if) ).

fof(fact_mult__divide__mult__cancel__left,axiom,
    ! [X26,X25,X24,X15] :
      ( class_Fields_Ofield__inverse__zero(X15)
     => ( X24 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X26)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),X26) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).

fof(fact_mult__divide__mult__cancel__right,axiom,
    ! [X26,X25,X24,X15] :
      ( class_Fields_Ofield__inverse__zero(X15)
     => ( X24 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X24)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),X26) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).

fof(fact_div__mult__mult1,axiom,
    ! [X26,X25,X24,X15] :
      ( class_Divides_Osemiring__div(X15)
     => ( X24 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X26)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),X25),X26) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__mult1) ).

fof(fact_div__mult__mult2,axiom,
    ! [X26,X25,X24,X15] :
      ( class_Divides_Osemiring__div(X15)
     => ( X24 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X24)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),X25),X26) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__mult2) ).

fof(fact_nat__rec__Suc,axiom,
    ! [X111,X88,X89,X5] : hAPP(c_Nat_Onat_Onat__rec(X5,X89,X88),hAPP(c_Nat_OSuc,X111)) = hAPP(hAPP(X88,X111),hAPP(c_Nat_Onat_Onat__rec(X5,X89,X88),X111)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__rec__Suc) ).

fof(fact_trans__less__add1,axiom,
    ! [X99,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X101))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),X99))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).

fof(fact_termination__basic__simps_I1_J,axiom,
    ! [X23,X22,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),X22))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X23))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).

fof(fact_trans__less__add2,axiom,
    ! [X99,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X101))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X101))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).

fof(fact_termination__basic__simps_I2_J,axiom,
    ! [X22,X23,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),X23))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X23))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).

fof(fact_trans__le__add1,axiom,
    ! [X99,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X101))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),X99))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).

fof(fact_termination__basic__simps_I3_J,axiom,
    ! [X23,X22,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14),X22))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X23))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).

fof(fact_trans__le__add2,axiom,
    ! [X99,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X101))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X101))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).

fof(fact_termination__basic__simps_I4_J,axiom,
    ! [X22,X23,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14),X23))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X23))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).

fof(fact_mod__mult__self2,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X24)),X26) = c_Divides_Odiv__class_Omod(X15,X25,X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self2) ).

fof(fact_mod__mult__self1,axiom,
    ! [X26,X24,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X24),X26)),X26) = c_Divides_Odiv__class_Omod(X15,X25,X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self1) ).

fof(fact_less__Suc__eq__0__disj,axiom,
    ! [X76,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),hAPP(c_Nat_OSuc,X76)))
    <=> ( X45 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [X124] :
            ( X45 = hAPP(c_Nat_OSuc,X124)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X124),X76)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).

fof(fact_rotate1__hd__tl,axiom,
    ! [X15,X221] :
      ( X221 != c_List_Olist_ONil(X15)
     => hAPP(c_List_Orotate1(X15),X221) = hAPP(hAPP(c_List_Oappend(X15),hAPP(c_List_Otl(X15),X221)),hAPP(hAPP(c_List_Olist_OCons(X15),hAPP(c_List_Ohd(X15),X221)),c_List_Olist_ONil(X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__hd__tl) ).

fof(fact_fun__upd__def,axiom,
    ! [X17,X2,X16,X5,X6,X12] :
      ( ( X12 = X6
       => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),X2),X6),X17),X12) = X17 )
      & ( X12 != X6
       => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),X2),X6),X17),X12) = hAPP(X2,X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__def) ).

fof(fact_fun__upd__other,axiom,
    ! [X27,X2,X16,X5,X12,X37] :
      ( X37 != X12
     => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),X2),X12),X27),X37) = hAPP(X2,X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__other) ).

fof(fact_fun__upd__apply,axiom,
    ! [X27,X2,X16,X5,X12,X37] :
      ( ( X37 = X12
       => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),X2),X12),X27),X37) = X27 )
      & ( X37 != X12
       => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),X2),X12),X27),X37) = hAPP(X2,X37) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__apply) ).

fof(fact_setsum__set__upto__conv__listsum__int,axiom,
    ! [X115,X70,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(X70,X115))) = hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X5),X2),c_List_Oupto(X70,X115))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__set__upto__conv__listsum__int) ).

fof(fact_interv__listsum__conv__setsum__set__int,axiom,
    ! [X97,X30,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(X30,X97))) = 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(X30,X97))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_interv__listsum__conv__setsum__set__int) ).

fof(fact_min__max_Osup_Oassoc,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X25),X26)),X24) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X25),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X26),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup_Oassoc) ).

fof(fact_min__max_Osup__assoc,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),X22)),X23) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X22),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__assoc) ).

fof(fact_min__max_Oinf__assoc,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),X22)),X23) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X22),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__assoc) ).

fof(fact_min__max_Oinf_Oassoc,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X25),X26)),X24) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X25),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X26),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf_Oassoc) ).

fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Groups_Oab__semigroup__add(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26)),X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X26),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26)),X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X26),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

fof(fact_power__commutes,axiom,
    ! [X98,X25,X15] :
      ( class_Groups_Omonoid__mult(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)),X25) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__commutes) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
    ! [X117,X118,X119,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X119),X118)),X117) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X119),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X118),X117)) ),
    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,
    ! [X24,X26,X25,X15] :
      ( class_Groups_Oab__semigroup__mult(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26)),X24) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).

fof(fact_inf_Oassoc,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X25),X26)),X24) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X25),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X26),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oassoc) ).

fof(fact_inf__assoc,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X22)),X23) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X22),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__assoc) ).

fof(fact_inf__sup__aci_I2_J,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Lattices_Olattice(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X22)),X23) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X22),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I2_J) ).

fof(fact_inf__sup__aci_I6_J,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Lattices_Olattice(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X22)),X23) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X22),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I6_J) ).

fof(fact_sup_Oassoc,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X25),X26)),X24) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X25),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X26),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup_Oassoc) ).

fof(fact_sup__assoc,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X22)),X23) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X22),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__assoc) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
    ! [X41,X24,X25,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X24),X41)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X24)),X41) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

fof(fact_times__divide__eq__right,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Rings_Odivision__ring(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X26),X24)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26)),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
    ! [X116,X117,X119,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X119),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X117),X116)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X119),X117)),X116) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).

fof(fact_last__conv__nth,axiom,
    ! [X15,X221] :
      ( X221 != c_List_Olist_ONil(X15)
     => c_List_Olast(X15,X221) = hAPP(hAPP(c_List_Onth(X15),X221),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),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,
    ! [X112,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X112))
       => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),c_Nat_Osemiring__1__class_ONats(X5))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nats__number__of) ).

fof(fact_card__Pow,axiom,
    ! [X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => hAPP(c_Finite__Set_Ocard(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OPow(X5),X11)) = 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),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Pow) ).

fof(fact_atLeast__Suc,axiom,
    ! [X30] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X30)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X30),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,
    ! [X13,X11,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Compl) ).

fof(fact_Diff__eq,axiom,
    ! [X13,X11,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__eq) ).

fof(fact_zero__less__two,axiom,
    ! [X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),c_Groups_Oone__class_Oone(X15)),c_Groups_Oone__class_Oone(X15)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).

fof(fact_card__greaterThanLessThan__int,axiom,
    ! [X66,X97] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X97,X66)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X66),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X97),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__greaterThanLessThan__int) ).

fof(fact_nth__replicate,axiom,
    ! [X14,X15,X98,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X98))
     => hAPP(hAPP(c_List_Onth(X15),c_List_Oreplicate(X15,X98,X14)),X102) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__replicate) ).

fof(fact_gfp__upperbound,axiom,
    ! [X2,X31,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X31),hAPP(X2,X31)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X31),c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X2))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gfp__upperbound) ).

fof(fact_min__max_Osup__Inf__absorb,axiom,
    ! [X6,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X11)) = X6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__Inf__absorb) ).

fof(fact_min__max_Oinf__Sup__absorb,axiom,
    ! [X6,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X6),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X11)) = 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,
    ! [X13,X11,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__triv) ).

fof(fact_insort__not__Nil,axiom,
    ! [X212,X6,X2,X5,X16] :
      ( class_Orderings_Olinorder(X16)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X16,X2),X6),X212) != c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__not__Nil) ).

fof(fact_setprod__constant,axiom,
    ! [X27,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),hAPP(c_COMBK(X16,X5),X27)),X11) = hAPP(hAPP(c_Power_Opower__class_Opower(X16),X27),hAPP(c_Finite__Set_Ocard(X5),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__constant) ).

fof(fact_fold1__insert__idem,axiom,
    ! [X12,X11,X5] :
      ( class_Lattices_Oab__semigroup__idem__mult(X5)
     => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
         => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__insert__idem) ).

fof(fact_ivl__disj__int_I11_J,axiom,
    ! [X66,X45,X97,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,X97),X45)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X45),X66)) = 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,
    ! [X76,X45] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X45),hAPP(c_Nat_OSuc,X76)) = 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),X45),X76)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc) ).

fof(fact_append__assoc,axiom,
    ! [X242,X225,X221,X15] : hAPP(hAPP(c_List_Oappend(X15),hAPP(hAPP(c_List_Oappend(X15),X221),X225)),X242) = hAPP(hAPP(c_List_Oappend(X15),X221),hAPP(hAPP(c_List_Oappend(X15),X225),X242)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__assoc) ).

fof(fact_append__Cons,axiom,
    ! [X225,X221,X14,X15] : hAPP(hAPP(c_List_Oappend(X15),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)),X225) = hAPP(hAPP(c_List_Olist_OCons(X15),X14),hAPP(hAPP(c_List_Oappend(X15),X221),X225)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Cons) ).

fof(fact_take__Suc,axiom,
    ! [X98,X15,X221] :
      ( X221 != c_List_Olist_ONil(X15)
     => hAPP(hAPP(c_List_Otake(X15),hAPP(c_Nat_OSuc,X98)),X221) = hAPP(hAPP(c_List_Olist_OCons(X15),hAPP(c_List_Ohd(X15),X221)),hAPP(hAPP(c_List_Otake(X15),X98),hAPP(c_List_Otl(X15),X221))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Suc) ).

fof(fact_image__atLeastZeroLessThan__int,axiom,
    ! [X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X66))
     => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X66) = 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,X66))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__atLeastZeroLessThan__int) ).

fof(fact_nth__Cons_H,axiom,
    ! [X221,X14,X15,X98] :
      ( ( X98 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(X15),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)),X98) = X14 )
      & ( X98 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(X15),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)),X98) = hAPP(hAPP(c_List_Onth(X15),X221),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),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,
    ! [X21,X16,X5,X11] :
      ( ( X11 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(X5,X16,hAPP(c_COMBK(X16,X5),X21)),X11) = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)) )
      & ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(X5,X16,hAPP(c_COMBK(X16,X5),X21)),X11) = hAPP(hAPP(c_Set_Oinsert(X16),X21),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__constant__conv) ).

fof(fact_listsum__distinct__conv__setsum__set,axiom,
    ! [X2,X212,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),X212))
       => hAPP(c_List_Omonoid__add__class_Olistsum(X16),hAPP(hAPP(c_List_Omap(X5,X16),X2),X212)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),hAPP(c_List_Oset(X5),X212)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__distinct__conv__setsum__set) ).

fof(fact_power__mult,axiom,
    ! [X98,X99,X25,X15] :
      ( class_Groups_Omonoid__mult(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),X98)) = hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X99)),X98) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
    ! [X128,X129,X14,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),X129)),X128) = hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X129),X128)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).

fof(fact_mod__minus__eq,axiom,
    ! [X26,X25,X15] :
      ( class_Divides_Oring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25),X26) = c_Divides_Odiv__class_Omod(X15,hAPP(c_Groups_Ouminus__class_Ouminus(X15),c_Divides_Odiv__class_Omod(X15,X25,X26)),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__minus__eq) ).

fof(fact_tl__take,axiom,
    ! [X221,X98,X15] : hAPP(c_List_Otl(X15),hAPP(hAPP(c_List_Otake(X15),X98),X221)) = hAPP(hAPP(c_List_Otake(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X15),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl__take) ).

fof(fact_abs__power__minus,axiom,
    ! [X98,X25,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)),X98)) = hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__power__minus) ).

fof(fact_fun__upd__same,axiom,
    ! [X27,X12,X2,X5,X16] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X16,X5),X2),X12),X27),X12) = X27,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__same) ).

fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
    ! [X11,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),X11) = hAPP(c_Finite__Set_Ocard(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
       => X11 = 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,
    ! [X221,X14,X15,X98] :
      ( ( X98 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(X15),X98),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221) )
      & ( X98 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(X15),X98),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = hAPP(hAPP(c_List_Odrop(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X221) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__Cons_H) ).

fof(fact_neg__zminus__int,axiom,
    ! [X98] : 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,X98))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__zminus__int) ).

fof(fact_insert__code,axiom,
    ! [X12,X11,X27,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X5),X27),X11),X12))
    <=> ( X27 = X12
        | hBOOL(hAPP(X11,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__code) ).

fof(fact_lessThan__iff,axiom,
    ! [X30,X70,X5] :
      ( class_Orderings_Oord(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X70),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X30)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X70),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__iff) ).

fof(fact_greaterThan__iff,axiom,
    ! [X30,X70,X5] :
      ( class_Orderings_Oord(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X70),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X30)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),X70)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThan__iff) ).

fof(fact_atMost__iff,axiom,
    ! [X30,X70,X5] :
      ( class_Orderings_Oord(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X70),hAPP(c_SetInterval_Oord__class_OatMost(X5),X30)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X70),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__iff) ).

fof(fact_atLeast__iff,axiom,
    ! [X30,X70,X5] :
      ( class_Orderings_Oord(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X70),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X30)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X30),X70)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast__iff) ).

fof(fact_image__uminus__greaterThanAtMost,axiom,
    ! [X27,X12,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,X12,X27)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X27)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__greaterThanAtMost) ).

fof(fact_folding__one__idem_Oin__idem,axiom,
    ! [X12,X11,X90,X2,X5] :
      ( c_Finite__Set_Ofolding__one__idem(X5,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(hAPP(X2,X12),hAPP(X90,X11)) = hAPP(X90,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oin__idem) ).

fof(fact_Max__ge,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),c_Big__Operators_Olinorder__class_OMax(X5,X11))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max__ge) ).

fof(fact_listsum__setsum__nth,axiom,
    ! [X212,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),X212) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(c_List_Onth(X5),X212)),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)),X212))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__setsum__nth) ).

fof(fact_zdiff__int,axiom,
    ! [X99,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X99))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X99)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X98)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__int) ).

fof(fact_odd__nonzero,axiom,
    ! [X23] : 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)),X23)),X23) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).

fof(fact_Field__def,axiom,
    ! [X34,X5] : hAPP(c_Relation_OField(X5),X34) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X5),X34)),hAPP(c_Relation_ORange(X5,X5),X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__def) ).

fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
    ! [X76,X45] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X45,X76) = 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),X45),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X76))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I2_J) ).

fof(fact_div__mult__self1__is__m,axiom,
    ! [X99,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X98))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X99)),X98) = X99 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self1__is__m) ).

fof(fact_div__mult__self__is__m,axiom,
    ! [X99,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X98))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),X98)),X98) = X99 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self__is__m) ).

fof(fact_zmod__zminus2__eq__if,axiom,
    ! [X26,X25] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26)),X26) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus2__eq__if) ).

fof(fact_subset__UNIV,axiom,
    ! [X11,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),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,
    ! [X100,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X102),X101))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),X100))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X102),X100)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).

fof(fact_le__trans,axiom,
    ! [X100,X101,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X101))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X101),X100))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X100)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
    ! [X99,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X99),X99) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),c_Groups_Oone__class_Oone(X15)),c_Groups_Oone__class_Oone(X15))),X99) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

fof(fact_less__add__eq__less,axiom,
    ! [X98,X99,X103,X100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X100),X103))
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X103) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),X98)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).

fof(fact_Suc__lessD,axiom,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X99)),X98))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).

fof(fact_less__eq__Suc__le,axiom,
    ! [X45,X76] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),X45))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X76)),X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).

fof(fact_Suc__le__eq,axiom,
    ! [X76,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X45)),X76))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__eq) ).

fof(fact_Suc__le__lessD,axiom,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X99)),X98))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).

fof(fact_Suc__leD,axiom,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X99)),X98))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leD) ).

fof(fact_drop__drop,axiom,
    ! [X221,X99,X98,X15] : hAPP(hAPP(c_List_Odrop(X15),X98),hAPP(hAPP(c_List_Odrop(X15),X99),X221)) = hAPP(hAPP(c_List_Odrop(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X99)),X221),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__drop) ).

fof(fact_take__take,axiom,
    ! [X221,X99,X98,X15] : hAPP(hAPP(c_List_Otake(X15),X98),hAPP(hAPP(c_List_Otake(X15),X99),X221)) = hAPP(hAPP(c_List_Otake(X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X98),X99)),X221),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__take) ).

fof(fact_Inf__lower,axiom,
    ! [X11,X12,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Complete__Lattice_OInf__class_OInf(X5,X11)),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__lower) ).

fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
    ! [X29] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
         => hBOOL(hAPP(X29,X3)) )
    <=> ! [X3] : hBOOL(hAPP(X29,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,
    ! [X22,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14),X22)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X14)),hAPP(c_Int_Onat,X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__div__distrib) ).

fof(fact_nat__mult__distrib,axiom,
    ! [X139,X23] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X139)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X23)),hAPP(c_Int_Onat,X139)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__distrib) ).

fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
    ! [X76,X45] :
      ( c_Nat__Transfer_Ois__nat(X45)
     => ( c_Nat__Transfer_Ois__nat(X76)
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X45,X76) = 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,X45),hAPP(c_Int_Onat,X76))) ) ),
    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,
    ! [X98,X99,X100] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),X99),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__distrib2) ).

fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
    ! [X13,X11] :
      ( X11 = X13
    <=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X11) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I3_J) ).

fof(fact_set__append,axiom,
    ! [X214,X212,X5] : hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Oappend(X5),X212),X214)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X212)),hAPP(c_List_Oset(X5),X214)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__append) ).

fof(fact_Suc__mono,axiom,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X99)),hAPP(c_Nat_OSuc,X98))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).

fof(fact_power__inject__exp,axiom,
    ! [X76,X45,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),X45) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X76)
        <=> X45 = X76 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__exp) ).

fof(fact_listset_Osimps_I2_J,axiom,
    ! [X238,X11,X5] : c_List_Olistset(X5,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X5,tc_HOL_Obool)),X11),X238)) = c_List_Oset__Cons(X5,X11,c_List_Olistset(X5,X238)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listset_Osimps_I2_J) ).

fof(fact_Sup__fold__sup,axiom,
    ! [X11,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => c_Complete__Lattice_OSup__class_OSup(X5,X11) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),c_Orderings_Obot__class_Obot(X5)),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fold__sup) ).

fof(fact_Inf__fold__inf,axiom,
    ! [X11,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => c_Complete__Lattice_OInf__class_OInf(X5,X11) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),c_Orderings_Otop__class_Otop(X5)),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fold__inf) ).

fof(fact_power__eq__if,axiom,
    ! [X129,X99] :
      ( ( X99 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X129),X99) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X99 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X129),X99) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X129),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X129),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),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,
    ! [X27,X12,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,X12,X27)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X27),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__atLeastAtMost) ).

fof(fact_image__uminus__greaterThanLessThan,axiom,
    ! [X27,X12,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,X12,X27)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X5,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X27),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__greaterThanLessThan) ).

fof(fact_lessThan__Suc__eq__insert__0,axiom,
    ! [X76] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X76)) = 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),X76))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__Suc__eq__insert__0) ).

fof(fact_div__mod__code__numeral__def,axiom,
    ! [X99,X98] : c_Code__Numeral_Odiv__mod__code__numeral(X98,X99) = 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),X98),X99)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X98,X99)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mod__code__numeral__def) ).

fof(fact_divmod__int__mod__div,axiom,
    ! [X128,X129] : c_Divides_Odivmod__int(X129,X128) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X129),X128)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X129,X128)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__mod__div) ).

fof(fact_zminus__zmod,axiom,
    ! [X99,X14] : 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,X14,X99)),X99) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X14),X99),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zmod) ).

fof(fact_transfer__nat__int__relations_I1_J,axiom,
    ! [X27,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X27))
       => ( hAPP(c_Int_Onat,X12) = hAPP(c_Int_Onat,X27)
        <=> X12 = X27 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I1_J) ).

fof(fact_eq__nat__nat__iff,axiom,
    ! [X170,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X170))
       => ( hAPP(c_Int_Onat,X37) = hAPP(c_Int_Onat,X170)
        <=> X37 = X170 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__nat__nat__iff) ).

fof(fact_zless__iff__Suc__zadd,axiom,
    ! [X37,X112] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X112),X37))
    <=> ? [X107] : X37 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X112),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X107))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__iff__Suc__zadd) ).

fof(fact_div__mod__equality_H,axiom,
    ! [X98,X99] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),X98)),X98) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mod__equality_H) ).

fof(fact_le__add__diff__inverse2,axiom,
    ! [X99,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X99))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98)),X98) = X99 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).

fof(fact_zero__less__int__conv,axiom,
    ! [X76] :
      ( 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),X76)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__int__conv) ).

fof(fact_int__eq__iff__number__of,axiom,
    ! [X56,X45] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X45) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X56)
    <=> ( X45 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),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),X56))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__eq__iff__number__of) ).

fof(fact_ranI,axiom,
    ! [X16,X17,X5,X6,X45] :
      ( hAPP(X45,X6) = hAPP(c_Option_Ooption_OSome(X5),X17)
     => hBOOL(hAPP(hAPP(c_member(X5),X17),c_Map_Oran(X16,X5,X45))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ranI) ).

fof(fact_domI,axiom,
    ! [X16,X17,X5,X6,X45] :
      ( hAPP(X45,X6) = hAPP(c_Option_Ooption_OSome(X5),X17)
     => hBOOL(hAPP(hAPP(c_member(X16),X6),c_Map_Odom(X16,X5,X45))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_domI) ).

fof(fact_finite__Pow__iff,axiom,
    ! [X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OPow(X5),X11)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Pow__iff) ).

fof(fact_DomainP_Ointros,axiom,
    ! [X16,X5,X17,X6,X34] :
      ( hBOOL(hAPP(hAPP(X34,X6),X17))
     => hBOOL(hAPP(c_Predicate_ODomainP(X5,X16,X34),X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).

fof(fact_RangeP_Ointros,axiom,
    ! [X16,X5,X17,X6,X34] :
      ( hBOOL(hAPP(hAPP(X34,X6),X17))
     => hBOOL(hAPP(c_Predicate_ORangeP(X5,X16,X34),X17)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).

fof(fact_enum__option__def,axiom,
    ! [X5] :
      ( class_Enum_Oenum(X5)
     => c_Enum_Oenum__class_Oenum(tc_Option_Ooption(X5)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(X5)),c_Option_Ooption_ONone(X5)),hAPP(hAPP(c_List_Omap(X5,tc_Option_Ooption(X5)),c_Option_Ooption_OSome(X5)),c_Enum_Oenum__class_Oenum(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__option__def) ).

fof(fact_length__splice,axiom,
    ! [X225,X221,X15] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),c_List_Osplice(X15,X221,X225)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X225)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__splice) ).

fof(fact_length__greater__0__conv,axiom,
    ! [X212,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)),X212)))
    <=> X212 != 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,
    ! [X66,X97,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,X97),X66)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X66)) = 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,
    ! [X76,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),hAPP(c_Nat_OSuc,X45)))
      <=> X76 = X45 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).

fof(fact_mod__pos__pos__trivial,axiom,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),X26))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26) = X25 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__pos__trivial) ).

fof(fact_atMost__Int__atLeast,axiom,
    ! [X76,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),X76)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X76)) = hAPP(hAPP(c_Set_Oinsert(X5),X76),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,
    ! [X225,X221,X15] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),hAPP(hAPP(c_List_Oappend(X15),X221),X225)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X225)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__append) ).

fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
    ! [X13,X11] :
      ( c_Nat__Transfer_Onat__set(X11)
     => ( c_Nat__Transfer_Onat__set(X13)
       => ( X11 = X13
        <=> hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X11) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X13) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I3_J) ).

fof(fact_setprod__zero,axiom,
    ! [X2,X11,X5,X16] :
      ( class_Rings_Ocomm__semiring__1(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ? [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
              & hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X16) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),X11) = c_Groups_Ozero__class_Ozero(X16) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__zero) ).

fof(fact_nat__mult__div__cancel__disj,axiom,
    ! [X98,X99,X100] :
      ( ( X100 = 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),X100),X99)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),X98)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X100 != 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),X100),X99)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X100),X98)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),X98) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__div__cancel__disj) ).

fof(fact_Pow__top,axiom,
    ! [X11,X5] : hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Set_OPow(X5),X11))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__top) ).

fof(fact_rev_Osimps_I2_J,axiom,
    ! [X221,X14,X15] : hAPP(c_List_Orev(X15),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = hAPP(hAPP(c_List_Oappend(X15),hAPP(c_List_Orev(X15),X221)),hAPP(hAPP(c_List_Olist_OCons(X15),X14),c_List_Olist_ONil(X15))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev_Osimps_I2_J) ).

fof(fact_zdiv__eq__0__iff,axiom,
    ! [X30,X70] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X70),X30) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> ( X30 = 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)),X70))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X70),X30)) )
        | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X70),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),X70)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).

fof(fact_div__pos__pos__trivial,axiom,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),X26))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__pos__trivial) ).

fof(fact_Inf__le__Sup,axiom,
    ! [X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != 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,X11)),c_Big__Operators_Olattice__class_OSup__fin(X5,X11))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__le__Sup) ).

fof(fact_map__replicate__const,axiom,
    ! [X278,X30,X5,X16] : hAPP(hAPP(c_List_Omap(X16,X5),hAPP(c_COMBK(X5,X16),X30)),X278) = c_List_Oreplicate(X5,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X278),X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__replicate__const) ).

fof(fact_equivp__transp,axiom,
    ! [X37,X27,X12,X36,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X36)
     => ( hBOOL(hAPP(hAPP(X36,X12),X27))
       => ( hBOOL(hAPP(hAPP(X36,X27),X37))
         => hBOOL(hAPP(hAPP(X36,X12),X37)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__transp) ).

fof(fact_folding__one__idem_Oinsert__idem,axiom,
    ! [X12,X11,X90,X2,X5] :
      ( c_Finite__Set_Ofolding__one__idem(X5,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(X90,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(X2,X12),hAPP(X90,X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oinsert__idem) ).

fof(fact_mod__minus__cong,axiom,
    ! [X81,X26,X25,X15] :
      ( class_Divides_Oring__div(X15)
     => ( c_Divides_Odiv__class_Omod(X15,X25,X26) = c_Divides_Odiv__class_Omod(X15,X81,X26)
       => c_Divides_Odiv__class_Omod(X15,hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25),X26) = c_Divides_Odiv__class_Omod(X15,hAPP(c_Groups_Ouminus__class_Ouminus(X15),X81),X26) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__minus__cong) ).

fof(fact_sublists__powset,axiom,
    ! [X212,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,X212))) = hAPP(c_Set_OPow(X5),hAPP(c_List_Oset(X5),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublists__powset) ).

fof(fact_Union__def,axiom,
    ! [X35,X5] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X35) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X35),c_COMBI(tc_fun(X5,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__def) ).

fof(fact_Inter__def,axiom,
    ! [X35,X5] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X35) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X35),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,
    ! [X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X37)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> X37 = 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,
    ! [X76] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X76)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__le__0__conv) ).

fof(fact_empty__map__add,axiom,
    ! [X45,X16,X5] : c_Map_Omap__add(X5,X16,hAPP(c_COMBK(tc_Option_Ooption(X16),X5),c_Option_Ooption_ONone(X16)),X45) = X45,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__map__add) ).

fof(fact_map__add__empty,axiom,
    ! [X45,X16,X5] : c_Map_Omap__add(X5,X16,X45,hAPP(c_COMBK(tc_Option_Ooption(X16),X5),c_Option_Ooption_ONone(X16))) = X45,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__add__empty) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
    ! [X98,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))
     => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X14)),X98) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J) ).

fof(fact_nat__power__eq,axiom,
    ! [X98,X23] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X23),X98)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X23)),X98) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__eq) ).

fof(fact_diff__cancel,axiom,
    ! [X98,X99,X100] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),X99)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),X98)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel) ).

fof(fact_diff__cancel2,axiom,
    ! [X98,X100,X99] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X100)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X100)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel2) ).

fof(fact_zpower__zpower,axiom,
    ! [X23,X22,X14] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14),X22)),X23) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X23)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zpower) ).

fof(fact_zadd__assoc,axiom,
    ! [X135,X133,X134] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X134),X133)),X135) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X134),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X133),X135)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).

fof(fact_nat__add__assoc,axiom,
    ! [X100,X98,X99] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X98)),X100) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X100)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).

fof(fact_zmult__assoc,axiom,
    ! [X135,X133,X134] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X134),X133)),X135) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X134),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X133),X135)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).

fof(fact_nat__mult__assoc,axiom,
    ! [X100,X98,X99] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),X98)),X100) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X100)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).

fof(fact_diff__diff__left,axiom,
    ! [X100,X101,X102] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X102),X101)),X100) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X102),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),X100)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__left) ).

fof(fact_div__mult2__eq,axiom,
    ! [X24,X26,X25] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X24)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X25),X26)),X24),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult2__eq) ).

fof(fact_ball__empty,axiom,
    ! [X29,X5,X3] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
     => hBOOL(hAPP(X29,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ball__empty) ).

fof(fact_ivl__disj__int_I3_J,axiom,
    ! [X66,X97,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),X97)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X97,X66)) = 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,
    ! [X66,X97,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),X97)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X97,X66)) = 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,
    ! [X66,X97,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),X97)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X97,X66)) = 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,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),X25))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26) = X25 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__neg__neg__trivial) ).

fof(fact_set__map,axiom,
    ! [X212,X2,X16,X5] : hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Omap(X16,X5),X2),X212)) = hAPP(c_Set_Oimage(X16,X5,X2),hAPP(c_List_Oset(X16),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__map) ).

fof(fact_exists1__code,axiom,
    ! [X29,X5] :
      ( class_Enum_Oenum(X5)
     => ( ? [X3] :
            ( hBOOL(hAPP(X29,X3))
            & ! [X33] :
                ( hBOOL(hAPP(X29,X33))
               => X33 = X3 ) )
      <=> c_List_Olist__ex1(X5,X29,c_Enum_Oenum__class_Oenum(X5)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exists1__code) ).

fof(fact_append__take__drop__id,axiom,
    ! [X221,X98,X15] : hAPP(hAPP(c_List_Oappend(X15),hAPP(hAPP(c_List_Otake(X15),X98),X221)),hAPP(hAPP(c_List_Odrop(X15),X98),X221)) = X221,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__take__drop__id) ).

fof(fact_mod__Suc__eq__Suc__mod,axiom,
    ! [X98,X99] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X99),X98) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98)),X98),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__Suc__eq__Suc__mod) ).

fof(fact_less__0__number__of,axiom,
    ! [X56] :
      ( 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),X56)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X56)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__0__number__of) ).

fof(fact_list__ex__append,axiom,
    ! [X214,X212,X29,X5] :
      ( c_List_Olist__ex(X5,X29,hAPP(hAPP(c_List_Oappend(X5),X212),X214))
    <=> ( c_List_Olist__ex(X5,X29,X212)
        | c_List_Olist__ex(X5,X29,X214) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__append) ).

fof(fact_div__neg__neg__trivial,axiom,
    ! [X26,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),X25))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26) = 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,
    ! [X221,X14,X98,X15] : hAPP(hAPP(c_List_Otake(X15),hAPP(c_Nat_OSuc,X98)),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = hAPP(hAPP(c_List_Olist_OCons(X15),X14),hAPP(hAPP(c_List_Otake(X15),X98),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Suc__Cons) ).

fof(fact_small__lazy__prod__def,axiom,
    ! [X41,X5,X15] :
      ( ( class_Lazy__Sequence_Osmall__lazy(X15)
        & class_Lazy__Sequence_Osmall__lazy(X5) )
     => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(X15,X5),X41) = c_Lazy__Sequence_Oproduct(X15,X5,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X15,X41),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X5,X41)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small__lazy__prod__def) ).

fof(fact_map__eq__imp__length__eq,axiom,
    ! [X214,X1,X38,X212,X2,X5,X16] :
      ( hAPP(hAPP(c_List_Omap(X16,X5),X2),X212) = hAPP(hAPP(c_List_Omap(X38,X5),X1),X214)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X38)),X214) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__eq__imp__length__eq) ).

fof(fact_length__sublists,axiom,
    ! [X221,X15] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X15))),c_Enum_Osublists(X15,X221)) = 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(X15)),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__sublists) ).

fof(fact_transfer__int__nat__set__return__embed,axiom,
    ! [X11] : 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)),X11)) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__set__return__embed) ).

fof(fact_fst__eqD,axiom,
    ! [X25,X22,X14,X5,X15] :
      ( hAPP(c_Product__Type_Ofst(X15,X5),hAPP(hAPP(c_Product__Type_OPair(X15,X5),X14),X22)) = X25
     => X14 = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__eqD) ).

fof(fact_snd__eqD,axiom,
    ! [X25,X22,X14,X15,X5] :
      ( hAPP(c_Product__Type_Osnd(X5,X15),hAPP(hAPP(c_Product__Type_OPair(X5,X15),X14),X22)) = X25
     => X22 = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__eqD) ).

fof(fact_transfer__nat__int__set__return__embed,axiom,
    ! [X11] :
      ( c_Nat__Transfer_Onat__set(X11)
     => 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),X11)) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__set__return__embed) ).

fof(fact_finite__Field,axiom,
    ! [X34,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X34))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Relation_OField(X5),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Field) ).

fof(fact_image__uminus__atLeastLessThan,axiom,
    ! [X27,X12,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,X12),X27)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X5,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X27),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__atLeastLessThan) ).

fof(fact_strict__mono__imp__inj__on,axiom,
    ! [X11,X2,X5,X16] :
      ( ( class_Orderings_Oorder(X16)
        & class_Orderings_Olinorder(X5) )
     => ( c_Orderings_Oorder__class_Ostrict__mono(X5,X16,X2)
       => c_Fun_Oinj__on(X5,X16,X2,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_strict__mono__imp__inj__on) ).

fof(fact_Suc__lessI,axiom,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
     => ( hAPP(c_Nat_OSuc,X99) != X98
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X99)),X98)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).

fof(fact_finite__nat__set__iff__bounded,axiom,
    ! [X93] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X93))
    <=> ? [X94] :
        ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X93))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X94)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).

fof(fact_finite__nat__set__iff__bounded__le,axiom,
    ! [X93] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X93))
    <=> ? [X94] :
        ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X93))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X94)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).

fof(fact_diff__number__of__eq,axiom,
    ! [X132,X126,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X126)),hAPP(c_Int_Onumber__class_Onumber__of(X15),X132)) = hAPP(c_Int_Onumber__class_Onumber__of(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X126),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X132))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__number__of__eq) ).

fof(fact_distinct__n__lists,axiom,
    ! [X98,X221,X15] :
      ( hBOOL(hAPP(c_List_Odistinct(X15),X221))
     => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X15)),c_Enum_On__lists(X15,X98,X221))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__n__lists) ).

fof(fact_max__of__mono,axiom,
    ! [X76,X45,X2,X5,X16] :
      ( ( class_Orderings_Olinorder(X16)
        & class_Orderings_Olinorder(X5) )
     => ( c_Orderings_Oorder__class_Omono(X5,X16,X2)
       => hAPP(hAPP(c_Orderings_Oord__class_Omax(X16),hAPP(X2,X45)),hAPP(X2,X76)) = hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X45),X76)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__of__mono) ).

fof(fact_min__of__mono,axiom,
    ! [X76,X45,X2,X5,X16] :
      ( ( class_Orderings_Olinorder(X16)
        & class_Orderings_Olinorder(X5) )
     => ( c_Orderings_Oorder__class_Omono(X5,X16,X2)
       => hAPP(hAPP(c_Orderings_Oord__class_Omin(X16),hAPP(X2,X45)),hAPP(X2,X76)) = hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X45),X76)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__of__mono) ).

fof(fact_zero__less__nat__eq,axiom,
    ! [X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X37)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__nat__eq) ).

fof(fact_butlast__snoc,axiom,
    ! [X14,X221,X15] : c_List_Obutlast(X15,hAPP(hAPP(c_List_Oappend(X15),X221),hAPP(hAPP(c_List_Olist_OCons(X15),X14),c_List_Olist_ONil(X15)))) = X221,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__snoc) ).

fof(fact_last__snoc,axiom,
    ! [X14,X221,X15] : c_List_Olast(X15,hAPP(hAPP(c_List_Oappend(X15),X221),hAPP(hAPP(c_List_Olist_OCons(X15),X14),c_List_Olist_ONil(X15)))) = X14,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__snoc) ).

fof(fact_rtrancl__idemp__self__comp,axiom,
    ! [X36,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),c_Transitive__Closure_Ortrancl(X5,X36)),c_Transitive__Closure_Ortrancl(X5,X36)) = c_Transitive__Closure_Ortrancl(X5,X36),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__idemp__self__comp) ).

fof(fact_fst__def,axiom,
    ! [X161,X16,X5] : hAPP(c_Product__Type_Ofst(X5,X16),X161) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,X5),c_COMBK(X5,X16)),X161),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__def) ).

fof(fact_finite__acyclic__wf__converse,axiom,
    ! [X34,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X34))
     => ( c_Wellfounded_Oacyclic(X5,X34)
       => c_Wellfounded_Owf(X5,hAPP(c_Relation_Oconverse(X5,X5),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__acyclic__wf__converse) ).

fof(fact_order__eq__iff,axiom,
    ! [X27,X12,X5] :
      ( class_Orderings_Oorder(X5)
     => ( X12 = X27
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X27),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).

fof(fact_order__antisym__conv,axiom,
    ! [X12,X27,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X27),X12))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27))
        <=> X12 = X27 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).

fof(fact_order__antisym,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Oorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X14))
         => X14 = X22 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).

fof(fact_xt1_I5_J,axiom,
    ! [X14,X22,X15] :
      ( class_Orderings_Oorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22))
         => X14 = X22 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).

fof(fact_le__mod__geq,axiom,
    ! [X99,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X99))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98),X98) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__mod__geq) ).

fof(fact_in__set__insert,axiom,
    ! [X212,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => c_List_Oinsert(X5,X12,X212) = X212 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__insert) ).

fof(fact_Suc__diff__le,axiom,
    ! [X99,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X99))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X99)),X98) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__le) ).

fof(fact_abs__ge__minus__self,axiom,
    ! [X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)),hAPP(c_Groups_Oabs__class_Oabs(X15),X25))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__minus__self) ).

fof(fact_zero__le__square,axiom,
    ! [X25,X15] :
      ( class_Rings_Olinordered__ring(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X25))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).

fof(fact_less__add__one,axiom,
    ! [X25,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),c_Groups_Oone__class_Oone(X15)))) ),
    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,X17,X34,X5] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X34),X17))
     => ( hBOOL(hAPP(hAPP(X34,X6),X17))
       => hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X34),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__downward) ).

fof(fact_hd__in__set,axiom,
    ! [X5,X212] :
      ( X212 != c_List_Olist_ONil(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_List_Ohd(X5),X212)),hAPP(c_List_Oset(X5),X212))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__in__set) ).

fof(fact_lazy__sequence_Osize_I4_J,axiom,
    ! [X271,X25,X15] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X15)),c_Lazy__Sequence_Olazy__sequence_OInsert(X15,X25,X271)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X15)),X271)),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,
    ! [X128,X14,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),X128)),X14) = hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),hAPP(c_Nat_OSuc,X128)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).

fof(fact_power__Suc2,axiom,
    ! [X98,X25,X15] :
      ( class_Groups_Omonoid__mult(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),hAPP(c_Nat_OSuc,X98)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc2) ).

fof(fact_sorted__list__of__set__sort__remdups,axiom,
    ! [X212,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Olinorder__class_Osorted__list__of__set(X5,hAPP(c_List_Oset(X5),X212)) = c_List_Olinorder__class_Osort__key(X5,X5,c_COMBI(X5),c_List_Oremdups(X5,X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__list__of__set__sort__remdups) ).

fof(fact_map__upd__triv,axiom,
    ! [X16,X12,X5,X30,X10] :
      ( hAPP(X10,X30) = hAPP(c_Option_Ooption_OSome(X5),X12)
     => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X16,tc_Option_Ooption(X5)),X10),X30),hAPP(c_Option_Ooption_OSome(X5),X12)) = X10 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__upd__triv) ).

fof(fact_list_Osize_I4_J,axiom,
    ! [X226,X25,X15] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),hAPP(hAPP(c_List_Olist_OCons(X15),X25),X226)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X226)),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,
    ! [X221,X98,X15] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X15))),c_Enum_On__lists(X15,X98,X221)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),X98),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__n__lists) ).

fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
    ! [X29] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
          & hBOOL(hAPP(X29,X3)) )
    <=> ? [X3] : hBOOL(hAPP(X29,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,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X99)),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).

fof(fact_Max_Oin__idem,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X12),c_Big__Operators_Olinorder__class_OMax(X5,X11)) = c_Big__Operators_Olinorder__class_OMax(X5,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oin__idem) ).

fof(fact_Min_Oin__idem,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X12),c_Big__Operators_Olinorder__class_OMin(X5,X11)) = c_Big__Operators_Olinorder__class_OMin(X5,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oin__idem) ).

fof(fact_Inf__fin_Oin__idem,axiom,
    ! [X12,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X12),c_Big__Operators_Olattice__class_OInf__fin(X5,X11)) = c_Big__Operators_Olattice__class_OInf__fin(X5,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oin__idem) ).

fof(fact_Sup__fin_Oin__idem,axiom,
    ! [X12,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X12),c_Big__Operators_Olattice__class_OSup__fin(X5,X11)) = c_Big__Operators_Olattice__class_OSup__fin(X5,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oin__idem) ).

fof(fact_Sup__upper,axiom,
    ! [X11,X12,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),c_Complete__Lattice_OSup__class_OSup(X5,X11))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__upper) ).

fof(fact_list__ex__simps_I1_J,axiom,
    ! [X212,X12,X29,X5] :
      ( c_List_Olist__ex(X5,X29,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212))
    <=> ( hBOOL(hAPP(X29,X12))
        | c_List_Olist__ex(X5,X29,X212) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__simps_I1_J) ).

fof(fact_ivl__disj__int_I2_J,axiom,
    ! [X66,X97,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),X97)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X97),X66)) = 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,
    ! [X11,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),X11)))
    <=> ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__gt__0__iff) ).

fof(fact_nth__Cons__Suc,axiom,
    ! [X98,X221,X14,X15] : hAPP(hAPP(c_List_Onth(X15),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)),hAPP(c_Nat_OSuc,X98)) = hAPP(hAPP(c_List_Onth(X15),X221),X98),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__Cons__Suc) ).

fof(fact_map__tl,axiom,
    ! [X212,X2,X5,X16] : hAPP(hAPP(c_List_Omap(X16,X5),X2),hAPP(c_List_Otl(X16),X212)) = hAPP(c_List_Otl(X5),hAPP(hAPP(c_List_Omap(X16,X5),X2),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__tl) ).

fof(fact_rev__map,axiom,
    ! [X212,X2,X16,X5] : hAPP(c_List_Orev(X5),hAPP(hAPP(c_List_Omap(X16,X5),X2),X212)) = hAPP(hAPP(c_List_Omap(X16,X5),X2),hAPP(c_List_Orev(X16),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__map) ).

fof(fact_ex__nat,axiom,
    ! [X29] :
      ( ? [X32] : hBOOL(hAPP(X29,X32))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
          & hBOOL(hAPP(X29,hAPP(c_Int_Onat,X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__nat) ).

fof(fact_card__ge__0__finite,axiom,
    ! [X11,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),X11)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).

fof(fact_list__all__append,axiom,
    ! [X214,X212,X29,X5] :
      ( c_List_Olist__all(X5,X29,hAPP(hAPP(c_List_Oappend(X5),X212),X214))
    <=> ( c_List_Olist__all(X5,X29,X212)
        & c_List_Olist__all(X5,X29,X214) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__append) ).

fof(fact_Suc__pred,axiom,
    ! [X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X98))
     => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X98 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred) ).

fof(fact_singleton__inject,axiom,
    ! [X17,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),X17),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))
     => X6 = X17 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__inject) ).

fof(fact_of__nat__inverse,axiom,
    ! [X27] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X27),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,X27)) = X27 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__inverse) ).

fof(fact_divide__eq__eq__number__of,axiom,
    ! [X112,X21,X17,X5] :
      ( ( class_Fields_Ofield__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X17),X21) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)
      <=> ( ( X21 != c_Groups_Ozero__class_Ozero(X5)
           => X17 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),X21) )
          & ( X21 = c_Groups_Ozero__class_Ozero(X5)
           => hAPP(c_Int_Onumber__class_Onumber__of(X5),X112) = 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,
    ! [X21,X17,X112,X5] :
      ( ( class_Fields_Ofield__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X112) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X17),X21)
      <=> ( ( X21 != c_Groups_Ozero__class_Ozero(X5)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),X21) = X17 )
          & ( X21 = c_Groups_Ozero__class_Ozero(X5)
           => hAPP(c_Int_Onumber__class_Onumber__of(X5),X112) = 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,
    ! [X76,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),hAPP(c_Nat_OSuc,X76)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76))
        | X45 = hAPP(c_Nat_OSuc,X76) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__eq) ).

fof(fact_append__butlast__last__id,axiom,
    ! [X15,X221] :
      ( X221 != c_List_Olist_ONil(X15)
     => hAPP(hAPP(c_List_Oappend(X15),c_List_Obutlast(X15,X221)),hAPP(hAPP(c_List_Olist_OCons(X15),c_List_Olast(X15,X221)),c_List_Olist_ONil(X15))) = X221 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__butlast__last__id) ).

fof(fact_pair__collapse,axiom,
    ! [X129,X5,X15] : hAPP(hAPP(c_Product__Type_OPair(X15,X5),hAPP(c_Product__Type_Ofst(X15,X5),X129)),hAPP(c_Product__Type_Osnd(X15,X5),X129)) = X129,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__collapse) ).

fof(fact_surjective__pairing,axiom,
    ! [X5,X15,X104] : X104 = hAPP(hAPP(c_Product__Type_OPair(X15,X5),hAPP(c_Product__Type_Ofst(X15,X5),X104)),hAPP(c_Product__Type_Osnd(X15,X5),X104)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surjective__pairing) ).

fof(fact_insort__key_Osimps_I1_J,axiom,
    ! [X12,X2,X5,X16] :
      ( class_Orderings_Olinorder(X16)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X16,X2),X12),c_List_Olist_ONil(X5)) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Olist_ONil(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__key_Osimps_I1_J) ).

fof(fact_fun__upd__idem__iff,axiom,
    ! [X27,X12,X2,X16,X5] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),X2),X12),X27) = X2
    <=> hAPP(X2,X12) = X27 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).

fof(fact_distinct__insert,axiom,
    ! [X14,X221,X15] :
      ( hBOOL(hAPP(c_List_Odistinct(X15),X221))
     => hBOOL(hAPP(c_List_Odistinct(X15),c_List_Oinsert(X15,X14,X221))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__insert) ).

fof(fact_distinct__takeWhile,axiom,
    ! [X29,X212,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X212))
     => hBOOL(hAPP(c_List_Odistinct(X5),c_List_OtakeWhile(X5,X29,X212))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__takeWhile) ).

fof(fact_distinct__remove1,axiom,
    ! [X14,X221,X15] :
      ( hBOOL(hAPP(c_List_Odistinct(X15),X221))
     => hBOOL(hAPP(c_List_Odistinct(X15),c_List_Oremove1(X15,X14,X221))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__remove1) ).

fof(fact_distinct__sublistI,axiom,
    ! [X68,X212,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X212))
     => hBOOL(hAPP(c_List_Odistinct(X5),c_List_Osublist(X5,X212,X68))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__sublistI) ).

fof(fact__03,axiom,
    ! [X274,X270,X14,X15] : c_Lazy__Sequence_Oappend(X15,c_Lazy__Sequence_Olazy__sequence_OInsert(X15,X14,X270),X274) = c_Lazy__Sequence_Olazy__sequence_OInsert(X15,X14,c_Lazy__Sequence_Oappend(X15,X270,X274)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__03) ).

fof(fact_remove1__commute,axiom,
    ! [X242,X22,X14,X15] : c_List_Oremove1(X15,X14,c_List_Oremove1(X15,X22,X242)) = c_List_Oremove1(X15,X22,c_List_Oremove1(X15,X14,X242)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__commute) ).

fof(fact_fun__left__comm_Ofun__left__comm,axiom,
    ! [X37,X27,X12,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X16,X2)
     => hAPP(hAPP(X2,X12),hAPP(hAPP(X2,X27),X37)) = hAPP(hAPP(X2,X27),hAPP(hAPP(X2,X12),X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm) ).

fof(fact_inf__Sup__absorb,axiom,
    ! [X6,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X6),c_Big__Operators_Olattice__class_OSup__fin(X5,X11)) = X6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Sup__absorb) ).

fof(fact_sup__Inf__absorb,axiom,
    ! [X6,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X6),c_Big__Operators_Olattice__class_OInf__fin(X5,X11)) = 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_le__maxI1,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__maxI1) ).

fof(fact_le__maxI2,axiom,
    ! [X14,X22,X15] :
      ( class_Orderings_Olinorder(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__maxI2) ).

fof(fact_inf__sup__ord_I3_J,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Olattice(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I3_J) ).

fof(fact_sup__ge1,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__ge1) ).

fof(fact_inf__sup__ord_I4_J,axiom,
    ! [X14,X22,X15] :
      ( class_Lattices_Olattice(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I4_J) ).

fof(fact_sup__ge2,axiom,
    ! [X14,X22,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X22))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__ge2) ).

fof(fact_mem__Collect__eq,axiom,
    ! [X29,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Set_OCollect(X5),X29)))
    <=> hBOOL(hAPP(X29,X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__Collect__eq) ).

fof(fact_CollectD,axiom,
    ! [X29,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Set_OCollect(X5),X29)))
     => hBOOL(hAPP(X29,X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_CollectD) ).

fof(fact_CollectE,axiom,
    ! [X29,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Set_OCollect(X5),X29)))
     => hBOOL(hAPP(X29,X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_CollectE) ).

fof(fact_Suc__nat__eq__nat__zadd1,axiom,
    ! [X23] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))
     => hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X23)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__nat__eq__nat__zadd1) ).

fof(fact_remove1_Osimps_I2_J,axiom,
    ! [X221,X15,X22,X14] :
      ( ( X14 = X22
       => c_List_Oremove1(X15,X14,hAPP(hAPP(c_List_Olist_OCons(X15),X22),X221)) = X221 )
      & ( X14 != X22
       => c_List_Oremove1(X15,X14,hAPP(hAPP(c_List_Olist_OCons(X15),X22),X221)) = hAPP(hAPP(c_List_Olist_OCons(X15),X22),c_List_Oremove1(X15,X14,X221)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1_Osimps_I2_J) ).

fof(fact_less__Suc__eq,axiom,
    ! [X76,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),hAPP(c_Nat_OSuc,X76)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76))
        | X45 = X76 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).

fof(fact_Image__Id__on,axiom,
    ! [X13,X11,X5] : hAPP(c_Relation_OImage(X5,X5,c_Relation_OId__on(X5,X11)),X13) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Id__on) ).

fof(fact_min__max_Osup_Oleft__commute,axiom,
    ! [X24,X25,X26,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X26),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X25),X24)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X25),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X26),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup_Oleft__commute) ).

fof(fact_min__max_Osup__left__commute,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X22),X23)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X22),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__left__commute) ).

fof(fact_min__max_Oinf__left__commute,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X22),X23)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X22),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__left__commute) ).

fof(fact_min__max_Oinf_Oleft__commute,axiom,
    ! [X24,X25,X26,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X26),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X25),X24)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X25),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X26),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf_Oleft__commute) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
    ! [X41,X24,X25,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X24),X41)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X24),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X41)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
    ! [X116,X117,X119,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X119),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X117),X116)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X117),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X119),X116)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).

fof(fact_inf_Oleft__commute,axiom,
    ! [X24,X25,X26,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X26),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X25),X24)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X25),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X26),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oleft__commute) ).

fof(fact_inf__left__commute,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X22),X23)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__left__commute) ).

fof(fact_inf__sup__aci_I3_J,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Lattices_Olattice(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X22),X23)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I3_J) ).

fof(fact_inf__sup__aci_I7_J,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Lattices_Olattice(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X22),X23)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X22),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I7_J) ).

fof(fact_sup_Oleft__commute,axiom,
    ! [X24,X25,X26,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X26),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X25),X24)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X25),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X26),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup_Oleft__commute) ).

fof(fact_sup__left__commute,axiom,
    ! [X23,X22,X14,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X22),X23)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X22),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__left__commute) ).

fof(fact_add__minus__cancel,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Ogroup__add(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)),X26)) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__minus__cancel) ).

fof(fact_nat__mult__eq__cancel1,axiom,
    ! [X76,X45,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30))
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X45) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X76)
      <=> X45 = X76 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).

fof(fact_less__Suc__eq__le,axiom,
    ! [X76,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),hAPP(c_Nat_OSuc,X76)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).

fof(fact_one__div__nat__number__of,axiom,
    ! [X169] : 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),X169)) = 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),X169))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__div__nat__number__of) ).

fof(fact_split__nat,axiom,
    ! [X70,X29] :
      ( hBOOL(hAPP(X29,hAPP(c_Int_Onat,X70)))
    <=> ( ! [X107] :
            ( X70 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X107)
           => hBOOL(hAPP(X29,X107)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X70),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__nat) ).

fof(fact_distinct__drop,axiom,
    ! [X102,X221,X15] :
      ( hBOOL(hAPP(c_List_Odistinct(X15),X221))
     => hBOOL(hAPP(c_List_Odistinct(X15),hAPP(hAPP(c_List_Odrop(X15),X102),X221))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__drop) ).

fof(fact_distinct__take,axiom,
    ! [X102,X221,X15] :
      ( hBOOL(hAPP(c_List_Odistinct(X15),X221))
     => hBOOL(hAPP(c_List_Odistinct(X15),hAPP(hAPP(c_List_Otake(X15),X102),X221))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__take) ).

fof(fact_finite_OinsertI,axiom,
    ! [X6,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Set_Oinsert(X5),X6),X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite_OinsertI) ).

fof(fact_image__Suc__atLeastAtMost,axiom,
    ! [X115,X70] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X70,X115)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X70),hAPP(c_Nat_OSuc,X115)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Suc__atLeastAtMost) ).

fof(fact_INT__empty,axiom,
    ! [X13,X5,X16] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))),X13) = 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,
    ! [X132,X126] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X126),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X132))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__numeral__code_I6_J) ).

fof(fact_Compl__eq__Diff__UNIV,axiom,
    ! [X11,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__eq__Diff__UNIV) ).

fof(fact_map__butlast,axiom,
    ! [X212,X2,X5,X16] : hAPP(hAPP(c_List_Omap(X16,X5),X2),c_List_Obutlast(X16,X212)) = c_List_Obutlast(X5,hAPP(hAPP(c_List_Omap(X16,X5),X2),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__butlast) ).

fof(fact_Min__in,axiom,
    ! [X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olinorder__class_OMin(X5,X11)),X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min__in) ).

fof(fact_Max__in,axiom,
    ! [X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olinorder__class_OMax(X5,X11)),X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max__in) ).

fof(fact_all__nat,axiom,
    ! [X29] :
      ( ! [X32] : hBOOL(hAPP(X29,X32))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
         => hBOOL(hAPP(X29,hAPP(c_Int_Onat,X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nat) ).

fof(fact_insertI1,axiom,
    ! [X13,X6,X5] : hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI1) ).

fof(fact_mod__Suc,axiom,
    ! [X98,X99] :
      ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98)) = X98
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X99),X98) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98)) != X98
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X99),X98) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98)) ) ),
    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,
    ! [X11,X27,X12,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X12),hAPP(hAPP(c_Set_Oinsert(X5),X27),X11)) = hAPP(hAPP(c_Set_Oinsert(X5),X27),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__commute) ).

fof(fact_folding__one_Osingleton,axiom,
    ! [X12,X90,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X90)
     => hAPP(X90,hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Osingleton) ).

fof(fact_diff__Suc__eq__diff__pred,axiom,
    ! [X98,X99] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),hAPP(c_Nat_OSuc,X98)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X98),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).

fof(fact_fold__empty,axiom,
    ! [X37,X2,X5,X16] : hAPP(hAPP(c_Finite__Set_Ofold(X16,X5,X2),X37),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))) = X37,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__empty) ).

fof(fact_length__drop,axiom,
    ! [X221,X98,X15] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),hAPP(hAPP(c_List_Odrop(X15),X98),X221)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),X98),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__drop) ).

fof(fact_length__take,axiom,
    ! [X221,X98,X15] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),hAPP(hAPP(c_List_Otake(X15),X98),X221)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),X98),
    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,
    ! [X221,X98,X15] : hAPP(hAPP(c_List_Otake(X15),X98),hAPP(c_List_Otl(X15),X221)) = hAPP(c_List_Otl(X15),hAPP(hAPP(c_List_Otake(X15),hAPP(c_Nat_OSuc,X98)),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__tl) ).

fof(fact_enum__prod__def,axiom,
    ! [X5,X15] :
      ( ( class_Enum_Oenum(X15)
        & class_Enum_Oenum(X5) )
     => c_Enum_Oenum__class_Oenum(tc_prod(X15,X5)) = c_Enum_Oproduct(X15,X5,c_Enum_Oenum__class_Oenum(X15),c_Enum_Oenum__class_Oenum(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__prod__def) ).

fof(fact_less__iff__Suc__add,axiom,
    ! [X76,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76))
    <=> ? [X109] : X76 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X109)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).

fof(fact_drop__replicate,axiom,
    ! [X14,X100,X102,X15] : hAPP(hAPP(c_List_Odrop(X15),X102),c_List_Oreplicate(X15,X100,X14)) = c_List_Oreplicate(X15,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X100),X102),X14),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__replicate) ).

fof(fact_take__replicate,axiom,
    ! [X14,X100,X102,X15] : hAPP(hAPP(c_List_Otake(X15),X102),c_List_Oreplicate(X15,X100,X14)) = c_List_Oreplicate(X15,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X102),X100),X14),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__replicate) ).

fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
    ! [X76] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X76) = 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),X76))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I1_J) ).

fof(fact_list__all__simps_I1_J,axiom,
    ! [X212,X12,X29,X5] :
      ( c_List_Olist__all(X5,X29,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212))
    <=> ( hBOOL(hAPP(X29,X12))
        & c_List_Olist__all(X5,X29,X212) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__simps_I1_J) ).

fof(fact_nonzero__abs__divide,axiom,
    ! [X25,X26,X15] :
      ( class_Fields_Olinordered__field(X15)
     => ( X26 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),X26)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),hAPP(c_Groups_Oabs__class_Oabs(X15),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__abs__divide) ).

fof(fact_card_Oneutral,axiom,
    ! [X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
         => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
       => hAPP(c_Finite__Set_Ocard(X5),X11) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oneutral) ).

fof(fact_Compl__disjoint,axiom,
    ! [X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11)) = 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,
    ! [X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11)) = 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,X16,X5] : c_Fun_Oinj__on(X5,X16,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,
    ! [X132,X23] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23),X132))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X132),X23))
       => X23 = X132 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).

fof(fact_le__antisym,axiom,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X98))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X99))
       => X99 = X98 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).

fof(fact_zmod__minus1,axiom,
    ! [X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X26) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__minus1) ).

fof(fact_Min__insert,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X12),c_Big__Operators_Olinorder__class_OMin(X5,X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min__insert) ).

fof(fact_Max__insert,axiom,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X12),c_Big__Operators_Olinorder__class_OMax(X5,X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max__insert) ).

fof(fact_Sup__fin_Oinsert__idem,axiom,
    ! [X12,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != 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),X12),X11)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X12),c_Big__Operators_Olattice__class_OSup__fin(X5,X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oinsert__idem) ).

fof(fact_Inf__fin_Oinsert__idem,axiom,
    ! [X12,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != 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),X12),X11)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X12),c_Big__Operators_Olattice__class_OInf__fin(X5,X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oinsert__idem) ).

fof(fact_Un__empty,axiom,
    ! [X13,X11,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ( X11 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        & X13 = 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,
    ! [X225,X221,X15] :
      ( class_Groups_Omonoid__add(X15)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X15),hAPP(hAPP(c_List_Oappend(X15),X221),X225)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_List_Omonoid__add__class_Olistsum(X15),X221)),hAPP(c_List_Omonoid__add__class_Olistsum(X15),X225)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__append) ).

fof(fact_abs__divide,axiom,
    ! [X26,X25,X15] :
      ( class_Fields_Olinordered__field__inverse__zero(X15)
     => hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),X26)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),hAPP(c_Groups_Oabs__class_Oabs(X15),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__divide) ).

fof(fact_abs__mult,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),hAPP(c_Groups_Oabs__class_Oabs(X15),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult) ).

fof(fact_minus__max__eq__min,axiom,
    ! [X22,X14,X15] :
      ( class_Groups_Olinordered__ab__group__add(X15)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),X22)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X14)),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__max__eq__min) ).

fof(fact_minus__min__eq__max,axiom,
    ! [X22,X14,X15] :
      ( class_Groups_Olinordered__ab__group__add(X15)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),X22)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X14)),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__min__eq__max) ).

fof(fact_minus__add__distrib,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Oab__group__add(X15)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__distrib) ).

fof(fact_minus__add,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Ogroup__add(X15)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X26)),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add) ).

fof(fact_compl__inf,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Oboolean__algebra(X15)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X14)),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__inf) ).

fof(fact_compl__sup,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Oboolean__algebra(X15)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X14)),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__sup) ).

fof(fact_Cantors__paradox,axiom,
    ! [X11,X5] :
      ~ ? [X43] : hAPP(c_Set_Oimage(X5,tc_fun(X5,tc_HOL_Obool),X43),X11) = hAPP(c_Set_OPow(X5),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cantors__paradox) ).

fof(fact_equalityD1,axiom,
    ! [X5,X13,X11] :
      ( X11 = X13
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD1) ).

fof(fact_equalityD2,axiom,
    ! [X5,X13,X11] :
      ( X11 = X13
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD2) ).

fof(fact_last__in__set,axiom,
    ! [X5,X235] :
      ( X235 != c_List_Olist_ONil(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),c_List_Olast(X5,X235)),hAPP(c_List_Oset(X5),X235))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__in__set) ).

fof(fact_Suc__mult__cancel1,axiom,
    ! [X76,X45,X30] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),X45) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),X76)
    <=> X45 = X76 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).

fof(fact_Pair__eq,axiom,
    ! [X138,X82,X17,X6,X16,X5] :
      ( hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17) = hAPP(hAPP(c_Product__Type_OPair(X5,X16),X82),X138)
    <=> ( X6 = X82
        & X17 = X138 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__eq) ).

fof(fact_Pair__inject,axiom,
    ! [X143,X81,X26,X25,X5,X15] :
      ( hAPP(hAPP(c_Product__Type_OPair(X15,X5),X25),X26) = hAPP(hAPP(c_Product__Type_OPair(X15,X5),X81),X143)
     => ~ ( X25 = X81
         => X26 != X143 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__inject) ).

fof(fact_zmod__zminus1__eq__if,axiom,
    ! [X26,X25] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26) = 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),X25),X26) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26) != 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),X25),X26) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26),c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus1__eq__if) ).

fof(fact_subset__refl,axiom,
    ! [X11,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__refl) ).

fof(fact_image__Suc__atLeastLessThan,axiom,
    ! [X115,X70] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X70),X115)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X70)),hAPP(c_Nat_OSuc,X115)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Suc__atLeastLessThan) ).

fof(fact_rev__append,axiom,
    ! [X225,X221,X15] : hAPP(c_List_Orev(X15),hAPP(hAPP(c_List_Oappend(X15),X221),X225)) = hAPP(hAPP(c_List_Oappend(X15),hAPP(c_List_Orev(X15),X225)),hAPP(c_List_Orev(X15),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__append) ).

fof(fact_rotate__simps,axiom,
    ! [X221,X14,X5,X15] :
      ( hAPP(c_List_Orotate1(X15),c_List_Olist_ONil(X15)) = c_List_Olist_ONil(X15)
      & hAPP(c_List_Orotate1(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X14),X221)) = hAPP(hAPP(c_List_Oappend(X5),X221),hAPP(hAPP(c_List_Olist_OCons(X5),X14),c_List_Olist_ONil(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__simps) ).

fof(fact_less__SucI,axiom,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),hAPP(c_Nat_OSuc,X98))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).

fof(fact_le__imp__less__Suc,axiom,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X98))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),hAPP(c_Nat_OSuc,X98))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).

fof(fact_le__SucI,axiom,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X98))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),hAPP(c_Nat_OSuc,X98))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucI) ).

fof(fact_greaterThanAtMost__upto,axiom,
    ! [X115,X70] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X70,X115) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X70),c_Groups_Oone__class_Oone(tc_Int_Oint)),X115)),
    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,
    ! [X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),X26) = 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,
    ! [X13,X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X13),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__commute) ).

fof(fact_Un__commute,axiom,
    ! [X13,X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X13),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__commute) ).

fof(fact_zero__less__imp__eq__int,axiom,
    ! [X100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X100))
     => ? [X107] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X107))
          & X100 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X107) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__imp__eq__int) ).

fof(fact_frac__eq__eq,axiom,
    ! [X112,X12,X37,X27,X5] :
      ( class_Fields_Ofield(X5)
     => ( X27 != c_Groups_Ozero__class_Ozero(X5)
       => ( X37 != c_Groups_Ozero__class_Ozero(X5)
         => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X12),X27) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X112),X37)
          <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X37) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X112),X27) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__eq__eq) ).

fof(fact_zmult__div__cancel,axiom,
    ! [X99,X98] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X98),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X99),X98)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X99),c_Divides_Odiv__class_Omod(tc_Int_Oint,X99,X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__div__cancel) ).

fof(fact_mult__div__cancel,axiom,
    ! [X99,X98] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),X98)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__div__cancel) ).

fof(fact_div__code__numeral__def,axiom,
    ! [X99,X98] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X98),X99) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X98)),hAPP(c_Code__Numeral_Onat__of,X99))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__code__numeral__def) ).

fof(fact_plus__code__numeral__def,axiom,
    ! [X99,X98] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X98),X99) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X98)),hAPP(c_Code__Numeral_Onat__of,X99))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__code__numeral__def) ).

fof(fact_times__code__numeral__def,axiom,
    ! [X99,X98] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X98),X99) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X98)),hAPP(c_Code__Numeral_Onat__of,X99))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__code__numeral__def) ).

fof(fact_minus__code__numeral__def,axiom,
    ! [X99,X98] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X98),X99) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X98)),hAPP(c_Code__Numeral_Onat__of,X99))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__code__numeral__def) ).

fof(fact_le__add__diff__inverse,axiom,
    ! [X99,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X99))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98)) = X99 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).

fof(fact_diff__diff__cancel,axiom,
    ! [X98,X102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X98))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),X102)) = X102 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).

fof(fact_nat__case__Suc,axiom,
    ! [X111,X88,X89,X5] : c_Nat_Onat_Onat__case(X5,X89,X88,hAPP(c_Nat_OSuc,X111)) = hAPP(X88,X111),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__Suc) ).

fof(fact_listsum__eq__0__nat__iff__nat,axiom,
    ! [X224] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X224) = 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),X224)))
         => 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_xt1_I11_J,axiom,
    ! [X25,X26,X15] :
      ( class_Orderings_Oorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),X25))
       => ( X25 != X26
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),X25)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).

fof(fact_order__le__neq__trans,axiom,
    ! [X26,X25,X15] :
      ( class_Orderings_Oorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26))
       => ( X25 != X26
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).

fof(fact_order__le__imp__less__or__eq,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Oorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
          | X14 = X22 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).

fof(fact_order__neq__le__trans,axiom,
    ! [X26,X25,X15] :
      ( class_Orderings_Oorder(X15)
     => ( X25 != X26
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).

fof(fact_order__le__less,axiom,
    ! [X27,X12,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X12),X27))
          | X12 = X27 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).

fof(fact_order__less__le,axiom,
    ! [X27,X12,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X12),X27))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27))
          & X12 != X27 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).

fof(fact_xt1_I12_J,axiom,
    ! [X26,X25,X15] :
      ( class_Orderings_Oorder(X15)
     => ( X25 != X26
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),X25))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),X25)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).

fof(fact_add__number__of__eq,axiom,
    ! [X132,X126,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X126)),hAPP(c_Int_Onumber__class_Onumber__of(X15),X132)) = hAPP(c_Int_Onumber__class_Onumber__of(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X126),X132)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__eq) ).

fof(fact_arith__simps_I32_J,axiom,
    ! [X132,X126,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X126)),hAPP(c_Int_Onumber__class_Onumber__of(X15),X132)) = hAPP(c_Int_Onumber__class_Onumber__of(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X126),X132)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I32_J) ).

fof(fact_of__nat__add,axiom,
    ! [X98,X99,X15] :
      ( class_Rings_Osemiring__1(X15)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X98)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),X99)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__add) ).

fof(fact_of__nat__mult,axiom,
    ! [X98,X99,X15] :
      ( class_Rings_Osemiring__1(X15)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),X98)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),X99)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__mult) ).

fof(fact_of__int__add,axiom,
    ! [X23,X132,X15] :
      ( class_Rings_Oring__1(X15)
     => hAPP(c_Int_Oring__1__class_Oof__int(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X132),X23)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Int_Oring__1__class_Oof__int(X15),X132)),hAPP(c_Int_Oring__1__class_Oof__int(X15),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__add) ).

fof(fact_of__int__mult,axiom,
    ! [X23,X132,X15] :
      ( class_Rings_Oring__1(X15)
     => hAPP(c_Int_Oring__1__class_Oof__int(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X132),X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Int_Oring__1__class_Oof__int(X15),X132)),hAPP(c_Int_Oring__1__class_Oof__int(X15),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__mult) ).

fof(fact_of__int__diff,axiom,
    ! [X23,X132,X15] :
      ( class_Rings_Oring__1(X15)
     => hAPP(c_Int_Oring__1__class_Oof__int(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X132),X23)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),hAPP(c_Int_Oring__1__class_Oof__int(X15),X132)),hAPP(c_Int_Oring__1__class_Oof__int(X15),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__diff) ).

fof(fact_number__of__add,axiom,
    ! [X132,X126,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(c_Int_Onumber__class_Onumber__of(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X126),X132)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X126)),hAPP(c_Int_Onumber__class_Onumber__of(X15),X132)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__add) ).

fof(fact_number__of__mult,axiom,
    ! [X132,X126,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(c_Int_Onumber__class_Onumber__of(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X126),X132)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X126)),hAPP(c_Int_Onumber__class_Onumber__of(X15),X132)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__mult) ).

fof(fact_number__of__diff,axiom,
    ! [X132,X126,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(c_Int_Onumber__class_Onumber__of(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X126),X132)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X126)),hAPP(c_Int_Onumber__class_Onumber__of(X15),X132)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__diff) ).

fof(fact_product_Osimps_I1_J,axiom,
    ! [X237,X5,X15] : c_Enum_Oproduct(X15,X5,c_List_Olist_ONil(X15),X237) = c_List_Olist_ONil(tc_prod(X15,X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_product_Osimps_I1_J) ).

fof(fact_minus1__divide,axiom,
    ! [X14,X15] :
      ( ( class_Fields_Ofield__inverse__zero(X15)
        & class_Int_Onumber__ring(X15) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OMin)),X14) = hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),c_Groups_Oone__class_Oone(X15)),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus1__divide) ).

fof(fact_setsum__0,axiom,
    ! [X11,X16,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),hAPP(c_COMBK(X5,X16),c_Groups_Ozero__class_Ozero(X5))),X11) = c_Groups_Ozero__class_Ozero(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__0) ).

fof(fact_setprod__1,axiom,
    ! [X11,X16,X5] :
      ( class_Groups_Ocomm__monoid__mult(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16,X5),hAPP(c_COMBK(X5,X16),c_Groups_Oone__class_Oone(X5))),X11) = c_Groups_Oone__class_Oone(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__1) ).

fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
    ! [X66,X97] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X97),c_Groups_Oone__class_Oone(tc_Int_Oint))),X66) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X97,X66),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastPlusOneLessThan__greaterThanLessThan__int) ).

fof(fact_order__less__imp__le,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Opreorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).

fof(fact_tl__replicate,axiom,
    ! [X14,X15,X98] :
      ( X98 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Otl(X15),c_List_Oreplicate(X15,X98,X14)) = c_List_Oreplicate(X15,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl__replicate) ).

fof(fact_negateSnd__eq,axiom,
    ! [X123,X128] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X128),X123)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X128),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X123)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negateSnd__eq) ).

fof(fact_abs__power__minus__one,axiom,
    ! [X98,X15] :
      ( ( class_Int_Onumber__ring(X15)
        & class_Rings_Olinordered__idom(X15) )
     => hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OMin)),X98)) = c_Groups_Oone__class_Oone(X15) ),
    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,
    ! [X13,X11] :
      ( c_Nat__Transfer_Onat__set(X11)
     => ( c_Nat__Transfer_Onat__set(X13)
       => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X11),X13)) ) ),
    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,
    ! [X13,X11] :
      ( c_Nat__Transfer_Onat__set(X11)
     => ( c_Nat__Transfer_Onat__set(X13)
       => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X11),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J) ).

fof(fact_zle__iff__zadd,axiom,
    ! [X37,X112] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X112),X37))
    <=> ? [X107] : X37 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X112),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X107)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__iff__zadd) ).

fof(fact_map__replicate,axiom,
    ! [X12,X76,X2,X5,X16] : hAPP(hAPP(c_List_Omap(X16,X5),X2),c_List_Oreplicate(X16,X76,X12)) = c_List_Oreplicate(X5,X76,hAPP(X2,X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__replicate) ).

fof(fact_filter__remove1,axiom,
    ! [X212,X12,X28,X5] : hAPP(c_List_Ofilter(X5,X28),c_List_Oremove1(X5,X12,X212)) = c_List_Oremove1(X5,X12,hAPP(c_List_Ofilter(X5,X28),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__remove1) ).

fof(fact_snoc__eq__iff__butlast,axiom,
    ! [X214,X12,X212,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X212),hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Olist_ONil(X5))) = X214
    <=> ( X214 != c_List_Olist_ONil(X5)
        & c_List_Obutlast(X5,X214) = X212
        & c_List_Olast(X5,X214) = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snoc__eq__iff__butlast) ).

fof(fact_negD,axiom,
    ! [X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ? [X107] : X14 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X107))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negD) ).

fof(fact_of__nat__in__Nats,axiom,
    ! [X76,X5] :
      ( class_Rings_Osemiring__1(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X76)),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,
    ! [X76,X5] :
      ( class_Rings_Oring__1(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X76)),c_Int_Oring__1__class_OInts(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__of__nat) ).

fof(fact_Ints__of__int,axiom,
    ! [X37,X5] :
      ( class_Rings_Oring__1(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),X37)),c_Int_Oring__1__class_OInts(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__of__int) ).

fof(fact_Ints__number__of,axiom,
    ! [X112,X5] :
      ( class_Int_Onumber__ring(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),c_Int_Oring__1__class_OInts(X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__number__of) ).

fof(fact_Suc__diff__1,axiom,
    ! [X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X98))
     => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X98 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__1) ).

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

fof(fact_nat__of,axiom,
    ! [X12] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X12)),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,
    ! [X26,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),c_Divides_Odiv__class_Omod(X15,X25,X26)),X26) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__div__trivial) ).

fof(fact_negDivAlg__minus1,axiom,
    ! [X26] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X26) = 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),X26),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg__minus1) ).

fof(fact_set__replicate__Suc,axiom,
    ! [X12,X76,X5] : hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,hAPP(c_Nat_OSuc,X76),X12)) = hAPP(hAPP(c_Set_Oinsert(X5),X12),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,
    ! [X27,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))
     => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X12,X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__function__closures) ).

fof(fact_hb__map_Osimps_I1_J,axiom,
    ! [X2,X5,X16] : c_Lazy__Sequence_Ohb__map(X16,X5,X2,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(X16))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hb__map_Osimps_I1_J) ).

fof(fact_min__max_OSup__fin_Osingleton,axiom,
    ! [X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Osingleton) ).

fof(fact_min__max_OInf__fin_Osingleton,axiom,
    ! [X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Osingleton) ).

fof(fact_int__one__le__iff__zero__less,axiom,
    ! [X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X37))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).

fof(fact_Int__empty__left,axiom,
    ! [X13,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))),X13) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__empty__left) ).

fof(fact_empty__Diff,axiom,
    ! [X11,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))),X11) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__Diff) ).

fof(fact_Un__UNIV__left,axiom,
    ! [X13,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))),X13) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__UNIV__left) ).

fof(fact_Sigma__empty1,axiom,
    ! [X13,X16,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X16),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X13) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__empty1) ).

fof(fact_le__add1,axiom,
    ! [X99,X98] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X99))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).

fof(fact_le__add2,axiom,
    ! [X99,X98] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X98))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).

fof(fact_le__square,axiom,
    ! [X99] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),X99))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).

fof(fact_divide__eq__eq__number__of1,axiom,
    ! [X6,X112,X17,X5] :
      ( ( class_Fields_Ofield__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X17),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)) = X6
      <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X112) != c_Groups_Ozero__class_Ozero(X5)
           => X17 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)) )
          & ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X112) = 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,
    ! [X112,X17,X6,X5] :
      ( ( class_Fields_Ofield__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( X6 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X17),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112))
      <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X112) != c_Groups_Ozero__class_Ozero(X5)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)) = X17 )
          & ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X112) = 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,
    ! [X29,X76,X45] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76))
       => hBOOL(hAPP(hAPP(X29,X76),X45)) )
     => ( ( X45 = X76
         => hBOOL(hAPP(hAPP(X29,X76),X45)) )
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),X45))
           => hBOOL(hAPP(hAPP(X29,X76),X45)) )
         => hBOOL(hAPP(hAPP(X29,X76),X45)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
    ! [X11] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X11) = 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)),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) ).

fof(fact_append__eq__appendI,axiom,
    ! [X241,X225,X242,X244,X221,X15] :
      ( hAPP(hAPP(c_List_Oappend(X15),X221),X244) = X242
     => ( X225 = hAPP(hAPP(c_List_Oappend(X15),X244),X241)
       => hAPP(hAPP(c_List_Oappend(X15),X221),X225) = hAPP(hAPP(c_List_Oappend(X15),X242),X241) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__appendI) ).

fof(fact_Cons__eq__appendI,axiom,
    ! [X242,X221,X225,X244,X14,X15] :
      ( hAPP(hAPP(c_List_Olist_OCons(X15),X14),X244) = X225
     => ( X221 = hAPP(hAPP(c_List_Oappend(X15),X244),X242)
       => hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221) = hAPP(hAPP(c_List_Oappend(X15),X225),X242) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__eq__appendI) ).

fof(fact_zadd__left__commute,axiom,
    ! [X23,X22,X14] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X14),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22),X23)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X14),X23)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).

fof(fact_nat__add__left__commute,axiom,
    ! [X23,X22,X14] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X23)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),X23)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).

fof(fact_atLeastLessThan__upto,axiom,
    ! [X115,X70] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X70),X115) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X70,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X115),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,
    ! [X99,X98] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),X99)),X99) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X98),X99),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__minus__add__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_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_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_elem__set,axiom,
    ! [X83,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),c_Option_Oset(X5,X83)))
    <=> X83 = hAPP(c_Option_Ooption_OSome(X5),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_elem__set) ).

fof(fact_div__mult__self1__is__id,axiom,
    ! [X25,X26,X15] :
      ( class_Divides_Osemiring__div(X15)
     => ( X26 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X25)),X26) = X25 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self1__is__id) ).

fof(fact_div__mult__self2__is__id,axiom,
    ! [X25,X26,X15] :
      ( class_Divides_Osemiring__div(X15)
     => ( X26 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26)),X26) = X25 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self2__is__id) ).

fof(fact_le__imp__diff__is__add,axiom,
    ! [X30,X115,X70] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X70),X115))
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X115),X70) = X30
      <=> X115 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X70) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).

fof(fact_zmod__zminus2,axiom,
    ! [X26,X25] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26)) = 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),X25),X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus2) ).

fof(fact_remove1__remdups,axiom,
    ! [X14,X221,X15] :
      ( hBOOL(hAPP(c_List_Odistinct(X15),X221))
     => c_List_Oremove1(X15,X14,c_List_Oremdups(X15,X221)) = c_List_Oremdups(X15,c_List_Oremove1(X15,X14,X221)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__remdups) ).

fof(fact_insert__dom,axiom,
    ! [X16,X27,X5,X12,X2] :
      ( hAPP(X2,X12) = hAPP(c_Option_Ooption_OSome(X5),X27)
     => hAPP(hAPP(c_Set_Oinsert(X16),X12),c_Map_Odom(X16,X5,X2)) = c_Map_Odom(X16,X5,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__dom) ).

fof(fact_Nitpick_Owf_H__def,axiom,
    ! [X34,X5] :
      ( c_Nitpick_Owf_H(X5,X34)
    <=> ( c_Wellfounded_Oacyclic(X5,X34)
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X34))
          | 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,
    ! [X34,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X34))
     => ( c_Wellfounded_Owf(X5,X34)
      <=> c_Wellfounded_Oacyclic(X5,X34) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__iff__acyclic__if__finite) ).

fof(fact_finite__acyclic__wf,axiom,
    ! [X34,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X34))
     => ( c_Wellfounded_Oacyclic(X5,X34)
       => c_Wellfounded_Owf(X5,X34) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__acyclic__wf) ).

fof(fact_inj__on__rev,axiom,
    ! [X11,X5] : c_Fun_Oinj__on(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Orev(X5),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__rev) ).

fof(conj_5,conjecture,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).

fof(fact_Least__le,axiom,
    ! [X30,X29,X5] :
      ( class_Orderings_Owellorder(X5)
     => ( hBOOL(hAPP(X29,X30))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Orderings_Oord__class_OLeast(X5,X29)),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Least__le) ).

fof(fact_distinct__filter,axiom,
    ! [X29,X212,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X212))
     => hBOOL(hAPP(c_List_Odistinct(X5),hAPP(c_List_Ofilter(X5,X29),X212))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__filter) ).

fof(fact_equivp__def,axiom,
    ! [X36,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X36)
    <=> ! [X3,X33] :
          ( hBOOL(hAPP(hAPP(X36,X3),X33))
        <=> hAPP(X36,X3) = hAPP(X36,X33) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__def) ).

fof(fact_diff__add__cancel,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Ogroup__add(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X25),X26)),X26) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__cancel) ).

fof(fact_add__diff__cancel,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Ogroup__add(X15)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26)),X26) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__cancel) ).

fof(fact_sort__key__simps_I1_J,axiom,
    ! [X2,X5,X16] :
      ( class_Orderings_Olinorder(X16)
     => c_List_Olinorder__class_Osort__key(X5,X16,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,
    ! [X36,X16,X5] : hAPP(c_Set_Oimage(tc_prod(X5,X16),X5,c_Product__Type_Ofst(X5,X16)),X36) = hAPP(c_Relation_ODomain(X5,X16),X36),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__eq__Domain) ).

fof(fact_snd__eq__Range,axiom,
    ! [X36,X5,X16] : hAPP(c_Set_Oimage(tc_prod(X16,X5),X5,c_Product__Type_Osnd(X16,X5)),X36) = hAPP(c_Relation_ORange(X16,X5),X36),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__eq__Range) ).

fof(fact_total__on__converse,axiom,
    ! [X34,X11,X5] :
      ( c_Relation_Ototal__on(X5,X11,hAPP(c_Relation_Oconverse(X5,X5),X34))
    <=> c_Relation_Ototal__on(X5,X11,X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__converse) ).

fof(fact_refl__on__converse,axiom,
    ! [X34,X11,X5] :
      ( c_Relation_Orefl__on(X5,X11,hAPP(c_Relation_Oconverse(X5,X5),X34))
    <=> c_Relation_Orefl__on(X5,X11,X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__converse) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
    ! [X11] :
      ( c_Nat__Transfer_Onat__set(X11)
     => hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X11) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X11)) ),
    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,
    ! [X12,X11] :
      ( c_Nat__Transfer_Onat__set(X11)
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X12),X11))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J) ).

fof(fact_nat__set__def,axiom,
    ! [X35] :
      ( c_Nat__Transfer_Onat__set(X35)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),X35))
         => 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,
    ! [X11,X5] : hAPP(c_Finite__Set_Ocard(X5),X11) = 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))),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__eq__setsum) ).

fof(fact_divmod__nat__rel__unique,axiom,
    ! [X160,X159,X98,X99] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X99,X98),X159))
     => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X99,X98),X160))
       => X159 = X160 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__unique) ).

fof(fact_inj__uminus,axiom,
    ! [X11,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => c_Fun_Oinj__on(X5,X5,c_Groups_Ouminus__class_Ouminus(X5),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__uminus) ).

fof(fact_mod__code__numeral__def,axiom,
    ! [X99,X98] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X98,X99) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X98),hAPP(c_Code__Numeral_Onat__of,X99))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__code__numeral__def) ).

fof(fact_nth__Cons__0,axiom,
    ! [X221,X14,X15] : hAPP(hAPP(c_List_Onth(X15),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X14,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__Cons__0) ).

fof(fact_image__is__empty,axiom,
    ! [X11,X2,X5,X16] :
      ( hAPP(c_Set_Oimage(X16,X5,X2),X11) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> X11 = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__is__empty) ).

fof(fact_empty__is__image,axiom,
    ! [X11,X2,X16,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X16,X5,X2),X11)
    <=> X11 = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__is__image) ).

fof(fact_inj__Some,axiom,
    ! [X11,X5] : c_Fun_Oinj__on(X5,tc_Option_Ooption(X5),c_Option_Ooption_OSome(X5),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__Some) ).

fof(fact_listrelp_ONil,axiom,
    ! [X34,X5] : c_List_Olistrelp(X5,X34,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,
    ! [X34,X5] : c_List_Olistrelp(X5,X34,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,X16,X5,X212] :
      ( X212 != c_List_Olist_ONil(X5)
     => hAPP(c_List_Ohd(X16),hAPP(hAPP(c_List_Omap(X5,X16),X2),X212)) = hAPP(X2,hAPP(c_List_Ohd(X5),X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__map) ).

fof(fact_of__nat__aux_Osimps_I1_J,axiom,
    ! [X70,X171,X5] :
      ( class_Rings_Osemiring__1(X5)
     => c_Nat_Osemiring__1__class_Oof__nat__aux(X5,X171,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X70) = X70 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I1_J) ).

fof(fact_atLeastAtMost__singleton__iff,axiom,
    ! [X21,X17,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X17) = hAPP(hAPP(c_Set_Oinsert(X5),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))
      <=> ( X6 = X17
          & X17 = X21 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton__iff) ).

fof(fact_neg__single__def,axiom,
    ! [X262,X263,X264,X12,X5] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X5),X12),X264),X263),X262) = c_New__DSequence_Oneg__single(X5,X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__single__def) ).

fof(fact_pos__single__def,axiom,
    ! [X262,X263,X264,X12,X5] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X5),X12),X264),X263),X262) = c_New__DSequence_Opos__single(X5,X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__single__def) ).

fof(fact_power__abs,axiom,
    ! [X98,X25,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)) = hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),X98) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__abs) ).

fof(fact_minus__divide__left,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Odivision__ring(X15)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),X26)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__left) ).

fof(fact_minus__mult__left,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Oring(X15)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__left) ).

fof(fact_power_Opower_Opower__0,axiom,
    ! [X6,X136,X137,X5] : hAPP(hAPP(c_Power_Opower_Opower(X5,X137,X136),X6),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X137,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).

fof(fact_maps__simps_I2_J,axiom,
    ! [X2,X5,X16] : c_List_Omaps(X16,X5,X2,c_List_Olist_ONil(X16)) = c_List_Olist_ONil(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_maps__simps_I2_J) ).

fof(fact_map__filter__simps_I2_J,axiom,
    ! [X2,X5,X16] : c_List_Omap__filter(X16,X5,X2,c_List_Olist_ONil(X16)) = c_List_Olist_ONil(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__filter__simps_I2_J) ).

fof(fact_atLeastatMost__empty,axiom,
    ! [X6,X17,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),X6))
       => c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X17) = 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,
    ! [X30,X97,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X97),X30))
       => c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X30,X97) = 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,
    ! [X30,X97,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X97),X30))
       => c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X30,X97) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanLessThan__empty) ).

fof(fact_tl__append2,axiom,
    ! [X225,X15,X221] :
      ( X221 != c_List_Olist_ONil(X15)
     => hAPP(c_List_Otl(X15),hAPP(hAPP(c_List_Oappend(X15),X221),X225)) = hAPP(hAPP(c_List_Oappend(X15),hAPP(c_List_Otl(X15),X221)),X225) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl__append2) ).

fof(fact_zmod__zdiv__trivial,axiom,
    ! [X26,X25] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26)),X26) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zdiv__trivial) ).

fof(fact_Pair__fst__snd__eq,axiom,
    ! [X16,X5,X10,X84] :
      ( X84 = X10
    <=> ( hAPP(c_Product__Type_Ofst(X5,X16),X84) = hAPP(c_Product__Type_Ofst(X5,X16),X10)
        & hAPP(c_Product__Type_Osnd(X5,X16),X84) = hAPP(c_Product__Type_Osnd(X5,X16),X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__fst__snd__eq) ).

fof(fact_prod__eqI,axiom,
    ! [X128,X129,X5,X15] :
      ( hAPP(c_Product__Type_Ofst(X15,X5),X129) = hAPP(c_Product__Type_Ofst(X15,X5),X128)
     => ( hAPP(c_Product__Type_Osnd(X15,X5),X129) = hAPP(c_Product__Type_Osnd(X15,X5),X128)
       => X129 = X128 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod__eqI) ).

fof(fact_inj__on__id,axiom,
    ! [X11,X5] : c_Fun_Oinj__on(X5,X5,c_Fun_Oid(X5),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__id) ).

fof(fact_inj__on__id2,axiom,
    ! [X11,X5] : c_Fun_Oinj__on(X5,X5,c_COMBI(X5),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__id2) ).

fof(fact_sgn__times,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => c_Groups_Osgn__class_Osgn(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),c_Groups_Osgn__class_Osgn(X15,X25)),c_Groups_Osgn__class_Osgn(X15,X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__times) ).

fof(fact_sorted__distinct__set__unique,axiom,
    ! [X214,X212,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,X212)
       => ( hBOOL(hAPP(c_List_Odistinct(X5),X212))
         => ( c_List_Olinorder__class_Osorted(X5,X214)
           => ( hBOOL(hAPP(c_List_Odistinct(X5),X214))
             => ( hAPP(c_List_Oset(X5),X212) = hAPP(c_List_Oset(X5),X214)
               => X212 = X214 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__distinct__set__unique) ).

fof(fact_drop__Suc__Cons,axiom,
    ! [X221,X14,X98,X15] : hAPP(hAPP(c_List_Odrop(X15),hAPP(c_Nat_OSuc,X98)),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = hAPP(hAPP(c_List_Odrop(X15),X98),X221),
    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,
    ! [X26,X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X25),X26)) = hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X26),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__commute) ).

fof(fact_code__numeral_Orecs_I1_J,axiom,
    ! [X88,X89,X5] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X5,X89,X88,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X89,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Orecs_I1_J) ).

fof(fact_code__numeral_Osimps_I4_J,axiom,
    ! [X88,X89,X5] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X5,X89,X88,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X89,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I4_J) ).

fof(fact_nat__case__0,axiom,
    ! [X88,X89,X5] : c_Nat_Onat_Onat__case(X5,X89,X88,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X89,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__0) ).

fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
    ! [X22,X14] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X14),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
    ! [X22,X14] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).

fof(fact_zadd__int,axiom,
    ! [X98,X99] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X99)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X98)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__int) ).

fof(fact_plus__numeral__code_I9_J,axiom,
    ! [X132,X126] : 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),X132)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X126),X132)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__numeral__code_I9_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
    ! [X22,X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).

fof(fact_zmult__int,axiom,
    ! [X98,X99] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X99)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X98)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__int) ).

fof(fact_times__numeral__code_I5_J,axiom,
    ! [X132,X126] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X126),X132)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__numeral__code_I5_J) ).

fof(fact_zdiv__int,axiom,
    ! [X26,X25] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X25),X26)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__int) ).

fof(fact_int__mult,axiom,
    ! [X98,X99] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),X98)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X99)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__mult) ).

fof(fact_zminus__zadd__distrib,axiom,
    ! [X132,X23] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23),X132)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X132)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).

fof(fact_Int__UNIV__left,axiom,
    ! [X13,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))),X13) = X13,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__UNIV__left) ).

fof(fact_Un__empty__left,axiom,
    ! [X13,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))),X13) = X13,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__empty__left) ).

fof(fact_pos__zmult__eq__1__iff,axiom,
    ! [X76,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45))
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X45),X76) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      <=> ( X45 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & X76 = 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__list__update,axiom,
    ! [X14,X102,X221,X15] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),hAPP(hAPP(c_List_Olist__update(X15,X221),X102),X14)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__list__update) ).

fof(fact_length__map,axiom,
    ! [X212,X2,X16,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Omap(X16,X5),X2),X212)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__map) ).

fof(fact_of__nat__power,axiom,
    ! [X98,X99,X15] :
      ( class_Rings_Osemiring__1(X15)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X99),X98)) = hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),X99)),X98) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__power) ).

fof(fact_of__int__power,axiom,
    ! [X98,X23,X15] :
      ( class_Rings_Oring__1(X15)
     => hAPP(c_Int_Oring__1__class_Oof__int(X15),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X23),X98)) = hAPP(hAPP(c_Power_Opower__class_Opower(X15),hAPP(c_Int_Oring__1__class_Oof__int(X15),X23)),X98) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__power) ).

fof(fact_zless__le,axiom,
    ! [X112,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),X112))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X37),X112))
        & X37 != X112 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).

fof(fact_le__neq__implies__less,axiom,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X98))
     => ( X99 != X98
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).

fof(fact_le__eq__less__or__eq,axiom,
    ! [X76,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76))
        | X45 = X76 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).

fof(fact_nat__less__le,axiom,
    ! [X76,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76))
        & X45 != X76 ) ),
    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,
    ! [X221,X15] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),hAPP(c_List_Otl(X15),X221)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),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,
    ! [X37,X12,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm__idem(X5,X16,X2)
     => hAPP(hAPP(X2,X12),hAPP(hAPP(X2,X12),X37)) = hAPP(hAPP(X2,X12),X37) ),
    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,
    ! [X19] : 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)),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J) ).

fof(fact_finite__atLeastAtMost__int,axiom,
    ! [X66,X97] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X97,X66))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastAtMost__int) ).

fof(fact_finite__greaterThanAtMost__int,axiom,
    ! [X66,X97] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X97,X66))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost__int) ).

fof(fact_finite__greaterThanLessThan__int,axiom,
    ! [X66,X97] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X97,X66))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan__int) ).

fof(fact_finite__atLeastAtMost,axiom,
    ! [X66,X97] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X97,X66))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastAtMost) ).

fof(fact_finite__greaterThanAtMost,axiom,
    ! [X66,X97] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X97,X66))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost) ).

fof(fact_finite__greaterThanLessThan,axiom,
    ! [X66,X97] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X97,X66))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan) ).

fof(fact_less__Suc0,axiom,
    ! [X76] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    <=> X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).

fof(fact_inj__Suc,axiom,
    ! [X93] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X93),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__Suc) ).

fof(fact_less__or__eq__imp__le,axiom,
    ! [X98,X99] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
        | X99 = X98 )
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).

fof(fact_less__imp__le__nat,axiom,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).

fof(fact_termination__basic__simps_I5_J,axiom,
    ! [X22,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),X22))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).

fof(fact_atLeastLessThan__empty,axiom,
    ! [X6,X17,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),X6))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X17) = 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,
    ! [X27,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_fequal,X27)))
    <=> X12 = X27 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem) ).

fof(fact_last__map,axiom,
    ! [X2,X16,X5,X212] :
      ( X212 != c_List_Olist_ONil(X5)
     => c_List_Olast(X16,hAPP(hAPP(c_List_Omap(X5,X16),X2),X212)) = hAPP(X2,c_List_Olast(X5,X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__map) ).

fof(fact_minus__add__cancel,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Ogroup__add(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26)) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__cancel) ).

fof(fact_ex__in__conv,axiom,
    ! [X11,X5] :
      ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
    <=> X11 != 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,
    ! [X23,X15] :
      ( class_Rings_Oring__1(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),hAPP(c_Int_Onat,X23)) = hAPP(c_Int_Oring__1__class_Oof__int(X15),X23) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__nat) ).

fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
    ! [X22,X14] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X14,X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I2_J) ).

fof(fact_zmod__zminus__zminus,axiom,
    ! [X26,X25] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus__zminus) ).

fof(fact_zmod__int,axiom,
    ! [X26,X25] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25,X26)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__int) ).

fof(fact_distinct__listsum__conv__Setsum,axiom,
    ! [X212,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),X212))
       => hAPP(c_List_Omonoid__add__class_Olistsum(X5),X212) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X5),c_COMBI(X5)),hAPP(c_List_Oset(X5),X212)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__listsum__conv__Setsum) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
    ! [X128,X14,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),X128)) = hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),hAPP(c_Nat_OSuc,X128)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).

fof(fact_power__Suc,axiom,
    ! [X98,X25,X15] :
      ( class_Power_Opower(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),hAPP(c_Nat_OSuc,X98)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
    ! [X128,X14,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),hAPP(c_Nat_OSuc,X128)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),X128)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).

fof(fact_image__uminus__atLeast,axiom,
    ! [X12,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),X12)) = hAPP(c_SetInterval_Oord__class_OatMost(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__atLeast) ).

fof(fact_image__uminus__greaterThan,axiom,
    ! [X12,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),X12)) = hAPP(c_SetInterval_Oord__class_OlessThan(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__greaterThan) ).

fof(fact_image__uminus__atMost,axiom,
    ! [X12,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),X12)) = hAPP(c_SetInterval_Oord__class_OatLeast(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__atMost) ).

fof(fact_image__uminus__lessThan,axiom,
    ! [X12,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),X12)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__lessThan) ).

fof(fact_replicate__Suc,axiom,
    ! [X14,X98,X15] : c_List_Oreplicate(X15,hAPP(c_Nat_OSuc,X98),X14) = hAPP(hAPP(c_List_Olist_OCons(X15),X14),c_List_Oreplicate(X15,X98,X14)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__Suc) ).

fof(fact_set__replicate,axiom,
    ! [X12,X5,X76] :
      ( X76 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X76,X12)) = hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__replicate) ).

fof(fact_set__replicate__conv__if,axiom,
    ! [X12,X5,X76] :
      ( ( X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X76,X12)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) )
      & ( X76 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X76,X12)) = hAPP(hAPP(c_Set_Oinsert(X5),X12),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_abs__of__pos,axiom,
    ! [X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
       => hAPP(c_Groups_Oabs__class_Oabs(X15),X25) = X25 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__pos) ).

fof(fact_abs__of__nonneg,axiom,
    ! [X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
       => hAPP(c_Groups_Oabs__class_Oabs(X15),X25) = X25 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).

fof(fact_abs__of__neg,axiom,
    ! [X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),c_Groups_Ozero__class_Ozero(X15)))
       => hAPP(c_Groups_Oabs__class_Oabs(X15),X25) = hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__neg) ).

fof(fact_abs__of__nonpos,axiom,
    ! [X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),c_Groups_Ozero__class_Ozero(X15)))
       => hAPP(c_Groups_Oabs__class_Oabs(X15),X25) = hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25) ) ),
    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,
    ! [X25,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),c_Groups_Ozero__class_Ozero(X15)))
       => c_Groups_Osgn__class_Osgn(X15,X25) = hAPP(c_Groups_Ouminus__class_Ouminus(X15),c_Groups_Oone__class_Oone(X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__neg) ).

fof(fact_equivp__symp,axiom,
    ! [X27,X12,X36,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X36)
     => ( hBOOL(hAPP(hAPP(X36,X12),X27))
       => hBOOL(hAPP(hAPP(X36,X27),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__symp) ).

fof(fact_New__DSequence_Oneg__union__def,axiom,
    ! [X70,X27,X12,X5] : hAPP(c_New__DSequence_Oneg__union(X5,X12,X27),X70) = c_Lazy__Sequence_Oappend(tc_Option_Ooption(X5),hAPP(X12,X70),hAPP(X27,X70)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__union__def) ).

fof(fact_length__butlast,axiom,
    ! [X221,X15] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),c_List_Obutlast(X15,X221)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__butlast) ).

fof(fact_lists_ONil,axiom,
    ! [X11,X5] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_List_Olists(X5,X11))),
    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,
    ! [X25,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X25))
       => c_Groups_Osgn__class_Osgn(X15,X25) = c_Groups_Oone__class_Oone(X15) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__pos) ).

fof(fact_nonzero__minus__divide__divide,axiom,
    ! [X25,X26,X15] :
      ( class_Rings_Odivision__ring(X15)
     => ( X26 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X26)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),X26) ) ),
    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,X29] :
      ( hBOOL(hAPP(X29,X6))
     => hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Set_OCollect(X5),X29))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_CollectI) ).

fof(fact_distinct__rev,axiom,
    ! [X212,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(c_List_Orev(X5),X212)))
    <=> hBOOL(hAPP(c_List_Odistinct(X5),X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__rev) ).

fof(fact_distinct1__rotate,axiom,
    ! [X212,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(c_List_Orotate1(X5),X212)))
    <=> hBOOL(hAPP(c_List_Odistinct(X5),X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct1__rotate) ).

fof(fact_quotient__empty,axiom,
    ! [X34,X5] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X34) = 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,
    ! [X16,X5] : hAPP(c_Product__Type_Oprod_Oprod__case(X5,X16,tc_prod(X5,X16)),c_Product__Type_OPair(X5,X16)) = c_Fun_Oid(tc_prod(X5,X16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__Pair) ).

fof(fact_min__max_Ole__iff__sup,axiom,
    ! [X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27))
      <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X12),X27) = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__iff__sup) ).

fof(fact_min__max_Osup__absorb2,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22))
       => hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),X22) = X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__absorb2) ).

fof(fact_min__max_Osup__absorb1,axiom,
    ! [X14,X22,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X14))
       => hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),X22) = X14 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__absorb1) ).

fof(fact_min__max_Ole__iff__inf,axiom,
    ! [X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27))
      <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X12),X27) = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__iff__inf) ).

fof(fact_min__max_Oinf__absorb1,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22))
       => hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),X22) = X14 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__absorb1) ).

fof(fact_min__max_Oinf__absorb2,axiom,
    ! [X14,X22,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X14))
       => hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),X22) = X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__absorb2) ).

fof(fact_le__iff__inf,axiom,
    ! [X27,X12,X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27))
      <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X12),X27) = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__inf) ).

fof(fact_inf__absorb1,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X22) = X14 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__absorb1) ).

fof(fact_inf__absorb2,axiom,
    ! [X14,X22,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X14))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X22) = X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__absorb2) ).

fof(fact_le__iff__sup,axiom,
    ! [X27,X12,X5] :
      ( class_Lattices_Osemilattice__sup(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27))
      <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X12),X27) = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__sup) ).

fof(fact_sup__absorb2,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X22) = X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__absorb2) ).

fof(fact_sup__absorb1,axiom,
    ! [X14,X22,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X14))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X22) = X14 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__absorb1) ).

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_Min_Osingleton,axiom,
    ! [X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Osingleton) ).

fof(fact_Max_Osingleton,axiom,
    ! [X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Osingleton) ).

fof(fact_Sup__fin_Osingleton,axiom,
    ! [X12,X5] :
      ( class_Lattices_Olattice(X5)
     => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Osingleton) ).

fof(fact_Inf__fin_Osingleton,axiom,
    ! [X12,X5] :
      ( class_Lattices_Olattice(X5)
     => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Osingleton) ).

fof(fact_mult__Suc,axiom,
    ! [X98,X99] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X99)),X98) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc) ).

fof(fact_cut,axiom,
    ! [X4,X7,X9,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X9,X7)
     => ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X9)
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cut) ).

fof(fact_diff__add__inverse,axiom,
    ! [X99,X98] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X99)),X98) = X99,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).

fof(fact_diff__add__inverse2,axiom,
    ! [X98,X99] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X98)),X98) = X99,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).

fof(fact_New__DSequence_Opos__union__def,axiom,
    ! [X70,X275,X253,X5] : hAPP(c_New__DSequence_Opos__union(X5,X253,X275),X70) = c_Lazy__Sequence_Oappend(X5,hAPP(X253,X70),hAPP(X275,X70)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__union__def) ).

fof(fact_Union__quotient,axiom,
    ! [X34,X11,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X11,X34)
     => c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X11),X34)) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__quotient) ).

fof(fact_minus__divide__divide,axiom,
    ! [X26,X25,X15] :
      ( class_Fields_Ofield__inverse__zero(X15)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X26)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__divide) ).

fof(fact_abs__mult__self,axiom,
    ! [X25,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__self) ).

fof(fact_minus__mult__minus,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Oring(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X26)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__minus) ).

fof(fact_minus__mult__commute,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Oring(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)),X26) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__commute) ).

fof(fact_wfP__accp__iff,axiom,
    ! [X34,X5] :
      ( c_Wellfounded_OwfP(X5,X34)
    <=> ! [X32] : hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X34),X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__accp__iff) ).

fof(fact_nonzero__minus__divide__right,axiom,
    ! [X25,X26,X15] :
      ( class_Rings_Odivision__ring(X15)
     => ( X26 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),X26)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__minus__divide__right) ).

fof(fact_quotient__is__empty2,axiom,
    ! [X34,X11,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X11),X34)
    <=> X11 = 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,
    ! [X34,X11,X5] :
      ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X11),X34) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))
    <=> X11 = 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,
    ! [X66,X97] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X97,X66)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X66),X97)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__greaterThanAtMost__int) ).

fof(fact_linorder__neq__iff,axiom,
    ! [X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( X12 != X27
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X12),X27))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X27),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).

fof(fact_linorder__less__linear,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
        | X14 = X22
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).

fof(fact_mod__mod__trivial,axiom,
    ! [X26,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,c_Divides_Odiv__class_Omod(X15,X25,X26),X26) = c_Divides_Odiv__class_Omod(X15,X25,X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mod__trivial) ).

fof(fact_Int__empty__right,axiom,
    ! [X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),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_Diff__UNIV,axiom,
    ! [X11,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),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_Un__UNIV__right,axiom,
    ! [X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),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_Domain__empty,axiom,
    ! [X16,X5] : hAPP(c_Relation_ODomain(X5,X16),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X16),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,X16] : hAPP(c_Relation_ORange(X16,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X16,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_fun__upd__triv,axiom,
    ! [X12,X2,X16,X5] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),X2),X12),hAPP(X2,X12)) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__triv) ).

fof(fact_fst__conv,axiom,
    ! [X26,X25,X5,X15] : hAPP(c_Product__Type_Ofst(X15,X5),hAPP(hAPP(c_Product__Type_OPair(X15,X5),X25),X26)) = X25,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__conv) ).

fof(fact_snd__conv,axiom,
    ! [X26,X25,X15,X5] : hAPP(c_Product__Type_Osnd(X5,X15),hAPP(hAPP(c_Product__Type_OPair(X5,X15),X25),X26)) = X26,
    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,
    ! [X76,X45] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76))
    <=> ? [X109] : X76 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X109) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).

fof(fact_insert__absorb,axiom,
    ! [X11,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
     => hAPP(hAPP(c_Set_Oinsert(X5),X6),X11) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb) ).

fof(fact_the__elem__eq,axiom,
    ! [X12,X5] : c_Set_Othe__elem(X5,hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__elem__eq) ).

fof(fact_linorder__le__less__linear,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).

fof(fact_linorder__linear,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).

fof(fact_fun__upd__idem,axiom,
    ! [X5,X16,X27,X12,X2] :
      ( hAPP(X2,X12) = X27
     => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X16,X5),X2),X12),X27) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem) ).

fof(fact_listsum__simps_I2_J,axiom,
    ! [X221,X14,X15] :
      ( class_Groups_Omonoid__add(X15)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X15),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X14),hAPP(c_List_Omonoid__add__class_Olistsum(X15),X221)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__simps_I2_J) ).

fof(fact_minus__divide__right,axiom,
    ! [X26,X25,X15] :
      ( class_Fields_Ofield__inverse__zero(X15)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),X26)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__right) ).

fof(fact_minus__mult__right,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Oring(X15)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__right) ).

fof(fact_option_Osize_I2_J,axiom,
    ! [X6,X92,X5] : c_Option_Ooption_Ooption__size(X5,X92,hAPP(c_Option_Ooption_OSome(X5),X6)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X92,X6)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option_Osize_I2_J) ).

fof(fact_partition_Osimps_I1_J,axiom,
    ! [X29,X5] : c_List_Opartition(X5,X29,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,
    ! [X221,X14,X15] : hAPP(hAPP(c_List_Otake(X15),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = hAPP(hAPP(c_List_Olist_OCons(X15),X14),c_List_Olist_ONil(X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__1__Cons) ).

fof(fact_wf__inv__image,axiom,
    ! [X2,X16,X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => c_Wellfounded_Owf(X16,hAPP(hAPP(c_Relation_Oinv__image(X5,X16),X34),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__inv__image) ).

fof(fact_rp__inv__image__rp,axiom,
    ! [X2,X16,X29,X5] :
      ( c_FunDef_Oreduction__pair(X5,X29)
     => c_FunDef_Oreduction__pair(X16,hAPP(hAPP(c_FunDef_Orp__inv__image(X5,X16),X29),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp__inv__image__rp) ).

fof(fact_mod__add__self1,axiom,
    ! [X25,X26,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X26),X25),X26) = c_Divides_Odiv__class_Omod(X15,X25,X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__self1) ).

fof(fact_mod__add__self2,axiom,
    ! [X26,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26),X26) = c_Divides_Odiv__class_Omod(X15,X25,X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__self2) ).

fof(fact_nth__via__drop,axiom,
    ! [X225,X22,X221,X98,X15] :
      ( hAPP(hAPP(c_List_Odrop(X15),X98),X221) = hAPP(hAPP(c_List_Olist_OCons(X15),X22),X225)
     => hAPP(hAPP(c_List_Onth(X15),X221),X98) = X22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__via__drop) ).

fof(fact_max__Suc__Suc,axiom,
    ! [X98,X99] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X99)),hAPP(c_Nat_OSuc,X98)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X99),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__Suc__Suc) ).

fof(fact_min__Suc__Suc,axiom,
    ! [X98,X99] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X99)),hAPP(c_Nat_OSuc,X98)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X99),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__Suc__Suc) ).

fof(fact_plus__code__numeral__code,axiom,
    ! [X99,X98] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X98)),hAPP(c_Code__Numeral_Oof__nat,X99)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X99)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__code__numeral__code) ).

fof(fact_times__code__numeral__code,axiom,
    ! [X99,X98] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X98)),hAPP(c_Code__Numeral_Oof__nat,X99)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X99)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__code__numeral__code) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
    ! [X98,X14] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14)),X98) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X14),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).

fof(fact_zpower__int,axiom,
    ! [X98,X99] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X99)),X98) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X99),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__int) ).

fof(fact_zmult__zminus,axiom,
    ! [X132,X23] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23)),X132) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X132)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zminus) ).

fof(fact_int__power,axiom,
    ! [X98,X99] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X99),X98)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X99)),X98),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__power) ).

fof(fact_List_Oset__insert,axiom,
    ! [X212,X12,X5] : hAPP(c_List_Oset(X5),c_List_Oinsert(X5,X12,X212)) = hAPP(hAPP(c_Set_Oinsert(X5),X12),hAPP(c_List_Oset(X5),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Oset__insert) ).

fof(fact_splice_Osimps_I2_J,axiom,
    ! [X277,X126,X15] : c_List_Osplice(X15,hAPP(hAPP(c_List_Olist_OCons(X15),X126),X277),c_List_Olist_ONil(X15)) = hAPP(hAPP(c_List_Olist_OCons(X15),X126),X277),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I2_J) ).

fof(fact_abs__ge__zero,axiom,
    ! [X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(c_Groups_Oabs__class_Oabs(X15),X25))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__zero) ).

fof(fact_zero__le__imp__of__nat,axiom,
    ! [X99,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),X99))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__imp__of__nat) ).

fof(fact_of__nat__0__le__iff,axiom,
    ! [X98,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),X98))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__0__le__iff) ).

fof(fact_in__enum,axiom,
    ! [X12,X5] :
      ( class_Enum_Oenum(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),c_Enum_Oenum__class_Oenum(X5)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__enum) ).

fof(fact_min__max_Osup_Oleft__idem,axiom,
    ! [X26,X25,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X25),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X25),X26)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X25),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup_Oleft__idem) ).

fof(fact_min__max_Osup__left__idem,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),X22)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__left__idem) ).

fof(fact_min__max_Oinf__left__idem,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),X22)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__left__idem) ).

fof(fact_min__max_Oinf_Oleft__idem,axiom,
    ! [X26,X25,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X25),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X25),X26)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X25),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf_Oleft__idem) ).

fof(fact_mult__left__idem,axiom,
    ! [X26,X25,X15] :
      ( class_Lattices_Oab__semigroup__idem__mult(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__idem) ).

fof(fact_inf_Oleft__idem,axiom,
    ! [X26,X25,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X25),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X25),X26)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X25),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oleft__idem) ).

fof(fact_inf__left__idem,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__left__idem) ).

fof(fact_inf__sup__aci_I4_J,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Olattice(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I4_J) ).

fof(fact_inf__sup__aci_I8_J,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Olattice(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I8_J) ).

fof(fact_sup_Oleft__idem,axiom,
    ! [X26,X25,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X25),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X25),X26)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X25),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup_Oleft__idem) ).

fof(fact_sup__left__idem,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X22)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__left__idem) ).

fof(fact_finite__sorted__distinct__unique,axiom,
    ! [X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ? [X3] :
            ( hAPP(c_List_Oset(X5),X3) = X11
            & c_List_Olinorder__class_Osorted(X5,X3)
            & hBOOL(hAPP(c_List_Odistinct(X5),X3))
            & ! [X33] :
                ( ( hAPP(c_List_Oset(X5),X33) = X11
                  & c_List_Olinorder__class_Osorted(X5,X33)
                  & hBOOL(hAPP(c_List_Odistinct(X5),X33)) )
               => X33 = X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__sorted__distinct__unique) ).

fof(fact_drop__tl,axiom,
    ! [X221,X98,X15] : hAPP(hAPP(c_List_Odrop(X15),X98),hAPP(c_List_Otl(X15),X221)) = hAPP(c_List_Otl(X15),hAPP(hAPP(c_List_Odrop(X15),X98),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__tl) ).

fof(fact_tl__drop,axiom,
    ! [X221,X98,X15] : hAPP(c_List_Otl(X15),hAPP(hAPP(c_List_Odrop(X15),X98),X221)) = hAPP(hAPP(c_List_Odrop(X15),X98),hAPP(c_List_Otl(X15),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl__drop) ).

fof(fact_List_Oset_Osimps_I2_J,axiom,
    ! [X212,X12,X5] : hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = hAPP(hAPP(c_Set_Oinsert(X5),X12),hAPP(c_List_Oset(X5),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Oset_Osimps_I2_J) ).

fof(fact_card__atLeastAtMost,axiom,
    ! [X66,X97] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X97,X66)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X66)),X97),
    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_map__of_Osimps_I1_J,axiom,
    ! [X185,X5,X15] : hAPP(hAPP(c_Map_Omap__of(X15,X5),c_List_Olist_ONil(tc_prod(X15,X5))),X185) = c_Option_Ooption_ONone(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of_Osimps_I1_J) ).

fof(fact_map__of__Cons__code_I1_J,axiom,
    ! [X100,X15,X5] : hAPP(hAPP(c_Map_Omap__of(X5,X15),c_List_Olist_ONil(tc_prod(X5,X15))),X100) = c_Option_Ooption_ONone(X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__of__Cons__code_I1_J) ).

fof(fact_some__eq__ex,axiom,
    ! [X5,X29] :
      ( hBOOL(hAPP(X29,c_Hilbert__Choice_OEps(X5,X29)))
    <=> ? [X32] : hBOOL(hAPP(X29,X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__eq__ex) ).

fof(fact_partition__filter1,axiom,
    ! [X212,X29,X5] : hAPP(c_Product__Type_Ofst(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Opartition(X5,X29,X212)) = hAPP(c_List_Ofilter(X5,X29),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition__filter1) ).

fof(fact_iso__tuple__UNIV__I,axiom,
    ! [X12,X5] : hBOOL(hAPP(hAPP(c_member(X5),X12),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,
    ! [X12,X5] : hBOOL(hAPP(hAPP(c_member(X5),X12),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,
    ! [X13,X11,X5] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X13)
    <=> X11 = X13 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__eq__Compl__iff) ).

fof(fact_fun__Compl__def,axiom,
    ! [X12,X11,X16,X5] :
      ( class_Groups_Ouminus(X5)
     => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X16,X5)),X11),X12) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(X11,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__Compl__def) ).

fof(fact_uminus__apply,axiom,
    ! [X12,X11,X16,X5] :
      ( class_Groups_Ouminus(X5)
     => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X16,X5)),X11),X12) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(X11,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__apply) ).

fof(fact_nat__0__le,axiom,
    ! [X23] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X23)) = X23 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__le) ).

fof(fact_tsub__eq,axiom,
    ! [X14,X22] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22),X14))
     => c_Nat__Transfer_Otsub(X14,X22) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X14),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tsub__eq) ).

fof(fact_subtract__code__numeral__code,axiom,
    ! [X99,X98] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,X98)),hAPP(c_Code__Numeral_Oof__nat,X99)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),X99)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subtract__code__numeral__code) ).

fof(fact_full__small__int__def,axiom,
    ! [X20,X2] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,X2,X20) = c_Smallcheck_Ofull__small_H(X2,hAPP(c_Code__Numeral_Oint__of,X20),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X20))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_full__small__int__def) ).

fof(fact_int__eq__iff,axiom,
    ! [X37,X45] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X45) = X37
    <=> ( X45 = hAPP(c_Int_Onat,X37)
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__eq__iff) ).

fof(fact_semilattice__big_OF__eq,axiom,
    ! [X11,X90,X2,X5] :
      ( c_Big__Operators_Osemilattice__big(X5,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(X90,X11) = hAPP(c_Finite__Set_Ofold1(X5,X2),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semilattice__big_OF__eq) ).

fof(fact_folding__one_Oeq__fold,axiom,
    ! [X11,X90,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(X90,X11) = hAPP(c_Finite__Set_Ofold1(X5,X2),X11) ) ),
    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,
    ! [X11,X12,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X12),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Set_Oinsert(X5),X12),X11),
    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,
    ! [X67,X5,X11,X16] :
      ( class_Complete__Lattice_Ocomplete__lattice(X16)
     => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X16),X11),hAPP(c_COMBK(X16,X5),X67)) = X67 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__const) ).

fof(fact_SUP__const,axiom,
    ! [X67,X5,X11,X16] :
      ( class_Complete__Lattice_Ocomplete__lattice(X16)
     => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X16),X11),hAPP(c_COMBK(X16,X5),X67)) = X67 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__const) ).

fof(fact_compl__unique,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Oboolean__algebra(X15)
     => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X22) = c_Orderings_Obot__class_Obot(X15)
       => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X22) = c_Orderings_Otop__class_Otop(X15)
         => hAPP(c_Groups_Ouminus__class_Ouminus(X15),X14) = X22 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__unique) ).

fof(fact_mult__Suc__right,axiom,
    ! [X98,X99] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),hAPP(c_Nat_OSuc,X98)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc__right) ).

fof(fact_finite__atLeastZeroLessThan__int,axiom,
    ! [X66] : 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)),X66))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastZeroLessThan__int) ).

fof(fact_transpose_Osimps_I2_J,axiom,
    ! [X255,X15] : c_List_Otranspose(X15,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X15)),c_List_Olist_ONil(X15)),X255)) = c_List_Otranspose(X15,X255),
    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,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98) = X99 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less) ).

fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
    ! [X66,X97] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X97),c_Groups_Oone__class_Oone(tc_Int_Oint)),X66) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X97,X66),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastPlusOneAtMost__greaterThanAtMost__int) ).

fof(fact_Sup__insert,axiom,
    ! [X11,X6,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OSup__class_OSup(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X6),c_Complete__Lattice_OSup__class_OSup(X5,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__insert) ).

fof(fact_Inf__insert,axiom,
    ! [X11,X6,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OInf__class_OInf(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X6),c_Complete__Lattice_OInf__class_OInf(X5,X11)) ),
    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_small__int__def,axiom,
    ! [X20,X2] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),X2),X20) = c_Smallcheck_Osmall_H(X2,hAPP(c_Code__Numeral_Oint__of,X20),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X20))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small__int__def) ).

fof(fact_insert__remdups,axiom,
    ! [X221,X14,X15] : c_List_Oinsert(X15,X14,c_List_Oremdups(X15,X221)) = c_List_Oremdups(X15,c_List_Oinsert(X15,X14,X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__remdups) ).

fof(fact_list__all__rev,axiom,
    ! [X212,X29,X5] :
      ( c_List_Olist__all(X5,X29,hAPP(c_List_Orev(X5),X212))
    <=> c_List_Olist__all(X5,X29,X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__rev) ).

fof(fact_list__ex__rev,axiom,
    ! [X212,X29,X5] :
      ( c_List_Olist__ex(X5,X29,hAPP(c_List_Orev(X5),X212))
    <=> c_List_Olist__ex(X5,X29,X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__rev) ).

fof(fact_butlast__append,axiom,
    ! [X221,X15,X225] :
      ( ( X225 = c_List_Olist_ONil(X15)
       => c_List_Obutlast(X15,hAPP(hAPP(c_List_Oappend(X15),X221),X225)) = c_List_Obutlast(X15,X221) )
      & ( X225 != c_List_Olist_ONil(X15)
       => c_List_Obutlast(X15,hAPP(hAPP(c_List_Oappend(X15),X221),X225)) = hAPP(hAPP(c_List_Oappend(X15),X221),c_List_Obutlast(X15,X225)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__append) ).

fof(fact_butlast_Osimps_I2_J,axiom,
    ! [X14,X15,X221] :
      ( ( X221 = c_List_Olist_ONil(X15)
       => c_List_Obutlast(X15,hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = c_List_Olist_ONil(X15) )
      & ( X221 != c_List_Olist_ONil(X15)
       => c_List_Obutlast(X15,hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = hAPP(hAPP(c_List_Olist_OCons(X15),X14),c_List_Obutlast(X15,X221)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast_Osimps_I2_J) ).

fof(fact_vimage__UNIV,axiom,
    ! [X2,X16,X5] : hAPP(c_Set_Ovimage(X5,X16,X2),c_Orderings_Otop__class_Otop(tc_fun(X16,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,X16,X5] : hAPP(c_Set_Ovimage(X5,X16,X2),c_Orderings_Obot__class_Obot(tc_fun(X16,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,
    ! [X36,X5,X16] : hAPP(c_Relation_OImage(X16,X5,X36),c_Orderings_Obot__class_Obot(tc_fun(X16,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_image__empty,axiom,
    ! [X2,X5,X16] : hAPP(c_Set_Oimage(X16,X5,X2),c_Orderings_Obot__class_Obot(tc_fun(X16,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,
    ! [X34,X11,X5] :
      ( c_Relation_Orefl__on(X5,X11,X34)
     => c_Relation_Orefl__on(tc_List_Olist(X5),c_List_Olists(X5,X11),c_List_Olistrel(X5,X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__refl__on) ).

fof(fact_equiv__listrel,axiom,
    ! [X34,X11,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X11,X34)
     => c_Equiv__Relations_Oequiv(tc_List_Olist(X5),c_List_Olists(X5,X11),c_List_Olistrel(X5,X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__listrel) ).

fof(fact_mem__def,axiom,
    ! [X11,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
    <=> hBOOL(hAPP(X11,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).

fof(fact_div__less,axiom,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),X98) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__less) ).

fof(fact_equal__int__def,axiom,
    ! [X97,X30] :
      ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X30),X97))
    <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X30),X97) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__int__def) ).

fof(fact_diff__is__0__eq_H,axiom,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X98))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).

fof(fact_diff__is__0__eq,axiom,
    ! [X76,X45] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X45),X76) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).

fof(fact_Int__UNIV__right,axiom,
    ! [X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__UNIV__right) ).

fof(fact_Diff__empty,axiom,
    ! [X11,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__empty) ).

fof(fact_Un__empty__right,axiom,
    ! [X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__empty__right) ).

fof(fact_double__complement,axiom,
    ! [X11,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)),X11)) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).

fof(fact_rel__pow__1,axiom,
    ! [X36,X5] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X36) = X36,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__1) ).

fof(fact_ran__empty,axiom,
    ! [X5,X16] : c_Map_Oran(X16,X5,hAPP(c_COMBK(tc_Option_Ooption(X5),X16),c_Option_Ooption_ONone(X5))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ran__empty) ).

fof(fact_dom__empty,axiom,
    ! [X16,X5] : c_Map_Odom(X5,X16,hAPP(c_COMBK(tc_Option_Ooption(X16),X5),c_Option_Ooption_ONone(X16))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dom__empty) ).

fof(fact_list__update__id,axiom,
    ! [X102,X221,X15] : hAPP(hAPP(c_List_Olist__update(X15,X221),X102),hAPP(hAPP(c_List_Onth(X15),X221),X102)) = X221,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__id) ).

fof(fact_square__eq__iff,axiom,
    ! [X17,X6,X5] :
      ( class_Rings_Oidom(X5)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X17)
      <=> ( X6 = X17
          | X6 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X17) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__iff) ).

fof(fact_add__Suc,axiom,
    ! [X98,X99] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X99)),X98) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).

fof(fact_drop__butlast,axiom,
    ! [X221,X98,X15] : hAPP(hAPP(c_List_Odrop(X15),X98),c_List_Obutlast(X15,X221)) = c_List_Obutlast(X15,hAPP(hAPP(c_List_Odrop(X15),X98),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__butlast) ).

fof(fact_butlast__drop,axiom,
    ! [X221,X98,X15] : c_List_Obutlast(X15,hAPP(hAPP(c_List_Odrop(X15),X98),X221)) = hAPP(hAPP(c_List_Odrop(X15),X98),c_List_Obutlast(X15,X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__drop) ).

fof(fact_code__numeral__not__eq__zero,axiom,
    ! [X70] :
      ( X70 != 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)),X70)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral__not__eq__zero) ).

fof(fact_Domain__empty__iff,axiom,
    ! [X34,X16,X5] :
      ( hAPP(c_Relation_ODomain(X5,X16),X34) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> X34 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X16),tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__empty__iff) ).

fof(fact_Range__empty__iff,axiom,
    ! [X34,X5,X16] :
      ( hAPP(c_Relation_ORange(X16,X5),X34) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> X34 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X16,X5),tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__empty__iff) ).

fof(fact_abs__zmult__eq__1,axiom,
    ! [X98,X99] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X99),X98)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
     => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X99) = 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,
    ! [X22,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14),X22))
      | X14 = X22
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).

fof(fact_nat__neq__iff,axiom,
    ! [X76,X45] :
      ( X45 != X76
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),X45)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).

fof(fact_card__atLeastLessThan__int,axiom,
    ! [X66,X97] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X97),X66)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X66),X97)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atLeastLessThan__int) ).

fof(fact_abs__ge__self,axiom,
    ! [X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),hAPP(c_Groups_Oabs__class_Oabs(X15),X25))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__self) ).

fof(fact_card__greaterThanLessThan,axiom,
    ! [X66,X97] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X97,X66)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X66),hAPP(c_Nat_OSuc,X97)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__greaterThanLessThan) ).

fof(fact_zle__linear,axiom,
    ! [X132,X23] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23),X132))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X132),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).

fof(fact_nat__le__linear,axiom,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X98))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X99)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).

fof(fact_zdiv__zminus__zminus,axiom,
    ! [X26,X25] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus__zminus) ).

fof(fact_zdiv__zminus2,axiom,
    ! [X26,X25] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25)),X26),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus2) ).

fof(fact_drop__Suc,axiom,
    ! [X221,X98,X15] : hAPP(hAPP(c_List_Odrop(X15),hAPP(c_Nat_OSuc,X98)),X221) = hAPP(hAPP(c_List_Odrop(X15),X98),hAPP(c_List_Otl(X15),X221)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__Suc) ).

fof(fact_dom__eq__empty__conv,axiom,
    ! [X2,X16,X5] :
      ( c_Map_Odom(X5,X16,X2) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> X2 = hAPP(c_COMBK(tc_Option_Ooption(X16),X5),c_Option_Ooption_ONone(X16)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dom__eq__empty__conv) ).

fof(fact_gr0__conv__Suc,axiom,
    ! [X76] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X76))
    <=> ? [X94] : X76 = hAPP(c_Nat_OSuc,X94) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).

fof(fact_min__max_OSup__fin_OF__eq,axiom,
    ! [X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X11) = hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omax(X5)),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_OF__eq) ).

fof(fact_min__max_OInf__fin_OF__eq,axiom,
    ! [X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X11) = hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__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_distinct__tl,axiom,
    ! [X221,X15] :
      ( hBOOL(hAPP(c_List_Odistinct(X15),X221))
     => hBOOL(hAPP(c_List_Odistinct(X15),hAPP(c_List_Otl(X15),X221))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__tl) ).

fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
    ! [X66,X97] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X97),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X66),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X97,X66),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThanPlusOne__atLeastAtMost__int) ).

fof(fact_neg__def,axiom,
    ! [X167] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X167))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X167),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__def) ).

fof(fact_card__distinct,axiom,
    ! [X212,X5] :
      ( hAPP(c_Finite__Set_Ocard(X5),hAPP(c_List_Oset(X5),X212)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)
     => hBOOL(hAPP(c_List_Odistinct(X5),X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__distinct) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
    ! [X22,X14] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14),X22)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J) ).

fof(fact_singleton__rev__conv,axiom,
    ! [X212,X12,X5] :
      ( hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Olist_ONil(X5)) = hAPP(c_List_Orev(X5),X212)
    <=> X212 = hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Olist_ONil(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__rev__conv) ).

fof(fact_rev__singleton__conv,axiom,
    ! [X12,X212,X5] :
      ( hAPP(c_List_Orev(X5),X212) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Olist_ONil(X5))
    <=> X212 = hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Olist_ONil(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__singleton__conv) ).

fof(fact_listrel1__converse,axiom,
    ! [X34,X5] : c_List_Olistrel1(X5,hAPP(c_Relation_Oconverse(X5,X5),X34)) = hAPP(c_Relation_Oconverse(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel1(X5,X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__converse) ).

fof(fact_minus__diff__eq,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Oab__group__add(X15)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X25),X26)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X26),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__diff__eq) ).

fof(fact_rev__replicate,axiom,
    ! [X14,X98,X15] : hAPP(c_List_Orev(X15),c_List_Oreplicate(X15,X98,X14)) = c_List_Oreplicate(X15,X98,X14),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__replicate) ).

fof(fact_acc__wfD,axiom,
    ! [X12,X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => hBOOL(hAPP(hAPP(c_member(X5),X12),c_Wellfounded_Oacc(X5,X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__wfD) ).

fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
    ! [X14,X15] :
      ( class_Rings_Ocomm__ring__1(X15)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X15),X14) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),c_Groups_Oone__class_Oone(X15))),X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).

fof(fact_finite__atLeastLessThan__int,axiom,
    ! [X66,X97] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X97),X66))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastLessThan__int) ).

fof(fact_finite__atLeastLessThan,axiom,
    ! [X66,X97] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X97),X66))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).

fof(fact_list__all__iff__all__interval__int,axiom,
    ! [X115,X70,X29] :
      ( c_List_Olist__all(tc_Int_Oint,X29,c_List_Oupto(X70,X115))
    <=> c_List_Oall__interval__int(X29,X70,X115) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__iff__all__interval__int) ).

fof(fact_enum__all,axiom,
    ! [X29,X5] :
      ( class_Enum_Oenum(X5)
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X5),X29))
      <=> ! [X32] : hBOOL(hAPP(X29,X32)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__all) ).

fof(fact_all__code,axiom,
    ! [X29,X5] :
      ( class_Enum_Oenum(X5)
     => ( ! [X32] : hBOOL(hAPP(X29,X32))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X5),X29)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__code) ).

fof(fact_nat_Osize_I4_J,axiom,
    ! [X131] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,X131)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X131)),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_order__less__imp__not__eq2,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Oorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
       => X22 != X14 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).

fof(fact_order__less__imp__not__eq,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Oorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
       => X14 != X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).

fof(fact_less__imp__neq,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Oorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
       => X14 != X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).

fof(fact_replicate__eq__replicate,axiom,
    ! [X27,X76,X12,X45,X5] :
      ( c_List_Oreplicate(X5,X45,X12) = c_List_Oreplicate(X5,X76,X27)
    <=> ( X45 = X76
        & ( X45 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => X12 = X27 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__eq__replicate) ).

fof(fact_diff__eq__diff__eq,axiom,
    ! [X20,X21,X17,X6,X5] :
      ( class_Groups_Oab__group__add(X5)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X17) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X21),X20)
       => ( X6 = X17
        <=> X21 = X20 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).

fof(fact_equal__eq,axiom,
    ! [X27,X12,X5] :
      ( class_HOL_Oequal(X5)
     => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X5),X12),X27))
      <=> X12 = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__eq) ).

fof(fact_option__map__Some,axiom,
    ! [X12,X2,X5,X16] : hAPP(hAPP(c_Option_Omap(X16,X5),X2),hAPP(c_Option_Ooption_OSome(X16),X12)) = hAPP(c_Option_Ooption_OSome(X5),hAPP(X2,X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option__map__Some) ).

fof(fact_rev__filter,axiom,
    ! [X212,X29,X5] : hAPP(c_List_Orev(X5),hAPP(c_List_Ofilter(X5,X29),X212)) = hAPP(c_List_Ofilter(X5,X29),hAPP(c_List_Orev(X5),X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__filter) ).

fof(fact_zmod__zminus1__not__zero,axiom,
    ! [X103,X100] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X100),X103) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,X100,X103) != 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,
    ! [X103,X100] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X100,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X103)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,X100,X103) != 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,
    ! [X76] :
      ( X76 != 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)),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).

fof(fact_n__lists__Nil,axiom,
    ! [X15,X98] :
      ( ( X98 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Enum_On__lists(X15,X98,c_List_Olist_ONil(X15)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X15)),c_List_Olist_ONil(X15)),c_List_Olist_ONil(tc_List_Olist(X15))) )
      & ( X98 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Enum_On__lists(X15,X98,c_List_Olist_ONil(X15)) = c_List_Olist_ONil(tc_List_Olist(X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__lists__Nil) ).

fof(fact_add__right__imp__eq,axiom,
    ! [X24,X25,X26,X15] :
      ( class_Groups_Ocancel__semigroup__add(X15)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X26),X25) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X24),X25)
       => X26 = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).

fof(fact_add__right__cancel,axiom,
    ! [X21,X6,X17,X5] :
      ( class_Groups_Ocancel__semigroup__add(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X17),X6) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X6)
      <=> X17 = X21 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).

fof(fact_add__imp__eq,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Groups_Ocancel__ab__semigroup__add(X15)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X24)
       => X26 = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).

fof(fact_add__left__imp__eq,axiom,
    ! [X24,X26,X25,X15] :
      ( class_Groups_Ocancel__semigroup__add(X15)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X24)
       => X26 = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).

fof(fact_add__left__cancel,axiom,
    ! [X21,X17,X6,X5] :
      ( class_Groups_Ocancel__semigroup__add(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X17) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X21)
      <=> X17 = X21 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).

fof(fact_lazy__sequence_Oinject,axiom,
    ! [X269,X82,X268,X6,X5] :
      ( c_Lazy__Sequence_Olazy__sequence_OInsert(X5,X6,X268) = c_Lazy__Sequence_Olazy__sequence_OInsert(X5,X82,X269)
    <=> ( X6 = X82
        & X268 = X269 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Oinject) ).

fof(fact_nat__0__iff,axiom,
    ! [X70] :
      ( hAPP(c_Int_Onat,X70) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X70),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__iff) ).

fof(fact_nat__le__0,axiom,
    ! [X23] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hAPP(c_Int_Onat,X23) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__0) ).

fof(fact_is__nat__def,axiom,
    ! [X12] :
      ( c_Nat__Transfer_Ois__nat(X12)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_is__nat__def) ).

fof(fact_add__Suc__right,axiom,
    ! [X98,X99] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),hAPP(c_Nat_OSuc,X98)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).

fof(fact_lexn_Osimps_I1_J,axiom,
    ! [X34,X5] : hAPP(c_List_Olexn(X5,X34),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_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
    ! [X23] : 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),X23))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).

fof(fact_zero__zle__int,axiom,
    ! [X98] : 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),X98))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__zle__int) ).

fof(fact_Diff__cancel,axiom,
    ! [X11,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X11) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__cancel) ).

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,
    ! [X17,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( X6 = X17
       => c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X17) = 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,
    ! [X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hAPP(c_List_Oset(X5),c_List_Olinorder__class_Osorted__list__of__set(X5,X11)) = X11
          & c_List_Olinorder__class_Osorted(X5,c_List_Olinorder__class_Osorted__list__of__set(X5,X11))
          & hBOOL(hAPP(c_List_Odistinct(X5),c_List_Olinorder__class_Osorted__list__of__set(X5,X11))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__list__of__set) ).

fof(fact_mod__mult__self1__is__0,axiom,
    ! [X25,X26,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X25),X26) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self1__is__0) ).

fof(fact_mod__mult__self2__is__0,axiom,
    ! [X26,X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26),X26) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self2__is__0) ).

fof(fact_distinct__butlast,axiom,
    ! [X15,X221] :
      ( X221 != c_List_Olist_ONil(X15)
     => ( hBOOL(hAPP(c_List_Odistinct(X15),X221))
       => hBOOL(hAPP(c_List_Odistinct(X15),c_List_Obutlast(X15,X221))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__butlast) ).

fof(fact_card__greaterThanAtMost,axiom,
    ! [X66,X97] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X97,X66)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X66),X97),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__greaterThanAtMost) ).

fof(fact_list_Oinject,axiom,
    ! [X220,X82,X213,X6,X5] :
      ( hAPP(hAPP(c_List_Olist_OCons(X5),X6),X213) = hAPP(hAPP(c_List_Olist_OCons(X5),X82),X220)
    <=> ( X6 = X82
        & X213 = X220 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Oinject) ).

fof(fact_append__same__eq,axiom,
    ! [X227,X212,X214,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X214),X212) = hAPP(hAPP(c_List_Oappend(X5),X227),X212)
    <=> X214 = X227 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__same__eq) ).

fof(fact_same__append__eq,axiom,
    ! [X227,X214,X212,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X212),X214) = hAPP(hAPP(c_List_Oappend(X5),X212),X227)
    <=> X214 = X227 ),
    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,
    ! [X102,X101] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X102))
     => c_List_Oupto(X102,X101) = 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,
    ! [X221,X15] : c_Enum_On__lists(X15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X221) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X15)),c_List_Olist_ONil(X15)),c_List_Olist_ONil(tc_List_Olist(X15))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__lists_Osimps_I1_J) ).

fof(fact_atMost__Suc,axiom,
    ! [X30] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__Suc) ).

fof(fact_eq__number__of__0,axiom,
    ! [X56] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X56),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__0) ).

fof(fact_neg__imp__number__of__eq__0,axiom,
    ! [X126] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
     => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126) = 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,
    ! [X56] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X56),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__0__number__of) ).

fof(fact_min__max_Osup__inf__absorb,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),X22)) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__inf__absorb) ).

fof(fact_min__max_Oinf__sup__absorb,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),X22)) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__sup__absorb) ).

fof(fact_inf__sup__absorb,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Olattice(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X22)) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__absorb) ).

fof(fact_sup__inf__absorb,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Olattice(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X22)) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__inf__absorb) ).

fof(fact_conversep__conversep,axiom,
    ! [X34,X5,X16] : c_Predicate_Oconversep(X16,X5,c_Predicate_Oconversep(X5,X16,X34)) = X34,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__conversep) ).

fof(fact_le__0__eq,axiom,
    ! [X76] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X76),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> X76 = 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,
    ! [X221,X14,X15] : hAPP(hAPP(c_List_Odrop(X15),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = X221,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__1__Cons) ).

fof(fact_diff__Suc__Suc,axiom,
    ! [X98,X99] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X99)),hAPP(c_Nat_OSuc,X98)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).

fof(fact_add__Suc__shift,axiom,
    ! [X98,X99] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X99)),X98) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),hAPP(c_Nat_OSuc,X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).

fof(fact_fold1__def,axiom,
    ! [X11,X2,X5] : hAPP(c_Finite__Set_Ofold1(X5,X2),X11) = c_HOL_OThe(X5,c_Finite__Set_Ofold1Set(X5,X2,X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__def) ).

fof(fact_zmod__eq__0__iff,axiom,
    ! [X20,X45] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X45,X20) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> ? [X150] : X45 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X150) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__eq__0__iff) ).

fof(fact_mod__eq__0__iff,axiom,
    ! [X20,X45] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X45,X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ? [X150] : X45 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X150) ),
    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,
    ! [X12,X11] :
      ( c_Nat__Transfer_Onat__set(X11)
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X12),X11))
       => c_Nat__Transfer_Ois__nat(X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J) ).

fof(fact_acyclic__converse,axiom,
    ! [X34,X5] :
      ( c_Wellfounded_Oacyclic(X5,hAPP(c_Relation_Oconverse(X5,X5),X34))
    <=> c_Wellfounded_Oacyclic(X5,X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__converse) ).

fof(fact_distinct__card,axiom,
    ! [X212,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X212))
     => hAPP(c_Finite__Set_Ocard(X5),hAPP(c_List_Oset(X5),X212)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__card) ).

fof(fact_length__remdups__eq,axiom,
    ! [X212,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremdups(X5,X212)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)
    <=> c_List_Oremdups(X5,X212) = X212 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__remdups__eq) ).

fof(fact_Domain__converse,axiom,
    ! [X34,X16,X5] : hAPP(c_Relation_ODomain(X5,X16),hAPP(c_Relation_Oconverse(X16,X5),X34)) = hAPP(c_Relation_ORange(X16,X5),X34),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__converse) ).

fof(fact_Range__converse,axiom,
    ! [X34,X5,X16] : hAPP(c_Relation_ORange(X16,X5),hAPP(c_Relation_Oconverse(X5,X16),X34)) = hAPP(c_Relation_ODomain(X5,X16),X34),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__converse) ).

fof(fact_remdups__filter,axiom,
    ! [X212,X29,X5] : c_List_Oremdups(X5,hAPP(c_List_Ofilter(X5,X29),X212)) = hAPP(c_List_Ofilter(X5,X29),c_List_Oremdups(X5,X212)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__filter) ).

fof(fact_rtrancl__converse,axiom,
    ! [X34,X5] : c_Transitive__Closure_Ortrancl(X5,hAPP(c_Relation_Oconverse(X5,X5),X34)) = hAPP(c_Relation_Oconverse(X5,X5),c_Transitive__Closure_Ortrancl(X5,X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__converse) ).

fof(fact_Range__def,axiom,
    ! [X34,X5,X16] : hAPP(c_Relation_ORange(X16,X5),X34) = hAPP(c_Relation_ODomain(X5,X16),hAPP(c_Relation_Oconverse(X16,X5),X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__def) ).

fof(fact_exists__code,axiom,
    ! [X29,X5] :
      ( class_Enum_Oenum(X5)
     => ( ? [X32] : hBOOL(hAPP(X29,X32))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X5),X29)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exists__code) ).

fof(fact_enum__ex,axiom,
    ! [X29,X5] :
      ( class_Enum_Oenum(X5)
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X5),X29))
      <=> ? [X32] : hBOOL(hAPP(X29,X32)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__ex) ).

fof(fact_list__update__nonempty,axiom,
    ! [X12,X30,X212,X5] :
      ( hAPP(hAPP(c_List_Olist__update(X5,X212),X30),X12) = c_List_Olist_ONil(X5)
    <=> X212 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__nonempty) ).

fof(fact_map__is__Nil__conv,axiom,
    ! [X212,X2,X5,X16] :
      ( hAPP(hAPP(c_List_Omap(X16,X5),X2),X212) = c_List_Olist_ONil(X5)
    <=> X212 = c_List_Olist_ONil(X16) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__is__Nil__conv) ).

fof(fact_option__map__is__None,axiom,
    ! [X215,X2,X5,X16] :
      ( hAPP(hAPP(c_Option_Omap(X16,X5),X2),X215) = c_Option_Ooption_ONone(X5)
    <=> X215 = c_Option_Ooption_ONone(X16) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option__map__is__None) ).

fof(fact_Nil__is__map__conv,axiom,
    ! [X212,X2,X16,X5] :
      ( c_List_Olist_ONil(X5) = hAPP(hAPP(c_List_Omap(X16,X5),X2),X212)
    <=> X212 = c_List_Olist_ONil(X16) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__is__map__conv) ).

fof(fact_Option_Oset_Osimps_I2_J,axiom,
    ! [X12,X5] : c_Option_Oset(X5,hAPP(c_Option_Ooption_OSome(X5),X12)) = hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Option_Oset_Osimps_I2_J) ).

fof(fact_diffs0__imp__equal,axiom,
    ! [X98,X99] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),X99) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => X99 = X98 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).

fof(fact_strict__mono__mono,axiom,
    ! [X2,X5,X16] :
      ( ( class_Orderings_Oorder(X16)
        & class_Orderings_Oorder(X5) )
     => ( c_Orderings_Oorder__class_Ostrict__mono(X5,X16,X2)
       => c_Orderings_Oorder__class_Omono(X5,X16,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_strict__mono__mono) ).

fof(fact_setsum__empty,axiom,
    ! [X2,X16,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__empty) ).

fof(fact_setsum_Oempty,axiom,
    ! [X1,X16,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16,X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Oempty) ).

fof(fact_setprod_Oempty,axiom,
    ! [X1,X16,X5] :
      ( class_Groups_Ocomm__monoid__mult(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16,X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Oempty) ).

fof(fact_setprod__empty,axiom,
    ! [X2,X16,X5] :
      ( class_Groups_Ocomm__monoid__mult(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16,X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__empty) ).

fof(fact_gr__implies__not0,axiom,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
     => X98 != 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,X21,X17,X5] :
      ( class_Fields_Ofield__inverse__zero(X5)
     => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X17),X21) = X6
      <=> ( ( X21 != c_Groups_Ozero__class_Ozero(X5)
           => X17 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21) )
          & ( X21 = 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,
    ! [X21,X17,X6,X5] :
      ( class_Fields_Ofield__inverse__zero(X5)
     => ( X6 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X17),X21)
      <=> ( ( X21 != c_Groups_Ozero__class_Ozero(X5)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21) = X17 )
          & ( X21 = 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,
    ! [X99,X15] :
      ( class_Rings_Osemiring__1(X15)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),hAPP(c_Nat_OSuc,X99)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),c_Groups_Oone__class_Oone(X15)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),X99)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__Suc) ).

fof(fact_zero__less__Suc,axiom,
    ! [X98] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X98))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).

fof(fact_less__not__refl3,axiom,
    ! [X104,X105] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X105),X104))
     => X105 != X104 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).

fof(fact_less__not__refl2,axiom,
    ! [X99,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X99))
     => X99 != X98 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).

fof(fact_atLeastLessThan__singleton,axiom,
    ! [X45] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45),hAPP(c_Nat_OSuc,X45)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X45),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,
    ! [X29,X212,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,X212)
       => c_List_Olinorder__class_Osorted(X5,c_List_OtakeWhile(X5,X29,X212)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__takeWhile) ).

fof(fact_sorted__remove1,axiom,
    ! [X25,X221,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( c_List_Olinorder__class_Osorted(X15,X221)
       => c_List_Olinorder__class_Osorted(X15,c_List_Oremove1(X15,X25,X221)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__remove1) ).

fof(fact_mult__cancel2,axiom,
    ! [X76,X30,X45] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X30) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X76),X30)
    <=> ( X45 = X76
        | X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).

fof(fact_nat__mult__eq__cancel__disj,axiom,
    ! [X76,X45,X30] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X45) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X76)
    <=> ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X45 = X76 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).

fof(fact_mult__cancel1,axiom,
    ! [X76,X45,X30] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X45) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X76)
    <=> ( X45 = X76
        | X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel1) ).

fof(fact_hd__append,axiom,
    ! [X225,X15,X221] :
      ( ( X221 = c_List_Olist_ONil(X15)
       => hAPP(c_List_Ohd(X15),hAPP(hAPP(c_List_Oappend(X15),X221),X225)) = hAPP(c_List_Ohd(X15),X225) )
      & ( X221 != c_List_Olist_ONil(X15)
       => hAPP(c_List_Ohd(X15),hAPP(hAPP(c_List_Oappend(X15),X221),X225)) = hAPP(c_List_Ohd(X15),X221) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__append) ).

fof(fact_mult__sgn__abs,axiom,
    ! [X14,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),c_Groups_Osgn__class_Osgn(X15,X14)),hAPP(c_Groups_Oabs__class_Oabs(X15),X14)) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__sgn__abs) ).

fof(fact_zero__less__one,axiom,
    ! [X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),c_Groups_Oone__class_Oone(X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__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_zero__le__one,axiom,
    ! [X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Ozero__class_Ozero(X15)),c_Groups_Oone__class_Oone(X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).

fof(fact_divide__eq__imp,axiom,
    ! [X25,X26,X24,X15] :
      ( class_Rings_Odivision__ring(X15)
     => ( X24 != c_Groups_Ozero__class_Ozero(X15)
       => ( X26 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X24)
         => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X26),X24) = X25 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__imp) ).

fof(fact_nonzero__divide__eq__eq,axiom,
    ! [X6,X17,X21,X5] :
      ( class_Rings_Odivision__ring(X5)
     => ( X21 != c_Groups_Ozero__class_Ozero(X5)
       => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X17),X21) = X6
        <=> X17 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).

fof(fact_nonzero__eq__divide__eq,axiom,
    ! [X17,X6,X21,X5] :
      ( class_Rings_Odivision__ring(X5)
     => ( X21 != c_Groups_Ozero__class_Ozero(X5)
       => ( X6 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X17),X21)
        <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21) = X17 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).

fof(fact_eq__divide__imp,axiom,
    ! [X26,X25,X24,X15] :
      ( class_Rings_Odivision__ring(X15)
     => ( X24 != c_Groups_Ozero__class_Ozero(X15)
       => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X24) = X26
         => X25 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X26),X24) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__imp) ).

fof(fact_diff__minus__eq__add,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Ogroup__add(X15)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X25),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X26)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).

fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
    ! [X22,X14,X15] :
      ( class_Rings_Ocomm__ring__1(X15)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X14),X22) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X14),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).

fof(fact_diff__def,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Ogroup__add(X15)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X25),X26) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__def) ).

fof(fact_ab__diff__minus,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Oab__group__add(X15)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X25),X26) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__diff__minus) ).

fof(fact_diff__eq,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Oboolean__algebra(X15)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X14),X22) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq) ).

fof(fact_mult__minus1,axiom,
    ! [X23,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OMin)),X23) = hAPP(c_Groups_Ouminus__class_Ouminus(X15),X23) ),
    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,
    ! [X225,X15,X221] :
      ( X221 != c_List_Olist_ONil(X15)
     => hAPP(c_List_Ohd(X15),hAPP(hAPP(c_List_Oappend(X15),X221),X225)) = hAPP(c_List_Ohd(X15),X221) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__append2) ).

fof(fact_lfp__unfold,axiom,
    ! [X2,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( c_Orderings_Oorder__class_Omono(X5,X5,X2)
       => c_Inductive_Ocomplete__lattice__class_Olfp(X5,X2) = hAPP(X2,c_Inductive_Ocomplete__lattice__class_Olfp(X5,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lfp__unfold) ).

fof(fact_gfp__unfold,axiom,
    ! [X2,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( c_Orderings_Oorder__class_Omono(X5,X5,X2)
       => c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X2) = hAPP(X2,c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gfp__unfold) ).

fof(fact_strict__mono__eq,axiom,
    ! [X27,X12,X2,X5,X16] :
      ( ( class_Orderings_Oorder(X16)
        & class_Orderings_Olinorder(X5) )
     => ( c_Orderings_Oorder__class_Ostrict__mono(X5,X16,X2)
       => ( hAPP(X2,X12) = hAPP(X2,X27)
        <=> X12 = X27 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_strict__mono__eq) ).

fof(fact_nat__add__right__cancel,axiom,
    ! [X76,X30,X45] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X30) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X76),X30)
    <=> X45 = X76 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).

fof(fact_nat__add__left__cancel,axiom,
    ! [X76,X45,X30] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X45) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X76)
    <=> X45 = X76 ),
    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,
    ! [X98,X221,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( c_List_Olinorder__class_Osorted(X15,X221)
       => c_List_Olinorder__class_Osorted(X15,hAPP(hAPP(c_List_Odrop(X15),X98),X221)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__drop) ).

fof(fact_sorted__take,axiom,
    ! [X98,X221,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( c_List_Olinorder__class_Osorted(X15,X221)
       => c_List_Olinorder__class_Osorted(X15,hAPP(hAPP(c_List_Otake(X15),X98),X221)) ) ),
    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,
    ! [X11,X5] : hAPP(c_Set_OPow(X5),X11) != 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,
    ! [X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X11) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb) ).

fof(fact_Un__absorb,axiom,
    ! [X11,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X11) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__absorb) ).

fof(fact_wf__in__rel,axiom,
    ! [X36,X5] :
      ( c_Wellfounded_Owf(X5,X36)
     => c_Wellfounded_OwfP(X5,c_FunDef_Oin__rel(X5,X5,X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__in__rel) ).

fof(fact_wf__mlex,axiom,
    ! [X2,X36,X5] :
      ( c_Wellfounded_Owf(X5,X36)
     => c_Wellfounded_Owf(X5,c_Wellfounded_Omlex__prod(X5,X2,X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__mlex) ).

fof(fact_Min_OF__eq,axiom,
    ! [X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => c_Big__Operators_Olinorder__class_OMin(X5,X11) = hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_OF__eq) ).

fof(fact_Max_OF__eq,axiom,
    ! [X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => c_Big__Operators_Olinorder__class_OMax(X5,X11) = hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omax(X5)),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_OF__eq) ).

fof(fact_Sup__fin_OF__eq,axiom,
    ! [X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => c_Big__Operators_Olattice__class_OSup__fin(X5,X11) = hAPP(c_Finite__Set_Ofold1(X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_OF__eq) ).

fof(fact_Inf__fin_OF__eq,axiom,
    ! [X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => c_Big__Operators_Olattice__class_OInf__fin(X5,X11) = hAPP(c_Finite__Set_Ofold1(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_OF__eq) ).

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

fof(fact_length__replicate,axiom,
    ! [X14,X98,X15] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),c_List_Oreplicate(X15,X98,X14)) = X98,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__replicate) ).

fof(fact_left__minus,axiom,
    ! [X25,X15] :
      ( class_Groups_Ogroup__add(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)),X25) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__minus) ).

fof(fact_ab__left__minus,axiom,
    ! [X25,X15] :
      ( class_Groups_Oab__group__add(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)),X25) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__left__minus) ).

fof(fact_compl__inf__bot,axiom,
    ! [X14,X15] :
      ( class_Lattices_Oboolean__algebra(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X14)),X14) = c_Orderings_Obot__class_Obot(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__inf__bot) ).

fof(fact_compl__sup__top,axiom,
    ! [X14,X15] :
      ( class_Lattices_Oboolean__algebra(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X14)),X14) = c_Orderings_Otop__class_Otop(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__sup__top) ).

fof(fact_last__append,axiom,
    ! [X221,X15,X225] :
      ( ( X225 = c_List_Olist_ONil(X15)
       => c_List_Olast(X15,hAPP(hAPP(c_List_Oappend(X15),X221),X225)) = c_List_Olast(X15,X221) )
      & ( X225 != c_List_Olist_ONil(X15)
       => c_List_Olast(X15,hAPP(hAPP(c_List_Oappend(X15),X221),X225)) = c_List_Olast(X15,X225) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__append) ).

fof(fact_last__appendL,axiom,
    ! [X221,X15,X225] :
      ( X225 = c_List_Olist_ONil(X15)
     => c_List_Olast(X15,hAPP(hAPP(c_List_Oappend(X15),X221),X225)) = c_List_Olast(X15,X221) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__appendL) ).

fof(fact_diff__add__0,axiom,
    ! [X99,X98] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X99)) = 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,
    ! [X76,X97,X5] : c_List_Osublist(X5,X97,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X76)) = hAPP(hAPP(c_List_Otake(X5),X76),X97),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__upt__eq__take) ).

fof(fact_bot__least,axiom,
    ! [X14,X15] :
      ( class_Orderings_Obot(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Orderings_Obot__class_Obot(X15)),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__least) ).

fof(fact_divmod__int__correct,axiom,
    ! [X25,X26] :
      ( X26 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X25,X26),c_Divides_Odivmod__int(X25,X26))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__correct) ).

fof(fact_pdivmod__posDivAlg,axiom,
    ! [X100,X103] :
      ( ( X103 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Opdivmod(X100,X103) = 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),X100)) )
      & ( X103 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Opdivmod(X100,X103) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X100),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X103)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__posDivAlg) ).

fof(fact_LeastI,axiom,
    ! [X30,X29,X5] :
      ( class_Orderings_Owellorder(X5)
     => ( hBOOL(hAPP(X29,X30))
       => hBOOL(hAPP(X29,c_Orderings_Oord__class_OLeast(X5,X29))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LeastI) ).

fof(fact_LeastI__ex,axiom,
    ! [X29,X5] :
      ( class_Orderings_Owellorder(X5)
     => ( ? [X32] : hBOOL(hAPP(X29,X32))
       => hBOOL(hAPP(X29,c_Orderings_Oord__class_OLeast(X5,X29))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LeastI__ex) ).

fof(fact_sorted__single,axiom,
    ! [X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => c_List_Olinorder__class_Osorted(X15,hAPP(hAPP(c_List_Olist_OCons(X15),X14),c_List_Olist_ONil(X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__single) ).

fof(fact_last__appendR,axiom,
    ! [X221,X15,X225] :
      ( X225 != c_List_Olist_ONil(X15)
     => c_List_Olast(X15,hAPP(hAPP(c_List_Oappend(X15),X221),X225)) = c_List_Olast(X15,X225) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__appendR) ).

fof(fact_last__ConsR,axiom,
    ! [X14,X15,X221] :
      ( X221 != c_List_Olist_ONil(X15)
     => c_List_Olast(X15,hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = c_List_Olast(X15,X221) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__ConsR) ).

fof(fact_last_Osimps,axiom,
    ! [X14,X15,X221] :
      ( ( X221 = c_List_Olist_ONil(X15)
       => c_List_Olast(X15,hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = X14 )
      & ( X221 != c_List_Olist_ONil(X15)
       => c_List_Olast(X15,hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = c_List_Olast(X15,X221) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last_Osimps) ).

fof(fact_nat__gcd_Osimps,axiom,
    ! [X14,X22] :
      ( ( X22 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Nitpick_Onat__gcd(X14,X22) = X14 )
      & ( X22 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Nitpick_Onat__gcd(X14,X22) = c_Nitpick_Onat__gcd(X22,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X14,X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__gcd_Osimps) ).

fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
    ! [X66,X97] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X97)),X66) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X97,X66),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastSucLessThan__greaterThanLessThan) ).

fof(fact_card__atLeastLessThan,axiom,
    ! [X66,X97] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X97),X66)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X66),X97),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atLeastLessThan) ).

fof(fact_eq__int__code_I5_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__int__code_I5_J) ).

fof(fact_eq__int__code_I2_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__int__code_I2_J) ).

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(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,
    ! [X225,X5,X15] : hAPP(hAPP(c_List_Ozip(X15,X5),c_List_Olist_ONil(X15)),X225) = c_List_Olist_ONil(tc_prod(X15,X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__Nil) ).

fof(fact_top1I,axiom,
    ! [X12,X5] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top1I) ).

fof(fact_vimage__id,axiom,
    ! [X11,X5] : hAPP(c_Set_Ovimage(X5,X5,c_Fun_Oid(X5)),X11) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__id) ).

fof(fact_vimage__ident,axiom,
    ! [X42,X5] : hAPP(c_Set_Ovimage(X5,X5,c_COMBI(X5)),X42) = X42,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__ident) ).

fof(fact_image__id,axiom,
    ! [X42,X5] : hAPP(c_Set_Oimage(X5,X5,c_Fun_Oid(X5)),X42) = X42,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__id) ).

fof(fact_image__ident,axiom,
    ! [X42,X5] : hAPP(c_Set_Oimage(X5,X5,c_COMBI(X5)),X42) = X42,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__ident) ).

fof(fact_def__lfp__unfold,axiom,
    ! [X2,X48,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( X48 = c_Inductive_Ocomplete__lattice__class_Olfp(X5,X2)
       => ( c_Orderings_Oorder__class_Omono(X5,X5,X2)
         => X48 = hAPP(X2,X48) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__lfp__unfold) ).

fof(fact_def__gfp__unfold,axiom,
    ! [X2,X11,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( X11 = c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X2)
       => ( c_Orderings_Oorder__class_Omono(X5,X5,X2)
         => X11 = hAPP(X2,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__gfp__unfold) ).

fof(fact_refl__rtrancl,axiom,
    ! [X34,X5] : c_Relation_Orefl__on(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__rtrancl) ).

fof(fact_hd__replicate,axiom,
    ! [X14,X15,X98] :
      ( X98 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Ohd(X15),c_List_Oreplicate(X15,X98,X14)) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__replicate) ).

fof(fact_Compl__atLeast,axiom,
    ! [X30,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X30)) = hAPP(c_SetInterval_Oord__class_OlessThan(X5),X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__atLeast) ).

fof(fact_Compl__greaterThan,axiom,
    ! [X30,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X30)) = hAPP(c_SetInterval_Oord__class_OatMost(X5),X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__greaterThan) ).

fof(fact_Compl__atMost,axiom,
    ! [X30,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X30)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__atMost) ).

fof(fact_Compl__lessThan,axiom,
    ! [X30,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X30)) = hAPP(c_SetInterval_Oord__class_OatLeast(X5),X30) ),
    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,
    ! [X11,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OSup__fin(X5,X11) = c_Complete__Lattice_OSup__class_OSup(X5,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin__Sup) ).

fof(fact_Inf__fin__Inf,axiom,
    ! [X11,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OInf__fin(X5,X11) = c_Complete__Lattice_OInf__class_OInf(X5,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin__Inf) ).

fof(fact_add__numeral__0,axiom,
    ! [X25,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OPls)),X25) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__numeral__0) ).

fof(fact_add__is__1,axiom,
    ! [X76,X45] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X76) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( ( X45 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( X45 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & X76 = 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,
    ! [X76,X45] :
      ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X76)
    <=> ( ( X45 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( X45 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & X76 = 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_tfl__some,axiom,
    ! [X5,X189] :
      ( ? [X3] : hBOOL(hAPP(X189,X3))
     => hBOOL(hAPP(X189,c_Hilbert__Choice_OEps(X5,X189))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__some) ).

fof(fact_someI,axiom,
    ! [X5,X12,X29] :
      ( hBOOL(hAPP(X29,X12))
     => hBOOL(hAPP(X29,c_Hilbert__Choice_OEps(X5,X29))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI) ).

fof(fact_someI__ex,axiom,
    ! [X5,X29] :
      ( ? [X32] : hBOOL(hAPP(X29,X32))
     => hBOOL(hAPP(X29,c_Hilbert__Choice_OEps(X5,X29))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI__ex) ).

fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
    ! [X66,X97] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X97),X66) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X97,X66),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastSucAtMost__greaterThanAtMost) ).

fof(fact_square__eq__1__iff,axiom,
    ! [X12,X5] :
      ( class_Rings_Oring__1__no__zero__divisors(X5)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X12) = c_Groups_Oone__class_Oone(X5)
      <=> ( X12 = c_Groups_Oone__class_Oone(X5)
          | X12 = 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,
    ! [X221,X5,X15] : hAPP(hAPP(c_List_Ozip(X15,X5),X221),c_List_Olist_ONil(X5)) = c_List_Olist_ONil(tc_prod(X15,X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip_Osimps_I1_J) ).

fof(fact_folding__one__idem_Oidem,axiom,
    ! [X12,X90,X2,X5] :
      ( c_Finite__Set_Ofolding__one__idem(X5,X2,X90)
     => hAPP(hAPP(X2,X12),X12) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).

fof(fact_sublists_Osimps_I1_J,axiom,
    ! [X15] : c_Enum_Osublists(X15,c_List_Olist_ONil(X15)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X15)),c_List_Olist_ONil(X15)),c_List_Olist_ONil(tc_List_Olist(X15))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublists_Osimps_I1_J) ).

fof(fact_top__greatest,axiom,
    ! [X14,X15] :
      ( class_Orderings_Otop(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),c_Orderings_Otop__class_Otop(X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__greatest) ).

fof(fact_last__ConsL,axiom,
    ! [X14,X15,X221] :
      ( X221 = c_List_Olist_ONil(X15)
     => c_List_Olast(X15,hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__ConsL) ).

fof(fact_last__replicate,axiom,
    ! [X14,X15,X98] :
      ( X98 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => c_List_Olast(X15,c_List_Oreplicate(X15,X98,X14)) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__replicate) ).

fof(fact_nat__rec__0,axiom,
    ! [X88,X89,X5] : hAPP(c_Nat_Onat_Onat__rec(X5,X89,X88),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X89,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__rec__0) ).

fof(fact_insert__not__empty,axiom,
    ! [X11,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),X11) != 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,
    ! [X11,X6,X5] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X5),X6),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__not__insert) ).

fof(fact_int__Suc,axiom,
    ! [X99] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X99)) = 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),X99)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__Suc) ).

fof(fact_diff__int__def__symmetric,axiom,
    ! [X132,X23] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X132)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23),X132),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).

fof(fact_diff__int__def,axiom,
    ! [X132,X23] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23),X132) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X132)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def) ).

fof(fact_tl_Osimps_I2_J,axiom,
    ! [X221,X14,X15] : hAPP(c_List_Otl(X15),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = X221,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl_Osimps_I2_J) ).

fof(fact_hd_Osimps,axiom,
    ! [X221,X14,X15] : hAPP(c_List_Ohd(X15),hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221)) = X14,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd_Osimps) ).

fof(fact_power__eq__0__iff,axiom,
    ! [X76,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),X76) = c_Groups_Ozero__class_Ozero(X5)
      <=> ( X6 = c_Groups_Ozero__class_Ozero(X5)
          & X76 != 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,
    ! [X22,X14] :
      ( c_Nat__Transfer_Ois__nat(X14)
     => ( c_Nat__Transfer_Ois__nat(X22)
       => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X14,X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I2_J) ).

fof(fact_divide__minus1,axiom,
    ! [X14,X15] :
      ( ( class_Fields_Ofield__inverse__zero(X15)
        & class_Int_Onumber__ring(X15) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X15),X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__minus1) ).

fof(fact_wf__lexn,axiom,
    ! [X76,X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => c_Wellfounded_Owf(tc_List_Olist(X5),hAPP(c_List_Olexn(X5,X34),X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__lexn) ).

fof(fact_list__update_Osimps_I1_J,axiom,
    ! [X126,X102,X15] : hAPP(hAPP(c_List_Olist__update(X15,c_List_Olist_ONil(X15)),X102),X126) = c_List_Olist_ONil(X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update_Osimps_I1_J) ).

fof(fact_list__update__code_I1_J,axiom,
    ! [X22,X102,X15] : hAPP(hAPP(c_List_Olist__update(X15,c_List_Olist_ONil(X15)),X102),X22) = c_List_Olist_ONil(X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__code_I1_J) ).

fof(fact_power__Suc__0,axiom,
    ! [X98] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X98) = 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,
    ! [X14,X15] : c_List_Oinsert(X15,X14,c_List_Olist_ONil(X15)) = hAPP(hAPP(c_List_Olist_OCons(X15),X14),c_List_Olist_ONil(X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Nil) ).

fof(fact_finite__set,axiom,
    ! [X212,X5] : hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_List_Oset(X5),X212))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__set) ).

fof(fact_converse__converse,axiom,
    ! [X34,X5,X16] : hAPP(c_Relation_Oconverse(X16,X5),hAPP(c_Relation_Oconverse(X5,X16),X34)) = X34,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__converse) ).

fof(fact_lessThan__Suc,axiom,
    ! [X30] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X30),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__Suc) ).

fof(fact_Field__converse,axiom,
    ! [X34,X5] : hAPP(c_Relation_OField(X5),hAPP(c_Relation_Oconverse(X5,X5),X34)) = hAPP(c_Relation_OField(X5),X34),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__converse) ).

fof(fact_of__int__minus,axiom,
    ! [X23,X15] :
      ( class_Rings_Oring__1(X15)
     => hAPP(c_Int_Oring__1__class_Oof__int(X15),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23)) = hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(c_Int_Oring__1__class_Oof__int(X15),X23)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__minus) ).

fof(fact_number__of__minus,axiom,
    ! [X132,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(c_Int_Onumber__class_Onumber__of(X15),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X132)) = hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X132)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__minus) ).

fof(fact_arith__simps_I30_J,axiom,
    ! [X132,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X132)) = hAPP(c_Int_Onumber__class_Onumber__of(X15),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X132)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I30_J) ).

fof(fact_nat__power__eq__Suc__0__iff,axiom,
    ! [X45,X12] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X45) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( X45 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X12 = 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,
    ! [X22,X14,X15] :
      ( class_Orderings_Opreorder(X15)
     => ( X14 = X22
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).

fof(fact_minus__unique,axiom,
    ! [X26,X25,X15] :
      ( class_Groups_Ogroup__add(X15)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X26) = c_Groups_Ozero__class_Ozero(X15)
       => hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25) = X26 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__unique) ).

fof(fact_eq__neg__iff__add__eq__0,axiom,
    ! [X17,X6,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( X6 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X17)
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X17) = 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,
    ! [X212,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremdups(X5,X212)) = hAPP(c_Finite__Set_Ocard(X5),hAPP(c_List_Oset(X5),X212)),
    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_hb__flat_Osimps_I1_J,axiom,
    ! [X15] : c_Lazy__Sequence_Ohb__flat(X15,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X15))))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hb__flat_Osimps_I1_J) ).

fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
    ! [X27,X12] :
      ( c_Nat__Transfer_Ois__nat(X12)
     => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X12,X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__function__closures) ).

fof(fact_mult__minus1__right,axiom,
    ! [X23,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X23),hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X15),X23) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__minus1__right) ).

fof(fact_mult__eq__1__iff,axiom,
    ! [X76,X45] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X76) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( X45 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        & X76 = 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,
    ! [X131] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X131)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X131)),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_equal__refl,axiom,
    ! [X14,X15] :
      ( class_HOL_Oequal(X15)
     => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X15),X14),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__refl) ).

fof(fact_order__refl,axiom,
    ! [X14,X15] :
      ( class_Orderings_Opreorder(X15)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).

fof(fact_card__atLeastZeroLessThan__int,axiom,
    ! [X66] : 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)),X66)) = hAPP(c_Int_Onat,X66),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atLeastZeroLessThan__int) ).

fof(fact_zadd__zminus__inverse2,axiom,
    ! [X23] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23)),X23) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).

fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
    ! [X66,X97] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X97),hAPP(c_Nat_OSuc,X66)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X97,X66),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThanSuc__atLeastAtMost) ).

fof(fact_mod__int__def,axiom,
    ! [X26,X25] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X26) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X25,X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__int__def) ).

fof(fact_min__max_Osup_Ocommute,axiom,
    ! [X26,X25,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X25),X26) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X26),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup_Ocommute) ).

fof(fact_min__max_Osup__commute,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),X22) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X22),X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__commute) ).

fof(fact_min__max_Oinf__commute,axiom,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),X22) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X22),X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__commute) ).

fof(fact_min__max_Oinf_Ocommute,axiom,
    ! [X26,X25,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X25),X26) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X26),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf_Ocommute) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
    ! [X24,X25,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X24),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X26),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

fof(fact_inf_Ocommute,axiom,
    ! [X26,X25,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X25),X26) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X26),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Ocommute) ).

fof(fact_inf__commute,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X22) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X22),X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__commute) ).

fof(fact_inf__sup__aci_I1_J,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Olattice(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X22) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X22),X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I1_J) ).

fof(fact_inf__sup__aci_I5_J,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Olattice(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X22) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X22),X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I5_J) ).

fof(fact_sup_Ocommute,axiom,
    ! [X26,X25,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X25),X26) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X26),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup_Ocommute) ).

fof(fact_sup__commute,axiom,
    ! [X22,X14,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X22) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X22),X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__commute) ).

fof(fact_nat__zminus__int,axiom,
    ! [X98] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X98))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zminus__int) ).

fof(fact_gr0I,axiom,
    ! [X98] :
      ( X98 != 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)),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).

fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
    ! [X22,X14] :
      ( c_Nat__Transfer_Ois__nat(X14)
     => ( c_Nat__Transfer_Ois__nat(X22)
       => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14),X22)) ) ),
    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_I1_J,axiom,
    ! [X22,X14] :
      ( c_Nat__Transfer_Ois__nat(X14)
     => ( c_Nat__Transfer_Ois__nat(X22)
       => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X14),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
    ! [X22,X14] :
      ( c_Nat__Transfer_Ois__nat(X14)
     => ( c_Nat__Transfer_Ois__nat(X22)
       => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J) ).

fof(fact_negative__eq__positive,axiom,
    ! [X45,X76] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X76)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X45)
    <=> ( X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & X45 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__eq__positive) ).

fof(fact_less__eq__nat_Osimps_I1_J,axiom,
    ! [X98] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).

fof(fact_le0,axiom,
    ! [X98] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).

fof(fact_total__on__empty,axiom,
    ! [X34,X5] : c_Relation_Ototal__on(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),X34),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__empty) ).

fof(fact_divisors__zero,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Ono__zero__divisors(X15)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26) = c_Groups_Ozero__class_Ozero(X15)
       => ( X25 = c_Groups_Ozero__class_Ozero(X15)
          | X26 = c_Groups_Ozero__class_Ozero(X15) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divisors__zero) ).

fof(fact_no__zero__divisors,axiom,
    ! [X26,X25,X15] :
      ( class_Rings_Ono__zero__divisors(X15)
     => ( X25 != c_Groups_Ozero__class_Ozero(X15)
       => ( X26 != c_Groups_Ozero__class_Ozero(X15)
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X26) != c_Groups_Ozero__class_Ozero(X15) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_no__zero__divisors) ).

fof(fact_mult__eq__0__iff,axiom,
    ! [X17,X6,X5] :
      ( class_Rings_Oring__no__zero__divisors(X5)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X17) = c_Groups_Ozero__class_Ozero(X5)
      <=> ( X6 = c_Groups_Ozero__class_Ozero(X5)
          | X17 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).

fof(fact_posDivAlg__0,axiom,
    ! [X26] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X26) = 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,
    ! [X26,X25] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X26) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X25,X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__int__def) ).

fof(fact_power__0__Suc,axiom,
    ! [X98,X15] :
      ( ( class_Power_Opower(X15)
        & class_Rings_Osemiring__0(X15) )
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),c_Groups_Ozero__class_Ozero(X15)),hAPP(c_Nat_OSuc,X98)) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__Suc) ).

fof(fact_divide__Numeral0,axiom,
    ! [X14,X15] :
      ( ( class_Fields_Ofield__inverse__zero(X15)
        & class_Int_Onumber__ring(X15) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X14),hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__Numeral0) ).

fof(fact_abs__sgn,axiom,
    ! [X100,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => hAPP(c_Groups_Oabs__class_Oabs(X15),X100) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X100),c_Groups_Osgn__class_Osgn(X15,X100)) ),
    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,
    ! [X212,X5] : hAPP(hAPP(c_List_Omap(X5,X5),c_COMBI(X5)),X212) = X212,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__ident) ).

fof(fact_accp__wfPD,axiom,
    ! [X12,X34,X5] :
      ( c_Wellfounded_OwfP(X5,X34)
     => hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X34),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__wfPD) ).

fof(fact_reflpE,axiom,
    ! [X12,X34,X5] :
      ( c_Predicate_Oreflp(X5,X34)
     => hBOOL(hAPP(hAPP(X34,X12),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reflpE) ).

fof(fact_equivp__reflp,axiom,
    ! [X12,X36,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X36)
     => hBOOL(hAPP(hAPP(X36,X12),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__reflp) ).

fof(fact_sublist__empty,axiom,
    ! [X212,X5] : c_List_Osublist(X5,X212,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,X17,X5] :
      ( class_Rings_Odivision__ring(X5)
     => ( X17 != c_Groups_Ozero__class_Ozero(X5)
       => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X6),X17) = c_Groups_Oone__class_Oone(X5)
        <=> X6 = X17 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse__eq) ).

fof(fact_length__rev,axiom,
    ! [X221,X15] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),hAPP(c_List_Orev(X15),X221)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__rev) ).

fof(fact_length__rotate1,axiom,
    ! [X221,X15] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),hAPP(c_List_Orotate1(X15),X221)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__rotate1) ).

fof(fact_exE__some,axiom,
    ! [X5,X21,X29] :
      ( ? [X32] : hBOOL(hAPP(X29,X32))
     => ( X21 = c_Hilbert__Choice_OEps(X5,X29)
       => hBOOL(hAPP(X29,X21)) ) ),
    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_option__map__None,axiom,
    ! [X2,X5,X16] : hAPP(hAPP(c_Option_Omap(X16,X5),X2),c_Option_Ooption_ONone(X16)) = c_Option_Ooption_ONone(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option__map__None) ).

fof(fact_map_Osimps_I1_J,axiom,
    ! [X2,X5,X16] : hAPP(hAPP(c_List_Omap(X16,X5),X2),c_List_Olist_ONil(X16)) = c_List_Olist_ONil(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map_Osimps_I1_J) ).

fof(fact_right__minus,axiom,
    ! [X25,X15] :
      ( class_Groups_Ogroup__add(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus) ).

fof(fact_inf__compl__bot,axiom,
    ! [X14,X15] :
      ( class_Lattices_Oboolean__algebra(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X14)) = c_Orderings_Obot__class_Obot(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__compl__bot) ).

fof(fact_sup__compl__top,axiom,
    ! [X14,X15] :
      ( class_Lattices_Oboolean__algebra(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X14)) = c_Orderings_Otop__class_Otop(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__compl__top) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
    ! [X98,X14] :
      ( c_Nat__Transfer_Ois__nat(X14)
     => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) ).

fof(fact_zmult__eq__1__iff,axiom,
    ! [X76,X45] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X45),X76) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    <=> ( ( X45 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & X76 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
        | ( X45 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
          & X76 = 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,
    ! [X27,X12,X5] :
      ( class_Lattices_Obounded__lattice__top(X5)
     => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X12),X27) = c_Orderings_Otop__class_Otop(X5)
      <=> ( X12 = c_Orderings_Otop__class_Otop(X5)
          & X27 = 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,
    ! [X27,X12,X5] :
      ( class_Lattices_Obounded__lattice__bot(X5)
     => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X12),X27) = c_Orderings_Obot__class_Obot(X5)
      <=> ( X12 = c_Orderings_Obot__class_Obot(X5)
          & X27 = 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,
    ! [X98,X25,X15] :
      ( class_Rings_Oring__1__no__zero__divisors(X15)
     => ( X25 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),X98) != c_Groups_Ozero__class_Ozero(X15) ) ),
    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,
    ! [X30] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X30))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atMost) ).

fof(fact_finite__lessThan,axiom,
    ! [X30] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X30))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__lessThan) ).

fof(fact_lfp__const,axiom,
    ! [X10,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Inductive_Ocomplete__lattice__class_Olfp(X5,hAPP(c_COMBK(X5,X5),X10)) = X10 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lfp__const) ).

fof(fact_minus__numeral__code_I5_J,axiom,
    ! [X132] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X132)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__numeral__code_I5_J) ).

fof(fact_right__minus__eq,axiom,
    ! [X17,X6,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X17) = c_Groups_Ozero__class_Ozero(X5)
      <=> X6 = X17 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus__eq) ).

fof(fact_eq__iff__diff__eq__0,axiom,
    ! [X17,X6,X5] :
      ( class_Groups_Oab__group__add(X5)
     => ( X6 = X17
      <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X17) = 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,
    ! [X98,X99] :
      ( X99 = X98
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X98)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).

fof(fact_take__eq__Nil,axiom,
    ! [X212,X76,X5] :
      ( hAPP(hAPP(c_List_Otake(X5),X76),X212) = c_List_Olist_ONil(X5)
    <=> ( X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X212 = 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,
    ! [X98,X99] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X99),X98) = c_Groups_Oone__class_Oone(tc_Int_Oint)
     => ( X99 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X99 = 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,X17,X5] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
     => ( X17 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X17),X6)
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).

fof(fact_replicate__empty,axiom,
    ! [X12,X76,X5] :
      ( c_List_Oreplicate(X5,X76,X12) = c_List_Olist_ONil(X5)
    <=> X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__empty) ).

fof(fact_empty__replicate,axiom,
    ! [X12,X76,X5] :
      ( c_List_Olist_ONil(X5) = c_List_Oreplicate(X5,X76,X12)
    <=> X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__replicate) ).

fof(fact_diff__Suc__1,axiom,
    ! [X98] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X98)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X98,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__1) ).

fof(fact_set__upto,axiom,
    ! [X115,X70] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X70,X115)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X70,X115),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__upto) ).

fof(fact_atLeastAtMost__upto,axiom,
    ! [X115,X70] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X70,X115) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X70,X115)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastAtMost__upto) ).

fof(fact_add__numeral__0__right,axiom,
    ! [X25,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OPls)) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__numeral__0__right) ).

fof(fact_eq__int__refl,axiom,
    ! [X100] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X100),X100)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__int__refl) ).

fof(fact_zle__refl,axiom,
    ! [X132] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X132),X132)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).

fof(fact_le__refl,axiom,
    ! [X98] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X98)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).

fof(fact_listsp_Oequations_I1_J,axiom,
    ! [X11,X5] : hBOOL(hAPP(c_List_Olistsp(X5,X11),c_List_Olist_ONil(X5))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_Oequations_I1_J) ).

fof(fact_listsp_ONil,axiom,
    ! [X11,X5] : hBOOL(hAPP(c_List_Olistsp(X5,X11),c_List_Olist_ONil(X5))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_ONil) ).

fof(fact_distinct__remdups,axiom,
    ! [X221,X15] : hBOOL(hAPP(c_List_Odistinct(X15),c_List_Oremdups(X15,X221))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__remdups) ).

fof(fact_append__is__Nil__conv,axiom,
    ! [X214,X212,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X212),X214) = c_List_Olist_ONil(X5)
    <=> ( X212 = c_List_Olist_ONil(X5)
        & X214 = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__is__Nil__conv) ).

fof(fact_Nil__is__append__conv,axiom,
    ! [X214,X212,X5] :
      ( c_List_Olist_ONil(X5) = hAPP(hAPP(c_List_Oappend(X5),X212),X214)
    <=> ( X212 = c_List_Olist_ONil(X5)
        & X214 = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__is__append__conv) ).

fof(fact_Domain__rtrancl,axiom,
    ! [X36,X5] : hAPP(c_Relation_ODomain(X5,X5),c_Transitive__Closure_Ortrancl(X5,X36)) = 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,
    ! [X36,X5] : hAPP(c_Relation_ORange(X5,X5),c_Transitive__Closure_Ortrancl(X5,X36)) = 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,
    ! [X287,X286,X5,X15] : hAPP(hAPP(c_COMBK(X15,X5),X286),X287) = X286,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).

fof(fact_lazy__sequence_Osimps_I3_J,axiom,
    ! [X283,X81,X15] : c_Lazy__Sequence_Olazy__sequence_OInsert(X15,X81,X283) != c_Lazy__Sequence_Olazy__sequence_OEmpty(X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Osimps_I3_J) ).

fof(fact_lazy__sequence_Osimps_I2_J,axiom,
    ! [X283,X81,X15] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X15) != c_Lazy__Sequence_Olazy__sequence_OInsert(X15,X81,X283),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Osimps_I2_J) ).

fof(fact_zdiv__minus1__right,axiom,
    ! [X25] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__minus1__right) ).

fof(fact_zadd__commute,axiom,
    ! [X132,X23] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23),X132) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X132),X23),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).

fof(fact_nat__add__commute,axiom,
    ! [X98,X99] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X98) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X99),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).

fof(fact_zmult__commute,axiom,
    ! [X132,X23] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X132) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X132),X23),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).

fof(fact_nat__mult__commute,axiom,
    ! [X98,X99] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),X98) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X99),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).

fof(fact_Nitpick_Ofrac__def,axiom,
    ! [X26,X25,X15] : hAPP(hAPP(c_Nitpick_Ofrac(X15),X25),X26) = c_Nitpick_OAbs__Frac(X15,c_Nitpick_Onorm__frac(X25,X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Ofrac__def) ).

fof(fact_diff__0,axiom,
    ! [X25,X15] :
      ( class_Groups_Ogroup__add(X15)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),c_Groups_Ozero__class_Ozero(X15)),X25) = hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0) ).

fof(fact_append__self__conv2,axiom,
    ! [X214,X212,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X212),X214) = X214
    <=> X212 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__self__conv2) ).

fof(fact_append__self__conv,axiom,
    ! [X214,X212,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X212),X214) = X212
    <=> X214 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__self__conv) ).

fof(fact_self__append__conv,axiom,
    ! [X214,X5,X212] :
      ( X212 = hAPP(hAPP(c_List_Oappend(X5),X212),X214)
    <=> X214 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__append__conv) ).

fof(fact_self__append__conv2,axiom,
    ! [X212,X5,X214] :
      ( X214 = hAPP(hAPP(c_List_Oappend(X5),X212),X214)
    <=> X212 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__append__conv2) ).

fof(fact_power__0__left,axiom,
    ! [X98,X15] :
      ( ( class_Power_Opower(X15)
        & class_Rings_Osemiring__0(X15) )
     => ( ( X98 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(hAPP(c_Power_Opower__class_Opower(X15),c_Groups_Ozero__class_Ozero(X15)),X98) = c_Groups_Oone__class_Oone(X15) )
        & ( X98 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(hAPP(c_Power_Opower__class_Opower(X15),c_Groups_Ozero__class_Ozero(X15)),X98) = c_Groups_Ozero__class_Ozero(X15) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left) ).

fof(fact_list_Osimps_I3_J,axiom,
    ! [X236,X81,X15] : hAPP(hAPP(c_List_Olist_OCons(X15),X81),X236) != c_List_Olist_ONil(X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I3_J) ).

fof(fact_list_Osimps_I2_J,axiom,
    ! [X236,X81,X15] : c_List_Olist_ONil(X15) != hAPP(hAPP(c_List_Olist_OCons(X15),X81),X236),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I2_J) ).

fof(fact_distinct__upto,axiom,
    ! [X101,X102] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X102,X101))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__upto) ).

fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
    ! [X34,X5] : c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X34)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__eq__rtrancl__listrel1) ).

fof(fact_min__ext__wf,axiom,
    ! [X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => c_Wellfounded_Owf(tc_fun(X5,tc_HOL_Obool),c_Wellfounded_Omin__ext(X5,X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__ext__wf) ).

fof(fact_max__ext__wf,axiom,
    ! [X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => c_Wellfounded_Owf(tc_fun(X5,tc_HOL_Obool),c_Wellfounded_Omax__ext(X5,X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ext__wf) ).

fof(fact_listsum__rev,axiom,
    ! [X221,X15] :
      ( class_Groups_Ocomm__monoid__add(X15)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X15),hAPP(c_List_Orev(X15),X221)) = hAPP(c_List_Omonoid__add__class_Olistsum(X15),X221) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__rev) ).

fof(fact_abs__idempotent,axiom,
    ! [X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)) = hAPP(c_Groups_Oabs__class_Oabs(X15),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__idempotent) ).

fof(fact_abs__of__nat,axiom,
    ! [X98,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),X98)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),X98) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nat) ).

fof(fact_abs__minus__cancel,axiom,
    ! [X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)) = hAPP(c_Groups_Oabs__class_Oabs(X15),X25) ),
    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,
    ! [X25] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,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,
    ! [X99] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,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,
    ! [X76,X45] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X76) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X45 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X76 = 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,
    ! [X221,X14,X15] : hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221) != X221,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self2) ).

fof(fact_not__Cons__self,axiom,
    ! [X14,X15,X221] : X221 != hAPP(hAPP(c_List_Olist_OCons(X15),X14),X221),
    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,
    ! [X12,X16,X5] :
      ( class_Orderings_Otop(X5)
     => hAPP(c_Orderings_Otop__class_Otop(tc_fun(X16,X5)),X12) = c_Orderings_Otop__class_Otop(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__apply) ).

fof(fact_bot__apply,axiom,
    ! [X12,X16,X5] :
      ( class_Orderings_Obot(X5)
     => hAPP(c_Orderings_Obot__class_Obot(tc_fun(X16,X5)),X12) = c_Orderings_Obot__class_Obot(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__apply) ).

fof(fact_bot__fun__def,axiom,
    ! [X12,X16,X5] :
      ( class_Orderings_Obot(X5)
     => hAPP(c_Orderings_Obot__class_Obot(tc_fun(X16,X5)),X12) = c_Orderings_Obot__class_Obot(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__fun__def) ).

fof(fact_minus__code__numeral__code,axiom,
    ! [X99,X98] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X98),X99) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,X98),X99),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__code__numeral__code) ).

fof(fact_sorted__tl,axiom,
    ! [X221,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( c_List_Olinorder__class_Osorted(X15,X221)
       => c_List_Olinorder__class_Osorted(X15,hAPP(c_List_Otl(X15),X221)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__tl) ).

fof(fact_remdups__id__iff__distinct,axiom,
    ! [X212,X5] :
      ( c_List_Oremdups(X5,X212) = X212
    <=> hBOOL(hAPP(c_List_Odistinct(X5),X212)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__id__iff__distinct) ).

fof(fact_distinct__remdups__id,axiom,
    ! [X221,X15] :
      ( hBOOL(hAPP(c_List_Odistinct(X15),X221))
     => c_List_Oremdups(X15,X221) = X221 ),
    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,
    ! [X98,X99] :
      ( X99 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),X98)
     => ( X98 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X99 = 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,
    ! [X15,X221] :
      ( X221 != c_List_Olist_ONil(X15)
     => hAPP(c_List_Ohd(X15),X221) = hAPP(hAPP(c_List_Onth(X15),X221),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,
    ! [X28,X29] :
      ( hBOOL(X29)
      | hBOOL(hAPP(hAPP(c_fimplies,X29),X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__1) ).

fof(fact_single__valued__Id__on,axiom,
    ! [X11,X5] : c_Relation_Osingle__valued(X5,X5,c_Relation_OId__on(X5,X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__Id__on) ).

fof(fact_refl__on__Id__on,axiom,
    ! [X11,X5] : c_Relation_Orefl__on(X5,X11,c_Relation_OId__on(X5,X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__Id__on) ).

fof(fact_add__is__0,axiom,
    ! [X76,X45] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X76) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X45 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & X76 = 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,
    ! [X76,X45] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X76) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    <=> ( X45 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        & X76 = 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,
    ! [X76,X45] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X76)
    <=> ( X45 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        & X76 = 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,
    ! [X27,X12,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Int_Oring__char__0(X5) )
     => ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X12) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X27)
      <=> X12 = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of) ).

fof(fact_converse__Id__on,axiom,
    ! [X11,X5] : hAPP(c_Relation_Oconverse(X5,X5),c_Relation_OId__on(X5,X11)) = c_Relation_OId__on(X5,X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__Id__on) ).

fof(help_c__fequal__2,axiom,
    ! [X27,X12] :
      ( X12 != X27
      | hBOOL(hAPP(hAPP(c_fequal,X12),X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).

fof(fact_of__int__of__nat__eq,axiom,
    ! [X98,X15] :
      ( class_Rings_Oring__1(X15)
     => hAPP(c_Int_Oring__1__class_Oof__int(X15),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X98)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),X98) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__of__nat__eq) ).

fof(fact_of__int__number__of__eq,axiom,
    ! [X126,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(c_Int_Oring__1__class_Oof__int(X15),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(X15),X126) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__number__of__eq) ).

fof(fact_set__empty2,axiom,
    ! [X212,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_List_Oset(X5),X212)
    <=> X212 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__empty2) ).

fof(fact_set__empty,axiom,
    ! [X212,X5] :
      ( hAPP(c_List_Oset(X5),X212) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> X212 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__empty) ).

fof(fact_set__rev,axiom,
    ! [X212,X5] : hAPP(c_List_Oset(X5),hAPP(c_List_Orev(X5),X212)) = hAPP(c_List_Oset(X5),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rev) ).

fof(fact_set__rotate1,axiom,
    ! [X212,X5] : hAPP(c_List_Oset(X5),hAPP(c_List_Orotate1(X5),X212)) = hAPP(c_List_Oset(X5),X212),
    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,
    ! [X98,X99] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X98) = X99
     => X98 = 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,
    ! [X15,X221] :
      ( X221 != c_List_Olist_ONil(X15)
     => hAPP(c_List_Ohd(X15),hAPP(c_List_Orev(X15),X221)) = c_List_Olast(X15,X221) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__rev) ).

fof(fact_last__rev,axiom,
    ! [X15,X221] :
      ( X221 != c_List_Olist_ONil(X15)
     => c_List_Olast(X15,hAPP(c_List_Orev(X15),X221)) = hAPP(c_List_Ohd(X15),X221) ),
    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,
    ! [X99] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X99,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__1) ).

fof(fact_Union__Pow__eq,axiom,
    ! [X11,X5] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_OPow(X5),X11)) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__Pow__eq) ).

fof(fact_divide__zero__left,axiom,
    ! [X25,X15] :
      ( class_Rings_Odivision__ring(X15)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),c_Groups_Ozero__class_Ozero(X15)),X25) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero__left) ).

fof(fact_div__0,axiom,
    ! [X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),c_Groups_Ozero__class_Ozero(X15)),X25) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__0) ).

fof(fact_power__one,axiom,
    ! [X98,X15] :
      ( class_Groups_Omonoid__mult(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),c_Groups_Oone__class_Oone(X15)),X98) = c_Groups_Oone__class_Oone(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).

fof(fact_mult__zero__left,axiom,
    ! [X25,X15] :
      ( class_Rings_Omult__zero(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),c_Groups_Ozero__class_Ozero(X15)),X25) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
    ! [X25,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),c_Groups_Ozero__class_Ozero(X15)),X25) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

fof(fact_inf__bot__left,axiom,
    ! [X14,X15] :
      ( class_Lattices_Obounded__lattice__bot(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),c_Orderings_Obot__class_Obot(X15)),X14) = c_Orderings_Obot__class_Obot(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__bot__left) ).

fof(fact_sup__top__left,axiom,
    ! [X14,X15] :
      ( class_Lattices_Obounded__lattice__top(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),c_Orderings_Otop__class_Otop(X15)),X14) = c_Orderings_Otop__class_Otop(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__top__left) ).

fof(fact_sorted__butlast,axiom,
    ! [X221,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( X221 != c_List_Olist_ONil(X15)
       => ( c_List_Olinorder__class_Osorted(X15,X221)
         => c_List_Olinorder__class_Osorted(X15,c_List_Obutlast(X15,X221)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__butlast) ).

fof(fact_of__int__m1,axiom,
    ! [X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(c_Int_Oring__1__class_Oof__int(X15),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(X15),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,
    ! [X15] :
      ( ( class_Int_Onumber__ring(X15)
        & class_Rings_Olinordered__idom(X15) )
     => hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OMin)) = c_Groups_Oone__class_Oone(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__one) ).

fof(fact_option_Osize_I4_J,axiom,
    ! [X25,X15] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X15)),hAPP(c_Option_Ooption_OSome(X15),X25)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option_Osize_I4_J) ).

fof(fact_atLeast0AtMost,axiom,
    ! [X76] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X76) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X76),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast0AtMost) ).

fof(fact_atLeast__eq__iff,axiom,
    ! [X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OatLeast(X5),X12) = hAPP(c_SetInterval_Oord__class_OatLeast(X5),X27)
      <=> X12 = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast__eq__iff) ).

fof(fact_greaterThan__eq__iff,axiom,
    ! [X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X12) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X27)
      <=> X12 = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThan__eq__iff) ).

fof(fact_atMost__eq__iff,axiom,
    ! [X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OatMost(X5),X12) = hAPP(c_SetInterval_Oord__class_OatMost(X5),X27)
      <=> X12 = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__eq__iff) ).

fof(fact_lessThan__eq__iff,axiom,
    ! [X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OlessThan(X5),X12) = hAPP(c_SetInterval_Oord__class_OlessThan(X5),X27)
      <=> X12 = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__eq__iff) ).

fof(fact_of__nat__eq__iff,axiom,
    ! [X76,X45,X5] :
      ( class_Nat_Osemiring__char__0(X5)
     => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X45) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X76)
      <=> X45 = X76 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__eq__iff) ).

fof(fact_of__int__eq__iff,axiom,
    ! [X37,X112,X5] :
      ( class_Int_Oring__char__0(X5)
     => ( hAPP(c_Int_Oring__1__class_Oof__int(X5),X112) = hAPP(c_Int_Oring__1__class_Oof__int(X5),X37)
      <=> X112 = X37 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__eq__iff) ).

fof(fact_compl__eq__compl__iff,axiom,
    ! [X27,X12,X5] :
      ( class_Lattices_Oboolean__algebra(X5)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(X5),X12) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X27)
      <=> X12 = X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).

fof(fact_neg__equal__iff__equal,axiom,
    ! [X17,X6,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X17)
      <=> X6 = X17 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).

fof(fact_add__0,axiom,
    ! [X25,X15] :
      ( class_Groups_Ocomm__monoid__add(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),c_Groups_Ozero__class_Ozero(X15)),X25) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).

fof(fact_add__0__left,axiom,
    ! [X25,X15] :
      ( class_Groups_Omonoid__add(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),c_Groups_Ozero__class_Ozero(X15)),X25) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
    ! [X25,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),c_Groups_Ozero__class_Ozero(X15)),X25) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
    ! [X25,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),c_Groups_Oone__class_Oone(X15)),X25) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).

fof(fact_mult__1__left,axiom,
    ! [X25,X15] :
      ( class_Groups_Omonoid__mult(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),c_Groups_Oone__class_Oone(X15)),X25) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).

fof(fact_mult__1,axiom,
    ! [X25,X15] :
      ( class_Groups_Ocomm__monoid__mult(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),c_Groups_Oone__class_Oone(X15)),X25) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).

fof(fact_inf__top__left,axiom,
    ! [X14,X15] :
      ( class_Lattices_Obounded__lattice__top(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),c_Orderings_Otop__class_Otop(X15)),X14) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__top__left) ).

fof(fact_sup__bot__left,axiom,
    ! [X14,X15] :
      ( class_Lattices_Obounded__lattice__bot(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),c_Orderings_Obot__class_Obot(X15)),X14) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__bot__left) ).

fof(fact_divide__self__if,axiom,
    ! [X25,X15] :
      ( class_Rings_Odivision__ring__inverse__zero(X15)
     => ( ( X25 = c_Groups_Ozero__class_Ozero(X15)
         => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),X25) = c_Groups_Ozero__class_Ozero(X15) )
        & ( X25 != c_Groups_Ozero__class_Ozero(X15)
         => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),X25) = c_Groups_Oone__class_Oone(X15) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self__if) ).

fof(fact_mod__0,axiom,
    ! [X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,c_Groups_Ozero__class_Ozero(X15),X25) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__0) ).

fof(fact_mod__by__1,axiom,
    ! [X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,X25,c_Groups_Oone__class_Oone(X15)) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__by__1) ).

fof(fact_sorted__remdups,axiom,
    ! [X103,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( c_List_Olinorder__class_Osorted(X15,X103)
       => c_List_Olinorder__class_Osorted(X15,c_List_Oremdups(X15,X103)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__remdups) ).

fof(fact_set__empty__eq,axiom,
    ! [X83,X5] :
      ( c_Option_Oset(X5,X83) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> X83 = c_Option_Ooption_ONone(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__empty__eq) ).

fof(fact_divide__zero,axiom,
    ! [X25,X15] :
      ( class_Rings_Odivision__ring__inverse__zero(X15)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),c_Groups_Ozero__class_Ozero(X15)) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero) ).

fof(fact_div__by__0,axiom,
    ! [X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),X25),c_Groups_Ozero__class_Ozero(X15)) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__0) ).

fof(fact_mult__zero__right,axiom,
    ! [X25,X15] :
      ( class_Rings_Omult__zero(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),c_Groups_Ozero__class_Ozero(X15)) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
    ! [X25,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),c_Groups_Ozero__class_Ozero(X15)) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

fof(fact_inf__bot__right,axiom,
    ! [X14,X15] :
      ( class_Lattices_Obounded__lattice__bot(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),c_Orderings_Obot__class_Obot(X15)) = c_Orderings_Obot__class_Obot(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__bot__right) ).

fof(fact_sup__top__right,axiom,
    ! [X14,X15] :
      ( class_Lattices_Obounded__lattice__top(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),c_Orderings_Otop__class_Otop(X15)) = c_Orderings_Otop__class_Otop(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__top__right) ).

fof(fact_wf__lex,axiom,
    ! [X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => c_Wellfounded_Owf(tc_List_Olist(X5),c_List_Olex(X5,X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__lex) ).

fof(fact_wf__lenlex,axiom,
    ! [X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => c_Wellfounded_Owf(tc_List_Olist(X5),c_List_Olenlex(X5,X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__lenlex) ).

fof(fact_eq__Nil__appendI,axiom,
    ! [X15,X225,X221] :
      ( X221 = X225
     => X221 = hAPP(hAPP(c_List_Oappend(X15),c_List_Olist_ONil(X15)),X225) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__Nil__appendI) ).

fof(fact_divide__self,axiom,
    ! [X25,X15] :
      ( class_Rings_Odivision__ring(X15)
     => ( X25 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),X25) = c_Groups_Oone__class_Oone(X15) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self) ).

fof(fact_div__self,axiom,
    ! [X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => ( X25 != c_Groups_Ozero__class_Ozero(X15)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),X25),X25) = c_Groups_Oone__class_Oone(X15) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__self) ).

fof(fact_mod__by__0,axiom,
    ! [X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,X25,c_Groups_Ozero__class_Ozero(X15)) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__by__0) ).

fof(fact__05,axiom,
    ! [X15] : hAPP(c_Lazy__Sequence_Oyield(X15),c_Lazy__Sequence_Olazy__sequence_OEmpty(X15)) = c_Option_Ooption_ONone(tc_prod(X15,tc_Lazy__Sequence_Olazy__sequence(X15))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__05) ).

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_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_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_Domain__Id__on,axiom,
    ! [X11,X5] : hAPP(c_Relation_ODomain(X5,X5),c_Relation_OId__on(X5,X11)) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Id__on) ).

fof(fact_Range__Id__on,axiom,
    ! [X11,X5] : hAPP(c_Relation_ORange(X5,X5),c_Relation_OId__on(X5,X11)) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Id__on) ).

fof(fact_power__0,axiom,
    ! [X25,X15] :
      ( class_Power_Opower(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
    ! [X14,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).

fof(fact_divide__1,axiom,
    ! [X25,X15] :
      ( class_Rings_Odivision__ring(X15)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15),X25),c_Groups_Oone__class_Oone(X15)) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__1) ).

fof(fact_div__by__1,axiom,
    ! [X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15),X25),c_Groups_Oone__class_Oone(X15)) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__1) ).

fof(fact_add_Ocomm__neutral,axiom,
    ! [X25,X15] :
      ( class_Groups_Ocomm__monoid__add(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),c_Groups_Ozero__class_Ozero(X15)) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).

fof(fact_add__0__right,axiom,
    ! [X25,X15] :
      ( class_Groups_Omonoid__add(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),c_Groups_Ozero__class_Ozero(X15)) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
    ! [X25,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),X25),c_Groups_Ozero__class_Ozero(X15)) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
    ! [X25,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),c_Groups_Oone__class_Oone(X15)) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

fof(fact_mult__1__right,axiom,
    ! [X25,X15] :
      ( class_Groups_Omonoid__mult(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),c_Groups_Oone__class_Oone(X15)) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).

fof(fact_mult_Ocomm__neutral,axiom,
    ! [X25,X15] :
      ( class_Groups_Ocomm__monoid__mult(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),c_Groups_Oone__class_Oone(X15)) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).

fof(fact_inf__top__right,axiom,
    ! [X14,X15] :
      ( class_Lattices_Obounded__lattice__top(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),c_Orderings_Otop__class_Otop(X15)) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__top__right) ).

fof(fact_diff__0__right,axiom,
    ! [X25,X15] :
      ( class_Groups_Ogroup__add(X15)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X25),c_Groups_Ozero__class_Ozero(X15)) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__right) ).

fof(fact_sup__bot__right,axiom,
    ! [X14,X15] :
      ( class_Lattices_Obounded__lattice__bot(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),c_Orderings_Obot__class_Obot(X15)) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__bot__right) ).

fof(fact_double__compl,axiom,
    ! [X14,X15] :
      ( class_Lattices_Oboolean__algebra(X15)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X14)) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__compl) ).

fof(fact_minus__minus,axiom,
    ! [X25,X15] :
      ( class_Groups_Ogroup__add(X15)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25)) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).

fof(fact_abs__int__eq,axiom,
    ! [X99] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X99)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X99),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__int__eq) ).

fof(fact_of__int__int__eq,axiom,
    ! [X98] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X98)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X98),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__int__eq) ).

fof(fact_set__remdups,axiom,
    ! [X212,X5] : hAPP(c_List_Oset(X5),c_List_Oremdups(X5,X212)) = hAPP(c_List_Oset(X5),X212),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__remdups) ).

fof(fact_mod__self,axiom,
    ! [X25,X15] :
      ( class_Divides_Osemiring__div(X15)
     => c_Divides_Odiv__class_Omod(X15,X25,X25) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__self) ).

fof(fact_rev__is__rev__conv,axiom,
    ! [X214,X212,X5] :
      ( hAPP(c_List_Orev(X5),X212) = hAPP(c_List_Orev(X5),X214)
    <=> X212 = X214 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__is__rev__conv) ).

fof(fact_option_Oinject,axiom,
    ! [X82,X6,X5] :
      ( hAPP(c_Option_Ooption_OSome(X5),X6) = hAPP(c_Option_Ooption_OSome(X5),X82)
    <=> X6 = X82 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option_Oinject) ).

fof(fact_inc__shift__def,axiom,
    ! [X100,X126] :
      ( ( X126 = X100
       => c_Random_Oinc__shift(X126,X100) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
      & ( X126 != X100
       => c_Random_Oinc__shift(X126,X100) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X100),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,
    ! [X225,X15] : hAPP(hAPP(c_List_Oappend(X15),c_List_Olist_ONil(X15)),X225) = X225,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Nil) ).

fof(fact_Suc__eq__plus1__left,axiom,
    ! [X98] : hAPP(c_Nat_OSuc,X98) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X98),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).

fof(fact_sublist__nil,axiom,
    ! [X11,X5] : c_List_Osublist(X5,c_List_Olist_ONil(X5),X11) = c_List_Olist_ONil(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__nil) ).

fof(fact_takeWhile_Osimps_I1_J,axiom,
    ! [X29,X5] : c_List_OtakeWhile(X5,X29,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,
    ! [X14,X15] : c_List_Oremove1(X15,X14,c_List_Olist_ONil(X15)) = c_List_Olist_ONil(X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1_Osimps_I1_J) ).

fof(fact_atLeastLessThan0,axiom,
    ! [X45] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45),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_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
    ! [X14,X15] :
      ( class_Rings_Ocomm__semiring__1(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).

fof(fact_power__one__right,axiom,
    ! [X25,X15] :
      ( class_Groups_Omonoid__mult(X15)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).

fof(fact_diff__self,axiom,
    ! [X25,X15] :
      ( class_Groups_Ogroup__add(X15)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15),X25),X25) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self) ).

fof(fact_list_Osize_I1_J,axiom,
    ! [X92,X5] : c_List_Olist_Olist__size(X5,X92,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_option_Osize_I1_J,axiom,
    ! [X92,X5] : c_Option_Ooption_Ooption__size(X5,X92,c_Option_Ooption_ONone(X5)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option_Osize_I1_J) ).

fof(fact_take__0,axiom,
    ! [X221,X15] : hAPP(hAPP(c_List_Otake(X15),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X221) = c_List_Olist_ONil(X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__0) ).

fof(fact_drop__Nil,axiom,
    ! [X98,X15] : hAPP(hAPP(c_List_Odrop(X15),X98),c_List_Olist_ONil(X15)) = c_List_Olist_ONil(X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__Nil) ).

fof(fact_take__Nil,axiom,
    ! [X98,X15] : hAPP(hAPP(c_List_Otake(X15),X98),c_List_Olist_ONil(X15)) = c_List_Olist_ONil(X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Nil) ).

fof(fact_minus__equation__iff,axiom,
    ! [X17,X6,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6) = X17
      <=> hAPP(c_Groups_Ouminus__class_Ouminus(X5),X17) = X6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__equation__iff) ).

fof(fact_equation__minus__iff,axiom,
    ! [X17,X6,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( X6 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X17)
      <=> X17 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equation__minus__iff) ).

fof(fact_enum__distinct,axiom,
    ! [X15] :
      ( class_Enum_Oenum(X15)
     => hBOOL(hAPP(c_List_Odistinct(X15),c_Enum_Oenum__class_Oenum(X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__distinct) ).

fof(fact_nat__list__def,axiom,
    ! [X97] :
      ( c_List_Onat__list(X97)
    <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X97)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__list__def) ).

fof(fact_card__atMost,axiom,
    ! [X66] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X66)) = hAPP(c_Nat_OSuc,X66),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atMost) ).

fof(fact_nat__of__number,axiom,
    ! [X100] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X100)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X100),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__number) ).

fof(fact_nat__number__of,axiom,
    ! [X132] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X132),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of) ).

fof(fact_nat__number__of__def,axiom,
    ! [X126] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__def) ).

fof(fact_Suc__eq__plus1,axiom,
    ! [X98] : hAPP(c_Nat_OSuc,X98) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).

fof(fact_replicate__0,axiom,
    ! [X14,X15] : c_List_Oreplicate(X15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) = c_List_Olist_ONil(X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__0) ).

fof(fact_splice_Osimps_I1_J,axiom,
    ! [X225,X15] : c_List_Osplice(X15,c_List_Olist_ONil(X15),X225) = X225,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I1_J) ).

fof(fact__04,axiom,
    ! [X274,X15] : c_Lazy__Sequence_Oappend(X15,c_Lazy__Sequence_Olazy__sequence_OEmpty(X15),X274) = X274,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__04) ).

fof(fact_splice__Nil2,axiom,
    ! [X221,X15] : c_List_Osplice(X15,X221,c_List_Olist_ONil(X15)) = X221,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice__Nil2) ).

fof(fact_sgn__sgn,axiom,
    ! [X25,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => c_Groups_Osgn__class_Osgn(X15,c_Groups_Osgn__class_Osgn(X15,X25)) = c_Groups_Osgn__class_Osgn(X15,X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__sgn) ).

fof(fact_list__all__simps_I2_J,axiom,
    ! [X29,X5] : c_List_Olist__all(X5,X29,c_List_Olist_ONil(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__simps_I2_J) ).

fof(fact_enum__UNIV,axiom,
    ! [X5] :
      ( class_Enum_Oenum(X5)
     => hAPP(c_List_Oset(X5),c_Enum_Oenum__class_Oenum(X5)) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__UNIV) ).

fof(fact_UNIV__enum,axiom,
    ! [X5] :
      ( class_Enum_Oenum(X5)
     => c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_List_Oset(X5),c_Enum_Oenum__class_Oenum(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__enum) ).

fof(fact_min__max_Osup_Oidem,axiom,
    ! [X25,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X25),X25) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup_Oidem) ).

fof(fact_Max_Oidem,axiom,
    ! [X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X14),X14) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oidem) ).

fof(fact_Min_Oidem,axiom,
    ! [X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X14),X14) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oidem) ).

fof(fact_min__max_Oinf_Oidem,axiom,
    ! [X25,X15] :
      ( class_Orderings_Olinorder(X15)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X25),X25) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf_Oidem) ).

fof(fact_times_Oidem,axiom,
    ! [X25,X15] :
      ( class_Lattices_Oab__semigroup__idem__mult(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X25) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times_Oidem) ).

fof(fact_mult__idem,axiom,
    ! [X14,X15] :
      ( class_Lattices_Oab__semigroup__idem__mult(X15)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),X14) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__idem) ).

fof(fact_inf_Oidem,axiom,
    ! [X25,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X25),X25) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oidem) ).

fof(fact_inf__idem,axiom,
    ! [X14,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X14) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__idem) ).

fof(fact_Inf__fin_Oidem,axiom,
    ! [X14,X15] :
      ( class_Lattices_Olattice(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X14),X14) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oidem) ).

fof(fact_Sup__fin_Oidem,axiom,
    ! [X14,X15] :
      ( class_Lattices_Olattice(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X14) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oidem) ).

fof(fact_sup_Oidem,axiom,
    ! [X25,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X25),X25) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup_Oidem) ).

fof(fact_sup__idem,axiom,
    ! [X14,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X14),X14) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__idem) ).

fof(fact_length__0__conv,axiom,
    ! [X212,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> X212 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__0__conv) ).

fof(fact_mult__Min,axiom,
    ! [X100] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X100) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X100),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Min) ).

fof(fact_atLeast0LessThan,axiom,
    ! [X76] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X76) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X76),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast0LessThan) ).

fof(fact_New__DSequence_Opos__single__def,axiom,
    ! [X267,X14,X15] : hAPP(c_New__DSequence_Opos__single(X15,X14),X267) = hAPP(c_Lazy__Sequence_Osingle(X15),X14),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__single__def) ).

fof(fact_drop__0,axiom,
    ! [X221,X15] : hAPP(hAPP(c_List_Odrop(X15),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X221) = X221,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__0) ).

fof(fact_append__Nil2,axiom,
    ! [X221,X15] : hAPP(hAPP(c_List_Oappend(X15),X221),c_List_Olist_ONil(X15)) = X221,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Nil2) ).

fof(fact_rev__rev__ident,axiom,
    ! [X221,X15] : hAPP(c_List_Orev(X15),hAPP(c_List_Orev(X15),X221)) = X221,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__rev__ident) ).

fof(fact_the_Osimps,axiom,
    ! [X14,X15] : hAPP(c_Option_Othe(X15),hAPP(c_Option_Ooption_OSome(X15),X14)) = X14,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the_Osimps) ).

fof(fact_small__lazy__int__def,axiom,
    ! [X41] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X41) = c_Lazy__Sequence_Osmall__lazy_H(X41,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X41)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small__lazy__int__def) ).

fof(fact_zmod__zero,axiom,
    ! [X26] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X26) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zero) ).

fof(fact_neg__nat,axiom,
    ! [X23] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X23))
     => hAPP(c_Int_Onat,X23) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__nat) ).

fof(fact_atLeast__Suc__greaterThan,axiom,
    ! [X30] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast__Suc__greaterThan) ).

fof(fact_lessThan__Suc__atMost,axiom,
    ! [X30] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__Suc__atMost) ).

fof(fact_less__eq__Suc__le__raw,axiom,
    ! [X76] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X76)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).

fof(fact_DIVISION__BY__ZERO,axiom,
    ! [X25] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      & c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DIVISION__BY__ZERO) ).

fof(fact_iszero__Numeral0,axiom,
    ! [X15] :
      ( class_Int_Onumber__ring(X15)
     => c_Int_Oiszero(X15,hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__Numeral0) ).

fof(fact_Option_Omap_Oid,axiom,
    ! [X5] : hAPP(c_Option_Omap(X5,X5),c_Fun_Oid(X5)) = c_Fun_Oid(tc_Option_Ooption(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Option_Omap_Oid) ).

fof(fact_Option_Omap_Oidentity,axiom,
    ! [X5] : hAPP(c_Option_Omap(X5,X5),c_COMBI(X5)) = c_Fun_Oid(tc_Option_Ooption(X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Option_Omap_Oidentity) ).

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_int__int__eq,axiom,
    ! [X76,X45] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X45) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X76)
    <=> X45 = X76 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__int__eq) ).

fof(fact_transfer__int__nat__relations_I1_J,axiom,
    ! [X27,X12] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X12) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X27)
    <=> X12 = X27 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I1_J) ).

fof(fact_zmod__self,axiom,
    ! [X25] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X25) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__self) ).

fof(fact_rev__swap,axiom,
    ! [X214,X212,X5] :
      ( hAPP(c_List_Orev(X5),X212) = X214
    <=> X212 = hAPP(c_List_Orev(X5),X214) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__swap) ).

fof(fact_min__0L,axiom,
    ! [X98] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X98) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__0L) ).

fof(fact_zdiv__zero,axiom,
    ! [X26] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zero) ).

fof(fact_mult__0,axiom,
    ! [X98] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X98) = 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,
    ! [X98] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X98) = 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,
    ! [X15] : hBOOL(hAPP(c_List_Odistinct(X15),c_List_Olist_ONil(X15))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct_Osimps_I1_J) ).

fof(fact_New__DSequence_Oneg__single__def,axiom,
    ! [X267,X14,X15] : hAPP(c_New__DSequence_Oneg__single(X15,X14),X267) = c_Lazy__Sequence_Ohb__single(X15,X14),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).

fof(fact_remdups__remdups,axiom,
    ! [X221,X15] : c_List_Oremdups(X15,c_List_Oremdups(X15,X221)) = c_List_Oremdups(X15,X221),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__remdups) ).

fof(fact_rtrancl__idemp,axiom,
    ! [X34,X5] : c_Transitive__Closure_Ortrancl(X5,c_Transitive__Closure_Ortrancl(X5,X34)) = c_Transitive__Closure_Ortrancl(X5,X34),
    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,
    ! [X98] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X98) = X98,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__0L) ).

fof(fact_zadd__0,axiom,
    ! [X23] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23) = X23,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).

fof(fact_plus__nat_Oadd__0,axiom,
    ! [X98] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X98) = X98,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).

fof(fact_zmult__1,axiom,
    ! [X23] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X23) = X23,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).

fof(fact_nat__mult__1,axiom,
    ! [X98] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X98) = X98,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).

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,
    ! [X25] :
      ( X25 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25),X25) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__self) ).

fof(fact_not__None__eq,axiom,
    ! [X5,X12] :
      ( X12 != c_Option_Ooption_ONone(X5)
    <=> ? [X33] : X12 = hAPP(c_Option_Ooption_OSome(X5),X33) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__None__eq) ).

fof(fact_not__Some__eq,axiom,
    ! [X5,X12] :
      ( ! [X33] : X12 != hAPP(c_Option_Ooption_OSome(X5),X33)
    <=> X12 = c_Option_Ooption_ONone(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Some__eq) ).

fof(fact_arith__simps_I31_J,axiom,
    ! [X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X15),c_Groups_Oone__class_Oone(X15)) = hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OMin) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I31_J) ).

fof(fact_number__of__Min,axiom,
    ! [X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(X15),c_Groups_Oone__class_Oone(X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Min) ).

fof(fact_min__0R,axiom,
    ! [X98] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X98),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,
    ! [X99] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X99),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,
    ! [X98] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X98),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X98,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__0R) ).

fof(fact_zadd__0__right,axiom,
    ! [X23] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X23,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).

fof(fact_Nat_Oadd__0__right,axiom,
    ! [X99] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X99,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).

fof(fact_zmult__1__right,axiom,
    ! [X23] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X23,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).

fof(fact_nat__mult__1__right,axiom,
    ! [X98] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X98,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).

fof(fact_minus__nat_Odiff__0,axiom,
    ! [X99] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X99,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).

fof(fact_card__lessThan,axiom,
    ! [X66] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X66)) = X66,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__lessThan) ).

fof(fact_zminus__zminus,axiom,
    ! [X23] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23)) = X23,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).

fof(fact_filter_Osimps_I1_J,axiom,
    ! [X29,X5] : hAPP(c_List_Ofilter(X5,X29),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,
    ! [X11,X5] :
      ( class_Finite__Set_Ofinite(X5)
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite) ).

fof(fact_finite__code,axiom,
    ! [X11,X5] :
      ( class_Finite__Set_Ofinite(X5)
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__code) ).

fof(fact_of__int__eq__0__iff,axiom,
    ! [X37,X5] :
      ( class_Int_Oring__char__0(X5)
     => ( hAPP(c_Int_Oring__1__class_Oof__int(X5),X37) = c_Groups_Ozero__class_Ozero(X5)
      <=> X37 = 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,
    ! [X37,X5] :
      ( class_Int_Oring__char__0(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Int_Oring__1__class_Oof__int(X5),X37)
      <=> X37 = 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,
    ! [X99] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X99) = 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,
    ! [X92,X5] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X5,X92),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,
    ! [X100,X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(c_Int_Onumber__class_Onumber__of(X15),X100) = hAPP(c_Int_Oring__1__class_Oof__int(X15),X100) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__eq) ).

fof(fact_Option_Oset_Osimps_I1_J,axiom,
    ! [X5] : c_Option_Oset(X5,c_Option_Ooption_ONone(X5)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Option_Oset_Osimps_I1_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,
    ! [X100] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X100),c_Int_OPls) = X100,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls__right) ).

fof(fact_diff__bin__simps_I1_J,axiom,
    ! [X100] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X100),c_Int_OPls) = X100,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I1_J) ).

fof(fact_nat__int,axiom,
    ! [X98] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X98)) = X98,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__int) ).

fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom,
    ! [X285,X284] :
      ( ( class_Lazy__Sequence_Osmall__lazy(X284)
        & class_Lazy__Sequence_Osmall__lazy(X285) )
     => class_Lazy__Sequence_Osmall__lazy(tc_prod(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Lazy__Sequence_Osmall__lazy) ).

fof(arity_fun__HOL_Oequal,axiom,
    ! [X285,X284] :
      ( ( class_Enum_Oenum(X284)
        & class_HOL_Oequal(X285) )
     => class_HOL_Oequal(tc_fun(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__HOL_Oequal) ).

fof(arity_prod__Smallcheck_Osmall,axiom,
    ! [X285,X284] :
      ( ( class_Smallcheck_Osmall(X284)
        & class_Smallcheck_Osmall(X285) )
     => class_Smallcheck_Osmall(tc_prod(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Smallcheck_Osmall) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
    ! [X22,X14] :
      ( c_Nat__Transfer_Ois__nat(X14)
     => ( c_Nat__Transfer_Ois__nat(X22)
       => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X14,X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J) ).

fof(arity_sum__Finite__Set_Ofinite,axiom,
    ! [X285,X284] :
      ( ( class_Finite__Set_Ofinite(X284)
        & class_Finite__Set_Ofinite(X285) )
     => class_Finite__Set_Ofinite(tc_sum(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).

fof(arity_prod__Finite__Set_Ofinite,axiom,
    ! [X285,X284] :
      ( ( class_Finite__Set_Ofinite(X284)
        & class_Finite__Set_Ofinite(X285) )
     => class_Finite__Set_Ofinite(tc_prod(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).

fof(arity_fun__Finite__Set_Ofinite,axiom,
    ! [X285,X284] :
      ( ( class_Finite__Set_Ofinite(X284)
        & class_Finite__Set_Ofinite(X285) )
     => class_Finite__Set_Ofinite(tc_fun(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).

fof(arity_sum__Enum_Oenum,axiom,
    ! [X285,X284] :
      ( ( class_Enum_Oenum(X284)
        & class_Enum_Oenum(X285) )
     => class_Enum_Oenum(tc_sum(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum__Enum_Oenum) ).

fof(arity_prod__Enum_Oenum,axiom,
    ! [X285,X284] :
      ( ( class_Enum_Oenum(X284)
        & class_Enum_Oenum(X285) )
     => class_Enum_Oenum(tc_prod(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Enum_Oenum) ).

fof(arity_fun__Enum_Oenum,axiom,
    ! [X285,X284] :
      ( ( class_Enum_Oenum(X284)
        & class_Enum_Oenum(X285) )
     => class_Enum_Oenum(tc_fun(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Enum_Oenum) ).

fof(fact_add__Pls,axiom,
    ! [X100] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X100) = X100,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls) ).

fof(fact_rev__is__Nil__conv,axiom,
    ! [X212,X5] :
      ( hAPP(c_List_Orev(X5),X212) = c_List_Olist_ONil(X5)
    <=> X212 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__is__Nil__conv) ).

fof(fact_rotate1__is__Nil__conv,axiom,
    ! [X212,X5] :
      ( hAPP(c_List_Orotate1(X5),X212) = c_List_Olist_ONil(X5)
    <=> X212 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__is__Nil__conv) ).

fof(fact_Nil__is__rev__conv,axiom,
    ! [X212,X5] :
      ( c_List_Olist_ONil(X5) = hAPP(c_List_Orev(X5),X212)
    <=> X212 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__is__rev__conv) ).

fof(fact_mult__Pls,axiom,
    ! [X132] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X132) = c_Int_OPls,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Pls) ).

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,
    ! [X15] : c_List_Otranspose(X15,c_List_Olist_ONil(tc_List_Olist(X15))) = c_List_Olist_ONil(tc_List_Olist(X15)),
    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,
    ! [X27,X12] :
      ( hAPP(c_Code__Numeral_Onat__of,X12) = hAPP(c_Code__Numeral_Onat__of,X27)
    <=> X12 = X27 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Onat__of__inject) ).

fof(fact_Code__Numeral_Onat__of__inject,axiom,
    ! [X97,X30] :
      ( hAPP(c_Code__Numeral_Onat__of,X30) = hAPP(c_Code__Numeral_Onat__of,X97)
    <=> X30 = X97 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Code__Numeral_Onat__of__inject) ).

fof(fact_Code__Numeral_Oof__nat__inject,axiom,
    ! [X45,X76] :
      ( hAPP(c_Code__Numeral_Oof__nat,X76) = hAPP(c_Code__Numeral_Oof__nat,X45)
    <=> X76 = X45 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__inject) ).

fof(fact_Rep__Integ__inject,axiom,
    ! [X27,X12] :
      ( hAPP(c_Int_ORep__Integ,X12) = hAPP(c_Int_ORep__Integ,X27)
    <=> X12 = X27 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).

fof(fact_Suc__inject,axiom,
    ! [X22,X14] :
      ( hAPP(c_Nat_OSuc,X14) = hAPP(c_Nat_OSuc,X22)
     => X14 = X22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).

fof(fact_nat_Oinject,axiom,
    ! [X110,X111] :
      ( hAPP(c_Nat_OSuc,X111) = hAPP(c_Nat_OSuc,X110)
    <=> X111 = X110 ),
    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,
    ! [X15] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X15)),c_Lazy__Sequence_Olazy__sequence_OEmpty(X15)) = 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,
    ! [X15] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),c_List_Olist_ONil(X15)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osize_I3_J) ).

fof(fact_option_Osize_I3_J,axiom,
    ! [X15] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X15)),c_Option_Ooption_ONone(X15)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option_Osize_I3_J) ).

fof(fact_wf__measures,axiom,
    ! [X261,X5] : c_Wellfounded_Owf(X5,c_List_Omeasures(X5,X261)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__measures) ).

fof(fact_sorted__upto,axiom,
    ! [X101,X102] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X102,X101)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__upto) ).

fof(fact_option_Osimps_I3_J,axiom,
    ! [X81,X15] : hAPP(c_Option_Ooption_OSome(X15),X81) != c_Option_Ooption_ONone(X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option_Osimps_I3_J) ).

fof(fact_option_Osimps_I2_J,axiom,
    ! [X81,X15] : c_Option_Ooption_ONone(X15) != hAPP(c_Option_Ooption_OSome(X15),X81),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option_Osimps_I2_J) ).

fof(fact_some__sym__eq__trivial,axiom,
    ! [X12,X5] : c_Hilbert__Choice_OEps(X5,hAPP(c_fequal,X12)) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__sym__eq__trivial) ).

fof(fact_the__sym__eq__trivial,axiom,
    ! [X12,X5] : c_HOL_OThe(X5,hAPP(c_fequal,X12)) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__sym__eq__trivial) ).

fof(fact_listsum__simps_I1_J,axiom,
    ! [X15] :
      ( class_Groups_Omonoid__add(X15)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X15),c_List_Olist_ONil(X15)) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__simps_I1_J) ).

fof(fact_abs__zero,axiom,
    ! [X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => hAPP(c_Groups_Oabs__class_Oabs(X15),c_Groups_Ozero__class_Ozero(X15)) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__zero) ).

fof(fact_abs__one,axiom,
    ! [X15] :
      ( class_Rings_Olinordered__idom(X15)
     => hAPP(c_Groups_Oabs__class_Oabs(X15),c_Groups_Oone__class_Oone(X15)) = c_Groups_Oone__class_Oone(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__one) ).

fof(fact_minus__zero,axiom,
    ! [X15] :
      ( class_Groups_Ogroup__add(X15)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X15),c_Groups_Ozero__class_Ozero(X15)) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__zero) ).

fof(fact_compl__top__eq,axiom,
    ! [X15] :
      ( class_Lattices_Oboolean__algebra(X15)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X15),c_Orderings_Otop__class_Otop(X15)) = c_Orderings_Obot__class_Obot(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__top__eq) ).

fof(fact_compl__bot__eq,axiom,
    ! [X15] :
      ( class_Lattices_Oboolean__algebra(X15)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X15),c_Orderings_Obot__class_Obot(X15)) = c_Orderings_Otop__class_Otop(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__bot__eq) ).

fof(arity_fun__Lattices_Obounded__lattice,axiom,
    ! [X284,X285] :
      ( class_Lattices_Obounded__lattice(X285)
     => class_Lattices_Obounded__lattice(tc_fun(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).

fof(arity_fun__Groups_Ouminus,axiom,
    ! [X284,X285] :
      ( class_Groups_Ouminus(X285)
     => class_Groups_Ouminus(tc_fun(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).

fof(arity_fun__Lattices_Oboolean__algebra,axiom,
    ! [X284,X285] :
      ( class_Lattices_Oboolean__algebra(X285)
     => class_Lattices_Oboolean__algebra(tc_fun(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).

fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
    ! [X284,X285] :
      ( class_Lattices_Obounded__lattice(X285)
     => class_Lattices_Obounded__lattice__top(tc_fun(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__top) ).

fof(arity_fun__Orderings_Otop,axiom,
    ! [X284,X285] :
      ( class_Orderings_Otop(X285)
     => class_Orderings_Otop(tc_fun(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).

fof(arity_fun__Lattices_Odistrib__lattice,axiom,
    ! [X284,X285] :
      ( class_Lattices_Odistrib__lattice(X285)
     => class_Lattices_Odistrib__lattice(tc_fun(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Odistrib__lattice) ).

fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
    ! [X284,X285] :
      ( class_Complete__Lattice_Ocomplete__lattice(X285)
     => class_Complete__Lattice_Ocomplete__lattice(tc_fun(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Complete__Lattice_Ocomplete__lattice) ).

fof(arity_fun__Lattices_Osemilattice__inf,axiom,
    ! [X284,X285] :
      ( class_Lattices_Olattice(X285)
     => class_Lattices_Osemilattice__inf(tc_fun(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).

fof(arity_fun__Groups_Ominus,axiom,
    ! [X284,X285] :
      ( class_Groups_Ominus(X285)
     => class_Groups_Ominus(tc_fun(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).

fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
    ! [X284,X285] :
      ( class_Lattices_Obounded__lattice(X285)
     => class_Lattices_Obounded__lattice__bot(tc_fun(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__bot) ).

fof(arity_fun__Lattices_Olattice,axiom,
    ! [X284,X285] :
      ( class_Lattices_Olattice(X285)
     => class_Lattices_Olattice(tc_fun(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).

fof(arity_fun__Lattices_Osemilattice__sup,axiom,
    ! [X284,X285] :
      ( class_Lattices_Olattice(X285)
     => class_Lattices_Osemilattice__sup(tc_fun(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__sup) ).

fof(arity_fun__Orderings_Oord,axiom,
    ! [X284,X285] :
      ( class_Orderings_Oord(X285)
     => class_Orderings_Oord(tc_fun(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).

fof(arity_fun__Orderings_Oorder,axiom,
    ! [X284,X285] :
      ( class_Orderings_Oorder(X285)
     => class_Orderings_Oorder(tc_fun(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).

fof(arity_fun__Orderings_Obot,axiom,
    ! [X284,X285] :
      ( class_Orderings_Obot(X285)
     => class_Orderings_Obot(tc_fun(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).

fof(arity_fun__Orderings_Opreorder,axiom,
    ! [X284,X285] :
      ( class_Orderings_Opreorder(X285)
     => class_Orderings_Opreorder(tc_fun(X284,X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).

fof(fact_wf__acyclic,axiom,
    ! [X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => c_Wellfounded_Oacyclic(X5,X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__acyclic) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
    ! [X23] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) ).

fof(fact_nat__of__of__nat,axiom,
    ! [X98] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X98)) = X98,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__of__nat) ).

fof(fact_of__nat__nat__of,axiom,
    ! [X100] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X100)) = X100,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__nat__of) ).

fof(fact_nat__of__inverse,axiom,
    ! [X14] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X14)) = X14,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__inverse) ).

fof(fact_Rep__Integ__inverse,axiom,
    ! [X12] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X12)) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__inverse) ).

fof(fact_iszero__def,axiom,
    ! [X37,X5] :
      ( class_Rings_Osemiring__1(X5)
     => ( c_Int_Oiszero(X5,X37)
      <=> X37 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__def) ).

fof(fact_int__eq__0__conv,axiom,
    ! [X76] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X76) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__eq__0__conv) ).

fof(fact_of__nat__0,axiom,
    ! [X15] :
      ( class_Rings_Osemiring__1(X15)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__0) ).

fof(fact_of__nat__1,axiom,
    ! [X15] :
      ( class_Rings_Osemiring__1(X15)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__1) ).

fof(fact_of__int__0,axiom,
    ! [X15] :
      ( class_Rings_Oring__1(X15)
     => hAPP(c_Int_Oring__1__class_Oof__int(X15),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__0) ).

fof(fact_of__int__1,axiom,
    ! [X15] :
      ( class_Rings_Oring__1(X15)
     => hAPP(c_Int_Oring__1__class_Oof__int(X15),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__1) ).

fof(fact_int__number__of__def,axiom,
    ! [X132] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X132),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__number__of__def) ).

fof(fact_remdups__eq__nil__iff,axiom,
    ! [X12,X5] :
      ( c_List_Oremdups(X5,X12) = c_List_Olist_ONil(X5)
    <=> X12 = 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,
    ! [X12,X5] :
      ( c_List_Olist_ONil(X5) = c_List_Oremdups(X5,X12)
    <=> X12 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__eq__nil__right__iff) ).

fof(fact_sgn0,axiom,
    ! [X15] :
      ( class_Groups_Osgn__if(X15)
     => c_Groups_Osgn__class_Osgn(X15,c_Groups_Ozero__class_Ozero(X15)) = c_Groups_Ozero__class_Ozero(X15) ),
    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,
    ! [X15] : hAPP(c_List_Orev(X15),c_List_Olist_ONil(X15)) = c_List_Olist_ONil(X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev_Osimps_I1_J) ).

fof(fact_tl_Osimps_I1_J,axiom,
    ! [X15] : hAPP(c_List_Otl(X15),c_List_Olist_ONil(X15)) = c_List_Olist_ONil(X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl_Osimps_I1_J) ).

fof(arity_Nitpick__Opair____box__Nat_Osize,axiom,
    ! [X285,X284] : class_Nat_Osize(tc_Nitpick_Opair__box(X284,X285)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nitpick__Opair____box__Nat_Osize) ).

fof(arity_sum__Nat_Osize,axiom,
    ! [X285,X284] : class_Nat_Osize(tc_sum(X284,X285)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum__Nat_Osize) ).

fof(arity_prod__Nat_Osize,axiom,
    ! [X285,X284] : class_Nat_Osize(tc_prod(X284,X285)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Nat_Osize) ).

fof(arity_Nitpick__Opair____box__HOL_Oequal,axiom,
    ! [X285,X284] : class_HOL_Oequal(tc_Nitpick_Opair__box(X284,X285)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nitpick__Opair____box__HOL_Oequal) ).

fof(arity_sum__HOL_Oequal,axiom,
    ! [X285,X284] : class_HOL_Oequal(tc_sum(X284,X285)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum__HOL_Oequal) ).

fof(arity_prod__HOL_Oequal,axiom,
    ! [X285,X284] : class_HOL_Oequal(tc_prod(X284,X285)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__HOL_Oequal) ).

fof(fact_number__of__Pls,axiom,
    ! [X15] :
      ( class_Int_Onumber__ring(X15)
     => hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OPls) = c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Pls) ).

fof(fact_semiring__norm_I112_J,axiom,
    ! [X15] :
      ( class_Int_Onumber__ring(X15)
     => c_Groups_Ozero__class_Ozero(X15) = hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OPls) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I112_J) ).

fof(fact_sorted_Oequations_I1_J,axiom,
    ! [X15] :
      ( class_Orderings_Olinorder(X15)
     => c_List_Olinorder__class_Osorted(X15,c_List_Olist_ONil(X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted_Oequations_I1_J) ).

fof(fact_sorted_ONil,axiom,
    ! [X15] :
      ( class_Orderings_Olinorder(X15)
     => c_List_Olinorder__class_Osorted(X15,c_List_Olist_ONil(X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted_ONil) ).

fof(fact_iszero__0,axiom,
    ! [X15] :
      ( class_Rings_Osemiring__1(X15)
     => c_Int_Oiszero(X15,c_Groups_Ozero__class_Ozero(X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__0) ).

fof(fact_New__DSequence_Opos__empty__def,axiom,
    ! [X267,X15] : hAPP(c_New__DSequence_Opos__empty(X15),X267) = c_Lazy__Sequence_Oempty(X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).

fof(fact_remdups_Osimps_I1_J,axiom,
    ! [X15] : c_List_Oremdups(X15,c_List_Olist_ONil(X15)) = c_List_Olist_ONil(X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups_Osimps_I1_J) ).

fof(fact_butlast_Osimps_I1_J,axiom,
    ! [X15] : c_List_Obutlast(X15,c_List_Olist_ONil(X15)) = c_List_Olist_ONil(X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast_Osimps_I1_J) ).

fof(fact_Suc__neq__Zero,axiom,
    ! [X99] : hAPP(c_Nat_OSuc,X99) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).

fof(fact_nat_Osimps_I3_J,axiom,
    ! [X122] : hAPP(c_Nat_OSuc,X122) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).

fof(fact_Suc__not__Zero,axiom,
    ! [X99] : hAPP(c_Nat_OSuc,X99) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).

fof(fact_Zero__neq__Suc,axiom,
    ! [X99] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X99),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).

fof(fact_nat_Osimps_I2_J,axiom,
    ! [X121] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X121),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).

fof(fact_Zero__not__Suc,axiom,
    ! [X99] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X99),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).

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_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_Suc__n__not__n,axiom,
    ! [X98] : hAPP(c_Nat_OSuc,X98) != X98,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).

fof(fact_n__not__Suc__n,axiom,
    ! [X98] : X98 != hAPP(c_Nat_OSuc,X98),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).

fof(fact_id__apply,axiom,
    ! [X14,X15] : hAPP(c_Fun_Oid(X15),X14) = X14,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__apply) ).

fof(fact_id__def,axiom,
    ! [X185,X15] : hAPP(c_Fun_Oid(X15),X185) = X185,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__def) ).

fof(help_c__COMBI__1,axiom,
    ! [X286,X15] : hAPP(c_COMBI(X15),X286) = X286,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).

fof(fact_Collect__def,axiom,
    ! [X29,X5] : hAPP(c_Set_OCollect(X5),X29) = X29,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).

fof(fact_zero__neq__one,axiom,
    ! [X15] :
      ( class_Rings_Ozero__neq__one(X15)
     => c_Groups_Ozero__class_Ozero(X15) != c_Groups_Oone__class_Oone(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).

fof(fact_one__neq__zero,axiom,
    ! [X15] :
      ( class_Rings_Ozero__neq__one(X15)
     => c_Groups_Oone__class_Oone(X15) != c_Groups_Ozero__class_Ozero(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).

fof(fact_wf__int__ge__less__than,axiom,
    ! [X20] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X20)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__int__ge__less__than) ).

fof(fact_wf__int__ge__less__than2,axiom,
    ! [X20] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X20)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__int__ge__less__than2) ).

fof(fact_number__of__is__id,axiom,
    ! [X100] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X100) = X100,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__is__id) ).

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

fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom,
    ! [X285] :
      ( class_Lazy__Sequence_Osmall__lazy(X285)
     => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_List__Olist__Lazy__Sequence_Osmall__lazy) ).

fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
    ! [X285] :
      ( class_Finite__Set_Ofinite(X285)
     => class_Finite__Set_Ofinite(tc_Option_Ooption(X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).

fof(arity_Option__Ooption__Enum_Oenum,axiom,
    ! [X285] :
      ( class_Enum_Oenum(X285)
     => class_Enum_Oenum(tc_Option_Ooption(X285)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option__Ooption__Enum_Oenum) ).

fof(fact_identity__equivp,axiom,
    ! [X5] : c_Equiv__Relations_Oequivp(X5,c_fequal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_identity__equivp) ).

fof(fact_equal,axiom,
    ! [X5] :
      ( class_HOL_Oequal(X5)
     => c_HOL_Oequal__class_Oequal(X5) = c_fequal ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal) ).

fof(fact_eq__equal,axiom,
    ! [X5] :
      ( class_HOL_Oequal(X5)
     => c_fequal = c_HOL_Oequal__class_Oequal(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__equal) ).

fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
    ! [X285] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X285)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Lazy____Sequence__Olazy____sequence__Nat_Osize) ).

fof(arity_List__Olist__Nat_Osize,axiom,
    ! [X285] : class_Nat_Osize(tc_List_Olist(X285)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_List__Olist__Nat_Osize) ).

fof(arity_Option__Ooption__Nat_Osize,axiom,
    ! [X285] : class_Nat_Osize(tc_Option_Ooption(X285)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option__Ooption__Nat_Osize) ).

fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
    ! [X285] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X285)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Hoare____Mirabelle__Otriple__Nat_Osize) ).

fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom,
    ! [X285] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(X285)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal) ).

fof(arity_List__Olist__HOL_Oequal,axiom,
    ! [X285] : class_HOL_Oequal(tc_List_Olist(X285)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_List__Olist__HOL_Oequal) ).

fof(arity_Option__Ooption__HOL_Oequal,axiom,
    ! [X285] : class_HOL_Oequal(tc_Option_Ooption(X285)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option__Ooption__HOL_Oequal) ).

fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom,
    ! [X285] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(X285)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Hoare____Mirabelle__Otriple__HOL_Oequal) ).

fof(help_c__fFalse__1,axiom,
    ~ hBOOL(c_fFalse),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fFalse__1) ).

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(conj_2,hypothesis,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).

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(conj_3,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).

fof(conj_0,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

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__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__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__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_eq__int__code_I6_J,axiom,
    hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__int__code_I6_J) ).

fof(fact_eq__int__code_I1_J,axiom,
    hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__int__code_I1_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_mono__Suc,axiom,
    c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mono__Suc) ).

fof(conj_4,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).

fof(conj_1,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,v_ts),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

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(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_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_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_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_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_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_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(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_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(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__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_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_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_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_Code____Evaluation__Oterm__HOL_Oequal,axiom,
    class_HOL_Oequal(tc_Code__Evaluation_Oterm),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Evaluation__Oterm__HOL_Oequal) ).

fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom,
    class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__HOL_Oequal) ).

fof(arity_Int__Oint__HOL_Oequal,axiom,
    class_HOL_Oequal(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__HOL_Oequal) ).

fof(arity_Product____Type__Ounit__HOL_Oequal,axiom,
    class_HOL_Oequal(tc_Product__Type_Ounit),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product____Type__Ounit__HOL_Oequal) ).

fof(arity_Nat__Onat__HOL_Oequal,axiom,
    class_HOL_Oequal(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__HOL_Oequal) ).

fof(arity_HOL__Obool__HOL_Oequal,axiom,
    class_HOL_Oequal(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__HOL_Oequal) ).

fof(arity_Int__Oint__Smallcheck_Osmall,axiom,
    class_Smallcheck_Osmall(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Smallcheck_Osmall) ).

fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom,
    class_Smallcheck_Osmall(tc_Product__Type_Ounit),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Smallcheck_Osmall) ).

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_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_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_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__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__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_Int__Oint__Rings_Oring__1,axiom,
    class_Rings_Oring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).

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__Power_Opower,axiom,
    class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Power_Opower) ).

fof(arity_Int__Oint__Power_Opower,axiom,
    class_Power_Opower(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).

fof(arity_Nat__Onat__Power_Opower,axiom,
    class_Power_Opower(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).

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),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).

fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict) ).

fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).

fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict) ).

fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).

fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
    class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring) ).

fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).

fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
    class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring) ).

fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).

fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).

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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_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
    class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__top) ).

fof(arity_HOL__Obool__Orderings_Otop,axiom,
    class_Orderings_Otop(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).

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_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_Int__Oint__Lattices_Odistrib__lattice,axiom,
    class_Lattices_Odistrib__lattice(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Odistrib__lattice) ).

fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
    class_Lattices_Odistrib__lattice(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Odistrib__lattice) ).

fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
    class_Lattices_Odistrib__lattice(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Odistrib__lattice) ).

fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
    class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice) ).

fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
    class_Lattices_Osemilattice__inf(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__inf) ).

fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
    class_Lattices_Osemilattice__inf(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__inf) ).

fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
    class_Lattices_Osemilattice__inf(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).

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_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
    class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).

fof(arity_Int__Oint__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Olattice) ).

fof(arity_Nat__Onat__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).

fof(arity_HOL__Obool__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).

fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
    class_Lattices_Osemilattice__sup(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__sup) ).

fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
    class_Lattices_Osemilattice__sup(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__sup) ).

fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
    class_Lattices_Osemilattice__sup(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).

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_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__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_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_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_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_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(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_5205,plain,
    ! [X30,X5] :
      ( class_Rings_Oring__1(X5)
     => ( ( X30 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(c_Int_Oring__1__class_Oof__int(X5),X30) = c_Groups_Ozero__class_Ozero(X5) )
        & ( X30 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
             => hAPP(c_Int_Oring__1__class_Oof__int(X5),X30) = 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),X30))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
             => hAPP(c_Int_Oring__1__class_Oof__int(X5),X30) = 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(X30,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_5206,plain,
    ! [X22,X14,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X14),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(X15),X22),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X15))) ),
    inference(fof_simplification,[status(thm)],[fact_not__sum__power2__lt__zero]) ).

fof(i_0_5207,plain,
    ! [X25,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Power_Opower__class_Opower(X15),X25),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X15))) ),
    inference(fof_simplification,[status(thm)],[fact_power2__less__0]) ).

fof(i_0_5208,plain,
    ! [X126,X132] :
      ( ( 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),X132)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X132))) = 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),X126),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)))),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),X132)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X132))) = 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),X126)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    inference(fof_simplification,[status(thm)],[fact_zmod__number__of__Bit1]) ).

fof(i_0_5209,plain,
    ! [X132,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),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126))))
         => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132),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),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)),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),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126))))
         => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132),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(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132),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__number__of]) ).

fof(i_0_5210,plain,
    ! [X132] :
      ( 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),X132)))
     => ( ( 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),X132))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)) = 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),X132))) )
        & ( ~ 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),X132))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)),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),X132)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_negDivAlg__eqn__1__number__of]) ).

fof(i_0_5211,plain,
    ! [X132,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),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
         => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132),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)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
         => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132),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(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132),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__number__of]) ).

fof(i_0_5212,plain,
    ! [X132] :
      ( 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),X132)))
     => ( ( 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),X132)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)) = 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),X132)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)),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),X132)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_posDivAlg__eqn__1__number__of]) ).

fof(i_0_5213,plain,
    ! [X25,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__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25),X26)))
         => c_Divides_OnegDivAlg(X25,X26) = 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),X25),X26)) )
        & ( ~ 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),X25),X26)))
         => c_Divides_OnegDivAlg(X25,X26) = hAPP(c_Divides_Oadjust(X26),c_Divides_OnegDivAlg(X25,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)))),X26))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_negDivAlg__eqn]) ).

fof(i_0_5214,plain,
    ! [X25,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),X25),X26))
         => c_Divides_OposDivAlg(X25,X26) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),X26))
         => c_Divides_OposDivAlg(X25,X26) = hAPP(c_Divides_Oadjust(X26),c_Divides_OposDivAlg(X25,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)))),X26))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_posDivAlg__eqn]) ).

fof(i_0_5215,plain,
    ! [X212,X29,X5] :
      ( c_List_OdropWhile(X5,X29,X212) != c_List_Olist_ONil(X5)
     => ~ hBOOL(hAPP(X29,hAPP(c_List_Ohd(X5),c_List_OdropWhile(X5,X29,X212)))) ),
    inference(fof_simplification,[status(thm)],[fact_hd__dropWhile]) ).

fof(i_0_5216,plain,
    ! [X56,X112,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),X112)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X56)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X112))) = hAPP(hAPP(c_HOL_OLet(X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X56)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X112))),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),X56)))),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),X112)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X56)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X112))) = c_Groups_Oone__class_Oone(X5) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_power__number__of__odd__number__of]) ).

fof(i_0_5217,plain,
    ! [X212,X29,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),c_List_OdropWhile(X5,X29,X212))))
         => ~ hBOOL(hAPP(X29,X3)) )
     => c_List_OtakeWhile(X5,X29,X212) = hAPP(c_List_Ofilter(X5,X29),X212) ),
    inference(fof_simplification,[status(thm)],[fact_takeWhile__eq__filter]) ).

fof(i_0_5218,plain,
    ! [X37,X112,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),X112)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),X37),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X112))) = hAPP(hAPP(c_HOL_OLet(X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X37),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X112))),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),X37))),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),X112)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),X37),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X112))) = c_Groups_Oone__class_Oone(X5) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_power__number__of__odd]) ).

fof(i_0_5219,plain,
    ! [X37,X112] :
      ( ( 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),X112)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X37),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X112))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X37),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X112))),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),X37))),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),X112)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X37),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X112))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(fof_simplification,[status(thm)],[fact_zpower__number__of__odd]) ).

fof(i_0_5220,plain,
    ! [X12,X34,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X5,X5),X34)),c_Transitive__Closure_Ortrancl(X5,X34)) = 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),X12),X12)),c_Transitive__Closure_Otrancl(X5,X34))) ),
    inference(fof_simplification,[status(thm)],[fact_irrefl__tranclI]) ).

fof(i_0_5221,plain,
    ! [X214,X29,X212,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => ( ~ hBOOL(hAPP(X29,X12))
       => c_List_OdropWhile(X5,X29,hAPP(hAPP(c_List_Oappend(X5),X212),X214)) = hAPP(hAPP(c_List_Oappend(X5),c_List_OdropWhile(X5,X29,X212)),X214) ) ),
    inference(fof_simplification,[status(thm)],[fact_dropWhile__append1]) ).

fof(i_0_5222,plain,
    ! [X34,X5] :
      ( c_Wellfounded_Oacyclic(X5,X34)
    <=> ! [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,X34))) ),
    inference(fof_simplification,[status(thm)],[fact_acyclic__def]) ).

fof(i_0_5223,plain,
    ! [X265,X266] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X266)),c_Int_OBit0(X265))),
    inference(fof_simplification,[status(thm)],[fact_eq__int__code_I15_J]) ).

fof(i_0_5224,plain,
    ! [X266] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X266)),c_Int_OPls)),
    inference(fof_simplification,[status(thm)],[fact_eq__int__code_I10_J]) ).

fof(i_0_5225,plain,
    ! [X126,X132] :
      ( ( 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),X132)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X126))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X132))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)) )
      & ( ~ 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),X132)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X126))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X132))) = 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),X126)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)) ) ),
    inference(fof_simplification,[status(thm)],[fact_zdiv__number__of__Bit1]) ).

fof(i_0_5226,plain,
    ! [X34,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,X34)))
     => c_Wellfounded_Oacyclic(X5,X34) ),
    inference(fof_simplification,[status(thm)],[fact_acyclicI]) ).

fof(i_0_5227,plain,
    ! [X212,X5,X12,X29] :
      ( ( hBOOL(hAPP(X29,X12))
       => c_List_OdropWhile(X5,X29,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = c_List_OdropWhile(X5,X29,X212) )
      & ( ~ hBOOL(hAPP(X29,X12))
       => c_List_OdropWhile(X5,X29,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212) ) ),
    inference(fof_simplification,[status(thm)],[fact_dropWhile_Osimps_I2_J]) ).

fof(i_0_5228,plain,
    ! [X112] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X112)))
       => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X112)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X112)))
       => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X112)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X112)),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_5229,plain,
    ! [X265,X266] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X266)),c_Int_OBit1(X265))),
    inference(fof_simplification,[status(thm)],[fact_eq__int__code_I14_J]) ).

fof(i_0_5230,plain,
    ! [X98,X99] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X98)))
       => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X98)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X98))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X98)))
       => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X98)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_upt__rec__number__of]) ).

fof(i_0_5231,plain,
    ! [X265] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X265))),
    inference(fof_simplification,[status(thm)],[fact_eq__int__code_I4_J]) ).

fof(i_0_5232,plain,
    ! [X132,X15] :
      ( ( class_Int_Onumber__ring(X15)
        & class_Int_Oring__char__0(X15) )
     => ~ c_Int_Oiszero(X15,hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OBit1(X132))) ),
    inference(fof_simplification,[status(thm)],[fact_iszero__number__of__Bit1]) ).

fof(i_0_5233,plain,
    ! [X214,X27,X212,X29,X5] :
      ( c_List_OdropWhile(X5,X29,X212) = hAPP(hAPP(c_List_Olist_OCons(X5),X27),X214)
    <=> ( X212 = hAPP(hAPP(c_List_Oappend(X5),c_List_OtakeWhile(X5,X29,X212)),hAPP(hAPP(c_List_Olist_OCons(X5),X27),X214))
        & ~ hBOOL(hAPP(X29,X27)) ) ),
    inference(fof_simplification,[status(thm)],[fact_dropWhile__eq__Cons__conv]) ).

fof(i_0_5234,plain,
    ! [X15] :
      ( class_Int_Onumber__ring(X15)
     => ~ c_Int_Oiszero(X15,hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OBit1(c_Int_OPls))) ),
    inference(fof_simplification,[status(thm)],[fact_not__iszero__Numeral1]) ).

fof(i_0_5235,plain,
    ! [X212,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => hAPP(c_List_OremoveAll(X5,X12),X212) = X212 ),
    inference(fof_simplification,[status(thm)],[fact_removeAll__id]) ).

fof(i_0_5236,plain,
    ! [X212,X5,X12,X29] :
      ( ~ hBOOL(hAPP(X29,X12))
     => hAPP(c_List_OremoveAll(X5,X12),hAPP(c_List_Ofilter(X5,X29),X212)) = hAPP(c_List_Ofilter(X5,X29),X212) ),
    inference(fof_simplification,[status(thm)],[fact_removeAll__filter__not]) ).

fof(i_0_5237,plain,
    ! [X98,X126] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),X98)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X98) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),X98)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X126))),X98) ) ),
    inference(fof_simplification,[status(thm)],[fact_Suc__nat__number__of__add]) ).

fof(i_0_5238,plain,
    ! [X101,X102] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X101))
       => c_List_Oupt(X102,hAPP(c_Nat_OSuc,X101)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X102,X101)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X101),c_List_Olist_ONil(tc_Nat_Onat))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X101))
       => c_List_Oupt(X102,hAPP(c_Nat_OSuc,X101)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_upt__Suc]) ).

fof(i_0_5239,plain,
    ! [X266] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X266)),c_Int_OMin)),
    inference(fof_simplification,[status(thm)],[fact_eq__int__code_I11_J]) ).

fof(i_0_5240,plain,
    ! [X101,X102] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X101))
       => c_List_Oupt(X102,X101) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X102),c_List_Oupt(hAPP(c_Nat_OSuc,X102),X101)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X101))
       => c_List_Oupt(X102,X101) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_upt__rec]) ).

fof(i_0_5241,plain,
    ! [X76,X30,X29] :
      ( epred2_3(X29,X30,X76)
    <=> ( ( X30 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(X29,X76)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))
         => ! [X145,X124] :
              ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X124))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X124),X30))
                & X76 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X145)),X124) )
             => hBOOL(hAPP(X29,X124)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [X145,X124] :
              ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),X124))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X124),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                & X76 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X145)),X124) )
             => hBOOL(hAPP(X29,X124)) ) ) ) ),
    introduced(definition) ).

fof(i_0_5242,plain,
    ! [X265] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X265))),
    inference(fof_simplification,[status(thm)],[fact_eq__int__code_I7_J]) ).

fof(i_0_5243,plain,
    ! [X76,X30,X29] :
      ( epred1_3(X29,X30,X76)
    <=> ( ( X30 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(X29,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)),X30))
         => ! [X145] :
              ( ? [X124] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X124))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X124),X30))
                  & X76 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X145)),X124) )
             => hBOOL(hAPP(X29,X145)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [X145] :
              ( ? [X124] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),X124))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X124),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & X76 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X145)),X124) )
             => hBOOL(hAPP(X29,X145)) ) ) ) ),
    introduced(definition) ).

fof(i_0_5244,plain,
    ! [X126] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X126),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),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),X126),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X126)) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__number__of__add__1]) ).

fof(i_0_5245,plain,
    ! [X126] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X126),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),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),X126),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X126)) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__number__of__diff__1]) ).

fof(i_0_5246,plain,
    ! [X126] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X126),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),X126)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X126),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),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X126)) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__1__add__number__of]) ).

fof(i_0_5247,plain,
    ! [X126] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X126)) ) ),
    inference(fof_simplification,[status(thm)],[fact_Suc__nat__number__of]) ).

fof(i_0_5248,plain,
    ! [X22,X15] : ~ hBOOL(hAPP(hAPP(c_List_Omember(X15),c_List_Olist_ONil(X15)),X22)),
    inference(fof_simplification,[status(thm)],[fact_member__rec_I2_J]) ).

fof(i_0_5249,plain,
    ! [X24967] : c_Divides_Oadjust(X24967) = 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)),X24967))))),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)),X24967))))),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_5250,plain,
    ! [X24819] : c_Int_Osucc(c_Int_OBit0(X24819)) = c_Int_OBit1(X24819),
    inference(variable_rename,[status(thm)],[fact_succ__Bit0]) ).

fof(i_0_5251,plain,
    ! [X24784] : c_Int_OBit0(X24784) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24784),X24784),
    inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).

fof(i_0_5252,plain,
    ! [X25033] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25033),c_Int_OMin) = c_Int_Osucc(X25033),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I2_J]) ).

fof(i_0_5253,plain,
    ! [X36,X1,X2,X55,X38,X21,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),X21),hAPP(c_Set_Oimage(tc_prod(X38,X55),tc_prod(X5,X16),c_Product__Type_Omap__pair(X38,X5,X55,X16,X2,X1)),X36)))
     => ~ ! [X3,X33] :
            ( X21 = hAPP(hAPP(c_Product__Type_OPair(X5,X16),hAPP(X2,X3)),hAPP(X1,X33))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X38,X55)),hAPP(hAPP(c_Product__Type_OPair(X38,X55),X3),X33)),X36)) ) ),
    inference(fof_simplification,[status(thm)],[fact_prod__fun__imageE]) ).

fof(i_0_5254,plain,
    ! [X27153,X27154] :
      ( ( X27154 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X27154,X27153) = 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)) )
      & ( X27153 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X27154,X27153) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X27154)
        | X27154 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X27153 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X27154,X27153) = 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,X27153))),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)),X27153)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X27154))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X27153),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X27154),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X27154,X27153)),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),X27153))))),c_Divides_Opdivmod(X27154,X27153))))
        | X27154 = 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_5255,plain,
    ! [X28072,X28073,X28074,X28075] : c_Product__Type_Oapsnd(X28075,X28074,X28073,X28072) = c_Product__Type_Omap__pair(X28073,X28073,X28075,X28074,c_Fun_Oid(X28073),X28072),
    inference(variable_rename,[status(thm)],[fact_apsnd__def]) ).

fof(i_0_5256,plain,
    ! [X27157,X27158] :
      ( ( X27158 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X27158,X27157) = 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)) )
      & ( X27157 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X27158,X27157) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X27158)
        | X27158 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X27157 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X27158,X27157) = 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,X27157))),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,X27158)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X27157))),c_Divides_Opdivmod(X27158,X27157)),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),X27157))))),c_Divides_Opdivmod(X27158,X27157))))
        | X27158 = 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_5257,plain,
    ! [X33551,X33552,X33553] : c_Nitpick_Oplus__frac(X33553,X33552,X33551) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X33553),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X33553),X33552),hAPP(c_Nitpick_Odenom(X33553),X33551))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X33553),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X33553),tc_Int_Oint),c_Nitpick_Ofrac(X33553)),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(X33553),X33552))),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(X33553),X33552))))),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(X33553),X33551))),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(X33553),X33551)))))),c_COMBI(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Oplus__frac__def]) ).

fof(i_0_5258,plain,
    ! [X33570] : c_Nitpick_Odenom(X33570) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X33570,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X33570)),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Odenom__def]) ).

fof(i_0_5259,plain,
    ! [X33571] : c_Nitpick_Onum(X33571) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X33571,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X33571)),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Onum__def]) ).

fof(i_0_5260,plain,
    ! [X28531,X28532,X28533,X28534] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28534,tc_fun(X28534,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X28534,tc_fun(tc_prod(X28534,X28534),tc_HOL_Obool),tc_fun(X28534,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28534,tc_fun(tc_fun(tc_prod(X28534,X28534),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28534,X28534),tc_HOL_Obool),tc_fun(X28534,tc_HOL_Obool)),X28534),c_COMBC(X28534,tc_fun(tc_prod(X28534,X28534),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28534,tc_prod(X28534,X28534)),tc_fun(X28534,tc_fun(tc_fun(tc_prod(X28534,X28534),tc_HOL_Obool),tc_HOL_Obool)),X28534),hAPP(c_COMBB(tc_prod(X28534,X28534),tc_fun(tc_fun(tc_prod(X28534,X28534),tc_HOL_Obool),tc_HOL_Obool),X28534),c_member(tc_prod(X28534,X28534)))),c_Product__Type_OPair(X28534,X28534)))),X28533)),c_fequal),X28532),X28531))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28534,X28534)),hAPP(hAPP(c_Product__Type_OPair(X28534,X28534),X28532),X28531)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28534,X28534),tc_HOL_Obool)),X28533),c_Relation_OId(X28534)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28534,X28534)),hAPP(hAPP(c_Product__Type_OPair(X28534,X28534),X28532),X28531)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28534,X28534),tc_HOL_Obool)),X28533),c_Relation_OId(X28534))))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28534,tc_fun(X28534,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X28534,tc_fun(tc_prod(X28534,X28534),tc_HOL_Obool),tc_fun(X28534,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28534,tc_fun(tc_fun(tc_prod(X28534,X28534),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28534,X28534),tc_HOL_Obool),tc_fun(X28534,tc_HOL_Obool)),X28534),c_COMBC(X28534,tc_fun(tc_prod(X28534,X28534),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28534,tc_prod(X28534,X28534)),tc_fun(X28534,tc_fun(tc_fun(tc_prod(X28534,X28534),tc_HOL_Obool),tc_HOL_Obool)),X28534),hAPP(c_COMBB(tc_prod(X28534,X28534),tc_fun(tc_fun(tc_prod(X28534,X28534),tc_HOL_Obool),tc_HOL_Obool),X28534),c_member(tc_prod(X28534,X28534)))),c_Product__Type_OPair(X28534,X28534)))),X28533)),c_fequal),X28532),X28531)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflcl__set__eq])]) ).

fof(i_0_5261,plain,
    ! [X28613] : c_Transitive__Closure_Ortrancl(X28613,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28613,X28613),tc_HOL_Obool))) = c_Relation_OId(X28613),
    inference(variable_rename,[status(thm)],[fact_rtrancl__empty]) ).

fof(i_0_5262,plain,
    ! [X24968,X24969,X24970] : hAPP(c_Divides_Oadjust(X24970),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X24969),X24968)) = 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),X24968),X24970)),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)))),X24969)),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)))),X24969)),X24968))),
    inference(variable_rename,[status(thm)],[fact_adjust__eq]) ).

fof(i_0_5263,plain,
    ! [X28527,X28528,X28529,X28530] : c_Transitive__Closure_Otrancl(X28530,hAPP(hAPP(c_Set_Oinsert(tc_prod(X28530,X28530)),hAPP(hAPP(c_Product__Type_OPair(X28530,X28530),X28529),X28528)),X28527)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28530,X28530),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X28530,X28527)),hAPP(c_Set_OCollect(tc_prod(X28530,X28530)),hAPP(c_Product__Type_Oprod_Oprod__case(X28530,X28530,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28530,tc_fun(X28530,tc_HOL_Obool),tc_fun(X28530,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X28530,tc_HOL_Obool),tc_fun(X28530,tc_HOL_Obool)),X28530),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X28530)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28530),c_fconj),hAPP(hAPP(c_COMBC(X28530,tc_fun(tc_prod(X28530,X28530),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X28530,X28530),tc_fun(tc_fun(tc_prod(X28530,X28530),tc_HOL_Obool),tc_HOL_Obool),X28530),c_member(tc_prod(X28530,X28530))),hAPP(hAPP(c_COMBC(X28530,X28530,tc_prod(X28530,X28530)),c_Product__Type_OPair(X28530,X28530)),X28529))),c_Transitive__Closure_Ortrancl(X28530,X28527))))),hAPP(hAPP(c_COMBC(X28530,tc_fun(tc_prod(X28530,X28530),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X28530,X28530),tc_fun(tc_fun(tc_prod(X28530,X28530),tc_HOL_Obool),tc_HOL_Obool),X28530),c_member(tc_prod(X28530,X28530))),hAPP(c_Product__Type_OPair(X28530,X28530),X28528))),c_Transitive__Closure_Ortrancl(X28530,X28527)))))),
    inference(variable_rename,[status(thm)],[fact_trancl__insert]) ).

fof(i_0_5264,plain,
    ! [X28626,X28627] : c_Transitive__Closure_Otrancl(X28627,X28626) = hAPP(hAPP(c_Relation_Orel__comp(X28627,X28627,X28627),X28626),c_Transitive__Closure_Ortrancl(X28627,X28626)),
    inference(variable_rename,[status(thm)],[fact_trancl__unfold__left]) ).

fof(i_0_5265,plain,
    ! [X24980,X24981] :
      ( ( X24980 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(c_Int_Oring__1__class_Oof__int(X24981),X24980) = c_Groups_Ozero__class_Ozero(X24981)
        | ~ class_Rings_Oring__1(X24981) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24980),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Oring__1__class_Oof__int(X24981),X24980) = hAPP(c_Groups_Ouminus__class_Ouminus(X24981),hAPP(c_Int_Oring__1__class_Oof__int(X24981),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24980)))
        | X24980 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ class_Rings_Oring__1(X24981) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24980),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Oring__1__class_Oof__int(X24981),X24980) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X24981),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X24981,X24981)),tc_fun(tc_Int_Oint,X24981)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X24981,X24981),X24981),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X24981,X24981)),tc_fun(tc_Int_Oint,X24981)),tc_Int_Oint),c_COMBB(tc_fun(X24981,X24981),X24981,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X24981,tc_fun(tc_fun(X24981,X24981),X24981),tc_Int_Oint),c_HOL_OLet(X24981,X24981)),c_Int_Oring__1__class_Oof__int(X24981)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X24981,X24981),tc_fun(X24981,X24981)),hAPP(hAPP(c_COMBB(tc_fun(X24981,tc_fun(X24981,X24981)),tc_fun(tc_fun(X24981,X24981),tc_fun(X24981,X24981)),tc_Int_Oint),c_COMBS(X24981,X24981,X24981)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X24981,X24981),tc_fun(X24981,tc_fun(X24981,X24981))),hAPP(hAPP(c_COMBB(tc_fun(X24981,tc_fun(X24981,X24981)),tc_fun(tc_fun(X24981,X24981),tc_fun(X24981,tc_fun(X24981,X24981))),tc_Int_Oint),c_COMBB(X24981,tc_fun(X24981,X24981),X24981)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X24981,tc_fun(X24981,X24981)),tc_Int_Oint),c_If(X24981)),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(X24981,X24981,X24981),c_Groups_Oplus__class_Oplus(X24981)),c_COMBI(X24981))))),hAPP(hAPP(c_COMBC(X24981,X24981,X24981),hAPP(hAPP(c_COMBB(X24981,tc_fun(X24981,X24981),X24981),c_Groups_Oplus__class_Oplus(X24981)),hAPP(hAPP(c_COMBS(X24981,X24981,X24981),c_Groups_Oplus__class_Oplus(X24981)),c_COMBI(X24981)))),c_Groups_Oone__class_Oone(X24981))))),c_Divides_Odivmod__int(X24980,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
        | X24980 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ class_Rings_Oring__1(X24981) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5205])])]) ).

fof(i_0_5266,plain,
    ! [X30043,X30044,X30045,X30046] : c_Map_Omap__add(X30046,X30045,X30044,hAPP(c_Map_Omap__of(X30046,X30045),X30043)) = c_List_Ofoldr(tc_prod(X30046,X30045),tc_fun(X30046,tc_Option_Ooption(X30045)),hAPP(c_Product__Type_Oprod_Oprod__case(X30046,X30045,tc_fun(tc_fun(X30046,tc_Option_Ooption(X30045)),tc_fun(X30046,tc_Option_Ooption(X30045)))),hAPP(hAPP(c_COMBC(X30046,tc_fun(X30045,tc_Option_Ooption(X30045)),tc_fun(X30045,tc_fun(tc_fun(X30046,tc_Option_Ooption(X30045)),tc_fun(X30046,tc_Option_Ooption(X30045))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X30045),tc_fun(tc_fun(X30046,tc_Option_Ooption(X30045)),tc_fun(X30046,tc_Option_Ooption(X30045)))),tc_fun(tc_fun(X30045,tc_Option_Ooption(X30045)),tc_fun(X30045,tc_fun(tc_fun(X30046,tc_Option_Ooption(X30045)),tc_fun(X30046,tc_Option_Ooption(X30045))))),X30046),c_COMBB(tc_Option_Ooption(X30045),tc_fun(tc_fun(X30046,tc_Option_Ooption(X30045)),tc_fun(X30046,tc_Option_Ooption(X30045))),X30045)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X30046,tc_Option_Ooption(X30045)),tc_fun(tc_Option_Ooption(X30045),tc_fun(X30046,tc_Option_Ooption(X30045)))),tc_fun(tc_Option_Ooption(X30045),tc_fun(tc_fun(X30046,tc_Option_Ooption(X30045)),tc_fun(X30046,tc_Option_Ooption(X30045)))),X30046),c_COMBC(tc_fun(X30046,tc_Option_Ooption(X30045)),tc_Option_Ooption(X30045),tc_fun(X30046,tc_Option_Ooption(X30045)))),hAPP(c_COMBC(tc_fun(X30046,tc_Option_Ooption(X30045)),X30046,tc_fun(tc_Option_Ooption(X30045),tc_fun(X30046,tc_Option_Ooption(X30045)))),c_Fun_Ofun__upd(X30046,tc_Option_Ooption(X30045)))))),c_Option_Ooption_OSome(X30045))),X30043,X30044),
    inference(variable_rename,[status(thm)],[fact_map__add__map__of__foldr]) ).

fof(i_0_5267,plain,
    ! [X32866,X32867,X32868,X32869,X32870] : c_List_Ofoldr(X32870,X32869,X32868,X32867,X32866) = hAPP(c_List_Ofoldl(X32869,X32870,hAPP(c_COMBC(X32870,X32869,X32869),X32868),X32866),hAPP(c_List_Orev(X32870),X32867)),
    inference(variable_rename,[status(thm)],[fact_foldr__foldl]) ).

fof(i_0_5268,plain,
    ! [X21,X17,X13,X11,X38,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X16,tc_fun(X38,tc_HOL_Obool))),X11),X13),X17),X21))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
           => ~ hBOOL(hAPP(hAPP(hAPP(X13,X3),X17),X21)) ) ),
    inference(fof_simplification,[status(thm)],[fact_SUP2__E]) ).

fof(i_0_5269,plain,
    ! [X24918,X24919,X24920] :
      ( ( X24919 = c_Groups_Ozero__class_Ozero(X24920)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24920),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24920),hAPP(hAPP(c_Power_Opower__class_Opower(X24920),X24919),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(X24920),X24918),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X24920)))
        | ~ class_Rings_Olinordered__idom(X24920) )
      & ( X24918 = c_Groups_Ozero__class_Ozero(X24920)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24920),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24920),hAPP(hAPP(c_Power_Opower__class_Opower(X24920),X24919),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(X24920),X24918),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X24920)))
        | ~ class_Rings_Olinordered__idom(X24920) )
      & ( X24919 != c_Groups_Ozero__class_Ozero(X24920)
        | X24918 != c_Groups_Ozero__class_Ozero(X24920)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24920),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24920),hAPP(hAPP(c_Power_Opower__class_Opower(X24920),X24919),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(X24920),X24918),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X24920)))
        | ~ class_Rings_Olinordered__idom(X24920) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__le__zero__iff])])]) ).

fof(i_0_5270,plain,
    ! [X24921,X24922,X24923] :
      ( ~ class_Rings_Olinordered__idom(X24923)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24923),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24923),hAPP(hAPP(c_Power_Opower__class_Opower(X24923),X24922),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(X24923),X24921),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X24923))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5206])]) ).

fof(i_0_5271,plain,
    ! [X32404,X32405,X32406,X32407] :
      ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X32407)),c_List_Otranspose__rel(X32407)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X32407)),hAPP(hAPP(c_List_Olist_OCons(X32407),X32406),X32405)),X32404)))
      | c_List_Otranspose(X32407,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X32407)),hAPP(hAPP(c_List_Olist_OCons(X32407),X32406),X32405)),X32404)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X32407)),hAPP(hAPP(c_List_Olist_OCons(X32407),X32406),c_List_Oconcat(X32407,hAPP(hAPP(c_List_Omap(tc_List_Olist(X32407),tc_List_Olist(X32407)),c_List_Olist_Olist__case(tc_List_Olist(X32407),X32407,c_List_Olist_ONil(X32407),hAPP(hAPP(c_COMBB(tc_List_Olist(X32407),tc_fun(tc_List_Olist(X32407),tc_List_Olist(X32407)),X32407),c_COMBK(tc_List_Olist(X32407),tc_List_Olist(X32407))),hAPP(hAPP(c_COMBC(X32407,tc_List_Olist(X32407),tc_List_Olist(X32407)),c_List_Olist_OCons(X32407)),c_List_Olist_ONil(X32407))))),X32404)))),c_List_Otranspose(X32407,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X32407)),X32405),c_List_Oconcat(tc_List_Olist(X32407),hAPP(hAPP(c_List_Omap(tc_List_Olist(X32407),tc_List_Olist(tc_List_Olist(X32407))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X32407)),X32407,c_List_Olist_ONil(tc_List_Olist(X32407)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X32407),tc_List_Olist(tc_List_Olist(X32407))),X32407),hAPP(hAPP(c_COMBC(tc_List_Olist(X32407),tc_List_Olist(tc_List_Olist(X32407)),tc_List_Olist(tc_List_Olist(X32407))),c_List_Olist_OCons(tc_List_Olist(X32407))),c_List_Olist_ONil(tc_List_Olist(X32407)))))),X32404))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I3_J])]) ).

fof(i_0_5272,plain,
    ! [X32335,X32336] : c_List_Oconcat(X32336,X32335) = hAPP(c_List_Ofoldl(tc_List_Olist(X32336),tc_List_Olist(X32336),c_List_Oappend(X32336),c_List_Olist_ONil(X32336)),X32335),
    inference(variable_rename,[status(thm)],[fact_concat__conv__foldl]) ).

fof(i_0_5273,plain,
    ! [X32385,X32386,X32387,X32388] : c_List_Otranspose(X32388,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X32388)),hAPP(hAPP(c_List_Olist_OCons(X32388),X32387),X32386)),X32385)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X32388)),hAPP(hAPP(c_List_Olist_OCons(X32388),X32387),c_List_Oconcat(X32388,hAPP(hAPP(c_List_Omap(tc_List_Olist(X32388),tc_List_Olist(X32388)),c_List_Olist_Olist__case(tc_List_Olist(X32388),X32388,c_List_Olist_ONil(X32388),hAPP(hAPP(c_COMBB(tc_List_Olist(X32388),tc_fun(tc_List_Olist(X32388),tc_List_Olist(X32388)),X32388),c_COMBK(tc_List_Olist(X32388),tc_List_Olist(X32388))),hAPP(hAPP(c_COMBC(X32388,tc_List_Olist(X32388),tc_List_Olist(X32388)),c_List_Olist_OCons(X32388)),c_List_Olist_ONil(X32388))))),X32385)))),c_List_Otranspose(X32388,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X32388)),X32386),c_List_Oconcat(tc_List_Olist(X32388),hAPP(hAPP(c_List_Omap(tc_List_Olist(X32388),tc_List_Olist(tc_List_Olist(X32388))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X32388)),X32388,c_List_Olist_ONil(tc_List_Olist(X32388)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X32388),tc_List_Olist(tc_List_Olist(X32388))),X32388),hAPP(hAPP(c_COMBC(tc_List_Olist(X32388),tc_List_Olist(tc_List_Olist(X32388)),tc_List_Olist(tc_List_Olist(X32388))),c_List_Olist_OCons(tc_List_Olist(X32388))),c_List_Olist_ONil(tc_List_Olist(X32388)))))),X32385))))),
    inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I3_J]) ).

fof(i_0_5274,plain,
    ! [X24951,X24952,X24953] :
      ( ~ class_Rings_Olinordered__idom(X24953)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24953),X24952),c_Groups_Ozero__class_Ozero(X24953)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24953),hAPP(hAPP(c_Power_Opower__class_Opower(X24953),X24952),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)))),X24951)))),c_Groups_Ozero__class_Ozero(X24953))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__power__less__zero])]) ).

fof(i_0_5275,plain,
    ! [X84,X34,X38,X209,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),X209),hAPP(hAPP(c_Relation_Orel__comp(X5,X38,X16),X34),X84)))
     => ~ ! [X3,X33,X44] :
            ( X209 = hAPP(hAPP(c_Product__Type_OPair(X5,X16),X3),X44)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X38)),hAPP(hAPP(c_Product__Type_OPair(X5,X38),X3),X33)),X34))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X38,X16)),hAPP(hAPP(c_Product__Type_OPair(X38,X16),X33),X44)),X84)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_rel__compE]) ).

fof(i_0_5276,plain,
    ! [X24948,X24949,X24950] :
      ( ~ class_Rings_Olinordered__idom(X24950)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24950),c_Groups_Ozero__class_Ozero(X24950)),hAPP(hAPP(c_Power_Opower__class_Opower(X24950),X24949),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)))),X24948)))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24950),c_Groups_Ozero__class_Ozero(X24950)),X24949)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__0__le__power__imp__0__le])]) ).

fof(i_0_5277,plain,
    ! [X214,X29,X212,X12,X5] :
      ( hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212) = hAPP(c_List_Ofilter(X5,X29),X214)
    <=> ? [X243,X248] :
          ( X214 = hAPP(hAPP(c_List_Oappend(X5),X243),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X248))
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X243)))
             => ~ hBOOL(hAPP(X29,X3)) )
          & hBOOL(hAPP(X29,X12))
          & X212 = hAPP(c_List_Ofilter(X5,X29),X248) ) ),
    inference(fof_simplification,[status(thm)],[fact_Cons__eq__filter__iff]) ).

fof(i_0_5278,plain,
    ! [X212,X12,X214,X29,X5] :
      ( hAPP(c_List_Ofilter(X5,X29),X214) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)
    <=> ? [X243,X248] :
          ( X214 = hAPP(hAPP(c_List_Oappend(X5),X243),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X248))
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X243)))
             => ~ hBOOL(hAPP(X29,X3)) )
          & hBOOL(hAPP(X29,X12))
          & X212 = hAPP(c_List_Ofilter(X5,X29),X248) ) ),
    inference(fof_simplification,[status(thm)],[fact_filter__eq__Cons__iff]) ).

fof(i_0_5279,plain,
    ! [X24927,X24928,X24929] :
      ( ~ class_Int_Onumber__ring(X24929)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X24929),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24929),X24928),X24927)),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(X24929),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24929),hAPP(hAPP(c_Power_Opower__class_Opower(X24929),X24928),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(X24929),X24927),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(X24929),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24929),hAPP(c_Int_Onumber__class_Onumber__of(X24929),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X24928)),X24927)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__sum])]) ).

fof(i_0_5280,plain,
    ! [X24945,X24946,X24947] :
      ( ~ class_Int_Onumber__ring(X24947)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X24947),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24947),X24946),X24945)),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(X24947),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24947),hAPP(hAPP(c_Power_Opower__class_Opower(X24947),X24946),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(X24947),X24945),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(X24947),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24947),hAPP(c_Int_Onumber__class_Onumber__of(X24947),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X24946)),X24945)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__diff])]) ).

fof(i_0_5281,plain,
    ! [X2,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
         => c_Nitpick_Osetsum_H(X5,X16,X2,X11) = hAPP(c_List_Omonoid__add__class_Olistsum(X16),hAPP(hAPP(c_List_Omap(X5,X16),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))),X11))),c_List_Odistinct(X5))))) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
         => c_Nitpick_Osetsum_H(X5,X16,X2,X11) = c_Groups_Ozero__class_Ozero(X16) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Nitpick_Osetsum_H__def]) ).

fof(i_0_5282,plain,
    ! [X24924,X24925,X24926] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24926),c_Groups_Ozero__class_Ozero(X24926)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24926),hAPP(hAPP(c_Power_Opower__class_Opower(X24926),X24925),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(X24926),X24924),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
        | X24925 != c_Groups_Ozero__class_Ozero(X24926)
        | X24924 != c_Groups_Ozero__class_Ozero(X24926)
        | ~ class_Rings_Olinordered__idom(X24926) )
      & ( X24925 = c_Groups_Ozero__class_Ozero(X24926)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24926),c_Groups_Ozero__class_Ozero(X24926)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24926),hAPP(hAPP(c_Power_Opower__class_Opower(X24926),X24925),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(X24926),X24924),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
        | ~ class_Rings_Olinordered__idom(X24926) )
      & ( X24924 = c_Groups_Ozero__class_Ozero(X24926)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24926),c_Groups_Ozero__class_Ozero(X24926)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24926),hAPP(hAPP(c_Power_Opower__class_Opower(X24926),X24925),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(X24926),X24924),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
        | ~ class_Rings_Olinordered__idom(X24926) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__gt__zero__iff])])]) ).

fof(i_0_5283,plain,
    ! [X32317,X32318,X32319,X32320] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32320)),X32319))),c_List_Ofoldr(tc_List_Olist(X32318),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X32318)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X32318))),X32317,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(X32320)),X32319)),c_List_Ofoldr(tc_List_Olist(X32318),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X32318)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X32318),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X32318)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X32318)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X32318),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X32318)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X32318),tc_List_Olist(X32318),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X32318)))),X32317),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(variable_rename,[status(thm)],[fact_transpose__aux__max]) ).

fof(i_0_5284,plain,
    ! [X32418,X32419,X32420,X32421] : hAPP(hAPP(c_List_Omap(tc_prod(X32421,tc_Nat_Onat),X32421),c_Product__Type_Ofst(X32421,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X32421,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X32421,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(X32421,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X32421,tc_Nat_Onat))),X32420)),hAPP(hAPP(c_List_Ozip(X32421,tc_Nat_Onat),X32419),c_List_Oupt(X32418,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32418),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32421)),X32419)))))) = hAPP(hAPP(c_List_Omap(tc_prod(X32421,tc_Nat_Onat),X32421),c_Product__Type_Ofst(X32421,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X32421,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X32421,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(X32421,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X32421,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(X32421,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X32421,tc_Nat_Onat))),X32418))),X32420)),hAPP(hAPP(c_List_Ozip(X32421,tc_Nat_Onat),X32419),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32421)),X32419))))),
    inference(variable_rename,[status(thm)],[fact_sublist__shift__lemma]) ).

fof(i_0_5285,plain,
    ! [X32611,X32612] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X32612),X32611)) = c_List_Oupt(X32612,X32611),
    inference(variable_rename,[status(thm)],[fact_sorted__list__of__set__range]) ).

fof(i_0_5286,plain,
    ! [X263,X1,X5,X264] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X264),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(X5,X1,X264,X263) = 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),X264),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(X5,X1,X264,X263) = 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,X263)),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),X264),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X263))),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_5287,plain,
    ! [X24697,X24698] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X24698)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24697)) = 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)))),X24698)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24697)),
    inference(variable_rename,[status(thm)],[fact_Suc__div__eq__add3__div__number__of]) ).

fof(i_0_5288,plain,
    ! [X24699,X24700] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X24700)))),X24699) = 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)))),X24700)),X24699),
    inference(variable_rename,[status(thm)],[fact_Suc__div__eq__add3__div]) ).

fof(i_0_5289,plain,
    ! [X32140,X32141] : hAPP(c_New__DSequence_Opos__not__seq(X32141),X32140) = c_Lazy__Sequence_Ohb__not__seq(hAPP(X32141,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)))),X32140))),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__not__seq__def]) ).

fof(i_0_5290,plain,
    ! [X161,X21,X38,X16,X37,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X37),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X16,X38,tc_fun(X5,tc_HOL_Obool)),X21),X161)))
     => ~ ! [X3,X33] :
            ( X161 = hAPP(hAPP(c_Product__Type_OPair(X16,X38),X3),X33)
           => ~ hBOOL(hAPP(hAPP(c_member(X5),X37),hAPP(hAPP(X21,X3),X33))) ) ),
    inference(fof_simplification,[status(thm)],[fact_mem__splitE]) ).

fof(i_0_5291,plain,
    ! [X56,X11,X12,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X16,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X16,X2,X37,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)),X56))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ~ ! [X33] :
                ( X56 = hAPP(hAPP(X2,X12),X33)
               => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X16,X2,X37,X11),X33)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE]) ).

fof(i_0_5292,plain,
    ! [X25090] :
      ( ( X25090 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_Code__Numeral_Oint__of,X25090) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X25090,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,X25090) = 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),X25090),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | X25090 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X25090,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,X25090) = 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),X25090),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))
        | X25090 = 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_5293,plain,
    ! [X24915,X24916,X24917] :
      ( ~ class_Rings_Olinordered__idom(X24917)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24917),c_Groups_Ozero__class_Ozero(X24917)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24917),hAPP(hAPP(c_Power_Opower__class_Opower(X24917),X24916),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(X24917),X24915),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_5294,plain,
    ! [X2,X16,X11,X5] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),hAPP(c_Set_Oimage(X5,X16,X2),X11)))
       => ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
            & ~ 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)),X11))),hAPP(hAPP(c_COMBC(X5,X16,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X16,tc_fun(X16,tc_HOL_Obool),X5),c_fequal),X2)),hAPP(X2,X3)))))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_pigeonhole__infinite]) ).

fof(i_0_5295,plain,
    ! [X32393,X32394,X32395] :
      ( ( c_List_Oconcat(X32395,X32394) != c_List_Oconcat(X32395,X32393)
        | X32394 = X32393
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32395))),X32394) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32395))),X32393)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32395),tc_List_Olist(X32395))),esk451_3(X32393,X32394,X32395)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X32395),tc_List_Olist(X32395))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X32395),tc_List_Olist(X32395)),X32394),X32393)))) )
      & ( X32394 != X32393
        | c_List_Oconcat(X32395,X32394) = c_List_Oconcat(X32395,X32393)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32395))),X32394) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32395))),X32393)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32395),tc_List_Olist(X32395))),esk451_3(X32393,X32394,X32395)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X32395),tc_List_Olist(X32395))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X32395),tc_List_Olist(X32395)),X32394),X32393)))) )
      & ( c_List_Oconcat(X32395,X32394) != c_List_Oconcat(X32395,X32393)
        | X32394 = X32393
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32395))),X32394) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32395))),X32393)
        | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X32395),tc_List_Olist(X32395),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X32395),tc_fun(tc_List_Olist(X32395),tc_Nat_Onat),tc_fun(tc_List_Olist(X32395),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X32395),tc_Nat_Onat),tc_fun(tc_List_Olist(X32395),tc_HOL_Obool)),tc_List_Olist(X32395)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X32395))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X32395)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X32395))))),c_Nat_Osize__class_Osize(tc_List_Olist(X32395)))),esk451_3(X32393,X32394,X32395))) )
      & ( X32394 != X32393
        | c_List_Oconcat(X32395,X32394) = c_List_Oconcat(X32395,X32393)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32395))),X32394) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32395))),X32393)
        | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X32395),tc_List_Olist(X32395),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X32395),tc_fun(tc_List_Olist(X32395),tc_Nat_Onat),tc_fun(tc_List_Olist(X32395),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X32395),tc_Nat_Onat),tc_fun(tc_List_Olist(X32395),tc_HOL_Obool)),tc_List_Olist(X32395)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X32395))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X32395)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X32395))))),c_Nat_Osize__class_Osize(tc_List_Olist(X32395)))),esk451_3(X32393,X32394,X32395))) ) ),
    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_5296,plain,
    ! [X32389,X32390,X32391] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32391),tc_List_Olist(X32391))),esk450_3(X32389,X32390,X32391)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X32391),tc_List_Olist(X32391))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X32391),tc_List_Olist(X32391)),X32390),X32389))))
        | X32390 = X32389
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32391))),X32390) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32391))),X32389)
        | c_List_Oconcat(X32391,X32390) != c_List_Oconcat(X32391,X32389) )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X32391),tc_List_Olist(X32391),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X32391),tc_fun(tc_List_Olist(X32391),tc_Nat_Onat),tc_fun(tc_List_Olist(X32391),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X32391),tc_Nat_Onat),tc_fun(tc_List_Olist(X32391),tc_HOL_Obool)),tc_List_Olist(X32391)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X32391))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X32391)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X32391))))),c_Nat_Osize__class_Osize(tc_List_Olist(X32391)))),esk450_3(X32389,X32390,X32391)))
        | X32390 = X32389
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32391))),X32390) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32391))),X32389)
        | c_List_Oconcat(X32391,X32390) != c_List_Oconcat(X32391,X32389) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_concat__injective])])])]) ).

fof(i_0_5297,plain,
    ! [X24726,X24727,X24728,X24729,X24730] : hAPP(c_Nat_Onat_Onat__rec(X24730,X24729,X24728),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24727)),X24726)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X24730),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X24727))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X24730,X24730),hAPP(hAPP(c_COMBC(tc_Int_Oint,X24730,tc_fun(X24730,X24730)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X24730,tc_fun(X24730,X24730)),tc_Int_Oint),c_If(X24730)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X24730,X24729,X24728),X24726))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X24730,X24730),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X24730,X24730),tc_Int_Oint),X24728),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)),X24726))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X24730,tc_Int_Oint),c_Nat_Onat_Onat__rec(X24730,X24729,X24728)),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)),X24726))))),
    inference(variable_rename,[status(thm)],[fact_nat__rec__add__eq__if]) ).

fof(i_0_5298,plain,
    ! [X25007] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25007),c_Int_OMin) = c_Int_Opred(X25007),
    inference(variable_rename,[status(thm)],[fact_add__Min__right]) ).

fof(i_0_5299,plain,
    ! [X24757,X24758] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24758),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)))),X24757)),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)))),X24758)) = 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),X24757),c_Groups_Oone__class_Oone(tc_Int_Oint)),X24758))),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_5300,plain,
    ! [X24963,X24964] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24964),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)))),X24963))),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)))),X24964)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24963),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24964) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__zdiv__mult__2])]) ).

fof(i_0_5301,plain,
    ! [X24965,X24966] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24966))
      | 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)))),X24965))),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)))),X24966)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24965),X24966) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zdiv__mult__2])]) ).

fof(i_0_5302,plain,
    ! [X24711,X24712] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24712) != hAPP(c_Nat_OSuc,X24711)
        | 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(X24712))),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)),X24711))))) )
      & ( ~ 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(X24712))),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)),X24711)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24712) = hAPP(c_Nat_OSuc,X24711) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__Suc])]) ).

fof(i_0_5303,plain,
    ! [X24709,X24710] :
      ( ( hAPP(c_Nat_OSuc,X24710) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24709)
        | 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(X24709))),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)),X24710))))) )
      & ( ~ 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(X24709))),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)),X24710)))))
        | hAPP(c_Nat_OSuc,X24710) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24709) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__eq__number__of])]) ).

fof(i_0_5304,plain,
    ! [X11,X5] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => c_Nitpick_Ocard_H(X5,X11) = 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))),X11))),c_List_Odistinct(X5)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => c_Nitpick_Ocard_H(X5,X11) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_Nitpick_Ocard_H__def]) ).

fof(i_0_5305,plain,
    ! [X70,X67] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X67))
     => 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)),X67))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X70)))) = 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)),X67))),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,X70))))) ),
    inference(fof_simplification,[status(thm)],[fact_card__less__Suc2]) ).

fof(i_0_5306,plain,
    ! [X24912,X24913,X24914] :
      ( ~ class_Rings_Olinordered__semidom(X24914)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24914),hAPP(hAPP(c_Power_Opower__class_Opower(X24914),X24913),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(X24914),X24912),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(X24914),c_Groups_Ozero__class_Ozero(X24914)),X24912))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24914),X24913),X24912)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__less__imp__less])]) ).

fof(i_0_5307,plain,
    ! [X24888,X24889,X24890] :
      ( ~ class_Rings_Olinordered__semidom(X24890)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24890),hAPP(hAPP(c_Power_Opower__class_Opower(X24890),X24889),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(X24890),X24888),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(X24890),c_Groups_Ozero__class_Ozero(X24890)),X24888))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24890),X24889),X24888)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__le__imp__le])]) ).

fof(i_0_5308,plain,
    ! [X13,X16,X20,X11,X21,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),X11))
           => hAPP(c_Set_Ovimage(X16,X5,hAPP(hAPP(c_COMBC(X16,X5,X5),hAPP(hAPP(c_COMBC(X16,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X16),c_If(X5)),hAPP(hAPP(c_COMBC(X16,tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool),c_member(X16)),X13))),X21)),X20)),X11) = c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X11))
           => hAPP(c_Set_Ovimage(X16,X5,hAPP(hAPP(c_COMBC(X16,X5,X5),hAPP(hAPP(c_COMBC(X16,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X16),c_If(X5)),hAPP(hAPP(c_COMBC(X16,tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool),c_member(X16)),X13))),X21)),X20)),X11) = X13 ) ) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),X11))
           => hAPP(c_Set_Ovimage(X16,X5,hAPP(hAPP(c_COMBC(X16,X5,X5),hAPP(hAPP(c_COMBC(X16,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X16),c_If(X5)),hAPP(hAPP(c_COMBC(X16,tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool),c_member(X16)),X13))),X21)),X20)),X11) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X16,tc_HOL_Obool)),X13) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X11))
           => hAPP(c_Set_Ovimage(X16,X5,hAPP(hAPP(c_COMBC(X16,X5,X5),hAPP(hAPP(c_COMBC(X16,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X16),c_If(X5)),hAPP(hAPP(c_COMBC(X16,tc_fun(X16,tc_HOL_Obool),tc_HOL_Obool),c_member(X16)),X13))),X21)),X20)),X11) = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_vimage__if]) ).

fof(i_0_5309,plain,
    ! [X24961,X24962] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24962))
      | 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)))),X24961)),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)))),X24962)) = 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,X24961,X24962))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmod__mult__2])]) ).

fof(i_0_5310,plain,
    ! [X24691,X24692] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X24692))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24691)) = 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)))),X24692),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24691)),
    inference(variable_rename,[status(thm)],[fact_Suc__mod__eq__add3__mod__number__of]) ).

fof(i_0_5311,plain,
    ! [X24930,X24931,X24932] :
      ( ~ class_Rings_Olinordered__idom(X24932)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24932),c_Groups_Ozero__class_Ozero(X24932)),hAPP(hAPP(c_Power_Opower__class_Opower(X24932),X24931),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)))),X24930)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__even__power_H])]) ).

fof(i_0_5312,plain,
    ! [X24693,X24694] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X24694))),X24693) = 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)))),X24694),X24693),
    inference(variable_rename,[status(thm)],[fact_Suc__mod__eq__add3__mod]) ).

fof(i_0_5313,plain,
    ! [X24695,X24696] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24696,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X24695)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24696,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)))),X24695)),
    inference(variable_rename,[status(thm)],[fact_mod__Suc__eq__mod__add3]) ).

fof(i_0_5314,plain,
    ! [X24701,X24702] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24702),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X24701)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24702),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)))),X24701)),
    inference(variable_rename,[status(thm)],[fact_div__Suc__eq__div__add3]) ).

fof(i_0_5315,plain,
    ! [X28476,X28477,X28478] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28478,X28478),tc_HOL_Obool)),X28477),X28476))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28478,X28478),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28478,X28478,X28478),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28478,X28478),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X28478,X28477)),X28476)),X28477)),X28476))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28478,X28478),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X28478,X28477)),X28476)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__Int__subset])]) ).

fof(i_0_5316,plain,
    ! [X21,X17,X6,X35,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X35))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X17)),X21)),X35) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(X17,X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X16),X21),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X35)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X35))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X17)),X21)),X35) = hAPP(hAPP(c_Power_Opower__class_Opower(X16),X21),hAPP(c_Finite__Set_Ocard(X5),X35)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__gen__delta]) ).

fof(i_0_5317,plain,
    ! [X17,X6,X35,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X35))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X17)),c_Groups_Ozero__class_Ozero(X16))),X35) = hAPP(X17,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X35))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X17)),c_Groups_Ozero__class_Ozero(X16))),X35) = c_Groups_Ozero__class_Ozero(X16) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__delta]) ).

fof(i_0_5318,plain,
    ! [X17,X6,X35,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X35))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X17)),c_Groups_Oone__class_Oone(X16))),X35) = hAPP(X17,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X35))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X17)),c_Groups_Oone__class_Oone(X16))),X35) = c_Groups_Oone__class_Oone(X16) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__delta]) ).

fof(i_0_5319,plain,
    ! [X24715,X24716] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24716)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24715)))
        | 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(X24715))),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),X24716)),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(X24715))),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),X24716)),c_Int_Onat)))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24716)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24715))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__number__of])]) ).

fof(i_0_5320,plain,
    ! [X24611,X24612] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24612)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24611)))
        | 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(X24611))),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),X24612)),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(X24611))),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),X24612)),c_Int_Onat)))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24612)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24611))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__number__of])]) ).

fof(i_0_5321,plain,
    ! [X27248,X27249,X27250,X27251,X27252,X27253,X27254] : hAPP(c_Product__Type_Oapsnd(X27254,X27253,X27252,X27251),hAPP(c_Product__Type_Oapfst(X27250,X27252,X27254,X27249),X27248)) = hAPP(c_Product__Type_Oapfst(X27250,X27252,X27253,X27249),hAPP(c_Product__Type_Oapsnd(X27254,X27253,X27250,X27251),X27248)),
    inference(variable_rename,[status(thm)],[fact_apsnd__apfst__commute]) ).

fof(i_0_5322,plain,
    ! [X28068,X28069,X28070,X28071] : c_Product__Type_Oapfst(X28071,X28070,X28069,X28068) = c_Product__Type_Omap__pair(X28071,X28070,X28069,X28069,X28068,c_Fun_Oid(X28069)),
    inference(variable_rename,[status(thm)],[fact_apfst__def]) ).

fof(i_0_5323,plain,
    ! [X34,X56,X66,X12,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),X12),X66)),hAPP(hAPP(c_List_Oappend(X5),X12),X56))),c_List_Olexord(X5,X34)))
     => ( ! [X74] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X74),X74)),X34))
       => 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)),X66),X56)),c_List_Olexord(X5,X34))) ) ),
    inference(fof_simplification,[status(thm)],[fact_lexord__append__leftD]) ).

fof(i_0_5324,plain,
    ! [X24894,X24895] :
      ( ~ class_Rings_Olinordered__idom(X24895)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24895),hAPP(hAPP(c_Power_Opower__class_Opower(X24895),X24894),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X24895))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5207])]) ).

fof(i_0_5325,plain,
    ! [X36,X76,X37,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X37)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X76),X36)))
     => ( ( X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => X12 != X37 )
       => ~ ! [X33,X94] :
              ( X76 = hAPP(c_Nat_OSuc,X94)
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X33)),X36))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X37)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X94),X36))) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_rel__pow__E2]) ).

fof(i_0_5326,plain,
    ! [X30200,X30201,X30202,X30203,X30204,X30205,X30206,X30208,X30209,X30210,X30211,X30212,X30213,X30214,X30215] :
      ( ( hAPP(X30202,X30201) = hAPP(c_Option_Ooption_OSome(X30206),esk397_7(X30200,X30201,X30202,X30203,X30204,X30205,X30206))
        | c_Map_Omap__comp(X30206,X30205,X30204,X30203,X30202,X30201) != hAPP(c_Option_Ooption_OSome(X30205),X30200) )
      & ( hAPP(X30203,esk397_7(X30200,X30201,X30202,X30203,X30204,X30205,X30206)) = hAPP(c_Option_Ooption_OSome(X30205),X30200)
        | c_Map_Omap__comp(X30206,X30205,X30204,X30203,X30202,X30201) != hAPP(c_Option_Ooption_OSome(X30205),X30200) )
      & ( hAPP(X30210,X30209) != hAPP(c_Option_Ooption_OSome(X30214),X30215)
        | hAPP(X30211,X30215) != hAPP(c_Option_Ooption_OSome(X30213),X30208)
        | c_Map_Omap__comp(X30214,X30213,X30212,X30211,X30210,X30209) = hAPP(c_Option_Ooption_OSome(X30213),X30208) ) ),
    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__comp__Some__iff])])])])])]) ).

fof(i_0_5327,plain,
    ! [X30135,X30136,X30137,X30138,X30139,X30140] : c_Map_Omap__comp(X30140,X30139,X30138,X30137,X30136,X30135) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X30139),X30140,c_Option_Ooption_ONone(X30139),X30137),hAPP(X30136,X30135)),
    inference(variable_rename,[status(thm)],[fact_map__comp__def]) ).

fof(i_0_5328,plain,
    ! [X24936,X24937,X24938] :
      ( ~ class_Groups_Omonoid__mult(X24938)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X24938),X24937),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)))),X24936))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24938),X24937),hAPP(hAPP(c_Power_Opower__class_Opower(X24938),hAPP(hAPP(c_Power_Opower__class_Opower(X24938),X24937),X24936)),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_5329,plain,
    ! [X33042,X33043,X33044] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X33044),X33043))
      | ~ hBOOL(hAPP(hAPP(c_member(X33044),X33042),hAPP(c_List_Oset(X33044),X33043)))
      | c_List_OtakeWhile(X33044,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33044),c_fNot),hAPP(hAPP(c_COMBC(X33044,X33044,tc_HOL_Obool),c_fequal),X33042)),hAPP(c_List_Orev(X33044),X33043)) = hAPP(c_List_Orev(X33044),hAPP(c_List_Otl(X33044),c_List_OdropWhile(X33044,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33044),c_fNot),hAPP(hAPP(c_COMBC(X33044,X33044,tc_HOL_Obool),c_fequal),X33042)),X33043))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__neq__rev])]) ).

fof(i_0_5330,plain,
    ! [X33092,X33093,X33094] : c_List_OdropWhile(X33094,X33093,X33092) = hAPP(hAPP(c_List_Odrop(X33094),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33094)),c_List_OtakeWhile(X33094,X33093,X33092))),X33092),
    inference(variable_rename,[status(thm)],[fact_dropWhile__eq__drop]) ).

fof(i_0_5331,plain,
    ! [X27170,X27171,X27172,X27173,X27174,X27175,X27176] : hAPP(c_Product__Type_Oapsnd(X27176,X27175,X27174,X27173),hAPP(c_Product__Type_Oapsnd(X27172,X27176,X27174,X27171),X27170)) = hAPP(c_Product__Type_Oapsnd(X27172,X27175,X27174,hAPP(c_Fun_Ocomp(X27176,X27175,X27172,X27173),X27171)),X27170),
    inference(variable_rename,[status(thm)],[fact_apsnd__compose]) ).

fof(i_0_5332,plain,
    ! [X27230,X27231,X27232,X27233,X27234,X27235,X27236] : hAPP(c_Product__Type_Oapfst(X27236,X27235,X27234,X27233),hAPP(c_Product__Type_Oapfst(X27232,X27236,X27234,X27231),X27230)) = hAPP(c_Product__Type_Oapfst(X27232,X27235,X27234,hAPP(c_Fun_Ocomp(X27236,X27235,X27232,X27233),X27231)),X27230),
    inference(variable_rename,[status(thm)],[fact_apfst__compose]) ).

fof(i_0_5333,plain,
    ! [X24898,X24899,X24900] :
      ( ( X24899 = c_Groups_Ozero__class_Ozero(X24900)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24900),hAPP(hAPP(c_Power_Opower__class_Opower(X24900),X24899),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(X24900),X24898),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X24900)
        | ~ class_Rings_Olinordered__idom(X24900) )
      & ( X24898 = c_Groups_Ozero__class_Ozero(X24900)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24900),hAPP(hAPP(c_Power_Opower__class_Opower(X24900),X24899),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(X24900),X24898),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X24900)
        | ~ class_Rings_Olinordered__idom(X24900) )
      & ( X24899 != c_Groups_Ozero__class_Ozero(X24900)
        | X24898 != c_Groups_Ozero__class_Ozero(X24900)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24900),hAPP(hAPP(c_Power_Opower__class_Opower(X24900),X24899),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(X24900),X24898),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X24900)
        | ~ class_Rings_Olinordered__idom(X24900) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__eq__zero__iff])])]) ).

fof(i_0_5334,plain,
    ! [X32490,X32491,X32492] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk452_3(X32490,X32491,X32492)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32491))),X32492)))
        | c_List_Otranspose(X32491,X32492) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X32491)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X32491)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X32491),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X32491)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X32491)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X32491),hAPP(hAPP(c_COMBB(tc_List_Olist(X32491),tc_fun(tc_Nat_Onat,X32491),tc_Nat_Onat),c_List_Onth(X32491)),hAPP(c_List_Onth(tc_List_Olist(X32491)),X32492))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32491))),X32492)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X32490))
        | X32492 = c_List_Olist_ONil(tc_List_Olist(X32491)) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32491)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X32491)),X32492),esk452_3(X32490,X32491,X32492))) != X32490
        | c_List_Otranspose(X32491,X32492) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X32491)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X32491)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X32491),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X32491)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X32491)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X32491),hAPP(hAPP(c_COMBB(tc_List_Olist(X32491),tc_fun(tc_Nat_Onat,X32491),tc_Nat_Onat),c_List_Onth(X32491)),hAPP(c_List_Onth(tc_List_Olist(X32491)),X32492))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32491))),X32492)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X32490))
        | X32492 = c_List_Olist_ONil(tc_List_Olist(X32491)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk452_3(X32490,X32491,X32492)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32491))),X32492)))
        | c_List_Otranspose(X32491,X32492) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X32491)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X32491)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X32491),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X32491)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X32491)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X32491),hAPP(hAPP(c_COMBB(tc_List_Olist(X32491),tc_fun(tc_Nat_Onat,X32491),tc_Nat_Onat),c_List_Onth(X32491)),hAPP(c_List_Onth(tc_List_Olist(X32491)),X32492))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32491))),X32492)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X32490))
        | X32490 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32491)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X32491)),X32492),esk452_3(X32490,X32491,X32492))) != X32490
        | c_List_Otranspose(X32491,X32492) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X32491)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X32491)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X32491),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X32491)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X32491)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X32491),hAPP(hAPP(c_COMBB(tc_List_Olist(X32491),tc_fun(tc_Nat_Onat,X32491),tc_Nat_Onat),c_List_Onth(X32491)),hAPP(c_List_Onth(tc_List_Olist(X32491)),X32492))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32491))),X32492)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X32490))
        | X32490 != 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_5335,plain,
    ! [X24759,X24760] :
      ( ( ~ 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),X24760)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X24759)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X24760))) = 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),X24759),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24760)))),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),X24760)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X24759)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X24760))) = 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),X24759)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24760)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5208])]) ).

fof(i_0_5336,plain,
    ! [X25286,X25287,X25288] :
      ( ( 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),esk157_3(X25286,X25287,X25288)),esk158_3(X25286,X25287,X25288))))
        | hBOOL(hAPP(hAPP(X25286,X25288),X25287))
        | ~ 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),X25288),X25287))) )
      & ( 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),esk157_3(X25286,X25287,X25288)),esk158_3(X25286,X25287,X25288))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk158_3(X25286,X25287,X25288)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(X25286,esk157_3(X25286,X25287,X25288)),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)))),esk158_3(X25286,X25287,X25288))))
        | hBOOL(hAPP(hAPP(X25286,X25288),X25287))
        | ~ 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),X25288),X25287))) )
      & ( ~ hBOOL(hAPP(hAPP(X25286,esk157_3(X25286,X25287,X25288)),esk158_3(X25286,X25287,X25288)))
        | hBOOL(hAPP(hAPP(X25286,X25288),X25287))
        | ~ 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),X25288),X25287))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg_Opinduct])])])]) ).

fof(i_0_5337,plain,
    ! [X17,X6,X35,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X35))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(c_fequal,X6))),X17)),c_Groups_Ozero__class_Ozero(X16))),X35) = hAPP(X17,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X35))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(c_fequal,X6))),X17)),c_Groups_Ozero__class_Ozero(X16))),X35) = c_Groups_Ozero__class_Ozero(X16) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__delta_H]) ).

fof(i_0_5338,plain,
    ! [X17,X6,X35,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X35))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X35))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(c_fequal,X6))),X17)),c_Groups_Oone__class_Oone(X16))),X35) = hAPP(X17,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X35))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),hAPP(hAPP(c_COMBC(X5,X16,X16),hAPP(hAPP(c_COMBS(X5,X16,tc_fun(X16,X16)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16,tc_fun(X16,X16)),X5),c_If(X16)),hAPP(c_fequal,X6))),X17)),c_Groups_Oone__class_Oone(X16))),X35) = c_Groups_Oone__class_Oone(X16) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__delta_H]) ).

fof(i_0_5339,plain,
    ! [X25085,X25086,X25087] :
      ( ( 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),esk148_3(X25085,X25086,X25087)),esk149_3(X25085,X25086,X25087))))
        | hBOOL(hAPP(hAPP(X25085,X25087),X25086))
        | ~ 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),X25087),X25086))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk148_3(X25085,X25086,X25087)),esk149_3(X25085,X25086,X25087)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk149_3(X25085,X25086,X25087)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(X25085,esk148_3(X25085,X25086,X25087)),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)))),esk149_3(X25085,X25086,X25087))))
        | hBOOL(hAPP(hAPP(X25085,X25087),X25086))
        | ~ 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),X25087),X25086))) )
      & ( ~ hBOOL(hAPP(hAPP(X25085,esk148_3(X25085,X25086,X25087)),esk149_3(X25085,X25086,X25087)))
        | hBOOL(hAPP(hAPP(X25085,X25087),X25086))
        | ~ 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),X25087),X25086))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg_Opinduct])])])]) ).

fof(i_0_5340,plain,
    ! [X34,X214,X27,X212,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)),X212),hAPP(hAPP(c_List_Olist_OCons(X5),X27),X214))),c_List_Olistrel(X5,X34)))
     => ~ ! [X3,X228] :
            ( X212 = hAPP(hAPP(c_List_Olist_OCons(X5),X3),X228)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X27)),X34))
             => ~ 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)),X228),X214)),c_List_Olistrel(X5,X34))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_listrel__Cons2]) ).

fof(i_0_5341,plain,
    ! [X36,X76,X37,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X37)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X76)),X36)))
     => ~ ! [X33] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X33)),X36))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X37)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X76),X36))) ) ),
    inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__E2]) ).

fof(i_0_5342,plain,
    ! [X33554,X33555,X33556] : c_Nitpick_Otimes__frac(X33556,X33555,X33554) = hAPP(hAPP(c_Nitpick_Ofrac(X33556),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X33556),X33555)),hAPP(c_Nitpick_Onum(X33556),X33554))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(X33556),X33555)),hAPP(c_Nitpick_Odenom(X33556),X33554))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Otimes__frac__def]) ).

fof(i_0_5343,plain,
    ! [X36,X76,X37,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X37)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X76),X36)))
     => ( ( X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => X12 != X37 )
       => ~ ! [X33,X94] :
              ( X76 = hAPP(c_Nat_OSuc,X94)
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X33)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X94),X36)))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X37)),X36)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_rel__pow__E]) ).

fof(i_0_5344,plain,
    ! [X36,X76,X37,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X37)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X76)),X36)))
     => ~ ! [X33] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X33)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X76),X36)))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X37)),X36)) ) ),
    inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__E]) ).

fof(i_0_5345,plain,
    ! [X24983,X24984] :
      ( ( ~ 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),X24983)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24984))))
        | c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24983),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24984)) = 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),X24983)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24984)))
        | ~ 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),X24984))) )
      & ( 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),X24983)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24984))))
        | c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24983),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24984)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24984)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24983),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),X24984))))
        | ~ 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),X24984))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5209])])]) ).

fof(i_0_5346,plain,
    ! [X25083,X25084] :
      ( ( ~ 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),X25084),X25083)))
        | c_Divides_OnegDivAlg(X25084,X25083) = 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),X25084),X25083))
        | ~ 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),X25084),X25083))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25083),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OnegDivAlg(X25084,X25083) = 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),X25084),X25083))
        | ~ 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),X25084),X25083))) )
      & ( 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),X25084),X25083)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25083),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OnegDivAlg(X25084,X25083) = hAPP(c_Divides_Oadjust(X25083),c_Divides_OnegDivAlg(X25084,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)))),X25083)))
        | ~ 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),X25084),X25083))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg_Opsimps])])]) ).

fof(i_0_5347,plain,
    ! [X24982] :
      ( ( ~ 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),X24982))))
        | c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24982)) = 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),X24982)))
        | ~ 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),X24982))) )
      & ( 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),X24982))))
        | c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24982)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24982)),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),X24982))))
        | ~ 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),X24982))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5210])])]) ).

fof(i_0_5348,plain,
    ! [X24978,X24979] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24979),X24978))
        | c_Divides_OposDivAlg(X24979,X24978) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24979)
        | ~ 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),X24979),X24978))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24978),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OposDivAlg(X24979,X24978) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24979)
        | ~ 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),X24979),X24978))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24979),X24978))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24978),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OposDivAlg(X24979,X24978) = hAPP(c_Divides_Oadjust(X24978),c_Divides_OposDivAlg(X24979,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)))),X24978)))
        | ~ 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),X24979),X24978))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg_Opsimps])])]) ).

fof(i_0_5349,plain,
    ! [X24976,X24977] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24976)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24977)))
        | c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24976),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24977)) = 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),X24976))
        | ~ 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),X24977))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24976)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24977)))
        | c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24976),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24977)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24977)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24976),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),X24977))))
        | ~ 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),X24977))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5211])])]) ).

fof(i_0_5350,plain,
    ! [X24933,X24934,X24935] :
      ( ~ class_Rings_Ocomm__semiring__1(X24935)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X24935),X24934),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)))),X24933))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24935),X24934),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24935),hAPP(hAPP(c_Power_Opower__class_Opower(X24935),X24934),X24933)),hAPP(hAPP(c_Power_Opower__class_Opower(X24935),X24934),X24933))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J])]) ).

fof(i_0_5351,plain,
    ! [X26421,X26422,X26423] : 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),X26423)),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))),X26422))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26421))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X26421)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26423),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26423),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),X26421),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X26422)))),
    inference(variable_rename,[status(thm)],[fact_arith__series__int]) ).

fof(i_0_5352,plain,
    ! [X24713,X24714] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24714)),hAPP(c_Nat_OSuc,X24713)))
        | 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(X24714))),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)),X24713)))) )
      & ( ~ 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(X24714))),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)),X24713))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24714)),hAPP(c_Nat_OSuc,X24713))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of__Suc])]) ).

fof(i_0_5353,plain,
    ! [X24609,X24610] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24610)),hAPP(c_Nat_OSuc,X24609)))
        | 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(X24610))),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)),X24609)))) )
      & ( ~ 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(X24610))),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)),X24609))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24610)),hAPP(c_Nat_OSuc,X24609))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__number__of__Suc])]) ).

fof(i_0_5354,plain,
    ! [X24971] :
      ( ( ~ 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),X24971)))
        | c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24971)) = 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),X24971))) )
      & ( 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),X24971)))
        | c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24971)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24971)),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),X24971))))
        | ~ 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),X24971))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5212])])]) ).

fof(i_0_5355,plain,
    ! [X25091,X25092] :
      ( ~ class_Rings_Osemiring__1(X25092)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25091))
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25092),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)))),X25091))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25092),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25092),hAPP(c_Int_Onat,X25091))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25092),hAPP(c_Int_Onat,X25091))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__double])]) ).

fof(i_0_5356,plain,
    ! [X25081,X25082] :
      ( ( ~ 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),X25081),X25082)))
        | c_Divides_OnegDivAlg(X25081,X25082) = 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),X25081),X25082))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25082)) )
      & ( 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),X25081),X25082)))
        | c_Divides_OnegDivAlg(X25081,X25082) = hAPP(c_Divides_Oadjust(X25082),c_Divides_OnegDivAlg(X25081,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)))),X25082)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25082)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5213])])]) ).

fof(i_0_5357,plain,
    ! [X25079,X25080] :
      ( ( ~ 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),X25080),X25079)))
        | c_Divides_OnegDivAlg(X25080,X25079) = 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),X25080),X25079)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25079),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OnegDivAlg(X25080,X25079) = 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),X25080),X25079)) )
      & ( 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),X25080),X25079)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25079),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OnegDivAlg(X25080,X25079) = hAPP(c_Divides_Oadjust(X25079),c_Divides_OnegDivAlg(X25080,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)))),X25079))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg_Osimps])])]) ).

fof(i_0_5358,plain,
    ! [X24974,X24975] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24974),X24975))
        | c_Divides_OposDivAlg(X24974,X24975) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24974)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24975)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24974),X24975))
        | c_Divides_OposDivAlg(X24974,X24975) = hAPP(c_Divides_Oadjust(X24975),c_Divides_OposDivAlg(X24974,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)))),X24975)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24975)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5214])])]) ).

fof(i_0_5359,plain,
    ! [X24972,X24973] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24973),X24972))
        | c_Divides_OposDivAlg(X24973,X24972) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24973) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24972),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OposDivAlg(X24973,X24972) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24973) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24973),X24972))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24972),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OposDivAlg(X24973,X24972) = hAPP(c_Divides_Oadjust(X24972),c_Divides_OposDivAlg(X24973,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)))),X24972))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg_Osimps])])]) ).

fof(i_0_5360,plain,
    ! [X24954,X24955] :
      ( ~ class_Rings_Oring__1(X24955)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X24955),hAPP(c_Groups_Ouminus__class_Ouminus(X24955),c_Groups_Oone__class_Oone(X24955))),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)))),X24954))) = hAPP(c_Groups_Ouminus__class_Ouminus(X24955),c_Groups_Oone__class_Oone(X24955)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus1__odd])]) ).

fof(i_0_5361,plain,
    ! [X24909,X24910,X24911] :
      ( ~ class_Rings_Oring__1(X24911)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X24911),hAPP(c_Groups_Ouminus__class_Ouminus(X24911),X24910)),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)))),X24909)) = hAPP(hAPP(c_Power_Opower__class_Opower(X24911),X24910),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)))),X24909)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus__even])]) ).

fof(i_0_5362,plain,
    ! [X25077,X25078] :
      ( ~ class_Int_Onumber__ring(X25078)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X25078),hAPP(c_Int_Onumber__class_Onumber__of(X25078),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)))),X25077))) = hAPP(c_Int_Onumber__class_Onumber__of(X25078),c_Int_OMin) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__m1__odd])]) ).

fof(i_0_5363,plain,
    ! [X24666] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X24666))) = 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)))),X24666),
    inference(variable_rename,[status(thm)],[fact_Suc3__eq__add__3]) ).

fof(i_0_5364,plain,
    ! [X11,X34,X16,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(c_Relation_OImage(X16,X5,X34),X11)))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X5)),hAPP(hAPP(c_Product__Type_OPair(X16,X5),X3),X17)),X34))
           => ~ hBOOL(hAPP(hAPP(c_member(X16),X3),X11)) ) ),
    inference(fof_simplification,[status(thm)],[fact_ImageE]) ).

fof(i_0_5365,plain,
    ! [X32401,X32402,X32403] : c_Enum_On__lists(X32403,hAPP(c_Nat_OSuc,X32402),X32401) = c_List_Oconcat(tc_List_Olist(X32403),hAPP(hAPP(c_List_Omap(tc_List_Olist(X32403),tc_List_Olist(tc_List_Olist(X32403))),hAPP(hAPP(c_COMBC(tc_List_Olist(X32403),tc_List_Olist(X32403),tc_List_Olist(tc_List_Olist(X32403))),hAPP(hAPP(c_COMBB(tc_fun(X32403,tc_List_Olist(X32403)),tc_fun(tc_List_Olist(X32403),tc_List_Olist(tc_List_Olist(X32403))),tc_List_Olist(X32403)),c_List_Omap(X32403,tc_List_Olist(X32403))),hAPP(c_COMBC(X32403,tc_List_Olist(X32403),tc_List_Olist(X32403)),c_List_Olist_OCons(X32403)))),X32401)),c_Enum_On__lists(X32403,X32402,X32401))),
    inference(variable_rename,[status(thm)],[fact_n__lists_Osimps_I2_J]) ).

fof(i_0_5366,plain,
    ! [X24717,X24718,X24719,X24720,X24721] : c_Nat_Onat_Onat__case(X24721,X24720,X24719,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24718)),X24717)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X24721),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X24718))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X24721,X24721),hAPP(hAPP(c_COMBC(tc_Int_Oint,X24721,tc_fun(X24721,X24721)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X24721,tc_fun(X24721,X24721)),tc_Int_Oint),c_If(X24721)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X24721,X24720,X24719,X24717))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X24721,tc_Int_Oint),X24719),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)),X24717)))),
    inference(variable_rename,[status(thm)],[fact_nat__case__add__eq__if]) ).

fof(i_0_5367,plain,
    ! [X24943] :
      ( ( ~ 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,X24943,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,X24943,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,X24943,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,X24943,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_5368,plain,
    ! [X27182,X27183,X27184,X27185,X27186,X27187] :
      ( ( hAPP(c_Product__Type_Oapsnd(X27187,X27186,X27185,X27184),X27183) != hAPP(c_Product__Type_Oapsnd(X27187,X27186,X27185,X27182),X27183)
        | hAPP(X27184,hAPP(c_Product__Type_Osnd(X27185,X27187),X27183)) = hAPP(X27182,hAPP(c_Product__Type_Osnd(X27185,X27187),X27183)) )
      & ( hAPP(X27184,hAPP(c_Product__Type_Osnd(X27185,X27187),X27183)) != hAPP(X27182,hAPP(c_Product__Type_Osnd(X27185,X27187),X27183))
        | hAPP(c_Product__Type_Oapsnd(X27187,X27186,X27185,X27184),X27183) = hAPP(c_Product__Type_Oapsnd(X27187,X27186,X27185,X27182),X27183) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_apsnd__eq__conv])]) ).

fof(i_0_5369,plain,
    ! [X27237,X27238,X27239,X27240,X27241,X27242] :
      ( ( hAPP(c_Product__Type_Oapfst(X27242,X27241,X27240,X27239),X27238) != hAPP(c_Product__Type_Oapfst(X27242,X27241,X27240,X27237),X27238)
        | hAPP(X27239,hAPP(c_Product__Type_Ofst(X27242,X27240),X27238)) = hAPP(X27237,hAPP(c_Product__Type_Ofst(X27242,X27240),X27238)) )
      & ( hAPP(X27239,hAPP(c_Product__Type_Ofst(X27242,X27240),X27238)) != hAPP(X27237,hAPP(c_Product__Type_Ofst(X27242,X27240),X27238))
        | hAPP(c_Product__Type_Oapfst(X27242,X27241,X27240,X27239),X27238) = hAPP(c_Product__Type_Oapfst(X27242,X27241,X27240,X27237),X27238) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_apfst__eq__conv])]) ).

fof(i_0_5370,plain,
    ! [X28684] : c_Relation_OId(X28684) = hAPP(c_Set_OCollect(tc_prod(X28684,X28684)),hAPP(hAPP(c_COMBB(tc_fun(X28684,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X28684,X28684)),c_HOL_OEx(X28684)),hAPP(hAPP(c_COMBC(tc_prod(X28684,X28684),tc_fun(X28684,tc_prod(X28684,X28684)),tc_fun(X28684,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X28684,X28684),tc_HOL_Obool),tc_fun(tc_fun(X28684,tc_prod(X28684,X28684)),tc_fun(X28684,tc_HOL_Obool)),tc_prod(X28684,X28684)),c_COMBB(tc_prod(X28684,X28684),tc_HOL_Obool,X28684)),c_fequal)),hAPP(hAPP(c_COMBS(X28684,X28684,tc_prod(X28684,X28684)),c_Product__Type_OPair(X28684,X28684)),c_COMBI(X28684))))),
    inference(variable_rename,[status(thm)],[fact_Id__def]) ).

fof(i_0_5371,plain,
    ! [X27212,X27213,X27214,X27215,X27216,X27217,X27218] : hAPP(c_Product__Type_Oapsnd(X27218,X27217,X27216,X27215),hAPP(c_Product__Type_Oapfst(X27214,X27216,X27218,X27213),X27212)) = hAPP(hAPP(c_Product__Type_OPair(X27216,X27217),hAPP(X27213,hAPP(c_Product__Type_Ofst(X27214,X27218),X27212))),hAPP(X27215,hAPP(c_Product__Type_Osnd(X27214,X27218),X27212))),
    inference(variable_rename,[status(thm)],[fact_apsnd__apfst]) ).

fof(i_0_5372,plain,
    ! [X27205,X27206,X27207,X27208,X27209,X27210,X27211] : hAPP(c_Product__Type_Oapfst(X27211,X27210,X27209,X27208),hAPP(c_Product__Type_Oapsnd(X27207,X27209,X27211,X27206),X27205)) = hAPP(hAPP(c_Product__Type_OPair(X27210,X27209),hAPP(X27208,hAPP(c_Product__Type_Ofst(X27211,X27207),X27205))),hAPP(X27206,hAPP(c_Product__Type_Osnd(X27211,X27207),X27205))),
    inference(variable_rename,[status(thm)],[fact_apfst__apsnd]) ).

fof(i_0_5373,plain,
    ! [X24882,X24883] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24883),c_Groups_Ozero__class_Ozero(X24883)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24883),X24882),hAPP(c_Int_Onumber__class_Onumber__of(X24883),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24883),c_Groups_Ozero__class_Ozero(X24883)),X24882))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24883)
        | ~ class_Int_Onumber__ring(X24883) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24883),c_Groups_Ozero__class_Ozero(X24883)),X24882))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24883),c_Groups_Ozero__class_Ozero(X24883)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24883),X24882),hAPP(c_Int_Onumber__class_Onumber__of(X24883),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24883)
        | ~ class_Int_Onumber__ring(X24883) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_half__gt__zero__iff])])]) ).

fof(i_0_5374,plain,
    ! [X25921,X25922] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25922)),hAPP(c_Nat_OSuc,X25921)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25922))),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,X25921))),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)),X25921)))),
    inference(variable_rename,[status(thm)],[fact_max__Suc__number__of]) ).

fof(i_0_5375,plain,
    ! [X24896,X24897] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24897),c_Groups_Ozero__class_Ozero(X24897)),hAPP(hAPP(c_Power_Opower__class_Opower(X24897),X24896),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | X24896 != c_Groups_Ozero__class_Ozero(X24897)
        | ~ class_Rings_Olinordered__idom(X24897) )
      & ( X24896 = c_Groups_Ozero__class_Ozero(X24897)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24897),c_Groups_Ozero__class_Ozero(X24897)),hAPP(hAPP(c_Power_Opower__class_Opower(X24897),X24896),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | ~ class_Rings_Olinordered__idom(X24897) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power2])])]) ).

fof(i_0_5376,plain,
    ! [X25293,X25294] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25294)),hAPP(c_Nat_OSuc,X25293)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25294))),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)),X25293)))),
    inference(variable_rename,[status(thm)],[fact_min__Suc__number__of]) ).

fof(i_0_5377,plain,
    ! [X24749,X24750,X24751,X24752] : hAPP(c_Nat_Onat_Onat__rec(X24752,X24751,X24750),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24749)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X24752),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X24749))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X24752,X24752),hAPP(hAPP(c_COMBC(tc_Int_Oint,X24752,tc_fun(X24752,X24752)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X24752,tc_fun(X24752,X24752)),tc_Int_Oint),c_If(X24752)),c_Nat__Numeral_Oneg)),X24751)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X24752,X24752),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X24752,X24752),tc_Int_Oint),X24750),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X24752,tc_Int_Oint),c_Nat_Onat_Onat__rec(X24752,X24751,X24750)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[fact_nat__rec__number__of]) ).

fof(i_0_5378,plain,
    ! [X32326,X32327] : c_List_Oconcat(X32327,hAPP(hAPP(c_List_Omap(tc_List_Olist(X32327),tc_List_Olist(X32327)),c_List_Olist_Olist__case(tc_List_Olist(X32327),X32327,c_List_Olist_ONil(X32327),hAPP(hAPP(c_COMBB(tc_List_Olist(X32327),tc_fun(tc_List_Olist(X32327),tc_List_Olist(X32327)),X32327),c_COMBK(tc_List_Olist(X32327),tc_List_Olist(X32327))),hAPP(hAPP(c_COMBC(X32327,tc_List_Olist(X32327),tc_List_Olist(X32327)),c_List_Olist_OCons(X32327)),c_List_Olist_ONil(X32327))))),X32326)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X32327),X32327),c_List_Ohd(X32327)),hAPP(c_List_Ofilter(tc_List_Olist(X32327),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X32327)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X32327),tc_List_Olist(X32327),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X32327)))),X32326)),
    inference(variable_rename,[status(thm)],[fact_transpose__aux__filter__head]) ).

fof(i_0_5379,plain,
    ! [X32408,X32409] : c_List_Oconcat(tc_List_Olist(X32409),hAPP(hAPP(c_List_Omap(tc_List_Olist(X32409),tc_List_Olist(tc_List_Olist(X32409))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X32409)),X32409,c_List_Olist_ONil(tc_List_Olist(X32409)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X32409),tc_List_Olist(tc_List_Olist(X32409))),X32409),hAPP(hAPP(c_COMBC(tc_List_Olist(X32409),tc_List_Olist(tc_List_Olist(X32409)),tc_List_Olist(tc_List_Olist(X32409))),c_List_Olist_OCons(tc_List_Olist(X32409))),c_List_Olist_ONil(tc_List_Olist(X32409)))))),X32408)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X32409),tc_List_Olist(X32409)),c_List_Otl(X32409)),hAPP(c_List_Ofilter(tc_List_Olist(X32409),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X32409)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X32409),tc_List_Olist(X32409),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X32409)))),X32408)),
    inference(variable_rename,[status(thm)],[fact_transpose__aux__filter__tail]) ).

fof(i_0_5380,plain,
    ! [X28562,X28563,X28564] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28564,X28564),tc_HOL_Obool)),c_Relation_OId(X28564)),X28563))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28564,X28564),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28564,X28564,X28564),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28564,X28564),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X28564,X28562)),X28563)),X28562)),X28563))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28564,X28564),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X28564,X28562)),X28563)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__Int__subset])]) ).

fof(i_0_5381,plain,
    ! [X34,X212,X214,X27,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),X27),X214)),X212)),c_List_Olistrel(X5,X34)))
     => ~ ! [X33,X229] :
            ( X212 = hAPP(hAPP(c_List_Olist_OCons(X5),X33),X229)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X27),X33)),X34))
             => ~ 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)),X214),X229)),c_List_Olistrel(X5,X34))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_listrel__Cons1]) ).

fof(i_0_5382,plain,
    ! [X24870,X24871,X24872] :
      ( ~ class_Groups_Omonoid__mult(X24872)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X24872),X24871),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)))),X24870)) = hAPP(hAPP(c_Power_Opower__class_Opower(X24872),hAPP(hAPP(c_Power_Opower__class_Opower(X24872),X24871),X24870)),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_5383,plain,
    ! [X32415,X32416,X32417] : c_List_Osublist(X32417,X32416,X32415) = hAPP(hAPP(c_List_Omap(tc_prod(X32417,tc_Nat_Onat),X32417),c_Product__Type_Ofst(X32417,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X32417,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X32417,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(X32417,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X32417,tc_Nat_Onat))),X32415)),hAPP(hAPP(c_List_Ozip(X32417,tc_Nat_Onat),X32416),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32417)),X32416))))),
    inference(variable_rename,[status(thm)],[fact_sublist__def]) ).

fof(i_0_5384,plain,
    ! [X51,X46,X47,X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,hAPP(hAPP(c_Set_Oinsert(X5),X47),X46)),X51))
    <=> ? [X74,X75] :
          ( hAPP(hAPP(c_Set_Oinsert(X5),X47),X46) = hAPP(hAPP(c_Set_Oinsert(X5),X74),X75)
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,X2,X74,X75),X51))
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X74),X75)) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold1Set_Oequations]) ).

fof(i_0_5385,plain,
    ! [X33562,X33563] : c_Nitpick_Ouminus__frac(X33563,X33562) = c_Nitpick_OAbs__Frac(X33563,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(X33563),X33562))),hAPP(c_Nitpick_Odenom(X33563),X33562))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Ouminus__frac__def]) ).

fof(i_0_5386,plain,
    ! [X27177,X27178,X27179,X27180,X27181] : hAPP(c_Product__Type_Osnd(X27181,X27180),hAPP(c_Product__Type_Oapsnd(X27179,X27180,X27181,X27178),X27177)) = hAPP(X27178,hAPP(c_Product__Type_Osnd(X27181,X27179),X27177)),
    inference(variable_rename,[status(thm)],[fact_snd__apsnd]) ).

fof(i_0_5387,plain,
    ! [X27243,X27244,X27245,X27246,X27247] : hAPP(c_Product__Type_Ofst(X27247,X27246),hAPP(c_Product__Type_Oapfst(X27245,X27247,X27246,X27244),X27243)) = hAPP(X27244,hAPP(c_Product__Type_Ofst(X27245,X27246),X27243)),
    inference(variable_rename,[status(thm)],[fact_fst__apfst]) ).

fof(i_0_5388,plain,
    ! [X27159,X27160,X27161,X27162,X27163] : hAPP(c_Product__Type_Ofst(X27163,X27162),hAPP(c_Product__Type_Oapsnd(X27161,X27162,X27163,X27160),X27159)) = hAPP(c_Product__Type_Ofst(X27163,X27161),X27159),
    inference(variable_rename,[status(thm)],[fact_fst__apsnd]) ).

fof(i_0_5389,plain,
    ! [X27219,X27220,X27221,X27222,X27223] : hAPP(c_Product__Type_Osnd(X27223,X27222),hAPP(c_Product__Type_Oapfst(X27221,X27223,X27222,X27220),X27219)) = hAPP(c_Product__Type_Osnd(X27221,X27222),X27219),
    inference(variable_rename,[status(thm)],[fact_snd__apfst]) ).

fof(i_0_5390,plain,
    ! [X29,X46,X47,X158] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X158),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X47),X46))))
     => ( ! [X43,X125,X145] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X43),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X125),X145))))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X125),X145))
               => ( hAPP(X43,X145) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
                 => hBOOL(hAPP(hAPP(hAPP(X29,X43),X125),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X145),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) )
             => hBOOL(hAPP(hAPP(hAPP(X29,X43),X125),X145)) ) )
       => hBOOL(hAPP(hAPP(hAPP(X29,X158),X47),X46)) ) ),
    inference(fof_simplification,[status(thm)],[fact_small_H_Opinduct]) ).

fof(i_0_5391,plain,
    ! [X24722,X24723,X24724,X24725] : c_Nat_Onat_Onat__case(X24725,X24724,X24723,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24722)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X24725),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X24722))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X24725,X24725),hAPP(hAPP(c_COMBC(tc_Int_Oint,X24725,tc_fun(X24725,X24725)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X24725,tc_fun(X24725,X24725)),tc_Int_Oint),c_If(X24725)),c_Nat__Numeral_Oneg)),X24724)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X24725,tc_Int_Oint),X24723),c_Int_Onat))),
    inference(variable_rename,[status(thm)],[fact_nat__case__number__of]) ).

fof(i_0_5392,plain,
    ! [X25923,X25924] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25924)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25923)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25923))),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,X25924))),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),X25924)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[fact_max__number__of__Suc]) ).

fof(i_0_5393,plain,
    ! [X25497,X25498] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25498)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25497)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X25497))),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),X25498)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[fact_min__number__of__Suc]) ).

fof(i_0_5394,plain,
    ! [X24956] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24956))
      | 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),X24956),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_5395,plain,
    ! [X24884,X24885] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X24885)
      | ~ class_Int_Onumber__ring(X24885)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24885),c_Groups_Ozero__class_Ozero(X24885)),X24884))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24885),c_Groups_Ozero__class_Ozero(X24885)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24885),X24884),hAPP(c_Int_Onumber__class_Onumber__of(X24885),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_5396,plain,
    ! [X24906,X24907,X24908] :
      ( ~ class_Rings_Ocomm__semiring__1(X24908)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X24908),X24907),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)))),X24906)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24908),hAPP(hAPP(c_Power_Opower__class_Opower(X24908),X24907),X24906)),hAPP(hAPP(c_Power_Opower__class_Opower(X24908),X24907),X24906)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J])]) ).

fof(i_0_5397,plain,
    ! [X24944] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X24944))
      | 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),X24944),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_5398,plain,
    ! [X24664,X24665] :
      ( ~ class_Groups_Omonoid__mult(X24665)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X24665),X24664),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(X24665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24665),X24664),X24664)),X24664) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power3__eq__cube])]) ).

fof(i_0_5399,plain,
    ! [X24886,X24887] :
      ( ~ class_Rings_Olinordered__idom(X24887)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24887),c_Groups_Ozero__class_Ozero(X24887)),hAPP(hAPP(c_Power_Opower__class_Opower(X24887),X24886),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_5400,plain,
    ! [X24939,X24940] :
      ( ~ class_Rings_Oring__1(X24940)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X24940),hAPP(c_Groups_Ouminus__class_Ouminus(X24940),c_Groups_Oone__class_Oone(X24940))),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)))),X24939)) = c_Groups_Oone__class_Oone(X24940) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus1__even])]) ).

fof(i_0_5401,plain,
    ! [X25075,X25076] :
      ( ~ class_Int_Onumber__ring(X25076)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X25076),hAPP(c_Int_Onumber__class_Onumber__of(X25076),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)))),X25075)) = c_Groups_Oone__class_Oone(X25076) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__m1__even])]) ).

fof(i_0_5402,plain,
    ! [X56,X168] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X168),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X168),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)) = 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),X56),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X168)))),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_5403,plain,
    ! [X33077,X33078,X33079,X33080,X33081] : c_List_OdropWhile(X33081,X33080,hAPP(hAPP(c_List_Omap(X33079,X33081),X33078),X33077)) = hAPP(hAPP(c_List_Omap(X33079,X33081),X33078),c_List_OdropWhile(X33079,hAPP(c_Fun_Ocomp(X33081,tc_HOL_Obool,X33079,X33080),X33078),X33077)),
    inference(variable_rename,[status(thm)],[fact_dropWhile__map]) ).

fof(i_0_5404,plain,
    ! [X37,X170] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X170))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X37)),hAPP(c_Int_Onat,X170)) = hAPP(c_Int_Onat,X37) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X170))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X37)),hAPP(c_Int_Onat,X170)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X37),X170)),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_5405,plain,
    ! [X33045,X33046,X33047] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X33047),X33046))
      | ~ hBOOL(hAPP(hAPP(c_member(X33047),X33045),hAPP(c_List_Oset(X33047),X33046)))
      | c_List_OdropWhile(X33047,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33047),c_fNot),hAPP(hAPP(c_COMBC(X33047,X33047,tc_HOL_Obool),c_fequal),X33045)),hAPP(c_List_Orev(X33047),X33046)) = hAPP(hAPP(c_List_Olist_OCons(X33047),X33045),hAPP(c_List_Orev(X33047),c_List_OtakeWhile(X33047,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33047),c_fNot),hAPP(hAPP(c_COMBC(X33047,X33047,tc_HOL_Obool),c_fequal),X33045)),X33046))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dropWhile__neq__rev])]) ).

fof(i_0_5406,plain,
    ! [X6,X12,X11,X17,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X17,X11),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X17),X11))
           => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X6,hAPP(hAPP(c_Set_Oinsert(X5),X17),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),X12)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold__graph__permute__diff]) ).

fof(i_0_5407,plain,
    ! [X32397,X32398,X32399,X32400] : c_List_Oconcat(X32400,hAPP(hAPP(c_List_Omap(X32399,tc_List_Olist(X32400)),hAPP(hAPP(c_COMBC(X32399,tc_List_Olist(X32400),tc_List_Olist(X32400)),hAPP(hAPP(c_COMBB(X32400,tc_fun(tc_List_Olist(X32400),tc_List_Olist(X32400)),X32399),c_List_Olist_OCons(X32400)),X32398)),c_List_Olist_ONil(X32400))),X32397)) = hAPP(hAPP(c_List_Omap(X32399,X32400),X32398),X32397),
    inference(variable_rename,[status(thm)],[fact_concat__map__singleton]) ).

fof(i_0_5408,plain,
    ! [X33567,X33568,X33569] :
      ( ( ~ c_Nitpick_Oless__eq__frac(X33569,X33568,X33567)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X33569),c_Nitpick_Oplus__frac(X33569,X33568,c_Nitpick_Ouminus__frac(X33569,X33567)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X33569),c_Nitpick_Oplus__frac(X33569,X33568,c_Nitpick_Ouminus__frac(X33569,X33567)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Nitpick_Oless__eq__frac(X33569,X33568,X33567) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__eq__frac__def])]) ).

fof(i_0_5409,plain,
    ! [X33564,X33565,X33566] :
      ( ( ~ c_Nitpick_Oless__frac(X33566,X33565,X33564)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X33566),c_Nitpick_Oplus__frac(X33566,X33565,c_Nitpick_Ouminus__frac(X33566,X33564)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X33566),c_Nitpick_Oplus__frac(X33566,X33565,c_Nitpick_Ouminus__frac(X33566,X33564)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Nitpick_Oless__frac(X33566,X33565,X33564) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__frac__def])]) ).

fof(i_0_5410,plain,
    ! [X24891,X24892,X24893] :
      ( ~ class_Rings_Olinordered__semidom(X24893)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X24893),X24892),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(X24893),X24891),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(X24893),c_Groups_Ozero__class_Ozero(X24893)),X24892))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24893),c_Groups_Ozero__class_Ozero(X24893)),X24891))
      | X24892 = X24891 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__imp__eq])]) ).

fof(i_0_5411,plain,
    ! [X24903] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24903),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      | X24903 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | X24903 = 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_5412,plain,
    ! [X24874] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X24874))),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),X24874),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_5413,plain,
    ! [X27146,X27147] :
      ( ~ class_Rings_Olinordered__idom(X27147)
      | hAPP(c_Groups_Oabs__class_Oabs(X27147),hAPP(hAPP(c_Power_Opower__class_Opower(X27147),X27146),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(X27147),X27146),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_5414,plain,
    ! [X33557,X33558,X33559] :
      ( ~ class_Rings_Oinverse(X33559)
      | ~ class_Rings_Oring__1(X33559)
      | c_Nitpick_Oof__frac(X33558,X33559,X33557) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X33559),hAPP(c_Int_Oring__1__class_Oof__int(X33559),hAPP(c_Nitpick_Onum(X33558),X33557))),hAPP(c_Int_Oring__1__class_Oof__int(X33559),hAPP(c_Nitpick_Odenom(X33558),X33557))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oof__frac__def])]) ).

fof(i_0_5415,plain,
    ! [X34,X201,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),X201),hAPP(c_Relation_Oconverse(X16,X5),X34)))
     => ~ ! [X3,X33] :
            ( X201 = hAPP(hAPP(c_Product__Type_OPair(X5,X16),X33),X3)
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X5)),hAPP(hAPP(c_Product__Type_OPair(X16,X5),X3),X33)),X34)) ) ),
    inference(fof_simplification,[status(thm)],[fact_converseE]) ).

fof(i_0_5416,plain,
    ! [X2,X76,X45,X5] :
      ( class_Groups_Oab__group__add(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76))
         => 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,X45,X76)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(X2,X45)),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X76),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76))
         => 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,X45,X76)) = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__natinterval__difff]) ).

fof(i_0_5417,plain,
    ! [X27,X2,X212,X214,X16,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)),X212))))
       => c_Map_Omap__upds(X5,X16,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),X2),X12),hAPP(c_Option_Ooption_OSome(X16),X27)),X212,X214) = c_Map_Omap__upds(X5,X16,X2,X212,X214) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)),X212))))
       => c_Map_Omap__upds(X5,X16,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),X2),X12),hAPP(c_Option_Ooption_OSome(X16),X27)),X212,X214) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),c_Map_Omap__upds(X5,X16,X2,X212,X214)),X12),hAPP(c_Option_Ooption_OSome(X16),X27)) ) ),
    inference(fof_simplification,[status(thm)],[fact_map__upd__upds__conv__if]) ).

fof(i_0_5418,plain,
    ! [X37,X27,X11,X17,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X17,X11),X27))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X17),X11))
         => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X37,hAPP(hAPP(c_Set_Oinsert(X5),X17),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X37),X27))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold__graph__insert__swap]) ).

fof(i_0_5419,plain,
    ! [X27,X37,X2,X16,X11,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X16,X2,X37,X11),X27))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X16,X2,X37,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)),hAPP(hAPP(X2,X12),X27))) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold__graph_OinsertI]) ).

fof(i_0_5420,plain,
    ! [X30240,X30241,X30242,X30243,X30244,X30245,X30247,X30248,X30249,X30250,X30251,X30252,X30253] :
      ( ( hAPP(X30241,X30240) = hAPP(c_Option_Ooption_OSome(X30245),esk398_6(X30240,X30241,X30242,X30243,X30244,X30245))
        | hAPP(X30241,X30240) = c_Option_Ooption_ONone(X30245)
        | c_Map_Omap__comp(X30245,X30244,X30243,X30242,X30241,X30240) != c_Option_Ooption_ONone(X30244) )
      & ( hAPP(X30242,esk398_6(X30240,X30241,X30242,X30243,X30244,X30245)) = c_Option_Ooption_ONone(X30244)
        | hAPP(X30241,X30240) = c_Option_Ooption_ONone(X30245)
        | c_Map_Omap__comp(X30245,X30244,X30243,X30242,X30241,X30240) != c_Option_Ooption_ONone(X30244) )
      & ( hAPP(X30248,X30247) != c_Option_Ooption_ONone(X30252)
        | c_Map_Omap__comp(X30252,X30251,X30250,X30249,X30248,X30247) = c_Option_Ooption_ONone(X30251) )
      & ( hAPP(X30248,X30247) != hAPP(c_Option_Ooption_OSome(X30252),X30253)
        | hAPP(X30249,X30253) != c_Option_Ooption_ONone(X30251)
        | c_Map_Omap__comp(X30252,X30251,X30250,X30249,X30248,X30247) = c_Option_Ooption_ONone(X30251) ) ),
    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__comp__None__iff])])])])])]) ).

fof(i_0_5421,plain,
    ! [X28999,X29000,X29001,X29002] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29002,X29002)),hAPP(hAPP(c_Product__Type_OPair(X29002,X29002),X29001),esk347_4(X28999,X29000,X29001,X29002))),X28999))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29002,X29002)),hAPP(hAPP(c_Product__Type_OPair(X29002,X29002),X29001),X29000)),c_Transitive__Closure_Otrancl(X29002,X28999))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29002,X29002)),hAPP(hAPP(c_Product__Type_OPair(X29002,X29002),esk347_4(X28999,X29000,X29001,X29002)),X29000)),c_Transitive__Closure_Ortrancl(X29002,X28999)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29002,X29002)),hAPP(hAPP(c_Product__Type_OPair(X29002,X29002),X29001),X29000)),c_Transitive__Closure_Otrancl(X29002,X28999))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclD])])])]) ).

fof(i_0_5422,plain,
    ! [X29004,X29005,X29006,X29007] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29007,X29007)),hAPP(hAPP(c_Product__Type_OPair(X29007,X29007),X29006),esk348_4(X29004,X29005,X29006,X29007))),c_Transitive__Closure_Ortrancl(X29007,X29004)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29007,X29007)),hAPP(hAPP(c_Product__Type_OPair(X29007,X29007),X29006),X29005)),c_Transitive__Closure_Otrancl(X29007,X29004))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29007,X29007)),hAPP(hAPP(c_Product__Type_OPair(X29007,X29007),esk348_4(X29004,X29005,X29006,X29007)),X29005)),X29004))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29007,X29007)),hAPP(hAPP(c_Product__Type_OPair(X29007,X29007),X29006),X29005)),c_Transitive__Closure_Otrancl(X29007,X29004))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclD2])])])]) ).

fof(i_0_5423,plain,
    ! [X27224,X27225,X27226,X27227,X27228,X27229] : hAPP(c_Product__Type_Oapfst(X27229,X27228,X27227,X27226),hAPP(hAPP(c_Product__Type_OPair(X27229,X27227),X27225),X27224)) = hAPP(hAPP(c_Product__Type_OPair(X27228,X27227),hAPP(X27226,X27225)),X27224),
    inference(variable_rename,[status(thm)],[fact_apfst__conv]) ).

fof(i_0_5424,plain,
    ! [X27164,X27165,X27166,X27167,X27168,X27169] : hAPP(c_Product__Type_Oapsnd(X27169,X27168,X27167,X27166),hAPP(hAPP(c_Product__Type_OPair(X27167,X27169),X27165),X27164)) = hAPP(hAPP(c_Product__Type_OPair(X27167,X27168),X27165),hAPP(X27166,X27164)),
    inference(variable_rename,[status(thm)],[fact_apsnd__conv]) ).

fof(i_0_5425,plain,
    ! [X234,X17,X45,X16,X235,X6,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_List_Oset(X5),X235)))
     => c_Map_Omap__upds(X5,X16,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),X45),X6),hAPP(c_Option_Ooption_OSome(X16),X17)),X235,X234) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),c_Map_Omap__upds(X5,X16,X45,X235,X234)),X6),hAPP(c_Option_Ooption_OSome(X16),X17)) ),
    inference(fof_simplification,[status(thm)],[fact_map__upds__twist]) ).

fof(i_0_5426,plain,
    ! [X212,X12,X29,X5] :
      ( c_List_Olist__ex1(X5,X29,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212))
    <=> ( ( hBOOL(hAPP(X29,X12))
         => 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),X29))),hAPP(c_fequal,X12)),X212) )
        & ( ~ hBOOL(hAPP(X29,X12))
         => c_List_Olist__ex1(X5,X29,X212) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_list__ex1__simps_I2_J]) ).

fof(i_0_5427,plain,
    ! [X32244,X32245] : c_List_Ofoldr(tc_List_Olist(X32245),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X32245)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X32245))),c_List_Otranspose(X32245,X32244),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32245))),hAPP(c_List_Ofilter(tc_List_Olist(X32245),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X32245)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X32245),tc_List_Olist(X32245),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X32245)))),X32244)),
    inference(variable_rename,[status(thm)],[fact_transpose__max__length]) ).

fof(i_0_5428,plain,
    ! [X33095,X33096,X33097,X33098] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33098),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33097)),c_List_OdropWhile(X33097,X33096,X33095))))
      | hAPP(hAPP(c_List_Onth(X33097),c_List_OdropWhile(X33097,X33096,X33095)),X33098) = hAPP(hAPP(c_List_Onth(X33097),X33095),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33098),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33097)),c_List_OtakeWhile(X33097,X33096,X33095)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dropWhile__nth])]) ).

fof(i_0_5429,plain,
    ! [X24875,X24876] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X24876)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X24875))) = 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),X24876),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24875))),
    inference(variable_rename,[status(thm)],[fact_zmod__number__of__Bit0]) ).

fof(i_0_5430,plain,
    ! [X27148,X27149] :
      ( ~ class_Rings_Olinordered__idom(X27149)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X27149),hAPP(c_Groups_Oabs__class_Oabs(X27149),X27148)),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(X27149),X27148),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_5431,plain,
    ! [X24866,X24867] :
      ( ~ class_Rings_Oring__1(X24867)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X24867),hAPP(c_Groups_Ouminus__class_Ouminus(X24867),X24866)),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(X24867),X24866),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_5432,plain,
    ! [X24873] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X24873)),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,X24873,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_5433,plain,
    ! [X29,X11,X90,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X90))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X90),X11))
       => ( hBOOL(hAPP(X29,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
         => ( ! [X74,X106] :
                ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X106))
               => ( hBOOL(hAPP(hAPP(c_member(X5),X74),X11))
                 => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X74),X106))
                   => ( hBOOL(hAPP(X29,X106))
                     => hBOOL(hAPP(X29,hAPP(hAPP(c_Set_Oinsert(X5),X74),X106))) ) ) ) )
           => hBOOL(hAPP(X29,X90)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_finite__subset__induct]) ).

fof(i_0_5434,plain,
    ! [X24851,X24852] :
      ( ~ class_Int_Onumber__ring(X24852)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24852),hAPP(c_Int_Onumber__class_Onumber__of(X24852),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X24851) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24852),X24851),X24851) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2])]) ).

fof(i_0_5435,plain,
    ! [X2,X29,X212,X5,X16] :
      ( class_Groups_Omonoid__add(X16)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
           => ( ~ hBOOL(hAPP(X29,X3))
             => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X16) ) )
       => hAPP(c_List_Omonoid__add__class_Olistsum(X16),hAPP(hAPP(c_List_Omap(X5,X16),X2),hAPP(c_List_Ofilter(X5,X29),X212))) = hAPP(c_List_Omonoid__add__class_Olistsum(X16),hAPP(hAPP(c_List_Omap(X5,X16),X2),X212)) ) ),
    inference(fof_simplification,[status(thm)],[fact_listsum__map__filter]) ).

fof(i_0_5436,plain,
    ! [X24868] : 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)))),X24868) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24868),X24868),
    inference(variable_rename,[status(thm)],[fact_nat__mult__2]) ).

fof(i_0_5437,plain,
    ! [X24864] : 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)))),X24864) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X24864)),
    inference(variable_rename,[status(thm)],[fact_add__2__eq__Suc]) ).

fof(i_0_5438,plain,
    ! [X33071,X33072,X33073] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33073)),c_List_OdropWhile(X33073,X33072,X33071))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33073)),X33071))),
    inference(variable_rename,[status(thm)],[fact_length__dropWhile__le]) ).

fof(i_0_5439,plain,
    ! [X12,X11,X90,X1,X37,X2,X16,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X16,X2,X37,X1,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X16),X12),X11))
         => hAPP(X90,hAPP(hAPP(c_Set_Oinsert(X16),X12),X11)) = hAPP(hAPP(X2,hAPP(X1,X12)),hAPP(X90,X11)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oinsert]) ).

fof(i_0_5440,plain,
    ! [X34,X16,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(c_Relation_ORange(X16,X5),X34)))
     => ~ ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X5)),hAPP(hAPP(c_Product__Type_OPair(X16,X5),X3),X17)),X34)) ),
    inference(fof_simplification,[status(thm)],[fact_RangeE]) ).

fof(i_0_5441,plain,
    ! [X28489,X28490,X28491,X28492,X28493] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28493,X28493)),hAPP(hAPP(c_Product__Type_OPair(X28493,X28493),X28492),X28491)),c_Transitive__Closure_Otrancl(X28493,X28490)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28493,X28493)),hAPP(hAPP(c_Product__Type_OPair(X28493,X28493),X28491),X28489)),c_Transitive__Closure_Otrancl(X28493,X28490)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28493,X28493)),hAPP(hAPP(c_Product__Type_OPair(X28493,X28493),X28492),X28489)),c_Transitive__Closure_Otrancl(X28493,X28490))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__trans])]) ).

fof(i_0_5442,plain,
    ! [X28794,X28795,X28796,X28797] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28797,X28797)),hAPP(hAPP(c_Product__Type_OPair(X28797,X28797),X28796),X28795)),hAPP(c_Relation_Oconverse(X28797,X28797),c_Transitive__Closure_Otrancl(X28797,X28794))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28797,X28797)),hAPP(hAPP(c_Product__Type_OPair(X28797,X28797),X28796),X28795)),c_Transitive__Closure_Otrancl(X28797,hAPP(c_Relation_Oconverse(X28797,X28797),X28794)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__converseI])]) ).

fof(i_0_5443,plain,
    ! [X28790,X28791,X28792,X28793] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28793,X28793)),hAPP(hAPP(c_Product__Type_OPair(X28793,X28793),X28792),X28791)),c_Transitive__Closure_Otrancl(X28793,hAPP(c_Relation_Oconverse(X28793,X28793),X28790))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28793,X28793)),hAPP(hAPP(c_Product__Type_OPair(X28793,X28793),X28792),X28791)),hAPP(c_Relation_Oconverse(X28793,X28793),c_Transitive__Closure_Otrancl(X28793,X28790)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__converseD])]) ).

fof(i_0_5444,plain,
    ! [X27,X45,X16,X18,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X18))
       => c_Map_Orestrict__map(X5,X16,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),X45),X12),X27),X18) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),c_Map_Orestrict__map(X5,X16,X45,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X18),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),X12),X27) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X18))
       => c_Map_Orestrict__map(X5,X16,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),X45),X12),X27),X18) = c_Map_Orestrict__map(X5,X16,X45,X18) ) ),
    inference(fof_simplification,[status(thm)],[fact_restrict__fun__upd]) ).

fof(i_0_5445,plain,
    ! [X12,X11,X6,X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,X2,X6,X11),X12))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)),X12)) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold1Set_Ointros]) ).

fof(i_0_5446,plain,
    ! [X33068,X33069,X33070] :
      ( c_List_OdropWhile(X33070,X33069,X33068) = c_List_Olist_ONil(X33070)
      | ~ hBOOL(hAPP(X33069,hAPP(c_List_Ohd(X33070),c_List_OdropWhile(X33070,X33069,X33068)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5215])]) ).

fof(i_0_5447,plain,
    ! [X24904,X24905] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X24905),X24904),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(X24905)
        | X24904 = c_Groups_Oone__class_Oone(X24905)
        | X24904 = hAPP(c_Groups_Ouminus__class_Ouminus(X24905),c_Groups_Oone__class_Oone(X24905))
        | ~ class_Rings_Oring__1__no__zero__divisors(X24905) )
      & ( X24904 != c_Groups_Oone__class_Oone(X24905)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X24905),X24904),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X24905)
        | ~ class_Rings_Oring__1__no__zero__divisors(X24905) )
      & ( X24904 != hAPP(c_Groups_Ouminus__class_Ouminus(X24905),c_Groups_Oone__class_Oone(X24905))
        | hAPP(hAPP(c_Power_Opower__class_Opower(X24905),X24904),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X24905)
        | ~ class_Rings_Oring__1__no__zero__divisors(X24905) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__1__iff])])]) ).

fof(i_0_5448,plain,
    ! [X24856,X24857] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X24857),X24856),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(X24857)
        | X24856 = c_Groups_Ozero__class_Ozero(X24857)
        | ~ class_Rings_Oring__1__no__zero__divisors(X24857) )
      & ( X24856 != c_Groups_Ozero__class_Ozero(X24857)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X24857),X24856),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X24857)
        | ~ class_Rings_Oring__1__no__zero__divisors(X24857) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__eq__power2])])]) ).

fof(i_0_5449,plain,
    ! [X33333,X33334,X33335,X33336] : hAPP(c_List_OremoveAll(X33336,X33335),hAPP(hAPP(c_List_Oappend(X33336),X33334),X33333)) = hAPP(hAPP(c_List_Oappend(X33336),hAPP(c_List_OremoveAll(X33336,X33335),X33334)),hAPP(c_List_OremoveAll(X33336,X33335),X33333)),
    inference(variable_rename,[status(thm)],[fact_removeAll__append]) ).

fof(i_0_5450,plain,
    ! [X33312,X33313] : c_List_OremoveAll(X33313,X33312) = c_List_Ofilter(X33313,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33313),c_fNot),hAPP(c_fequal,X33312))),
    inference(variable_rename,[status(thm)],[fact_removeAll__filter__not__eq]) ).

fof(i_0_5451,plain,
    ! [X32940,X32941,X32942] : hAPP(c_List_Orotate(X32942,X32941),hAPP(c_List_Orev(X32942),X32940)) = hAPP(c_List_Orev(X32942),hAPP(c_List_Orotate(X32942,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32942)),X32940)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X32941,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32942)),X32940)))),X32940)),
    inference(variable_rename,[status(thm)],[fact_rotate__rev]) ).

fof(i_0_5452,plain,
    ! [X31962,X31963] : c_List_Orotate(X31963,X31962) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X31963),tc_List_Olist(X31963)),X31962),c_List_Orotate1(X31963)),
    inference(variable_rename,[status(thm)],[fact_rotate__def]) ).

fof(i_0_5453,plain,
    ! [X37,X27,X12,X227,X212,X16,X214,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X214) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X212)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X227) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X212)
       => ( ~ hBOOL(hAPP(hAPP(c_member(X16),X12),hAPP(c_List_Oset(X16),X212)))
         => ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X16,tc_Option_Ooption(X5)),hAPP(c_Map_Omap__of(X16,X5),hAPP(hAPP(c_List_Ozip(X16,X5),X212),X214))),X12),hAPP(c_Option_Ooption_OSome(X5),X27)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X16,tc_Option_Ooption(X5)),hAPP(c_Map_Omap__of(X16,X5),hAPP(hAPP(c_List_Ozip(X16,X5),X212),X227))),X12),hAPP(c_Option_Ooption_OSome(X5),X37))
           => hAPP(c_Map_Omap__of(X16,X5),hAPP(hAPP(c_List_Ozip(X16,X5),X212),X214)) = hAPP(c_Map_Omap__of(X16,X5),hAPP(hAPP(c_List_Ozip(X16,X5),X212),X227)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_map__of__zip__upd]) ).

fof(i_0_5454,plain,
    ! [X28631,X28632,X28633,X28634,X28635] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28635,X28635)),hAPP(hAPP(c_Product__Type_OPair(X28635,X28635),X28634),X28633)),c_Transitive__Closure_Ortrancl(X28635,X28632)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28635,X28635)),hAPP(hAPP(c_Product__Type_OPair(X28635,X28635),X28633),X28631)),c_Transitive__Closure_Otrancl(X28635,X28632)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28635,X28635)),hAPP(hAPP(c_Product__Type_OPair(X28635,X28635),X28634),X28631)),c_Transitive__Closure_Otrancl(X28635,X28632))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__trancl__trancl])]) ).

fof(i_0_5455,plain,
    ! [X28636,X28637,X28638,X28639,X28640] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28640,X28640)),hAPP(hAPP(c_Product__Type_OPair(X28640,X28640),X28639),X28638)),c_Transitive__Closure_Otrancl(X28640,X28637)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28640,X28640)),hAPP(hAPP(c_Product__Type_OPair(X28640,X28640),X28638),X28636)),c_Transitive__Closure_Ortrancl(X28640,X28637)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28640,X28640)),hAPP(hAPP(c_Product__Type_OPair(X28640,X28640),X28639),X28636)),c_Transitive__Closure_Otrancl(X28640,X28637))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__rtrancl__trancl])]) ).

fof(i_0_5456,plain,
    ! [X28499,X28500,X28501,X28502,X28503] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28503,X28503)),hAPP(hAPP(c_Product__Type_OPair(X28503,X28503),X28502),X28501)),X28500))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28503,X28503)),hAPP(hAPP(c_Product__Type_OPair(X28503,X28503),X28501),X28499)),c_Transitive__Closure_Otrancl(X28503,X28500)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28503,X28503)),hAPP(hAPP(c_Product__Type_OPair(X28503,X28503),X28502),X28499)),c_Transitive__Closure_Otrancl(X28503,X28500))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__into__trancl2])]) ).

fof(i_0_5457,plain,
    ! [X28494,X28495,X28496,X28497,X28498] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28498,X28498)),hAPP(hAPP(c_Product__Type_OPair(X28498,X28498),X28497),X28496)),c_Transitive__Closure_Otrancl(X28498,X28495)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28498,X28498)),hAPP(hAPP(c_Product__Type_OPair(X28498,X28498),X28496),X28494)),X28495))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28498,X28498)),hAPP(hAPP(c_Product__Type_OPair(X28498,X28498),X28497),X28494)),c_Transitive__Closure_Otrancl(X28498,X28495))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Transitive__Closure_Otrancl__into__trancl])]) ).

fof(i_0_5458,plain,
    ! [X5,X6,X29] :
      ( ( hBOOL(hAPP(X29,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))),X29)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(X29,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))),X29)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    inference(fof_simplification,[status(thm)],[fact_Collect__conv__if]) ).

fof(i_0_5459,plain,
    ! [X30081,X30082,X30083,X30084,X30085,X30086,X30087] : c_List_Ofoldr(X30087,X30086,X30085,hAPP(hAPP(c_List_Omap(X30084,X30087),X30083),X30082),X30081) = c_List_Ofoldr(X30084,X30086,hAPP(c_Fun_Ocomp(X30087,tc_fun(X30086,X30086),X30084,X30085),X30083),X30082,X30081),
    inference(variable_rename,[status(thm)],[fact_foldr__map]) ).

fof(i_0_5460,plain,
    ! [X28515,X28516,X28517] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28517,X28517),tc_HOL_Obool)),X28516),hAPP(hAPP(c_Product__Type_OSigma(X28517,X28517),X28515),hAPP(c_COMBK(tc_fun(X28517,tc_HOL_Obool),X28517),X28515))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28517,X28517),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X28517,X28516)),hAPP(hAPP(c_Product__Type_OSigma(X28517,X28517),X28515),hAPP(c_COMBK(tc_fun(X28517,tc_HOL_Obool),X28517),X28515)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma])]) ).

fof(i_0_5461,plain,
    ! [X24103,X24104,X24105] :
      ( ( ~ 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),X24104)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(X24105),hAPP(c_Int_Onumber__class_Onumber__of(X24105),X24103)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X24104))) = hAPP(hAPP(c_HOL_OLet(X24105,X24105),hAPP(hAPP(c_Power_Opower__class_Opower(X24105),hAPP(c_Int_Onumber__class_Onumber__of(X24105),X24103)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24104))),hAPP(hAPP(c_COMBS(X24105,X24105,X24105),hAPP(hAPP(c_COMBB(X24105,tc_fun(X24105,X24105),X24105),c_Groups_Otimes__class_Otimes(X24105)),hAPP(c_Groups_Otimes__class_Otimes(X24105),hAPP(c_Int_Onumber__class_Onumber__of(X24105),X24103)))),c_COMBI(X24105)))
        | ~ class_Int_Onumber__ring(X24105) )
      & ( 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),X24104)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(X24105),hAPP(c_Int_Onumber__class_Onumber__of(X24105),X24103)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X24104))) = c_Groups_Oone__class_Oone(X24105)
        | ~ class_Int_Onumber__ring(X24105) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5216])])]) ).

fof(i_0_5462,plain,
    ! [X17,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),X17)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => c_Nitpick_Onorm__frac(X6,X17) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X17)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ( ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | X17 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(X6,X17) = 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)
                  | X17 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(X6,X17) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X6),X17)),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),X17))) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_norm__frac_Opsimps]) ).

fof(i_0_5463,plain,
    ! [X31624,X31625,X31626,X31627,X31628,X31629] : c_List_Ofoldr(X31629,X31628,X31627,hAPP(hAPP(c_List_Oappend(X31629),X31626),X31625),X31624) = c_List_Ofoldr(X31629,X31628,X31627,X31626,c_List_Ofoldr(X31629,X31628,X31627,X31625,X31624)),
    inference(variable_rename,[status(thm)],[fact_foldr__append]) ).

fof(i_0_5464,plain,
    ! [X13,X12,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),X13)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X13))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),X13)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X13))
         => ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
             => 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)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X13)) )
            & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13)) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_psubset__insert__iff]) ).

fof(i_0_5465,plain,
    ! [X27,X34,X5] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X34))
     => ~ 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)),X27),X27)),c_List_Olexord(X5,X34))) ),
    inference(fof_simplification,[status(thm)],[fact_lexord__irreflexive]) ).

fof(i_0_5466,plain,
    ! [X24833,X24834] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X24834)),c_Int_OBit1(X24833)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(X24834)),X24833)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I8_J]) ).

fof(i_0_5467,plain,
    ! [X11,X6,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,hAPP(hAPP(c_Set_Oinsert(X5),X6),X11))
    <=> ( c_Fun_Oinj__on(X5,X16,X2,X11)
        & ~ hBOOL(hAPP(hAPP(c_member(X16),hAPP(X2,X6)),hAPP(c_Set_Oimage(X5,X16,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),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_5468,plain,
    ! [X27902,X27903] : c_Product__Type_Oapfst(X27903,X27903,X27902,c_Fun_Oid(X27903)) = c_Fun_Oid(tc_prod(X27903,X27902)),
    inference(variable_rename,[status(thm)],[fact_apfst__id]) ).

fof(i_0_5469,plain,
    ! [X27925,X27926] : c_Product__Type_Oapsnd(X27926,X27926,X27925,c_Fun_Oid(X27926)) = c_Fun_Oid(tc_prod(X27925,X27926)),
    inference(variable_rename,[status(thm)],[fact_apsnd__id]) ).

fof(i_0_5470,plain,
    ! [X28620,X28621] : c_Transitive__Closure_Otrancl(X28621,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28621,X28621),tc_HOL_Obool)),X28620),c_Relation_OId(X28621))) = c_Transitive__Closure_Ortrancl(X28621,X28620),
    inference(variable_rename,[status(thm)],[fact_trancl__reflcl]) ).

fof(i_0_5471,plain,
    ! [X13,X12,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),X13)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => 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)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X13)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_subset__insert__iff]) ).

fof(i_0_5472,plain,
    ! [X24753,X24754] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X24754),X24753) != c_Groups_Oone__class_Oone(X24754)
        | c_Int_Oiszero(X24754,hAPP(c_Int_Onumber__class_Onumber__of(X24754),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24753),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
        | ~ class_Int_Onumber__ring(X24754) )
      & ( ~ c_Int_Oiszero(X24754,hAPP(c_Int_Onumber__class_Onumber__of(X24754),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24753),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(X24754),X24753) = c_Groups_Oone__class_Oone(X24754)
        | ~ class_Int_Onumber__ring(X24754) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I4_J])])]) ).

fof(i_0_5473,plain,
    ! [X24755,X24756] :
      ( ( c_Groups_Oone__class_Oone(X24756) != hAPP(c_Int_Onumber__class_Onumber__of(X24756),X24755)
        | c_Int_Oiszero(X24756,hAPP(c_Int_Onumber__class_Onumber__of(X24756),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),X24755))))
        | ~ class_Int_Onumber__ring(X24756) )
      & ( ~ c_Int_Oiszero(X24756,hAPP(c_Int_Onumber__class_Onumber__of(X24756),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),X24755))))
        | c_Groups_Oone__class_Oone(X24756) = hAPP(c_Int_Onumber__class_Onumber__of(X24756),X24755)
        | ~ class_Int_Onumber__ring(X24756) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I2_J])])]) ).

fof(i_0_5474,plain,
    ! [X70,X20,X2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X20),X70))))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20),X70))
         => c_Smallcheck_Osmall_H(X2,X20,X70) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20),X70))
         => c_Smallcheck_Osmall_H(X2,X20,X70) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X2,X20,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X70),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X2,X70)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_small_H_Opsimps]) ).

fof(i_0_5475,plain,
    ! [X6,X17] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Nitpick_Onorm__frac(X6,X17) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X17)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              | X17 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
           => c_Nitpick_Onorm__frac(X6,X17) = 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)
                | X17 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
           => c_Nitpick_Onorm__frac(X6,X17) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X6),X17)),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),X17))) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_norm__frac_Osimps]) ).

fof(i_0_5476,plain,
    ! [X33099,X33100,X33101] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33101),esk464_3(X33099,X33100,X33101)),hAPP(c_List_Oset(X33101),c_List_OdropWhile(X33101,X33100,X33099))))
        | c_List_OtakeWhile(X33101,X33100,X33099) = hAPP(c_List_Ofilter(X33101,X33100),X33099) )
      & ( hBOOL(hAPP(X33100,esk464_3(X33099,X33100,X33101)))
        | c_List_OtakeWhile(X33101,X33100,X33099) = hAPP(c_List_Ofilter(X33101,X33100),X33099) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5217])])])]) ).

fof(i_0_5477,plain,
    ! [X28650,X28651,X28652,X28653,X28654] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28654,X28654)),hAPP(hAPP(c_Product__Type_OPair(X28654,X28654),X28653),X28652)),X28651))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28654,X28654)),hAPP(hAPP(c_Product__Type_OPair(X28654,X28654),X28652),X28650)),c_Transitive__Closure_Ortrancl(X28654,X28651)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28654,X28654)),hAPP(hAPP(c_Product__Type_OPair(X28654,X28654),X28653),X28650)),c_Transitive__Closure_Otrancl(X28654,X28651))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl2])]) ).

fof(i_0_5478,plain,
    ! [X28641,X28642,X28643,X28644,X28645] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28645,X28645)),hAPP(hAPP(c_Product__Type_OPair(X28645,X28645),X28644),X28643)),c_Transitive__Closure_Ortrancl(X28645,X28642)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28645,X28645)),hAPP(hAPP(c_Product__Type_OPair(X28645,X28645),X28643),X28641)),X28642))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28645,X28645)),hAPP(hAPP(c_Product__Type_OPair(X28645,X28645),X28644),X28641)),c_Transitive__Closure_Otrancl(X28645,X28642))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl1])]) ).

fof(i_0_5479,plain,
    ! [X24211,X24212,X24213] :
      ( ( ~ 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),X24212)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(X24213),X24211),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X24212))) = hAPP(hAPP(c_HOL_OLet(X24213,X24213),hAPP(hAPP(c_Power_Opower__class_Opower(X24213),X24211),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24212))),hAPP(hAPP(c_COMBS(X24213,X24213,X24213),hAPP(hAPP(c_COMBB(X24213,tc_fun(X24213,X24213),X24213),c_Groups_Otimes__class_Otimes(X24213)),hAPP(c_Groups_Otimes__class_Otimes(X24213),X24211))),c_COMBI(X24213)))
        | ~ class_Int_Onumber__ring(X24213) )
      & ( 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),X24212)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(X24213),X24211),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X24212))) = c_Groups_Oone__class_Oone(X24213)
        | ~ class_Int_Onumber__ring(X24213) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5218])])]) ).

fof(i_0_5480,plain,
    ! [X24901,X24902] :
      ( ~ class_Groups_Omonoid__mult(X24902)
      | ~ class_Int_Onumber(X24902)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X24902),hAPP(c_Int_Onumber__class_Onumber__of(X24902),X24901)),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(X24902),hAPP(c_Int_Onumber__class_Onumber__of(X24902),X24901)),hAPP(c_Int_Onumber__class_Onumber__of(X24902),X24901)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__square__number__of])]) ).

fof(i_0_5481,plain,
    ! [X28504,X28505,X28506,X28507,X28508] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28508,X28508)),hAPP(hAPP(c_Product__Type_OPair(X28508,X28508),X28507),X28506)),X28505))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28508,X28508)),hAPP(hAPP(c_Product__Type_OPair(X28508,X28508),X28506),X28504)),X28505))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28508,X28508)),hAPP(hAPP(c_Product__Type_OPair(X28508,X28508),X28507),X28504)),c_Transitive__Closure_Otrancl(X28508,X28505))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__r__into__trancl])]) ).

fof(i_0_5482,plain,
    ! [X34,X16,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Relation_ODomain(X5,X16),X34)))
     => ~ ! [X33] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X33)),X34)) ),
    inference(fof_simplification,[status(thm)],[fact_DomainE]) ).

fof(i_0_5483,plain,
    ! [X24877] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24877),X24877)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X24877,
    inference(variable_rename,[status(thm)],[fact_add__self__div__2]) ).

fof(i_0_5484,plain,
    ! [X24853,X24854] :
      ( ~ class_Int_Onumber__ring(X24854)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24854),X24853),hAPP(c_Int_Onumber__class_Onumber__of(X24854),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24854),X24853),X24853) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2__right])]) ).

fof(i_0_5485,plain,
    ! [X24861,X24862] :
      ( ~ class_Groups_Omonoid__mult(X24862)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X24862),X24861),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(X24862),X24861),X24861) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__square])]) ).

fof(i_0_5486,plain,
    ! [X24859,X24860] :
      ( ~ class_Rings_Ocomm__semiring__1(X24860)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24860),X24859),X24859) = hAPP(hAPP(c_Power_Opower__class_Opower(X24860),X24859),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_5487,plain,
    ! [X6,X21,X17,X13,X11,X38,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_fun(X38,tc_HOL_Obool))),X11),X13),X17),X21))
     => ( ~ hBOOL(hAPP(hAPP(hAPP(X13,X6),X17),X21))
       => ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11)) ) ),
    inference(fof_simplification,[status(thm)],[fact_INF2__E]) ).

fof(i_0_5488,plain,
    ! [X24869] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24869),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),X24869),X24869),
    inference(variable_rename,[status(thm)],[fact_nat__mult__2__right]) ).

fof(i_0_5489,plain,
    ! [X24863] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24863),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,X24863)),
    inference(variable_rename,[status(thm)],[fact_add__2__eq__Suc_H]) ).

fof(i_0_5490,plain,
    ! [X24858] :
      ( ~ class_Rings_Osemiring__1(X24858)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X24858),c_Groups_Ozero__class_Ozero(X24858)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X24858) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__power2])]) ).

fof(i_0_5491,plain,
    ! [X24865] :
      ( ~ class_Rings_Osemiring__1(X24865)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X24865),c_Groups_Oone__class_Oone(X24865)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X24865) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__power2])]) ).

fof(i_0_5492,plain,
    ! [X24214,X24215] :
      ( ( ~ 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),X24215)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X24214),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X24215))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X24214),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24215))),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),X24214))),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),X24215)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X24214),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X24215))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5219])]) ).

fof(i_0_5493,plain,
    ! [X28509,X28510,X28511,X28512] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28512,X28512)),X28511),c_Transitive__Closure_Otrancl(X28512,X28510)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28512,X28512),tc_HOL_Obool)),X28510),X28509))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28512,X28512)),X28511),c_Transitive__Closure_Otrancl(X28512,X28509))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__mono])]) ).

fof(i_0_5494,plain,
    ! [X22,X14,X15] :
      ( class_Rings_Olinordered__ring(X15)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X22),X22))),c_Groups_Ozero__class_Ozero(X15))) ),
    inference(fof_simplification,[status(thm)],[fact_not__sum__squares__lt__zero]) ).

fof(i_0_5495,plain,
    ! [X28474,X28475] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28475,X28475),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X28475,X28474)),hAPP(hAPP(c_Product__Type_OSigma(X28475,X28475),hAPP(c_Relation_OField(X28475),X28474)),hAPP(c_COMBK(tc_fun(X28475,tc_HOL_Obool),X28475),hAPP(c_Relation_OField(X28475),X28474))))),
    inference(variable_rename,[status(thm)],[fact_trancl__subset__Field2]) ).

fof(i_0_5496,plain,
    ! [X27,X12,X13,X11,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),X11),X13),X12),X27))
     => ( ~ hBOOL(hAPP(hAPP(X11,X12),X27))
       => hBOOL(hAPP(hAPP(X13,X12),X27)) ) ),
    inference(fof_simplification,[status(thm)],[fact_sup2E]) ).

fof(i_0_5497,plain,
    ! [X28655,X28656,X28657,X28658] :
      ( ( X28657 != X28656
        | X28657 = X28656
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28658,X28658)),hAPP(hAPP(c_Product__Type_OPair(X28658,X28658),X28657),X28656)),c_Transitive__Closure_Ortrancl(X28658,X28655))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28658,X28658)),hAPP(hAPP(c_Product__Type_OPair(X28658,X28658),X28657),X28656)),c_Transitive__Closure_Otrancl(X28658,X28655)))
        | X28657 = X28656
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28658,X28658)),hAPP(hAPP(c_Product__Type_OPair(X28658,X28658),X28657),X28656)),c_Transitive__Closure_Ortrancl(X28658,X28655))) )
      & ( X28657 != X28656
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28658,X28658)),hAPP(hAPP(c_Product__Type_OPair(X28658,X28658),X28657),X28656)),c_Transitive__Closure_Ortrancl(X28658,X28655))) )
      & ( X28657 = X28656
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28658,X28658)),hAPP(hAPP(c_Product__Type_OPair(X28658,X28658),X28657),X28656)),c_Transitive__Closure_Otrancl(X28658,X28655)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28658,X28658)),hAPP(hAPP(c_Product__Type_OPair(X28658,X28658),X28657),X28656)),c_Transitive__Closure_Ortrancl(X28658,X28655))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__eq__or__trancl])])]) ).

fof(i_0_5498,plain,
    ! [X28543,X28544,X28545,X28546] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28546,X28546)),hAPP(hAPP(c_Product__Type_OPair(X28546,X28546),X28545),X28544)),c_Transitive__Closure_Otrancl(X28546,X28543)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28546,X28546)),hAPP(hAPP(c_Product__Type_OPair(X28546,X28546),X28545),X28544)),c_Transitive__Closure_Ortrancl(X28546,X28543))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__into__rtrancl])]) ).

fof(i_0_5499,plain,
    ! [X27,X12,X13,X11,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),X11),X13),X12),X27))
     => ~ ( hBOOL(hAPP(hAPP(X11,X12),X27))
         => ~ hBOOL(hAPP(hAPP(X13,X12),X27)) ) ),
    inference(fof_simplification,[status(thm)],[fact_inf2E]) ).

fof(i_0_5500,plain,
    ! [X33699,X33700] :
      ( ( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X33700)),c_Int_OBit1(X33699)))
        | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X33700),X33699)) )
      & ( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X33700),X33699))
        | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X33700)),c_Int_OBit1(X33699))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__int__code_I16_J])]) ).

fof(i_0_5501,plain,
    ! [X24121,X24122] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X24122)),c_Int_OBit1(X24121)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24122),X24121)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24122),X24121))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X24122)),c_Int_OBit1(X24121))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I17_J])]) ).

fof(i_0_5502,plain,
    ! [X24119,X24120] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X24120)),c_Int_OBit1(X24119)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24120),X24119)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24120),X24119))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X24120)),c_Int_OBit1(X24119))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I16_J])]) ).

fof(i_0_5503,plain,
    ! [X24117,X24118] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X24118)),c_Int_OBit1(X24117)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24118),X24117)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24118),X24117))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X24118)),c_Int_OBit1(X24117))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I16_J])]) ).

fof(i_0_5504,plain,
    ! [X24115,X24116] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X24116)),c_Int_OBit1(X24115)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24116),X24115)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24116),X24115))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X24116)),c_Int_OBit1(X24115))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I34_J])]) ).

fof(i_0_5505,plain,
    ! [X33323,X33324,X33325] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X33325),X33324))
      | hBOOL(hAPP(c_List_Odistinct(X33325),hAPP(c_List_OremoveAll(X33325,X33323),X33324))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__removeAll])]) ).

fof(i_0_5506,plain,
    ! [X33301,X33302,X33303,X33304,X33305] :
      ( ~ c_Fun_Oinj__on(X33305,X33304,X33303,hAPP(hAPP(c_Set_Oinsert(X33305),X33302),hAPP(c_List_Oset(X33305),X33301)))
      | hAPP(hAPP(c_List_Omap(X33305,X33304),X33303),hAPP(c_List_OremoveAll(X33305,X33302),X33301)) = hAPP(c_List_OremoveAll(X33304,hAPP(X33303,X33302)),hAPP(hAPP(c_List_Omap(X33305,X33304),X33303),X33301)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__removeAll__inj__on])]) ).

fof(i_0_5507,plain,
    ! [X28694,X28695,X28696] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28696,X28696),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X28696,X28696),X28695)),c_Transitive__Closure_Ortrancl(X28696,X28695)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28696,X28696),tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28696,X28696)),hAPP(hAPP(c_Product__Type_OPair(X28696,X28696),X28694),X28694)),c_Transitive__Closure_Otrancl(X28696,X28695))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5220])]) ).

fof(i_0_5508,plain,
    ! [X33082,X33083,X33084,X33085,X33086] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X33086),X33085),hAPP(c_List_Oset(X33086),X33084)))
      | hBOOL(hAPP(X33083,X33085))
      | c_List_OdropWhile(X33086,X33083,hAPP(hAPP(c_List_Oappend(X33086),X33084),X33082)) = hAPP(hAPP(c_List_Oappend(X33086),c_List_OdropWhile(X33086,X33083,X33084)),X33082) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5221])]) ).

fof(i_0_5509,plain,
    ! [X33425,X33426,X33427,X33428] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33428),esk480_4(X33425,X33426,X33427,X33428)),hAPP(c_List_Oset(X33428),X33427)))
        | c_List_OdropWhile(X33428,X33426,hAPP(hAPP(c_List_Oappend(X33428),X33427),X33425)) = c_List_OdropWhile(X33428,X33426,X33425) )
      & ( ~ hBOOL(hAPP(X33426,esk480_4(X33425,X33426,X33427,X33428)))
        | c_List_OdropWhile(X33428,X33426,hAPP(hAPP(c_List_Oappend(X33428),X33427),X33425)) = c_List_OdropWhile(X33428,X33426,X33425) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dropWhile__append2])])])]) ).

fof(i_0_5510,plain,
    ! [X33348,X33349,X33350,X33351,X33352] :
      ( ~ c_Fun_Oinj__on(X33352,X33351,X33350,c_Orderings_Otop__class_Otop(tc_fun(X33352,tc_HOL_Obool)))
      | hAPP(hAPP(c_List_Omap(X33352,X33351),X33350),hAPP(c_List_OremoveAll(X33352,X33349),X33348)) = hAPP(c_List_OremoveAll(X33351,hAPP(X33350,X33349)),hAPP(hAPP(c_List_Omap(X33352,X33351),X33350),X33348)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__removeAll__inj])]) ).

fof(i_0_5511,plain,
    ! [X212,X29,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,X29,X212))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
     => ~ hBOOL(hAPP(X29,hAPP(hAPP(c_List_Onth(X5),X212),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X29,X212))))) ),
    inference(fof_simplification,[status(thm)],[fact_nth__length__takeWhile]) ).

fof(i_0_5512,plain,
    ! [X32227,X32228] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32228))),c_List_Otranspose(X32228,X32227)) = c_List_Ofoldr(tc_List_Olist(X32228),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X32228)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X32228))),X32227,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_length__transpose]) ).

fof(i_0_5513,plain,
    ! [X28937,X28938,X28939,X28941,X28942,X28943,X28944] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk335_3(X28937,X28938,X28939)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28939,X28939)),X28938),c_Transitive__Closure_Otrancl(X28939,X28937))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28939,X28939)),X28938),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28939,X28939),tc_HOL_Obool),esk335_3(X28937,X28938,X28939)),X28937)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28939,X28939)),X28938),c_Transitive__Closure_Otrancl(X28939,X28937))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28944))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28943,X28943)),X28942),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28943,X28943),tc_HOL_Obool),X28944),X28941)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28943,X28943)),X28942),c_Transitive__Closure_Otrancl(X28943,X28941))) ) ),
    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_5514,plain,
    ! [X32374,X32375,X32376] : c_List_Oconcat(X32376,hAPP(hAPP(c_List_Oappend(tc_List_Olist(X32376)),X32375),X32374)) = hAPP(hAPP(c_List_Oappend(X32376),c_List_Oconcat(X32376,X32375)),c_List_Oconcat(X32376,X32374)),
    inference(variable_rename,[status(thm)],[fact_concat__append]) ).

fof(i_0_5515,plain,
    ! [X70,X6,X212,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X212))
     => ( ~ 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),X212)),hAPP(hAPP(c_Set_Oinsert(X5),hAPP(hAPP(c_List_Onth(X5),X212),X70)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
       => hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Olist__update(X5,X212),X70),X6))) ) ),
    inference(fof_simplification,[status(thm)],[fact_distinct__list__update]) ).

fof(i_0_5516,plain,
    ! [X11,X2,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(c_Set_Oimage(X16,X5,X2),X11))),hAPP(c_Finite__Set_Ocard(X16),X11)))
     => ~ c_Fun_Oinj__on(X16,X5,X2,X11) ),
    inference(fof_simplification,[status(thm)],[fact_pigeonhole]) ).

fof(i_0_5517,plain,
    ! [X28646,X28647,X28648,X28649] :
      ( ( X28648 != X28647
        | X28648 = X28647
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28649,X28649)),hAPP(hAPP(c_Product__Type_OPair(X28649,X28649),X28648),X28647)),c_Transitive__Closure_Ortrancl(X28649,X28646))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28649,X28649)),hAPP(hAPP(c_Product__Type_OPair(X28649,X28649),X28648),X28647)),c_Transitive__Closure_Otrancl(X28649,X28646)))
        | X28648 = X28647
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28649,X28649)),hAPP(hAPP(c_Product__Type_OPair(X28649,X28649),X28648),X28647)),c_Transitive__Closure_Ortrancl(X28649,X28646))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtranclD])])]) ).

fof(i_0_5518,plain,
    ! [X29,X212,X5,X76] :
      ( ! [X145] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X145),X76))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X145),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
           => hBOOL(hAPP(X29,hAPP(hAPP(c_List_Onth(X5),X212),X145))) ) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)))
         => ~ hBOOL(hAPP(X29,hAPP(hAPP(c_List_Onth(X5),X212),X76))) )
       => c_List_OtakeWhile(X5,X29,X212) = hAPP(hAPP(c_List_Otake(X5),X76),X212) ) ),
    inference(fof_simplification,[status(thm)],[fact_takeWhile__eq__take__P__nth]) ).

fof(i_0_5519,plain,
    ! [X28470,X28471,X28472,X28473] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28473,X28473)),hAPP(hAPP(c_Product__Type_OPair(X28473,X28473),X28472),X28471)),X28470))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28473,X28473)),hAPP(hAPP(c_Product__Type_OPair(X28473,X28473),X28472),X28471)),c_Transitive__Closure_Otrancl(X28473,X28470))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl_Or__into__trancl])]) ).

fof(i_0_5520,plain,
    ! [X112,X21,X17,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),X17),X21)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
      <=> ( ( 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),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),X21))) )
          & ( ~ 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),X21),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),X112)),X21)),X17)) )
              & ( ~ 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),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__less__eq__number__of]) ).

fof(i_0_5521,plain,
    ! [X112,X21,X17,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),X17),X21)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X21))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),X21))) )
          & ( ~ 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),X21),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),X112)),X21)),X17)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),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),X112))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__le__eq__number__of]) ).

fof(i_0_5522,plain,
    ! [X21,X17,X112,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),X112)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X17),X21)))
      <=> ( ( 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),X21)),X17)) )
          & ( ~ 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),X21),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),X21))) )
              & ( ~ 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),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__divide__eq__number__of]) ).

fof(i_0_5523,plain,
    ! [X21,X17,X112,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),X112)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X17),X21)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X21))
           => 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),X112)),X21)),X17)) )
          & ( ~ 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),X21),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),X21))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__divide__eq__number__of]) ).

fof(i_0_5524,plain,
    ! [X33375,X33376] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33376)),esk476_2(X33375,X33376)),hAPP(c_List_Oset(tc_List_Olist(X33376)),X33375)))
        | hBOOL(hAPP(c_List_Odistinct(X33376),c_List_Oconcat(X33376,X33375)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33376)),esk475_2(X33375,X33376)),hAPP(c_List_Oset(tc_List_Olist(X33376)),X33375)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X33376)),X33375)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33376)),esk477_2(X33375,X33376)),hAPP(c_List_Oset(tc_List_Olist(X33376)),X33375)))
        | hBOOL(hAPP(c_List_Odistinct(X33376),c_List_Oconcat(X33376,X33375)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33376)),esk475_2(X33375,X33376)),hAPP(c_List_Oset(tc_List_Olist(X33376)),X33375)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X33376)),X33375)) )
      & ( esk476_2(X33375,X33376) != esk477_2(X33375,X33376)
        | hBOOL(hAPP(c_List_Odistinct(X33376),c_List_Oconcat(X33376,X33375)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33376)),esk475_2(X33375,X33376)),hAPP(c_List_Oset(tc_List_Olist(X33376)),X33375)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X33376)),X33375)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33376,tc_HOL_Obool)),hAPP(c_List_Oset(X33376),esk476_2(X33375,X33376))),hAPP(c_List_Oset(X33376),esk477_2(X33375,X33376))) != c_Orderings_Obot__class_Obot(tc_fun(X33376,tc_HOL_Obool))
        | hBOOL(hAPP(c_List_Odistinct(X33376),c_List_Oconcat(X33376,X33375)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33376)),esk475_2(X33375,X33376)),hAPP(c_List_Oset(tc_List_Olist(X33376)),X33375)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X33376)),X33375)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33376)),esk476_2(X33375,X33376)),hAPP(c_List_Oset(tc_List_Olist(X33376)),X33375)))
        | hBOOL(hAPP(c_List_Odistinct(X33376),c_List_Oconcat(X33376,X33375)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X33376),esk475_2(X33375,X33376)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X33376)),X33375)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33376)),esk477_2(X33375,X33376)),hAPP(c_List_Oset(tc_List_Olist(X33376)),X33375)))
        | hBOOL(hAPP(c_List_Odistinct(X33376),c_List_Oconcat(X33376,X33375)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X33376),esk475_2(X33375,X33376)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X33376)),X33375)) )
      & ( esk476_2(X33375,X33376) != esk477_2(X33375,X33376)
        | hBOOL(hAPP(c_List_Odistinct(X33376),c_List_Oconcat(X33376,X33375)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X33376),esk475_2(X33375,X33376)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X33376)),X33375)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33376,tc_HOL_Obool)),hAPP(c_List_Oset(X33376),esk476_2(X33375,X33376))),hAPP(c_List_Oset(X33376),esk477_2(X33375,X33376))) != c_Orderings_Obot__class_Obot(tc_fun(X33376,tc_HOL_Obool))
        | hBOOL(hAPP(c_List_Odistinct(X33376),c_List_Oconcat(X33376,X33375)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X33376),esk475_2(X33375,X33376)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X33376)),X33375)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__concat])])])]) ).

fof(i_0_5525,plain,
    ! [X5,X6,X29] :
      ( ( hBOOL(hAPP(X29,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))),X29)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(X29,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))),X29)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    inference(fof_simplification,[status(thm)],[fact_Collect__conv__if2]) ).

fof(i_0_5526,plain,
    ! [X31988,X31989,X31990] : hAPP(c_List_Orotate(X31990,X31989),X31988) = hAPP(hAPP(c_List_Oappend(X31990),hAPP(hAPP(c_List_Odrop(X31990),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X31989,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31990)),X31988))),X31988)),hAPP(hAPP(c_List_Otake(X31990),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X31989,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31990)),X31988))),X31988)),
    inference(variable_rename,[status(thm)],[fact_rotate__drop__take]) ).

fof(i_0_5527,plain,
    ! [X28464,X28465,X28466,X28467,X28468] :
      ( ( ~ c_Wellfounded_Oacyclic(X28465,X28464)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28465,X28465)),hAPP(hAPP(c_Product__Type_OPair(X28465,X28465),X28466),X28466)),c_Transitive__Closure_Otrancl(X28465,X28464))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28468,X28468)),hAPP(hAPP(c_Product__Type_OPair(X28468,X28468),esk326_2(X28467,X28468)),esk326_2(X28467,X28468))),c_Transitive__Closure_Otrancl(X28468,X28467)))
        | c_Wellfounded_Oacyclic(X28468,X28467) ) ),
    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_5222])])])])]) ).

fof(i_0_5528,plain,
    ! [X214,X212,X27,X12,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X12),X27)),hAPP(c_List_Oset(tc_prod(X5,X16)),hAPP(hAPP(c_List_Ozip(X5,X16),X212),X214))))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
         => ~ hBOOL(hAPP(hAPP(c_member(X16),X27),hAPP(c_List_Oset(X16),X214))) ) ),
    inference(fof_simplification,[status(thm)],[fact_in__set__zipE]) ).

fof(i_0_5529,plain,
    ! [X33329,X33330,X33331,X33332] :
      ( ( X33332 != X33331
        | hAPP(c_List_OremoveAll(X33330,X33332),hAPP(hAPP(c_List_Olist_OCons(X33330),X33331),X33329)) = hAPP(c_List_OremoveAll(X33330,X33332),X33329) )
      & ( X33332 = X33331
        | hAPP(c_List_OremoveAll(X33330,X33332),hAPP(hAPP(c_List_Olist_OCons(X33330),X33331),X33329)) = hAPP(hAPP(c_List_Olist_OCons(X33330),X33331),hAPP(c_List_OremoveAll(X33330,X33332),X33329)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_removeAll_Osimps_I2_J])]) ).

fof(i_0_5530,plain,
    ! [X198,X199,X200,X16,X45,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X45),c_Map_Odom(X5,X16,X200)))
     => c_Map_Omap__add(X5,X16,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),X199),X45),hAPP(c_Option_Ooption_OSome(X16),X198)),X200) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),c_Map_Omap__add(X5,X16,X199,X200)),X45),hAPP(c_Option_Ooption_OSome(X16),X198)) ),
    inference(fof_simplification,[status(thm)],[fact_map__add__upd__left]) ).

fof(i_0_5531,plain,
    ! [X34,X12,X27,X5] :
      ( c_Wellfounded_Oacyclic(X5,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X27),X12)),X34))
    <=> ( c_Wellfounded_Oacyclic(X5,X34)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_Transitive__Closure_Ortrancl(X5,X34))) ) ),
    inference(fof_simplification,[status(thm)],[fact_acyclic__insert]) ).

fof(i_0_5532,plain,
    ! [X34,X12,X27,X5] :
      ( c_Wellfounded_Owf(X5,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X27),X12)),X34))
    <=> ( c_Wellfounded_Owf(X5,X34)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_Transitive__Closure_Ortrancl(X5,X34))) ) ),
    inference(fof_simplification,[status(thm)],[fact_wf__insert]) ).

fof(i_0_5533,plain,
    ! [X28513,X28514] : c_Transitive__Closure_Otrancl(X28514,X28513) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28514,X28514),tc_HOL_Obool)),X28513),hAPP(hAPP(c_Relation_Orel__comp(X28514,X28514,X28514),c_Transitive__Closure_Otrancl(X28514,X28513)),X28513)),
    inference(variable_rename,[status(thm)],[fact_trancl__unfold]) ).

fof(i_0_5534,plain,
    ! [X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
    <=> ! [X196] :
          ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),X196))
         => ? [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X196))
              & ! [X33] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X3)),X34))
                 => ~ hBOOL(hAPP(hAPP(c_member(X5),X33),X196)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_wf__eq__minimal]) ).

fof(i_0_5535,plain,
    ! [X24802,X24803] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X24803)),c_Int_OBit0(X24802)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24803),X24802)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24803),X24802))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X24803)),c_Int_OBit0(X24802))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I15_J])]) ).

fof(i_0_5536,plain,
    ! [X24800,X24801] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X24801)),c_Int_OBit0(X24800)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24801),X24800)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24801),X24800))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X24801)),c_Int_OBit0(X24800))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I16_J])]) ).

fof(i_0_5537,plain,
    ! [X24825,X24826] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X24826)),c_Int_OBit0(X24825)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24826),X24825)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24826),X24825))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X24826)),c_Int_OBit0(X24825))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I33_J])]) ).

fof(i_0_5538,plain,
    ! [X24823,X24824] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X24824)),c_Int_OBit0(X24823)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24824),X24823)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24824),X24823))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X24824)),c_Int_OBit0(X24823))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I15_J])]) ).

fof(i_0_5539,plain,
    ! [X45,X16,X18,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X18))
       => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),c_Map_Orestrict__map(X5,X16,X45,X18)),X12),c_Option_Ooption_ONone(X16)) = c_Map_Orestrict__map(X5,X16,X45,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X18),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X18))
       => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),c_Map_Orestrict__map(X5,X16,X45,X18)),X12),c_Option_Ooption_ONone(X16)) = c_Map_Orestrict__map(X5,X16,X45,X18) ) ),
    inference(fof_simplification,[status(thm)],[fact_fun__upd__None__restrict]) ).

fof(i_0_5540,plain,
    ! [X27198,X27199] : c_Nitpick_Oint__lcm(X27199,X27198) = 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),X27199)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X27198)))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Oint__lcm__def]) ).

fof(i_0_5541,plain,
    ! [X27196,X27197] : c_Nitpick_Onat__lcm(X27197,X27196) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27197),X27196)),c_Nitpick_Onat__gcd(X27197,X27196)),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Onat__lcm__def]) ).

fof(i_0_5542,plain,
    ! [X30288,X30289,X30290,X30291,X30292,X30293] : c_List_Ofoldr(X30293,X30292,X30291,hAPP(hAPP(c_List_Olist_OCons(X30293),X30290),X30289),X30288) = hAPP(hAPP(X30291,X30290),c_List_Ofoldr(X30293,X30292,X30291,X30289,X30288)),
    inference(variable_rename,[status(thm)],[fact_foldr_Osimps_I2_J]) ).

fof(i_0_5543,plain,
    ! [X12,X6,X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X12)),X34))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X6)),X34)) ) ),
    inference(fof_simplification,[status(thm)],[fact_wf__not__sym]) ).

fof(i_0_5544,plain,
    ! [X12,X6,X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X12)),X34))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X6)),X34)) ) ),
    inference(fof_simplification,[status(thm)],[fact_wf__asym]) ).

fof(i_0_5545,plain,
    ! [X162,X76,X45] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X45,X76),X162))
    <=> ( X45 = 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),X162)),X76)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X162))
        & ( X76 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X162) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( X76 != 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)),X76))
             => ( 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),X162)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X162)),X76)) ) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X76))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X162)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X162)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divmod__nat__rel__def]) ).

fof(i_0_5546,plain,
    ! [X6,X112,X17,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),X17),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112))),X6))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),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),X112))),X17)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),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_5547,plain,
    ! [X6,X112,X17,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),X17),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112))),X6))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),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),X112))),X17)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),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_5548,plain,
    ! [X24632] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(X24632)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24632))),
    inference(variable_rename,[status(thm)],[fact_minus__Bit1]) ).

fof(i_0_5549,plain,
    ! [X33705,X33706] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X33706)),c_Int_OBit0(X33705))),
    inference(variable_rename,[status(thm)],[i_0_5223]) ).

fof(i_0_5550,plain,
    ! [X29,X47,X158] :
      ( 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),X158),X47)))
     => ( ! [X125,X145] :
            ( 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),X125),X145)))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X125),X145))
               => hBOOL(hAPP(hAPP(X29,X125),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X145),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
             => hBOOL(hAPP(hAPP(X29,X125),X145)) ) )
       => hBOOL(hAPP(hAPP(X29,X158),X47)) ) ),
    inference(fof_simplification,[status(thm)],[fact_small__lazy_H_Opinduct]) ).

fof(i_0_5551,plain,
    ! [X28460,X28461] :
      ( ( ~ 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),X28461),X28460)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28461),X28460)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28461),X28460))
        | 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),X28461),X28460)),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_5552,plain,
    ! [X34,X11,X31,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X31),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X11),X34)))
     => ~ ! [X3] :
            ( X31 = hAPP(c_Relation_OImage(X5,X5,X34),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),X11)) ) ),
    inference(fof_simplification,[status(thm)],[fact_quotientE]) ).

fof(i_0_5553,plain,
    ! [X23764,X23765] :
      ( ( X23765 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Divides_Odivmod__nat(X23764,X23765) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23764) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23764),X23765))
        | c_Divides_Odivmod__nat(X23764,X23765) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23764) )
      & ( X23765 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23764),X23765))
        | c_Divides_Odivmod__nat(X23764,X23765) = 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),X23764),X23765),X23765)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__if])])]) ).

fof(i_0_5554,plain,
    ! [X23726,X23727] : c_Divides_Odivmod__nat(X23727,X23726) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X23727,X23726)),
    inference(variable_rename,[status(thm)],[fact_divmod__nat__def]) ).

fof(i_0_5555,plain,
    ! [X24186] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X24186)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24186),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24186),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X24186)),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_5556,plain,
    ! [X249,X250,X251,X252,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X252),X251) = hAPP(hAPP(c_List_Oappend(X5),X250),X249)
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X252)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X250)))
         => ( X252 = hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X252)),X250)
            & X251 = hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X252)),X250)),X249) ) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X252)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X250)))
         => ( hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X250)),X252) = X250
            & hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X250)),X252)),X251) = X249 ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_append__eq__append__conv__if]) ).

fof(i_0_5557,plain,
    ! [X33715] :
      ( ( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X33715)),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X33715),c_Int_OMin)) )
      & ( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X33715),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X33715)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__int__code_I12_J])]) ).

fof(i_0_5558,plain,
    ! [X25003] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X25003)),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25003),c_Int_OMin)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25003),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X25003)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I13_J])]) ).

fof(i_0_5559,plain,
    ! [X24627] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X24627)),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24627),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24627),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X24627)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I12_J])]) ).

fof(i_0_5560,plain,
    ! [X24645] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X24645)),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24645),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24645),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X24645)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I29_J])]) ).

fof(i_0_5561,plain,
    ! [X25000] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X25000)),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25000),c_Int_OMin)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25000),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X25000)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I30_J])]) ).

fof(i_0_5562,plain,
    ! [X24512] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X24512))))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24512))) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24512)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X24512)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit1])]) ).

fof(i_0_5563,plain,
    ! [X11,X2,X16,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(c_Set_Oimage(X16,X5,X2),X11)))
     => ~ ! [X3] :
            ( X17 = hAPP(X2,X3)
           => ~ hBOOL(hAPP(hAPP(c_member(X16),X3),X11)) ) ),
    inference(fof_simplification,[status(thm)],[fact_imageE]) ).

fof(i_0_5564,plain,
    ! [X32494,X32495] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32495)),c_List_Oremdups(X32495,c_List_Oconcat(X32495,X32494))) = hAPP(c_Finite__Set_Ocard(X32495),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X32495),tc_fun(X32495,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X32495)),X32494)),c_List_Oset(X32495))),
    inference(variable_rename,[status(thm)],[fact_length__remdups__concat]) ).

fof(i_0_5565,plain,
    ! [X33711] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X33711)),c_Int_OPls)),
    inference(variable_rename,[status(thm)],[i_0_5224]) ).

fof(i_0_5566,plain,
    ! [X24675,X24676] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24676),c_Groups_Oone__class_Oone(X24676)),hAPP(c_Int_Onumber__class_Onumber__of(X24676),X24675)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X24675))
        | ~ class_Int_Onumber__ring(X24676)
        | ~ class_Rings_Olinordered__idom(X24676) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X24675))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24676),c_Groups_Oone__class_Oone(X24676)),hAPP(c_Int_Onumber__class_Onumber__of(X24676),X24675)))
        | ~ class_Int_Onumber__ring(X24676)
        | ~ class_Rings_Olinordered__idom(X24676) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I2_J])])]) ).

fof(i_0_5567,plain,
    ! [X24671,X24672] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24672),c_Groups_Oone__class_Oone(X24672)),hAPP(c_Int_Onumber__class_Onumber__of(X24672),X24671)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X24671))
        | ~ class_Int_Onumber__ring(X24672)
        | ~ class_Rings_Olinordered__idom(X24672) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X24671))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24672),c_Groups_Oone__class_Oone(X24672)),hAPP(c_Int_Onumber__class_Onumber__of(X24672),X24671)))
        | ~ class_Int_Onumber__ring(X24672)
        | ~ class_Rings_Olinordered__idom(X24672) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I2_J])])]) ).

fof(i_0_5568,plain,
    ! [X112,X17,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),X17),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112))))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
           => 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),X112))),X17)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),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_5569,plain,
    ! [X112,X17,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),X17),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112))))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
           => 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),X112))),X17)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),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_5570,plain,
    ! [X16,X5,X11,X27,X12,X13] :
      ( ( ~ hBOOL(hAPP(hAPP(X13,X12),X27))
       => hBOOL(hAPP(hAPP(X11,X12),X27)) )
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),X11),X13),X12),X27)) ),
    inference(fof_simplification,[status(thm)],[fact_sup2CI]) ).

fof(i_0_5571,plain,
    ! [X36,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),c_Wellfounded_Oacc(X5,X36)))
     => ~ ! [X44] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X44),X12)),X36))
           => hBOOL(hAPP(hAPP(c_member(X5),X44),c_Wellfounded_Oacc(X5,X36))) ) ),
    inference(fof_simplification,[status(thm)],[fact_not__acc__down]) ).

fof(i_0_5572,plain,
    ! [X17,X11,X5] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X17),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(X5,X17,X11) = X17 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X17),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(X5,X17,X11) = 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)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X17),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ),
    inference(fof_simplification,[status(thm)],[fact_flat__lub__def]) ).

fof(i_0_5573,plain,
    ! [X24941,X24942] :
      ( ( ~ 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),X24942)))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X24941))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X24942))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24941)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24942)) )
      & ( 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),X24942)))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X24941))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X24942))) = 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),X24941)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24942)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5225])]) ).

fof(i_0_5574,plain,
    ! [X28827,X28828] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28828,X28828)),hAPP(hAPP(c_Product__Type_OPair(X28828,X28828),esk330_2(X28827,X28828)),esk330_2(X28827,X28828))),c_Transitive__Closure_Otrancl(X28828,X28827)))
      | c_Wellfounded_Oacyclic(X28828,X28827) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5226])])]) ).

fof(i_0_5575,plain,
    ! [X34,X212,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)),X212)),c_List_Olistrel1(X5,X34))),
    inference(fof_simplification,[status(thm)],[fact_not__Nil__listrel1]) ).

fof(i_0_5576,plain,
    ! [X34,X214,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)),X214)),c_List_Olex(X5,X34))),
    inference(fof_simplification,[status(thm)],[fact_Nil__notin__lex]) ).

fof(i_0_5577,plain,
    ! [X33779,X33780,X33781,X33782,X33783] :
      ( ( X33783 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_New__DSequence_Oneg__decr__bind(X33782,X33781,X33780,X33779),X33783) = c_Lazy__Sequence_Ohit__bound(X33781) )
      & ( X33783 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_New__DSequence_Oneg__decr__bind(X33782,X33781,X33780,X33779),X33783) = c_Lazy__Sequence_Ohb__bind(X33782,X33781,hAPP(X33780,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X33783),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X33782,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X33781))),X33779),X33783)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_New__DSequence_Oneg__decr__bind__def])]) ).

fof(i_0_5578,plain,
    ! [X33863,X33864,X33865,X33866] : c_Lazy__Sequence_Ohb__bind(X33866,X33865,X33864,X33863) = c_Lazy__Sequence_Ohb__flat(X33865,c_Lazy__Sequence_Ohb__map(X33866,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X33865)),X33863,X33864)),
    inference(variable_rename,[status(thm)],[fact_hb__bind__def]) ).

fof(i_0_5579,plain,
    ! [X27,X2,X16,X11,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hAPP(c_Set_Oimage(X5,X16,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),X2),X12),X27)),X11) = hAPP(hAPP(c_Set_Oinsert(X16),X27),hAPP(c_Set_Oimage(X5,X16,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hAPP(c_Set_Oimage(X5,X16,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),X2),X12),X27)),X11) = hAPP(c_Set_Oimage(X5,X16,X2),X11) ) ),
    inference(fof_simplification,[status(thm)],[fact_fun__upd__image]) ).

fof(i_0_5580,plain,
    ! [X34,X212,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)),X212),c_List_Olist_ONil(X5))),c_List_Olistrel1(X5,X34))),
    inference(fof_simplification,[status(thm)],[fact_not__listrel1__Nil]) ).

fof(i_0_5581,plain,
    ! [X34,X12,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)),X12),c_List_Olist_ONil(X5))),c_List_Olexord(X5,X34))),
    inference(fof_simplification,[status(thm)],[fact_lexord__Nil__right]) ).

fof(i_0_5582,plain,
    ! [X34,X212,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)),X212),c_List_Olist_ONil(X5))),c_List_Olex(X5,X34))),
    inference(fof_simplification,[status(thm)],[fact_Nil2__notin__lex]) ).

fof(i_0_5583,plain,
    ! [X32038,X32039,X32040] :
      ( ~ class_Groups_Omonoid__add(X32040)
      | hAPP(c_List_Ofoldl(X32040,X32040,c_Groups_Oplus__class_Oplus(X32040),X32039),X32038) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X32040),X32039),c_List_Ofoldr(X32040,X32040,c_Groups_Oplus__class_Oplus(X32040),X32038,c_Groups_Ozero__class_Ozero(X32040))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__foldr1__lemma])]) ).

fof(i_0_5584,plain,
    ! [X28628,X28629,X28630] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28630,X28630)),hAPP(hAPP(c_Product__Type_OPair(X28630,X28630),X28629),X28628)),c_Relation_OId(X28630)))
        | X28629 = X28628 )
      & ( X28629 != X28628
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28630,X28630)),hAPP(hAPP(c_Product__Type_OPair(X28630,X28630),X28629),X28628)),c_Relation_OId(X28630))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__in__Id__conv])]) ).

fof(i_0_5585,plain,
    ! [X29,X90,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X90))
     => ( hBOOL(hAPP(X29,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
       => ( ! [X3,X106] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X106))
             => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X106))
               => ( hBOOL(hAPP(X29,X106))
                 => hBOOL(hAPP(X29,hAPP(hAPP(c_Set_Oinsert(X5),X3),X106))) ) ) )
         => hBOOL(hAPP(X29,X90)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_finite__induct]) ).

fof(i_0_5586,plain,
    ! [X24855] :
      ( ~ class_Int_Onumber__ring(X24855)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24855),c_Groups_Oone__class_Oone(X24855)),c_Groups_Oone__class_Oone(X24855)) = hAPP(c_Int_Onumber__class_Onumber__of(X24855),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_5587,plain,
    ! [X214,X2,X16,X212,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => hAPP(c_Map_Omap__upds(X5,X16,X2,X212,X214),X12) = hAPP(X2,X12) ),
    inference(fof_simplification,[status(thm)],[fact_map__upds__apply__nontin]) ).

fof(i_0_5588,plain,
    ! [X12,X210,X5,X16] :
      ( hAPP(hAPP(c_Map_Omap__of(X16,X5),X210),X12) = c_Option_Ooption_ONone(X5)
    <=> ~ hBOOL(hAPP(hAPP(c_member(X16),X12),hAPP(c_Set_Oimage(tc_prod(X16,X5),X16,c_Product__Type_Ofst(X16,X5)),hAPP(c_List_Oset(tc_prod(X16,X5)),X210)))) ),
    inference(fof_simplification,[status(thm)],[fact_map__of__eq__None__iff]) ).

fof(i_0_5589,plain,
    ! [X33353,X33354,X33355] : hAPP(c_List_Oset(X33355),hAPP(c_List_OremoveAll(X33355,X33354),X33353)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X33355,tc_HOL_Obool)),hAPP(c_List_Oset(X33355),X33353)),hAPP(hAPP(c_Set_Oinsert(X33355),X33354),c_Orderings_Obot__class_Obot(tc_fun(X33355,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_set__removeAll]) ).

fof(i_0_5590,plain,
    ! [X1,X2,X16,X11,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => hAPP(c_Fun_Ooverride__on(X5,X16,X2,X1,X11),X6) = hAPP(X1,X6) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => hAPP(c_Fun_Ooverride__on(X5,X16,X2,X1,X11),X6) = hAPP(X2,X6) ) ),
    inference(fof_simplification,[status(thm)],[fact_override__on__def]) ).

fof(i_0_5591,plain,
    ! [X23705,X23706] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23706))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23706),X23705))
      | c_Divides_Odivmod__nat(X23705,X23706) = 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),X23705),X23706)),X23706))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23705),X23706),X23706)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__step])]) ).

fof(i_0_5592,plain,
    ! [X32871,X32872,X32873,X32874,X32875] : hAPP(c_List_Ofoldl(X32875,X32874,X32873,X32872),X32871) = c_List_Ofoldr(X32874,X32875,hAPP(c_COMBC(X32875,X32874,X32875),X32873),hAPP(c_List_Orev(X32874),X32871),X32872),
    inference(variable_rename,[status(thm)],[fact_foldl__foldr]) ).

fof(i_0_5593,plain,
    ! [X1,X2,X16,X11,X6,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
     => hAPP(c_Fun_Ooverride__on(X5,X16,X2,X1,X11),X6) = hAPP(X2,X6) ),
    inference(fof_simplification,[status(thm)],[fact_override__on__apply__notin]) ).

fof(i_0_5594,plain,
    ! [X33063,X33064,X33065] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X33065),X33064))
      | hBOOL(hAPP(c_List_Odistinct(X33065),c_List_OdropWhile(X33065,X33063,X33064))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__dropWhile])]) ).

fof(i_0_5595,plain,
    ! [X1,X11,X90,X37,X2,X16,X5] :
      ( c_Big__Operators_Ocomm__monoid__big(X5,X16,X2,X37,X90)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11))
         => hAPP(hAPP(X90,X1),X11) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X16,X2),X1),X37),X11) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11))
         => hAPP(hAPP(X90,X1),X11) = X37 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_comm__monoid__big_OF__eq]) ).

fof(i_0_5596,plain,
    ! [X22768,X22769,X22770,X22771] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22771,X22771)),hAPP(hAPP(c_Product__Type_OPair(X22771,X22771),X22770),X22769)),hAPP(c_Wellfounded_Omeasure(X22771),X22768)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X22768,X22770)),hAPP(X22768,X22769))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X22768,X22770)),hAPP(X22768,X22769)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X22771,X22771)),hAPP(hAPP(c_Product__Type_OPair(X22771,X22771),X22770),X22769)),hAPP(c_Wellfounded_Omeasure(X22771),X22768))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measure])]) ).

fof(i_0_5597,plain,
    ! [X25667] : c_Wellfounded_Omeasure(X25667) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X25667),c_Wellfounded_Oless__than),
    inference(variable_rename,[status(thm)],[fact_measure__def]) ).

fof(i_0_5598,plain,
    ! [X33799,X33800,X33801,X33802,X33803] : hAPP(c_New__DSequence_Oneg__bind(X33803,X33802,X33801,X33800),X33799) = c_Lazy__Sequence_Ohb__bind(X33803,X33802,hAPP(X33801,X33799),hAPP(hAPP(c_COMBC(X33803,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X33802))),X33800),X33799)),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Oneg__bind__def]) ).

fof(i_0_5599,plain,
    ! [X13,X11,X17,X6,X16,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X16)),hAPP(hAPP(c_Product__Type_OPair(X5,X16),X6),X17)),hAPP(hAPP(c_Product__Type_OSigma(X5,X16),X11),X13)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => ~ hBOOL(hAPP(hAPP(c_member(X16),X17),hAPP(X13,X6))) ) ),
    inference(fof_simplification,[status(thm)],[fact_SigmaE2]) ).

fof(i_0_5600,plain,
    ! [X32328,X32329,X32330,X32331] : hAPP(hAPP(c_List_Omap(X32331,X32330),X32329),c_List_Oconcat(X32331,X32328)) = c_List_Oconcat(X32330,hAPP(hAPP(c_List_Omap(tc_List_Olist(X32331),tc_List_Olist(X32330)),hAPP(c_List_Omap(X32331,X32330),X32329)),X32328)),
    inference(variable_rename,[status(thm)],[fact_map__concat]) ).

fof(i_0_5601,plain,
    ! [X24804,X24805] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X24805)),c_Int_OBit0(X24804)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24805),X24804)),
    inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit0]) ).

fof(i_0_5602,plain,
    ! [X24811,X24812] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X24812)),c_Int_OBit0(X24811)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24812),X24811)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I9_J]) ).

fof(i_0_5603,plain,
    ! [X212,X16,X12,X2,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X12)),hAPP(c_Set_Oimage(X16,X5,X2),hAPP(c_List_Oset(X16),X212))))
       => c_List_Olinorder__class_Oinsort__insert__key(X16,X5,X2,X12,X212) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X16,X5,X2),X12),X212) ) ),
    inference(fof_simplification,[status(thm)],[fact_insort__insert__insort__key]) ).

fof(i_0_5604,plain,
    ! [X28703,X28704,X28705] :
      ( ( ~ c_Relation_Ototal__on(X28705,X28704,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X28705,X28705),tc_HOL_Obool)),X28703),c_Relation_OId(X28705)))
        | c_Relation_Ototal__on(X28705,X28704,X28703) )
      & ( ~ c_Relation_Ototal__on(X28705,X28704,X28703)
        | c_Relation_Ototal__on(X28705,X28704,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X28705,X28705),tc_HOL_Obool)),X28703),c_Relation_OId(X28705))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__diff__Id])]) ).

fof(i_0_5605,plain,
    ! [X24683,X24684] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X24684))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24683)),X24684) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24683),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24684),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_5606,plain,
    ! [X24831,X24832] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X24832)),X24831) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24832),X24831))),X24831),
    inference(variable_rename,[status(thm)],[fact_mult__Bit1]) ).

fof(i_0_5607,plain,
    ! [X24847] :
      ( ( 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(X24847))))
        | ~ 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),X24847))) )
      & ( 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(X24847))))
        | ~ 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),X24847))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of1])])]) ).

fof(i_0_5608,plain,
    ! [X24835,X24836] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X24836)),c_Int_OBit1(X24835)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24836),c_Int_Osucc(X24835))),
    inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit1]) ).

fof(i_0_5609,plain,
    ! [X24829,X24830] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X24830)),c_Int_OBit1(X24829)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24830),X24829)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24830),X24829))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X24830)),c_Int_OBit1(X24829))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I15_J])]) ).

fof(i_0_5610,plain,
    ! [X24827,X24828] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X24828)),c_Int_OBit1(X24827)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24828),X24827)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24828),X24827))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X24828)),c_Int_OBit1(X24827))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I14_J])]) ).

fof(i_0_5611,plain,
    ! [X24796,X24797] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X24797)),c_Int_OBit1(X24796)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24797),X24796)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24797),X24796))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X24797)),c_Int_OBit1(X24796))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I32_J])]) ).

fof(i_0_5612,plain,
    ! [X24794,X24795] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X24795)),c_Int_OBit1(X24794)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24795),X24794)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24795),X24794))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X24795)),c_Int_OBit1(X24794))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I14_J])]) ).

fof(i_0_5613,plain,
    ! [X33059,X33060,X33061,X33062] :
      ( ( ~ hBOOL(hAPP(X33062,X33061))
        | c_List_OdropWhile(X33060,X33062,hAPP(hAPP(c_List_Olist_OCons(X33060),X33061),X33059)) = c_List_OdropWhile(X33060,X33062,X33059) )
      & ( hBOOL(hAPP(X33062,X33061))
        | c_List_OdropWhile(X33060,X33062,hAPP(hAPP(c_List_Olist_OCons(X33060),X33061),X33059)) = hAPP(hAPP(c_List_Olist_OCons(X33060),X33061),X33059) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5227])]) ).

fof(i_0_5614,plain,
    ! [X24508] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24508)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X24508)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24508)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X24508)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24508)),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_5228])]) ).

fof(i_0_5615,plain,
    ! [X28487,X28488] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28488,X28488)),c_Transitive__Closure_Otrancl(X28488,X28487)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28488,X28488)),X28487)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28488,X28488)),X28487))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28488,X28488)),c_Transitive__Closure_Otrancl(X28488,X28487))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__trancl])]) ).

fof(i_0_5616,plain,
    ! [X33707,X33708] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X33708)),c_Int_OBit1(X33707))),
    inference(variable_rename,[status(thm)],[i_0_5229]) ).

fof(i_0_5617,plain,
    ! [X13,X6,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X13))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13))) = 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)),X11),X13))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__Diff__insert]) ).

fof(i_0_5618,plain,
    ! [X32913,X32914] : hAPP(c_List_Orev(X32914),c_List_Oconcat(X32914,X32913)) = c_List_Oconcat(X32914,hAPP(hAPP(c_List_Omap(tc_List_Olist(X32914),tc_List_Olist(X32914)),c_List_Orev(X32914)),hAPP(c_List_Orev(tc_List_Olist(X32914)),X32913))),
    inference(variable_rename,[status(thm)],[fact_rev__concat]) ).

fof(i_0_5619,plain,
    ! [X37,X1,X6,X11,X5,X16] :
      ( class_Groups_Oab__semigroup__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X1),X37),hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(X1,X6)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X1),X37),X11)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold__image__insert]) ).

fof(i_0_5620,plain,
    ! [X32356,X32357,X32358] : hAPP(c_List_Ofilter(X32358,X32357),c_List_Oconcat(X32358,X32356)) = c_List_Oconcat(X32358,hAPP(hAPP(c_List_Omap(tc_List_Olist(X32358),tc_List_Olist(X32358)),c_List_Ofilter(X32358,X32357)),X32356)),
    inference(variable_rename,[status(thm)],[fact_filter__concat]) ).

fof(i_0_5621,plain,
    ! [X27,X12,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),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_5622,plain,
    ! [X6,X21,X17,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),X17),X21)),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),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21))) )
          & ( ~ 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),X21),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21)),X17)) )
              & ( ~ 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),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__less__eq]) ).

fof(i_0_5623,plain,
    ! [X6,X21,X17,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),X17),X21)),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__eq(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21))) )
          & ( ~ 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),X21),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),X21)),X17)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),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_5624,plain,
    ! [X31941,X31942,X31943] :
      ( ( ~ hBOOL(hAPP(c_List_Odistinct(X31943),hAPP(c_List_Orotate(X31943,X31942),X31941)))
        | hBOOL(hAPP(c_List_Odistinct(X31943),X31941)) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X31943),X31941))
        | hBOOL(hAPP(c_List_Odistinct(X31943),hAPP(c_List_Orotate(X31943,X31942),X31941))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__rotate])]) ).

fof(i_0_5625,plain,
    ! [X27,X36,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_Relation_ODomain(X5,X5),X36)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X27)),c_Transitive__Closure_Ortrancl(X5,X36)))
      <=> X12 = X27 ) ),
    inference(fof_simplification,[status(thm)],[fact_Not__Domain__rtrancl]) ).

fof(i_0_5626,plain,
    ! [X24806,X24807] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X24807)),c_Int_OBit1(X24806)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24807),X24806)),
    inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit1]) ).

fof(i_0_5627,plain,
    ! [X1,X11,X90,X37,X2,X16,X5] :
      ( c_Big__Operators_Ocomm__monoid__big(X5,X16,X2,X37,X90)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X11))
       => hAPP(hAPP(X90,X1),X11) = X37 ) ),
    inference(fof_simplification,[status(thm)],[fact_comm__monoid__big_Oinfinite]) ).

fof(i_0_5628,plain,
    ! [X24705,X24706] :
      ( ~ class_Int_Onumber__ring(X24706)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24706),hAPP(c_Int_Onumber__class_Onumber__of(X24706),X24705)),c_Groups_Oone__class_Oone(X24706)) = hAPP(c_Int_Onumber__class_Onumber__of(X24706),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24705),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_5629,plain,
    ! [X212,X12,X2,X5,X16] :
      ( class_Orderings_Olinorder(X16)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X16,X2),X12),X212)))
      <=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
          & hBOOL(hAPP(c_List_Odistinct(X5),X212)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_distinct__insort]) ).

fof(i_0_5630,plain,
    ! [X24707,X24708] :
      ( ~ class_Int_Onumber__ring(X24708)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24708),c_Groups_Oone__class_Oone(X24708)),hAPP(c_Int_Onumber__class_Onumber__of(X24708),X24707)) = hAPP(c_Int_Onumber__class_Onumber__of(X24708),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),X24707))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__special_I1_J])]) ).

fof(i_0_5631,plain,
    ! [X28479,X28480,X28481] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28481,X28481)),X28480),X28479))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28481,X28481)),X28480),c_Transitive__Closure_Otrancl(X28481,X28479))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__trancl_H])]) ).

fof(i_0_5632,plain,
    ! [X32341,X32342,X32343] : c_List_Oconcat(X32343,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X32343)),X32342),X32341)) = hAPP(hAPP(c_List_Oappend(X32343),X32342),c_List_Oconcat(X32343,X32341)),
    inference(variable_rename,[status(thm)],[fact_concat_Osimps_I2_J]) ).

fof(i_0_5633,plain,
    ! [X24679,X24680] :
      ( ~ class_Int_Onumber__ring(X24680)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24680),c_Groups_Oone__class_Oone(X24680)),hAPP(c_Int_Onumber__class_Onumber__of(X24680),X24679)) = hAPP(c_Int_Onumber__class_Onumber__of(X24680),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X24679)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I2_J])]) ).

fof(i_0_5634,plain,
    ! [X20,X21,X17,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,X17)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X21,X20)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X17))
            | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),X6))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),X20))
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X21),X6))
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),X20)) ) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),X20)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastatMost__psubset__iff]) ).

fof(i_0_5635,plain,
    ! [X32456,X32457] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32457)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32456)))
        | c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32457),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32456)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32457)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32457)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32456))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32457)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32456)))
        | c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32457),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32456)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5230])]) ).

fof(i_0_5636,plain,
    ! [X90,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X12),X90))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X12),X90)))
           => ! [X39] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X39),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X12),X90)))
               => ( X3 != X39
                 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X3),X39) = 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)),X12),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X90)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    inference(fof_simplification,[status(thm)],[fact_insert__partition]) ).

fof(i_0_5637,plain,
    ! [X28622,X28623] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28623,X28623),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X28623,X28622)),c_Relation_OId(X28623)) = c_Transitive__Closure_Ortrancl(X28623,X28622),
    inference(variable_rename,[status(thm)],[fact_reflcl__trancl]) ).

fof(i_0_5638,plain,
    ! [X14,X225,X221,X15,X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
       => hAPP(hAPP(c_List_Olist__update(X15,hAPP(hAPP(c_List_Oappend(X15),X221),X225)),X98),X14) = hAPP(hAPP(c_List_Oappend(X15),hAPP(hAPP(c_List_Olist__update(X15,X221),X98),X14)),X225) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
       => hAPP(hAPP(c_List_Olist__update(X15,hAPP(hAPP(c_List_Oappend(X15),X221),X225)),X98),X14) = hAPP(hAPP(c_List_Oappend(X15),X221),hAPP(hAPP(c_List_Olist__update(X15,X225),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221))),X14)) ) ),
    inference(fof_simplification,[status(thm)],[fact_list__update__append]) ).

fof(i_0_5639,plain,
    ! [X21,X17,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),X17),X21)))
      <=> ( ( 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21)),X17)) )
          & ( ~ 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),X21),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21))) )
              & ( ~ 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))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__divide__eq]) ).

fof(i_0_5640,plain,
    ! [X21,X17,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),X17),X21)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X21))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21)),X17)) )
          & ( ~ 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),X21),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X21))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__divide__eq]) ).

fof(i_0_5641,plain,
    ! [X24637,X24638] :
      ( ~ class_Int_Onumber__ring(X24638)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24638),hAPP(c_Int_Onumber__class_Onumber__of(X24638),c_Int_OBit1(c_Int_OPls))),X24637) = X24637 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1])]) ).

fof(i_0_5642,plain,
    ! [X115,X70,X29] :
      ( c_List_Olist__ex(tc_Int_Oint,X29,c_List_Oupto(X70,X115))
    <=> ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X29),X70,X115) ),
    inference(fof_simplification,[status(thm)],[fact_list__ex__iff__not__all__inverval__int]) ).

fof(i_0_5643,plain,
    ! [X31971,X31972,X31973] : c_List_Orotate(X31973,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31972),X31971)) = hAPP(c_Fun_Ocomp(tc_List_Olist(X31973),tc_List_Olist(X31973),tc_List_Olist(X31973),c_List_Orotate(X31973,X31972)),c_List_Orotate(X31973,X31971)),
    inference(variable_rename,[status(thm)],[fact_rotate__add]) ).

fof(i_0_5644,plain,
    ! [X20,X21,X17,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,X17)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X21,X20)))
      <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X17))
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X21),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X17),X20)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastatMost__subset__iff]) ).

fof(i_0_5645,plain,
    ! [X24677,X24678] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24678),hAPP(c_Int_Onumber__class_Onumber__of(X24678),X24677)),c_Groups_Oone__class_Oone(X24678)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24677),c_Int_OBit1(c_Int_OPls)))
        | ~ class_Int_Onumber__ring(X24678)
        | ~ class_Rings_Olinordered__idom(X24678) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24677),c_Int_OBit1(c_Int_OPls)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24678),hAPP(c_Int_Onumber__class_Onumber__of(X24678),X24677)),c_Groups_Oone__class_Oone(X24678)))
        | ~ class_Int_Onumber__ring(X24678)
        | ~ class_Rings_Olinordered__idom(X24678) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I4_J])])]) ).

fof(i_0_5646,plain,
    ! [X24673,X24674] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24674),hAPP(c_Int_Onumber__class_Onumber__of(X24674),X24673)),c_Groups_Oone__class_Oone(X24674)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24673),c_Int_OBit1(c_Int_OPls)))
        | ~ class_Int_Onumber__ring(X24674)
        | ~ class_Rings_Olinordered__idom(X24674) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24673),c_Int_OBit1(c_Int_OPls)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24674),hAPP(c_Int_Onumber__class_Onumber__of(X24674),X24673)),c_Groups_Oone__class_Oone(X24674)))
        | ~ class_Int_Onumber__ring(X24674)
        | ~ class_Rings_Olinordered__idom(X24674) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I4_J])])]) ).

fof(i_0_5647,plain,
    ! [X29009,X29010] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29010,X29010)),X29009),c_Relation_OId(X29010)))
      | X29009 = hAPP(hAPP(c_Product__Type_OPair(X29010,X29010),esk349_2(X29009,X29010)),esk349_2(X29009,X29010)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IdE])])]) ).

fof(i_0_5648,plain,
    ! [X25052] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X25052)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X25052)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I4_J]) ).

fof(i_0_5649,plain,
    ! [X28541,X28542] : hBOOL(hAPP(hAPP(c_member(tc_prod(X28542,X28542)),hAPP(hAPP(c_Product__Type_OPair(X28542,X28542),X28541),X28541)),c_Relation_OId(X28542))),
    inference(variable_rename,[status(thm)],[fact_IdI]) ).

fof(i_0_5650,plain,
    ! [X32332,X32333,X32334] : hAPP(c_List_Ofoldl(tc_List_Olist(X32334),tc_List_Olist(X32334),c_List_Oappend(X32334),X32333),X32332) = hAPP(hAPP(c_List_Oappend(X32334),X32333),c_List_Oconcat(X32334,X32332)),
    inference(variable_rename,[status(thm)],[fact_foldl__conv__concat]) ).

fof(i_0_5651,plain,
    ! [X24809,X24810] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X24810)),c_Int_OBit1(X24809)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24810),X24809)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I10_J]) ).

fof(i_0_5652,plain,
    ! [X212,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => c_List_Olinorder__class_Oinsort__insert__key(X5,X5,c_COMBI(X5),X12,X212) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X12),X212) ) ),
    inference(fof_simplification,[status(thm)],[fact_insort__insert__insort]) ).

fof(i_0_5653,plain,
    ! [X34,X5] :
      ( c_Relation_Oirrefl(X5,X34)
    <=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X34)) ),
    inference(fof_simplification,[status(thm)],[fact_irrefl__def]) ).

fof(i_0_5654,plain,
    ! [X6,X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X6)),X34)) ),
    inference(fof_simplification,[status(thm)],[fact_wf__not__refl]) ).

fof(i_0_5655,plain,
    ! [X6,X34,X5] :
      ( c_Wellfounded_Owf(X5,X34)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X6)),X34)) ),
    inference(fof_simplification,[status(thm)],[fact_wf__irrefl]) ).

fof(i_0_5656,plain,
    ! [X28581,X28582] : c_Transitive__Closure_Ortrancl(X28582,X28581) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28582,X28582),tc_HOL_Obool)),c_Relation_OId(X28582)),hAPP(hAPP(c_Relation_Orel__comp(X28582,X28582,X28582),c_Transitive__Closure_Ortrancl(X28582,X28581)),X28581)),
    inference(variable_rename,[status(thm)],[fact_rtrancl__unfold]) ).

fof(i_0_5657,plain,
    ! [X6,X13,X11,X16,X17,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16,tc_fun(X5,tc_HOL_Obool)),X11),X13)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X17),hAPP(X13,X6)))
       => ~ hBOOL(hAPP(hAPP(c_member(X16),X6),X11)) ) ),
    inference(fof_simplification,[status(thm)],[fact_INT__E]) ).

fof(i_0_5658,plain,
    ! [X33716] :
      ( ( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X33716)))
        | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X33716)) )
      & ( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X33716))
        | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X33716))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__int__code_I8_J])]) ).

fof(i_0_5659,plain,
    ! [X25002] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X25002)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X25002)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X25002))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X25002))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I9_J])]) ).

fof(i_0_5660,plain,
    ! [X25001] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X25001)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X25001)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X25001))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X25001))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I26_J])]) ).

fof(i_0_5661,plain,
    ! [X24646] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X24646)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X24646)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X24646))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X24646))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I5_J])]) ).

fof(i_0_5662,plain,
    ! [X24626] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X24626)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X24626)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X24626))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X24626))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I22_J])]) ).

fof(i_0_5663,plain,
    ! [X24848,X24849,X24850] :
      ( ~ class_Int_Onumber__ring(X24850)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X24850),hAPP(c_Int_Onumber__class_Onumber__of(X24850),X24849)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X24848))) = hAPP(hAPP(c_HOL_OLet(X24850,X24850),hAPP(hAPP(c_Power_Opower__class_Opower(X24850),hAPP(c_Int_Onumber__class_Onumber__of(X24850),X24849)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24848))),hAPP(hAPP(c_COMBS(X24850,X24850,X24850),c_Groups_Otimes__class_Otimes(X24850)),c_COMBI(X24850))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__number__of__even__number__of])]) ).

fof(i_0_5664,plain,
    ! [X12,X27,X11,X2,X16,X5] :
      ( c_Fun_Oinj__on(X5,X16,X2,X11)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X16),X27),hAPP(c_Set_Oimage(X5,X16,X2),X11)))
       => c_Fun_Oinj__on(X5,X16,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),X2),X12),X27),X11) ) ),
    inference(fof_simplification,[status(thm)],[fact_inj__on__fun__updI]) ).

fof(i_0_5665,plain,
    ! [X12,X27,X21] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X27))
       => 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)),X21)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X12),X27)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X21)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X27),X21)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X27))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X27))
           => 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)),X21)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X12),X27)) = 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),X12),X27))
           => 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)),X21)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X12),X27)) = 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_5666,plain,
    ! [X32036,X32037] :
      ( ~ class_Groups_Omonoid__add(X32037)
      | hAPP(c_List_Ofoldl(X32037,X32037,c_Groups_Oplus__class_Oplus(X32037),c_Groups_Ozero__class_Ozero(X32037)),X32036) = c_List_Ofoldr(X32037,X32037,c_Groups_Oplus__class_Oplus(X32037),X32036,c_Groups_Ozero__class_Ozero(X32037)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__foldr1])]) ).

fof(i_0_5667,plain,
    ! [X32484,X32485,X32486,X32487,X32488] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32488),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X32487),X32486)))
      | hAPP(hAPP(c_List_Onth(X32485),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X32485),X32484),c_List_Oupt(X32486,X32487))),X32488) = hAPP(X32484,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32486),X32488)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__map__upt])]) ).

fof(i_0_5668,plain,
    ! [X31946,X31947,X31948,X31949] : hAPP(c_List_Orotate(X31949,X31948),hAPP(c_List_Orotate(X31949,X31947),X31946)) = hAPP(c_List_Orotate(X31949,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31948),X31947)),X31946),
    inference(variable_rename,[status(thm)],[fact_rotate__rotate]) ).

fof(i_0_5669,plain,
    ! [X32012,X32013,X32014] :
      ( ~ class_Groups_Oab__semigroup__add(X32014)
      | c_List_Ofoldr(X32014,X32014,c_Groups_Oplus__class_Oplus(X32014),X32013,X32012) = hAPP(c_List_Ofoldl(X32014,X32014,c_Groups_Oplus__class_Oplus(X32014),X32012),X32013) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldr__conv__foldl])]) ).

fof(i_0_5670,plain,
    ! [X33712] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X33712))),
    inference(variable_rename,[status(thm)],[i_0_5231]) ).

fof(i_0_5671,plain,
    ! [X31916,X31917,X31918] : hAPP(c_List_Orotate(X31918,X31917),X31916) = hAPP(c_List_Orotate(X31918,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X31917,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31918)),X31916))),X31916),
    inference(variable_rename,[status(thm)],[fact_rotate__conv__mod]) ).

fof(i_0_5672,plain,
    ! [X2,X16,X212,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => hAPP(hAPP(c_Map_Omap__of(X5,X16),hAPP(hAPP(c_List_Ozip(X5,X16),X212),hAPP(hAPP(c_List_Omap(X5,X16),X2),X212))),X12) = hAPP(c_Option_Ooption_OSome(X16),hAPP(X2,X12)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => hAPP(hAPP(c_Map_Omap__of(X5,X16),hAPP(hAPP(c_List_Ozip(X5,X16),X212),hAPP(hAPP(c_List_Omap(X5,X16),X2),X212))),X12) = c_Option_Ooption_ONone(X16) ) ),
    inference(fof_simplification,[status(thm)],[fact_map__of__zip__map]) ).

fof(i_0_5673,plain,
    ! [X24843,X24844] :
      ( ~ class_Int_Onumber__ring(X24844)
      | ~ class_Int_Oring__char__0(X24844)
      | ~ c_Int_Oiszero(X24844,hAPP(c_Int_Onumber__class_Onumber__of(X24844),c_Int_OBit1(X24843))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5232])]) ).

fof(i_0_5674,plain,
    ! [X27,X45,X16,X11,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
     => hAPP(c_Set_Oimage(X5,tc_Option_Ooption(X16),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X16)),X45),X12),hAPP(c_Option_Ooption_OSome(X16),X27))),X11) = hAPP(c_Set_Oimage(X5,tc_Option_Ooption(X16),X45),X11) ),
    inference(fof_simplification,[status(thm)],[fact_image__map__upd]) ).

fof(i_0_5675,plain,
    ! [X24816] : c_Int_Opred(c_Int_OBit0(X24816)) = c_Int_OBit1(c_Int_Opred(X24816)),
    inference(variable_rename,[status(thm)],[fact_pred__Bit0]) ).

fof(i_0_5676,plain,
    ! [X6,X2,X11,X5,X16] :
      ( class_Fields_Ofield(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( hAPP(X2,X6) != c_Groups_Ozero__class_Ozero(X16)
         => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),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(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),X11)),hAPP(X2,X6)) )
            & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),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,X16),X2),X11) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__diff1]) ).

fof(i_0_5677,plain,
    ! [X28682,X28683] : c_Relation_Orefl__on(X28683,c_Orderings_Otop__class_Otop(tc_fun(X28683,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28683,X28683),tc_HOL_Obool)),X28682),c_Relation_OId(X28683))),
    inference(variable_rename,[status(thm)],[fact_refl__reflcl]) ).

fof(i_0_5678,plain,
    ! [X33048,X33049,X33050] : hAPP(hAPP(c_List_Oappend(X33050),c_List_OtakeWhile(X33050,X33049,X33048)),c_List_OdropWhile(X33050,X33049,X33048)) = X33048,
    inference(variable_rename,[status(thm)],[fact_takeWhile__dropWhile__id]) ).

fof(i_0_5679,plain,
    ! [X2,X6,X11,X5,X16] :
      ( class_Groups_Oab__group__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),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(X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X11)),hAPP(X2,X6)) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),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,X16),X2),X11) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__diff1]) ).

fof(i_0_5680,plain,
    ! [X32372,X32373] : hAPP(c_List_Oset(X32373),c_List_Oconcat(X32373,X32372)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X32373),tc_fun(X32373,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X32373)),X32372)),c_List_Oset(X32373)),
    inference(variable_rename,[status(thm)],[fact_set__concat]) ).

fof(i_0_5681,plain,
    ! [X32359,X32360] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32360)),c_List_Oconcat(X32360,X32359)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X32360),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X32360))),X32359)),
    inference(variable_rename,[status(thm)],[fact_length__concat]) ).

fof(i_0_5682,plain,
    ! [X6,X17,X13,X11,X16,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X16,tc_HOL_Obool)),X11),X13),X17))
     => ( ~ hBOOL(hAPP(hAPP(X13,X6),X17))
       => ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11)) ) ),
    inference(fof_simplification,[status(thm)],[fact_INF1__E]) ).

fof(i_0_5683,plain,
    ! [X32954,X32955,X32956] :
      ( ( X32955 != c_List_Olist_ONil(X32956)
        | c_List_Ofoldr(X32956,X32956,c_Orderings_Oord__class_Omax(X32956),X32955,X32954) = X32954
        | ~ c_List_Olinorder__class_Osorted(X32956,hAPP(c_List_Orev(X32956),X32955))
        | ~ class_Orderings_Olinorder(X32956) )
      & ( X32955 = c_List_Olist_ONil(X32956)
        | c_List_Ofoldr(X32956,X32956,c_Orderings_Oord__class_Omax(X32956),X32955,X32954) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X32956),hAPP(hAPP(c_List_Onth(X32956),X32955),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X32954)
        | ~ c_List_Olinorder__class_Osorted(X32956,hAPP(c_List_Orev(X32956),X32955))
        | ~ class_Orderings_Olinorder(X32956) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldr__max__sorted])])]) ).

fof(i_0_5684,plain,
    ! [X29,X212,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => ( ~ hBOOL(hAPP(X29,X12))
       => 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,X29),X212))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212))) ) ),
    inference(fof_simplification,[status(thm)],[fact_length__filter__less]) ).

fof(i_0_5685,plain,
    ! [X28575,X28576] : c_Transitive__Closure_Ortrancl(X28576,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X28576,X28576),tc_HOL_Obool)),X28575),c_Relation_OId(X28576))) = c_Transitive__Closure_Ortrancl(X28576,X28575),
    inference(variable_rename,[status(thm)],[fact_rtrancl__r__diff__Id]) ).

fof(i_0_5686,plain,
    ! [X28589,X28590] : c_Transitive__Closure_Ortrancl(X28590,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28590,X28590),tc_HOL_Obool)),X28589),c_Relation_OId(X28590))) = c_Transitive__Closure_Ortrancl(X28590,X28589),
    inference(variable_rename,[status(thm)],[fact_rtrancl__reflcl]) ).

fof(i_0_5687,plain,
    ! [X33087,X33088,X33089,X33090,X33091] :
      ( ( X33089 = hAPP(hAPP(c_List_Oappend(X33091),c_List_OtakeWhile(X33091,X33090,X33089)),hAPP(hAPP(c_List_Olist_OCons(X33091),X33088),X33087))
        | c_List_OdropWhile(X33091,X33090,X33089) != hAPP(hAPP(c_List_Olist_OCons(X33091),X33088),X33087) )
      & ( ~ hBOOL(hAPP(X33090,X33088))
        | c_List_OdropWhile(X33091,X33090,X33089) != hAPP(hAPP(c_List_Olist_OCons(X33091),X33088),X33087) )
      & ( X33089 != hAPP(hAPP(c_List_Oappend(X33091),c_List_OtakeWhile(X33091,X33090,X33089)),hAPP(hAPP(c_List_Olist_OCons(X33091),X33088),X33087))
        | hBOOL(hAPP(X33090,X33088))
        | c_List_OdropWhile(X33091,X33090,X33089) = hAPP(hAPP(c_List_Olist_OCons(X33091),X33088),X33087) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5233])])]) ).

fof(i_0_5688,plain,
    ! [X28685,X28686] : c_Relation_Oirrefl(X28686,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X28686,X28686),tc_HOL_Obool)),X28685),c_Relation_OId(X28686))),
    inference(variable_rename,[status(thm)],[fact_irrefl__diff__Id]) ).

fof(i_0_5689,plain,
    ! [X24878] :
      ( ~ class_Int_Onumber__ring(X24878)
      | ~ c_Int_Oiszero(X24878,hAPP(c_Int_Onumber__class_Onumber__of(X24878),c_Int_OBit1(c_Int_OPls))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5234])]) ).

fof(i_0_5690,plain,
    ! [X123,X128,X26,X25] :
      ( X25 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X128)),X123)
     => ( ( ( 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__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X123))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),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),X26),X123))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X123),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X25,X26),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X128),X123))) ) ),
    inference(fof_simplification,[status(thm)],[fact_divmod__int__relI]) ).

fof(i_0_5691,plain,
    ! [X25057] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X25057)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X25057)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I5_J]) ).

fof(i_0_5692,plain,
    ! [X2,X11,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => 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)),X11),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),X11)),hAPP(X2,X6)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => 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)),X11),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),X11) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__diff1__nat]) ).

fof(i_0_5693,plain,
    ! [X28766,X28767] :
      ( ~ c_Wellfounded_Owf(X28767,hAPP(c_Relation_Oconverse(X28767,X28767),X28766))
      | c_Wellfounded_Owf(X28767,hAPP(c_Relation_Oconverse(X28767,X28767),c_Transitive__Closure_Otrancl(X28767,X28766))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__converse__trancl])]) ).

fof(i_0_5694,plain,
    ! [X2,X70,X20] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20),X70))
       => c_Smallcheck_Osmall_H(X2,X20,X70) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20),X70))
       => c_Smallcheck_Osmall_H(X2,X20,X70) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X2,X20,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X70),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X2,X70)) ) ),
    inference(fof_simplification,[status(thm)],[fact_small_H_Osimps]) ).

fof(i_0_5695,plain,
    ! [X32344,X32345,X32346,X32347,X32348] :
      ( ( c_List_Oconcat(X32345,X32344) != c_List_Olist_ONil(X32345)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32345)),X32346),hAPP(c_List_Oset(tc_List_Olist(X32345)),X32344)))
        | X32346 = c_List_Olist_ONil(X32345) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32348)),esk448_2(X32347,X32348)),hAPP(c_List_Oset(tc_List_Olist(X32348)),X32347)))
        | c_List_Oconcat(X32348,X32347) = c_List_Olist_ONil(X32348) )
      & ( esk448_2(X32347,X32348) != c_List_Olist_ONil(X32348)
        | c_List_Oconcat(X32348,X32347) = c_List_Olist_ONil(X32348) ) ),
    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_5696,plain,
    ! [X32350,X32351,X32352,X32353,X32354] :
      ( ( c_List_Olist_ONil(X32351) != c_List_Oconcat(X32351,X32350)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32351)),X32352),hAPP(c_List_Oset(tc_List_Olist(X32351)),X32350)))
        | X32352 = c_List_Olist_ONil(X32351) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32354)),esk449_2(X32353,X32354)),hAPP(c_List_Oset(tc_List_Olist(X32354)),X32353)))
        | c_List_Olist_ONil(X32354) = c_List_Oconcat(X32354,X32353) )
      & ( esk449_2(X32353,X32354) != c_List_Olist_ONil(X32354)
        | c_List_Olist_ONil(X32354) = c_List_Oconcat(X32354,X32353) ) ),
    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_5697,plain,
    ! [X32433,X32434,X32435] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32435),X32434))
      | c_List_Oupt(X32435,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32434),X32433)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X32435,X32434)),c_List_Oupt(X32434,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32434),X32433))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__add__eq__append])]) ).

fof(i_0_5698,plain,
    ! [X2,X45,X76,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X76)),X45))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X45,hAPP(c_Nat_OSuc,X76))) = c_Groups_Ozero__class_Ozero(X5) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X76)),X45))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X45,hAPP(c_Nat_OSuc,X76))) = 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,X45,X76))),hAPP(X2,hAPP(c_Nat_OSuc,X76))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__cl__ivl__Suc]) ).

fof(i_0_5699,plain,
    ! [X13,X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
       => hBOOL(hAPP(hAPP(c_member(X5),X21),X13)) ) ),
    inference(fof_simplification,[status(thm)],[fact_UnE]) ).

fof(i_0_5700,plain,
    ! [X33051,X33052,X33053,X33054,X33055,X33056,X33057] :
      ( ( c_List_OdropWhile(X33053,X33052,X33051) != c_List_Olist_ONil(X33053)
        | ~ hBOOL(hAPP(hAPP(c_member(X33053),X33054),hAPP(c_List_Oset(X33053),X33051)))
        | hBOOL(hAPP(X33052,X33054)) )
      & ( hBOOL(hAPP(hAPP(c_member(X33057),esk463_3(X33055,X33056,X33057)),hAPP(c_List_Oset(X33057),X33055)))
        | c_List_OdropWhile(X33057,X33056,X33055) = c_List_Olist_ONil(X33057) )
      & ( ~ hBOOL(hAPP(X33056,esk463_3(X33055,X33056,X33057)))
        | c_List_OdropWhile(X33057,X33056,X33055) = c_List_Olist_ONil(X33057) ) ),
    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_5701,plain,
    ! [X33309,X33310,X33311] :
      ( hBOOL(hAPP(hAPP(c_member(X33311),X33310),hAPP(c_List_Oset(X33311),X33309)))
      | hAPP(c_List_OremoveAll(X33311,X33310),X33309) = X33309 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5235])]) ).

fof(i_0_5702,plain,
    ! [X12,X11,X90,X2,X16,X5] :
      ( c_Finite__Set_Ofolding(X5,X16,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(X90,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(c_Fun_Ocomp(X16,X16,X16,hAPP(X90,X11)),hAPP(X2,X12)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_folding_Oinsert]) ).

fof(i_0_5703,plain,
    ! [X33074,X33075,X33076] :
      ( ~ class_Orderings_Olinorder(X33076)
      | ~ c_List_Olinorder__class_Osorted(X33076,X33075)
      | c_List_Olinorder__class_Osorted(X33076,c_List_OdropWhile(X33076,X33074,X33075)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__dropWhile])]) ).

fof(i_0_5704,plain,
    ! [X212,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
    <=> ? [X229,X260] :
          ( X212 = hAPP(hAPP(c_List_Oappend(X5),X229),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X260))
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X260))) ) ),
    inference(fof_simplification,[status(thm)],[fact_in__set__conv__decomp__last]) ).

fof(i_0_5705,plain,
    ! [X212,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
    <=> ? [X229] :
          ( ? [X260] : X212 = hAPP(hAPP(c_List_Oappend(X5),X229),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X260))
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X229))) ) ),
    inference(fof_simplification,[status(thm)],[fact_in__set__conv__decomp__first]) ).

fof(i_0_5706,plain,
    ! [X24818] : c_Int_Osucc(c_Int_OBit1(X24818)) = c_Int_OBit0(c_Int_Osucc(X24818)),
    inference(variable_rename,[status(thm)],[fact_succ__Bit1]) ).

fof(i_0_5707,plain,
    ! [X24837,X24838,X24839] :
      ( ~ class_Int_Onumber__ring(X24839)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X24839),X24838),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X24837))) = hAPP(hAPP(c_HOL_OLet(X24839,X24839),hAPP(hAPP(c_Power_Opower__class_Opower(X24839),X24838),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24837))),hAPP(hAPP(c_COMBS(X24839,X24839,X24839),c_Groups_Otimes__class_Otimes(X24839)),c_COMBI(X24839))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__number__of__even])]) ).

fof(i_0_5708,plain,
    ! [X13,X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
        & ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X13)) ) ),
    inference(fof_simplification,[status(thm)],[fact_Diff__iff]) ).

fof(i_0_5709,plain,
    ! [X13,X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X13)) ),
    inference(fof_simplification,[status(thm)],[fact_DiffD2]) ).

fof(i_0_5710,plain,
    ! [X33314,X33315,X33316,X33317] :
      ( hBOOL(hAPP(X33317,X33316))
      | hAPP(c_List_OremoveAll(X33315,X33316),hAPP(c_List_Ofilter(X33315,X33317),X33314)) = hAPP(c_List_Ofilter(X33315,X33317),X33314) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5236])]) ).

fof(i_0_5711,plain,
    ! [X32540,X32541] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X32541),X32540) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(X32541)),c_List_Oembed__list(X32540))),
    inference(variable_rename,[status(thm)],[fact_transfer__nat__int__list__functions_I1_J]) ).

fof(i_0_5712,plain,
    ! [X32538] : c_List_Oreturn__list(X32538) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X32538),
    inference(variable_rename,[status(thm)],[fact_return__list__def]) ).

fof(i_0_5713,plain,
    ! [X32542] : c_List_Oembed__list(X32542) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X32542),
    inference(variable_rename,[status(thm)],[fact_embed__list__def]) ).

fof(i_0_5714,plain,
    ! [X30,X11,X5] :
      ( hAPP(c_Finite__Set_Ocard(X5),X11) = hAPP(c_Nat_OSuc,X30)
    <=> ? [X52,X127] :
          ( X11 = hAPP(hAPP(c_Set_Oinsert(X5),X52),X127)
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X52),X127))
          & hAPP(c_Finite__Set_Ocard(X5),X127) = X30
          & ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
           => X127 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__Suc__eq]) ).

fof(i_0_5715,plain,
    ! [X33337,X33338,X33339] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X33339),X33338))
      | c_List_Oremove1(X33339,X33337,X33338) = hAPP(c_List_OremoveAll(X33339,X33337),X33338) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__remove1__removeAll])]) ).

fof(i_0_5716,plain,
    ! [X32447,X32448,X32449] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32449),X32448)),X32447))
      | hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X32448),c_List_Oupt(X32449,X32447)) = c_List_Oupt(X32449,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32449),X32448)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__upt])]) ).

fof(i_0_5717,plain,
    ! [X31925,X31926,X31927,X31928,X31929] : hAPP(c_List_Orotate(X31929,X31928),hAPP(hAPP(c_List_Omap(X31927,X31929),X31926),X31925)) = hAPP(hAPP(c_List_Omap(X31927,X31929),X31926),hAPP(c_List_Orotate(X31927,X31928),X31925)),
    inference(variable_rename,[status(thm)],[fact_rotate__map]) ).

fof(i_0_5718,plain,
    ! [X28709,X28710] : c_Transitive__Closure_Otrancl(X28710,hAPP(c_Relation_Oconverse(X28710,X28710),X28709)) = hAPP(c_Relation_Oconverse(X28710,X28710),c_Transitive__Closure_Otrancl(X28710,X28709)),
    inference(variable_rename,[status(thm)],[fact_trancl__converse]) ).

fof(i_0_5719,plain,
    ! [X214,X16,X27,X12,X2,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X2,X12)),hAPP(X2,X27)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X16,X5,X2),X12),hAPP(hAPP(c_List_Olist_OCons(X16),X27),X214)) = hAPP(hAPP(c_List_Olist_OCons(X16),X12),hAPP(hAPP(c_List_Olist_OCons(X16),X27),X214)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X2,X12)),hAPP(X2,X27)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X16,X5,X2),X12),hAPP(hAPP(c_List_Olist_OCons(X16),X27),X214)) = hAPP(hAPP(c_List_Olist_OCons(X16),X27),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X16,X5,X2),X12),X214)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_insort__key_Osimps_I2_J]) ).

fof(i_0_5720,plain,
    ! [X98,X99] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X99)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X98)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X99),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X98)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X99)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X99)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X98))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X99)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X98)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X99),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X98)) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    inference(fof_simplification,[status(thm)],[fact_upto__rec__number__of]) ).

fof(i_0_5721,plain,
    ! [X13,X11,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),X13)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13)) ) ),
    inference(fof_simplification,[status(thm)],[fact_subset__insert]) ).

fof(i_0_5722,plain,
    ! [X13,X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
         => ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X13)) ) ),
    inference(fof_simplification,[status(thm)],[fact_IntE]) ).

fof(i_0_5723,plain,
    ! [X115,X70] :
      ( 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),X70),X115)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X70),X115))
         => c_List_Oupto(X70,X115) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X70),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X70),c_Groups_Oone__class_Oone(tc_Int_Oint)),X115)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X70),X115))
         => c_List_Oupto(X70,X115) = c_List_Olist_ONil(tc_Int_Oint) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_upto_Opsimps]) ).

fof(i_0_5724,plain,
    ! [X37,X12,X11,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X16,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),X37),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(X2,X12),hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),X37),X11)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__insert]) ).

fof(i_0_5725,plain,
    ! [X70,X20] :
      ( 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),X20),X70)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20),X70))
         => c_Lazy__Sequence_Osmall__lazy_H(X20,X70) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20),X70))
         => c_Lazy__Sequence_Osmall__lazy_H(X20,X70) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X70),c_Lazy__Sequence_Osmall__lazy_H(X20,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X70),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_small__lazy_H_Opsimps]) ).

fof(i_0_5726,plain,
    ! [X56,X2,X16,X212,X27,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X27),hAPP(c_List_Oset(X5),X212)))
     => hAPP(hAPP(c_List_Omap(X5,X16),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,X16),X2),X27),X56)),X212) = hAPP(hAPP(c_List_Omap(X5,X16),X2),X212) ),
    inference(fof_simplification,[status(thm)],[fact_map__fun__upd]) ).

fof(i_0_5727,plain,
    ! [X27,X212,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),c_List_Oremove1(X5,X27,X212)))) ),
    inference(fof_simplification,[status(thm)],[fact_notin__set__remove1]) ).

fof(i_0_5728,plain,
    ! [X68,X212,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),c_List_Osublist(X5,X212,X68)))) ),
    inference(fof_simplification,[status(thm)],[fact_notin__set__sublistI]) ).

fof(i_0_5729,plain,
    ! [X32477,X32478,X32479] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32479),X32478)),X32477))
      | hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X32479,X32477)),X32478) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32479),X32478) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__upt])]) ).

fof(i_0_5730,plain,
    ! [X24840,X24841] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X24841),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X24840))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X24841),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24840))),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_5731,plain,
    ! [X1,X2,X5,X16] :
      ( class_Orderings_Oord(X16)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,X16)),X2),X1))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X16)),X2),X1))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X16)),X1),X2)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).

fof(i_0_5732,plain,
    ! [X221,X14,X15,X102] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X102),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X15),X14)))
       => hAPP(c_Random_Opick(X15,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X15)),X14),X221)),X102) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X15),X14) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X102),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X15),X14)))
       => hAPP(c_Random_Opick(X15,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X15)),X14),X221)),X102) = hAPP(c_Random_Opick(X15,X221),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X102),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X15),X14))) ) ),
    inference(fof_simplification,[status(thm)],[fact_pick_Osimps]) ).

fof(i_0_5733,plain,
    ! [X12,X214,X16,X212,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16)),X214)
     => ( hAPP(hAPP(c_Map_Omap__of(X5,X16),hAPP(hAPP(c_List_Ozip(X5,X16),X212),X214)),X12) = c_Option_Ooption_ONone(X16)
      <=> ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212))) ) ),
    inference(fof_simplification,[status(thm)],[fact_map__of__zip__is__None]) ).

fof(i_0_5734,plain,
    ! [X19,X11,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X11),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X19)))
     => ~ ! [X195] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X11),X195))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X195),X19)) ) ),
    inference(fof_simplification,[status(thm)],[fact_UnionE]) ).

fof(i_0_5735,plain,
    ! [X33703,X33704] :
      ( ( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X33704)),c_Int_OBit0(X33703)))
        | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X33704),X33703)) )
      & ( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X33704),X33703))
        | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X33704)),c_Int_OBit0(X33703))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__int__code_I13_J])]) ).

fof(i_0_5736,plain,
    ! [X24778,X24779] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X24779)),c_Int_OBit0(X24778)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24779),X24778)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24779),X24778))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X24779)),c_Int_OBit0(X24778))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I13_J])]) ).

fof(i_0_5737,plain,
    ! [X24776,X24777] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X24777)),c_Int_OBit0(X24776)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24777),X24776)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24777),X24776))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X24777)),c_Int_OBit0(X24776))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I14_J])]) ).

fof(i_0_5738,plain,
    ! [X24774,X24775] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X24775)),c_Int_OBit0(X24774)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24775),X24774)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24775),X24774))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X24775)),c_Int_OBit0(X24774))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I31_J])]) ).

fof(i_0_5739,plain,
    ! [X24772,X24773] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X24773)),c_Int_OBit0(X24772)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24773),X24772)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24773),X24772))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X24773)),c_Int_OBit0(X24772))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I13_J])]) ).

fof(i_0_5740,plain,
    ! [X33318,X33319] : hAPP(c_List_OremoveAll(X33319,X33318),c_List_Olist_ONil(X33319)) = c_List_Olist_ONil(X33319),
    inference(variable_rename,[status(thm)],[fact_removeAll_Osimps_I1_J]) ).

fof(i_0_5741,plain,
    ! [X12,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),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),X11)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(X5),X11) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__Diff__singleton__if]) ).

fof(i_0_5742,plain,
    ! [X24681,X24682] :
      ( ~ class_Int_Onumber__ring(X24682)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24682),hAPP(c_Int_Onumber__class_Onumber__of(X24682),X24681)),c_Groups_Oone__class_Oone(X24682)) = hAPP(c_Int_Onumber__class_Onumber__of(X24682),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24681),c_Int_OBit1(c_Int_OPls))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I3_J])]) ).

fof(i_0_5743,plain,
    ! [X112,X56,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),X56)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X112)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X56))) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__number__of__eq__not__less]) ).

fof(i_0_5744,plain,
    ! [X27,X12,X16,X5] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_fun(X16,tc_HOL_Obool))),X12),X27)),
    inference(fof_simplification,[status(thm)],[fact_bot2E]) ).

fof(i_0_5745,plain,
    ! [X76,X29] :
      ( hBOOL(hAPP(X29,X76))
     => ( ~ hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
       => c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X29) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X29),c_Nat_OSuc))) ) ),
    inference(fof_simplification,[status(thm)],[fact_Least__Suc]) ).

fof(i_0_5746,plain,
    ! [X22,X151,X147,X148] :
      ( X148 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X147),X151)),X22)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X147))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22),X147)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X147))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X147),X22))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => ( X147 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => c_Divides_Odiv__class_Omod(tc_Int_Oint,X148,X147) = X22 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__mod__eq]) ).

fof(i_0_5747,plain,
    ! [X31365,X31366,X31367,X31368] : c_List_Ofoldr(X31368,X31367,X31366,c_List_Olist_ONil(X31368),X31365) = X31365,
    inference(variable_rename,[status(thm)],[fact_foldr_Osimps_I1_J]) ).

fof(i_0_5748,plain,
    ! [X33359,X33360,X33361,X33362] : c_List_Oconcat(X33362,hAPP(hAPP(c_List_Omap(X33361,tc_List_Olist(X33362)),X33360),X33359)) = c_List_Omaps(X33361,X33362,X33360,X33359),
    inference(variable_rename,[status(thm)],[fact_concat__map__maps]) ).

fof(i_0_5749,plain,
    ! [X33363,X33364,X33365,X33366] : c_List_Omaps(X33366,X33365,X33364,X33363) = c_List_Oconcat(X33365,hAPP(hAPP(c_List_Omap(X33366,tc_List_Olist(X33365)),X33364),X33363)),
    inference(variable_rename,[status(thm)],[fact_maps__def]) ).

fof(i_0_5750,plain,
    ! [X146,X22,X147,X148] :
      ( X148 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X147),X22)),X146)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X147))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X146))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X146),X147)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X147))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X147),X146))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X146),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => ( X147 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X148),X147) = X22 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__div__eq]) ).

fof(i_0_5751,plain,
    ! [X31964,X31965,X31966] : hAPP(c_List_Orotate(X31966,hAPP(c_Nat_OSuc,X31965)),X31964) = hAPP(c_List_Orotate1(X31966),hAPP(c_List_Orotate(X31966,X31965),X31964)),
    inference(variable_rename,[status(thm)],[fact_rotate__Suc]) ).

fof(i_0_5752,plain,
    ! [X37,X12,X11,X2,X16,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X16,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),X37),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X16,X2),hAPP(hAPP(X2,X12),X37)),X11) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__insert2]) ).

fof(i_0_5753,plain,
    ! [X32458,X32459,X32460,X32461] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32461),X32460))
        | c_List_Oupt(X32461,X32460) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X32459),X32458) )
      & ( X32461 = X32459
        | c_List_Oupt(X32461,X32460) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X32459),X32458) )
      & ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32461),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X32460) = X32458
        | c_List_Oupt(X32461,X32460) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X32459),X32458) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32461),X32460))
        | X32461 != X32459
        | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32461),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X32460) != X32458
        | c_List_Oupt(X32461,X32460) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X32459),X32458) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__eq__Cons__conv])])]) ).

fof(i_0_5754,plain,
    ! [X2,X45,X76,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),X45))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45),hAPP(c_Nat_OSuc,X76))) = c_Groups_Ozero__class_Ozero(X5) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),X45))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45),hAPP(c_Nat_OSuc,X76))) = 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,X45),X76))),hAPP(X2,X76)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__op__ivl__Suc]) ).

fof(i_0_5755,plain,
    ! [X12,X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13),X12))
     => ( ~ hBOOL(hAPP(X11,X12))
       => hBOOL(hAPP(X13,X12)) ) ),
    inference(fof_simplification,[status(thm)],[fact_sup1E]) ).

fof(i_0_5756,plain,
    ! [X24817] : c_Int_Opred(c_Int_OBit1(X24817)) = c_Int_OBit0(X24817),
    inference(variable_rename,[status(thm)],[fact_pred__Bit1]) ).

fof(i_0_5757,plain,
    ! [X100,X169,X126] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)),X100)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)),X100) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X169)))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)),X100)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),X100) )
          & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X169)))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)),X100)) = 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),X126),X169))),X100) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__number__of__add__left]) ).

fof(i_0_5758,plain,
    ! [X28482] : c_Transitive__Closure_Otrancl(X28482,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28482,X28482),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28482,X28482),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_trancl__empty]) ).

fof(i_0_5759,plain,
    ! [X32473,X32474,X32475,X32476] :
      ( ~ class_Groups_Ocomm__monoid__add(X32476)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X32476),X32475),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X32474,X32473))) = hAPP(c_List_Omonoid__add__class_Olistsum(X32476),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X32476),X32475),c_List_Oupt(X32474,X32473))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__set__upt__conv__listsum__nat])]) ).

fof(i_0_5760,plain,
    ! [X32469,X32470,X32471,X32472] :
      ( ~ class_Groups_Ocomm__monoid__add(X32472)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X32472),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X32472),X32471),c_List_Oupt(X32470,X32469))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X32472),X32471),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X32470,X32469))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_interv__listsum__conv__setsum__set__nat])]) ).

fof(i_0_5761,plain,
    ! [X12,X13,X11,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13),X12))
     => ~ ( hBOOL(hAPP(X11,X12))
         => ~ hBOOL(hAPP(X13,X12)) ) ),
    inference(fof_simplification,[status(thm)],[fact_inf1E]) ).

fof(i_0_5762,plain,
    ! [X31959,X31960,X31961] : hAPP(c_List_Orotate1(X31961),hAPP(c_List_Orotate(X31961,X31960),X31959)) = hAPP(c_List_Orotate(X31961,X31960),hAPP(c_List_Orotate1(X31961),X31959)),
    inference(variable_rename,[status(thm)],[fact_rotate1__rotate__swap]) ).

fof(i_0_5763,plain,
    ! [X24209,X24210] :
      ( ~ class_Int_Onumber__ring(X24210)
      | hAPP(c_Int_Onumber__class_Onumber__of(X24210),c_Int_OBit1(X24209)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24210),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24210),c_Groups_Oone__class_Oone(X24210)),hAPP(c_Int_Onumber__class_Onumber__of(X24210),X24209))),hAPP(c_Int_Onumber__class_Onumber__of(X24210),X24209)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit1])]) ).

fof(i_0_5764,plain,
    ! [X13,X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X13))
       => hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13))) ) ),
    inference(fof_simplification,[status(thm)],[fact_DiffI]) ).

fof(i_0_5765,plain,
    ! [X34198,X34199,X34200,X34201] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X34201,X34200,X34199,c_Code__Numeral_OSuc__code__numeral(X34198)) = hAPP(hAPP(X34199,X34198),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X34201,X34200,X34199,X34198)),
    inference(variable_rename,[status(thm)],[fact_code__numeral_Orecs_I2_J]) ).

fof(i_0_5766,plain,
    ! [X31298] : c_Code__Numeral_OSuc__code__numeral(X31298) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X31298))),
    inference(variable_rename,[status(thm)],[fact_Suc__code__numeral__def]) ).

fof(i_0_5767,plain,
    ! [X11,X5] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(c_Finite__Set_Ocard(X5),X11) = 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)),X11) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(c_Finite__Set_Ocard(X5),X11) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__def]) ).

fof(i_0_5768,plain,
    ! [X28567,X28568,X28569] : hAPP(hAPP(c_Relation_Orel__comp(X28569,X28569,X28568),c_Relation_OId(X28569)),X28567) = X28567,
    inference(variable_rename,[status(thm)],[fact_Id__O__R]) ).

fof(i_0_5769,plain,
    ! [X24651,X24652] :
      ( ~ class_Fields_Ofield(X24652)
      | ~ class_Int_Onumber__ring(X24652)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24652),X24651),hAPP(c_Int_Onumber__class_Onumber__of(X24652),c_Int_OBit1(c_Int_OPls))) = X24651 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__numeral__1])]) ).

fof(i_0_5770,plain,
    ! [X24649,X24650] :
      ( ~ class_Fields_Ofield(X24650)
      | ~ class_Int_Onumber__ring(X24650)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24650),X24649),hAPP(c_Int_Onumber__class_Onumber__of(X24650),c_Int_OBit1(c_Int_OPls))) = X24649 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__Numeral1])]) ).

fof(i_0_5771,plain,
    ! [X14,X26,X25,X15] :
      ( class_Lattices_Osemilattice__sup(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15),X25),X26)),X14))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X14))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),X14)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__supE]) ).

fof(i_0_5772,plain,
    ! [X14,X26,X25,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X25),X26)),X14))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X25),X14))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X26),X14)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_Ole__supE]) ).

fof(i_0_5773,plain,
    ! [X24635,X24636] :
      ( ~ class_Int_Onumber__ring(X24636)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24636),X24635),hAPP(c_Int_Onumber__class_Onumber__of(X24636),c_Int_OBit1(c_Int_OPls))) = X24635 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1__right])]) ).

fof(i_0_5774,plain,
    ! [X34081,X34082,X34083,X34084] :
      ( ( ~ hBOOL(hAPP(hAPP(c_List_Omember(X34084),hAPP(hAPP(c_List_Olist_OCons(X34084),X34083),X34082)),X34081))
        | X34083 = X34081
        | hBOOL(hAPP(hAPP(c_List_Omember(X34084),X34082),X34081)) )
      & ( X34083 != X34081
        | hBOOL(hAPP(hAPP(c_List_Omember(X34084),hAPP(hAPP(c_List_Olist_OCons(X34084),X34083),X34082)),X34081)) )
      & ( ~ hBOOL(hAPP(hAPP(c_List_Omember(X34084),X34082),X34081))
        | hBOOL(hAPP(hAPP(c_List_Omember(X34084),hAPP(hAPP(c_List_Olist_OCons(X34084),X34083),X34082)),X34081)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_member__rec_I1_J])])]) ).

fof(i_0_5775,plain,
    ! [X34085] : c_List_Omember(X34085) = c_List_Oset(X34085),
    inference(variable_rename,[status(thm)],[fact_member__set]) ).

fof(i_0_5776,plain,
    ! [X31907,X31908,X31909] :
      ( X31909 = c_List_Olist_ONil(X31908)
      | hAPP(c_List_Ohd(X31908),hAPP(c_List_Orotate(X31908,X31907),X31909)) = hAPP(hAPP(c_List_Onth(X31908),X31909),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X31907,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31908)),X31909))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__rotate__conv__nth])]) ).

fof(i_0_5777,plain,
    ! [X100,X169,X126] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X126),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)),X100)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X126),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)),X100)) = 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),X126),X169))),X100) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__number__of__mult__left]) ).

fof(i_0_5778,plain,
    ! [X31977,X31978,X31979] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31979)),X31978)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | hAPP(c_List_Orotate(X31979,X31977),X31978) = X31978 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__length01])]) ).

fof(i_0_5779,plain,
    ! [X13,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)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13)),X19) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X13),X19)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13)),X19) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X13),X19) ) ),
    inference(fof_simplification,[status(thm)],[fact_Int__insert__left]) ).

fof(i_0_5780,plain,
    ! [X11,X13,X21,X5] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X13))
       => hBOOL(hAPP(hAPP(c_member(X5),X21),X11)) )
     => hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13))) ),
    inference(fof_simplification,[status(thm)],[fact_UnCI]) ).

fof(i_0_5781,plain,
    ! [X207,X206,X16,X45,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X45),c_Map_Odom(X5,X16,X206)))
     => hAPP(c_Map_Omap__add(X5,X16,X206,X207),X45) = hAPP(X207,X45) ),
    inference(fof_simplification,[status(thm)],[fact_map__add__dom__app__simps_I2_J]) ).

fof(i_0_5782,plain,
    ! [X206,X207,X16,X45,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X45),c_Map_Odom(X5,X16,X207)))
     => hAPP(c_Map_Omap__add(X5,X16,X206,X207),X45) = hAPP(X206,X45) ),
    inference(fof_simplification,[status(thm)],[fact_map__add__dom__app__simps_I3_J]) ).

fof(i_0_5783,plain,
    ! [X25,X15] :
      ( class_Rings_Olinordered__ring(X15)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X25),X25)),c_Groups_Ozero__class_Ozero(X15))) ),
    inference(fof_simplification,[status(thm)],[fact_not__square__less__zero]) ).

fof(i_0_5784,plain,
    ! [X24791] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X24791)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24791),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24791),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X24791)),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_5785,plain,
    ! [X24813,X24814] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X24814))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X24813))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24814)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24813)),
    inference(variable_rename,[status(thm)],[fact_zdiv__number__of__Bit0]) ).

fof(i_0_5786,plain,
    ! [X98,X100,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X100)),X98))
     => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X98))
         => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X100),X98)) ) ),
    inference(fof_simplification,[status(thm)],[fact_add__leE]) ).

fof(i_0_5787,plain,
    ! [X33709] :
      ( ( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X33709)),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X33709),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X33709),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X33709)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__int__code_I9_J])]) ).

fof(i_0_5788,plain,
    ! [X24799] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X24799)),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24799),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24799),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X24799)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I10_J])]) ).

fof(i_0_5789,plain,
    ! [X25049] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X25049)),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25049),c_Int_OMin)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25049),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X25049)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I11_J])]) ).

fof(i_0_5790,plain,
    ! [X25004] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X25004)),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25004),c_Int_OMin)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25004),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X25004)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I28_J])]) ).

fof(i_0_5791,plain,
    ! [X24792] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X24792)),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24792),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24792),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X24792)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I27_J])]) ).

fof(i_0_5792,plain,
    ! [X24815] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X24815))))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24815))) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24815)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X24815)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit0])]) ).

fof(i_0_5793,plain,
    ! [X28565,X28566] : hAPP(c_Relation_OImage(X28566,X28566,c_Relation_OId(X28566)),X28565) = X28565,
    inference(variable_rename,[status(thm)],[fact_Image__Id]) ).

fof(i_0_5794,plain,
    ! [X11,X13,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X13))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)),X13) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X13))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)),X13) = hAPP(hAPP(c_Set_Oinsert(X5),X12),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X13)) ) ),
    inference(fof_simplification,[status(thm)],[fact_insert__Diff__if]) ).

fof(i_0_5795,plain,
    ! [X30235,X30236,X30237,X30238,X30239] : c_Map_Omap__comp(X30239,X30238,X30237,hAPP(c_COMBK(tc_Option_Ooption(X30238),X30239),c_Option_Ooption_ONone(X30238)),X30236,X30235) = c_Option_Ooption_ONone(X30238),
    inference(variable_rename,[status(thm)],[fact_map__comp__empty_I2_J]) ).

fof(i_0_5796,plain,
    ! [X30230,X30231,X30232,X30233,X30234] : c_Map_Omap__comp(X30234,X30233,X30232,X30231,hAPP(c_COMBK(tc_Option_Ooption(X30234),X30232),c_Option_Ooption_ONone(X30234)),X30230) = c_Option_Ooption_ONone(X30233),
    inference(variable_rename,[status(thm)],[fact_map__comp__empty_I1_J]) ).

fof(i_0_5797,plain,
    ! [X24630,X24631] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24631),X24630))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X24631)),X24630)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X24631)),X24630))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24631),X24630)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__pred__less])]) ).

fof(i_0_5798,plain,
    ! [X25058] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X25058)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X25058)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I6_J]) ).

fof(i_0_5799,plain,
    ! [X24520,X24521] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24521)))
        | hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24521)),X24520)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X24520) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24521)))
        | hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24521)),X24520)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X24521))),X24520) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5237])]) ).

fof(i_0_5800,plain,
    ! [X99,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),X99),X98))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),X98) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),X98) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98)),X98)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_div__if]) ).

fof(i_0_5801,plain,
    ! [X99,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),X99),X98))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),X98) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98)),X98)) ) ),
    inference(fof_simplification,[status(thm)],[fact_div__geq]) ).

fof(i_0_5802,plain,
    ! [X98] : ~ 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,X98))))),
    inference(fof_simplification,[status(thm)],[fact_not__zle__0__negative]) ).

fof(i_0_5803,plain,
    ! [X28587,X28588] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28588,X28588),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X28588,X28587)),c_Relation_OId(X28588)) = c_Transitive__Closure_Ortrancl(X28588,X28587),
    inference(variable_rename,[status(thm)],[fact_rtrancl__reflcl__absorb]) ).

fof(i_0_5804,plain,
    ! [X32431,X32432] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32432),X32431))
      | c_List_Oupt(X32432,hAPP(c_Nat_OSuc,X32431)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X32432,X32431)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X32431),c_List_Olist_ONil(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__Suc__append])]) ).

fof(i_0_5805,plain,
    ! [X32429,X32430] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32430),X32429))
        | c_List_Oupt(X32430,hAPP(c_Nat_OSuc,X32429)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X32430,X32429)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X32429),c_List_Olist_ONil(tc_Nat_Onat))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32430),X32429))
        | c_List_Oupt(X32430,hAPP(c_Nat_OSuc,X32429)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5238])]) ).

fof(i_0_5806,plain,
    ! [X13,X11,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) ) ),
    inference(fof_simplification,[status(thm)],[fact_Int__insert__right]) ).

fof(i_0_5807,plain,
    ! [X1,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),X11) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Oplus__class_Oplus(X16)),X1),c_Groups_Ozero__class_Ozero(X16)),X11) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),X11) = c_Groups_Ozero__class_Ozero(X16) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum_OF__eq]) ).

fof(i_0_5808,plain,
    ! [X1,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X11) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16,X5,c_Groups_Otimes__class_Otimes(X16)),X1),c_Groups_Oone__class_Oone(X16)),X11) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X11) = c_Groups_Oone__class_Oone(X16) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod_OF__eq]) ).

fof(i_0_5809,plain,
    ! [X225,X221,X15,X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
       => hAPP(hAPP(c_List_Onth(X15),hAPP(hAPP(c_List_Oappend(X15),X221),X225)),X98) = hAPP(hAPP(c_List_Onth(X15),X221),X98) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221)))
       => hAPP(hAPP(c_List_Onth(X15),hAPP(hAPP(c_List_Oappend(X15),X221),X225)),X98) = hAPP(hAPP(c_List_Onth(X15),X225),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15)),X221))) ) ),
    inference(fof_simplification,[status(thm)],[fact_nth__append]) ).

fof(i_0_5810,plain,
    ! [X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11)))
    <=> ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X11)) ),
    inference(fof_simplification,[status(thm)],[fact_Compl__iff]) ).

fof(i_0_5811,plain,
    ! [X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X11)) ),
    inference(fof_simplification,[status(thm)],[fact_ComplD]) ).

fof(i_0_5812,plain,
    ! [X11,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X11)) ),
    inference(fof_simplification,[status(thm)],[fact_ComplE]) ).

fof(i_0_5813,plain,
    ! [X24820] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X24820)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24820)),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_5814,plain,
    ! [X126,X120,X5] :
      ( ( class_Int_Onumber(X5)
        & class_Orderings_Oord(X5) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X120)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X120)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X126) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X120)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X120)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X120) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_max__number__of]) ).

fof(i_0_5815,plain,
    ! [X126,X120,X5] :
      ( ( class_Int_Onumber(X5)
        & class_Orderings_Oord(X5) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X120)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X120)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X120) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X120)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X120)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X126) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__number__of]) ).

fof(i_0_5816,plain,
    ! [X101,X102] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X101)),X102)),
    inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).

fof(i_0_5817,plain,
    ! [X102,X101] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),X102)),X102)),
    inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).

fof(i_0_5818,plain,
    ! [X214,X212,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => c_List_Oremove1(X5,X12,hAPP(hAPP(c_List_Oappend(X5),X212),X214)) = hAPP(hAPP(c_List_Oappend(X5),c_List_Oremove1(X5,X12,X212)),X214) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => c_List_Oremove1(X5,X12,hAPP(hAPP(c_List_Oappend(X5),X212),X214)) = hAPP(hAPP(c_List_Oappend(X5),X212),c_List_Oremove1(X5,X12,X214)) ) ),
    inference(fof_simplification,[status(thm)],[fact_remove1__append]) ).

fof(i_0_5819,plain,
    ! [X24690] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X24690))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24690) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24690) != 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(X24690)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__pred__iff__0])]) ).

fof(i_0_5820,plain,
    ! [X33713] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X33713)),c_Int_OMin)),
    inference(variable_rename,[status(thm)],[i_0_5239]) ).

fof(i_0_5821,plain,
    ! [X12,X2,X5] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X12)),
    inference(fof_simplification,[status(thm)],[fact_empty__fold1SetE]) ).

fof(i_0_5822,plain,
    ! [X24135,X24136] :
      ( ( c_Int_OBit1(X24136) != c_Int_OBit1(X24135)
        | X24136 = X24135 )
      & ( X24136 != X24135
        | c_Int_OBit1(X24136) = c_Int_OBit1(X24135) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I51_J])]) ).

fof(i_0_5823,plain,
    ! [X34037,X34038] : c_List_Oconcat(X34038,c_List_Oreplicate(tc_List_Olist(X34038),X34037,c_List_Olist_ONil(X34038))) = c_List_Olist_ONil(X34038),
    inference(variable_rename,[status(thm)],[fact_concat__replicate__trivial]) ).

fof(i_0_5824,plain,
    ! [X45,X16,X11,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hAPP(c_Map_Orestrict__map(X5,X16,X45,X11),X12) = hAPP(X45,X12) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hAPP(c_Map_Orestrict__map(X5,X16,X45,X11),X12) = c_Option_Ooption_ONone(X16) ) ),
    inference(fof_simplification,[status(thm)],[fact_restrict__map__def]) ).

fof(i_0_5825,plain,
    ! [X17,X6,X29] :
      ( hBOOL(hAPP(X29,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6),X17)))
    <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X17))
            & ~ hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
          | ? [X125] :
              ( X6 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X125)
              & ~ hBOOL(hAPP(X29,X125)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__diff__split__asm]) ).

fof(i_0_5826,plain,
    ! [X212,X12,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
        & hBOOL(hAPP(c_List_Odistinct(X5),X212)) ) ),
    inference(fof_simplification,[status(thm)],[fact_distinct_Osimps_I2_J]) ).

fof(i_0_5827,plain,
    ! [X2,X16,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Map_Odom(X5,X16,X2)))
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))
       => ? [X3] : hAPP(X2,X3) = c_Option_Ooption_ONone(X16) ) ),
    inference(fof_simplification,[status(thm)],[fact_finite__map__freshness]) ).

fof(i_0_5828,plain,
    ! [X31938,X31939,X31940] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31940)),hAPP(c_List_Orotate(X31940,X31939),X31938)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31940)),X31938),
    inference(variable_rename,[status(thm)],[fact_length__rotate]) ).

fof(i_0_5829,plain,
    ! [X33066,X33067] : c_List_OdropWhile(X33067,X33066,c_List_Olist_ONil(X33067)) = c_List_Olist_ONil(X33067),
    inference(variable_rename,[status(thm)],[fact_dropWhile_Osimps_I1_J]) ).

fof(i_0_5830,plain,
    ! [X11,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)),hAPP(hAPP(c_Set_Oinsert(X5),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X11 ),
    inference(fof_simplification,[status(thm)],[fact_Diff__insert__absorb]) ).

fof(i_0_5831,plain,
    ! [X1,X12,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16),hAPP(X1,X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),X11)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum_Oinsert]) ).

fof(i_0_5832,plain,
    ! [X2,X6,X90,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X90))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X90))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),hAPP(hAPP(c_Set_Oinsert(X5),X6),X90)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16),hAPP(X2,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X90)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__insert]) ).

fof(i_0_5833,plain,
    ! [X1,X12,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(X1,X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X11)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod_Oinsert]) ).

fof(i_0_5834,plain,
    ! [X2,X6,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16),hAPP(X2,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),X11)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__insert]) ).

fof(i_0_5835,plain,
    ! [X32424,X32425,X32426] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X32426),c_List_Oupt(X32425,X32424)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32425),X32426),X32424),
    inference(variable_rename,[status(thm)],[fact_drop__upt]) ).

fof(i_0_5836,plain,
    ! [X212,X29,X5] :
      ( hAPP(c_List_Ofilter(X5,X29),X212) = c_List_Olist_ONil(X5)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X212)))
         => ~ hBOOL(hAPP(X29,X3)) ) ),
    inference(fof_simplification,[status(thm)],[fact_filter__empty__conv]) ).

fof(i_0_5837,plain,
    ! [X99,X98] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X98)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X99)))),
    inference(fof_simplification,[status(thm)],[fact_not__int__zless__negative]) ).

fof(i_0_5838,plain,
    ! [X31950,X31951,X31952] : hAPP(c_List_Oset(X31952),hAPP(c_List_Orotate(X31952,X31951),X31950)) = hAPP(c_List_Oset(X31952),X31950),
    inference(variable_rename,[status(thm)],[fact_set__rotate]) ).

fof(i_0_5839,plain,
    ! [X5,X11,X12,X13] :
      ( ( ~ hBOOL(hAPP(X13,X12))
       => hBOOL(hAPP(X11,X12)) )
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X13),X12)) ),
    inference(fof_simplification,[status(thm)],[fact_sup1CI]) ).

fof(i_0_5840,plain,
    ! [X258,X259,X212,X29,X5] :
      ( c_List_Opartition(X5,X29,X212) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X259),X258)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X259)))
           => hBOOL(hAPP(X29,X3)) )
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X258)))
           => ~ hBOOL(hAPP(X29,X3)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_partition__P]) ).

fof(i_0_5841,plain,
    ! [X28483,X28484] : hAPP(c_Relation_ODomain(X28484,X28484),c_Transitive__Closure_Otrancl(X28484,X28483)) = hAPP(c_Relation_ODomain(X28484,X28484),X28483),
    inference(variable_rename,[status(thm)],[fact_trancl__domain]) ).

fof(i_0_5842,plain,
    ! [X28485,X28486] : hAPP(c_Relation_ORange(X28486,X28486),c_Transitive__Closure_Otrancl(X28486,X28485)) = hAPP(c_Relation_ORange(X28486,X28486),X28485),
    inference(variable_rename,[status(thm)],[fact_trancl__range]) ).

fof(i_0_5843,plain,
    ! [X168,X56] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X56),X168))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X56),c_Int_OPls)) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__nat__number__of]) ).

fof(i_0_5844,plain,
    ! [X24782,X24783] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X24783)),c_Int_OBit0(X24782)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24783),X24782)),
    inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit0]) ).

fof(i_0_5845,plain,
    ! [X24767,X24768] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X24768)),c_Int_OBit0(X24767)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24768),X24767)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I7_J]) ).

fof(i_0_5846,plain,
    ! [X12,X11,X90,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(X90,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,X2),X12),X11) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_folding__one_Oeq__fold_H]) ).

fof(i_0_5847,plain,
    ! [X12] :
      ~ ! [X33] :
          ( X12 = hAPP(c_Int_OAbs__Integ,X33)
         => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X33),c_Int_OInteg)) ),
    inference(fof_simplification,[status(thm)],[fact_Abs__Integ__cases]) ).

fof(i_0_5848,plain,
    ! [X32452,X32453] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32453),X32452))
        | c_List_Oupt(X32453,X32452) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X32453),c_List_Oupt(hAPP(c_Nat_OSuc,X32453),X32452)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32453),X32452))
        | c_List_Oupt(X32453,X32452) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5240])]) ).

fof(i_0_5849,plain,
    ! [X32450,X32451] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32451),X32450))
      | c_List_Oupt(X32451,X32450) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X32451),c_List_Oupt(hAPP(c_Nat_OSuc,X32451),X32450)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__conv__Cons])]) ).

fof(i_0_5850,plain,
    ! [X30216,X30217,X30218,X30219,X30220,X30221,X30222] :
      ( hAPP(X30222,X30221) != hAPP(c_Option_Ooption_OSome(X30220),X30219)
      | c_Map_Omap__comp(X30220,X30218,X30217,X30216,X30222,X30221) = hAPP(X30216,X30219) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__comp__simps_I2_J])]) ).

fof(i_0_5851,plain,
    ! [X212,X2,X5,X12,X29,X16] :
      ( class_Orderings_Olinorder(X16)
     => ( ~ hBOOL(hAPP(X29,X12))
       => hAPP(c_List_Ofilter(X5,X29),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X16,X2),X12),X212)) = hAPP(c_List_Ofilter(X5,X29),X212) ) ),
    inference(fof_simplification,[status(thm)],[fact_filter__insort__triv]) ).

fof(i_0_5852,plain,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X12),X11) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold_H]) ).

fof(i_0_5853,plain,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X12),X11) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold_H]) ).

fof(i_0_5854,plain,
    ! [X11,X5] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    inference(fof_simplification,[status(thm)],[fact_not__psubset__empty]) ).

fof(i_0_5855,plain,
    ! [X45,X16,X11,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
     => hAPP(c_Map_Orestrict__map(X5,X16,X45,X11),X12) = c_Option_Ooption_ONone(X16) ),
    inference(fof_simplification,[status(thm)],[fact_restrict__out]) ).

fof(i_0_5856,plain,
    ! [X6,X11,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
         => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Groups_Otimes__class_Otimes(X5)),X6),X11) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold1__eq__fold]) ).

fof(i_0_5857,plain,
    ! [X24821,X24822] :
      ( ~ class_Int_Onumber__ring(X24822)
      | hAPP(c_Int_Onumber__class_Onumber__of(X24822),c_Int_OBit0(X24821)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24822),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24822),c_Groups_Ozero__class_Ozero(X24822)),hAPP(c_Int_Onumber__class_Onumber__of(X24822),X24821))),hAPP(c_Int_Onumber__class_Onumber__of(X24822),X24821)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit0])]) ).

fof(i_0_5858,plain,
    ! [X32464,X32465] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X32465),hAPP(c_List_Onth(X32465),X32464)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32465)),X32464))) = X32464,
    inference(variable_rename,[status(thm)],[fact_map__nth]) ).

fof(i_0_5859,plain,
    ! [X26,X25,X14,X15] :
      ( class_Lattices_Osemilattice__inf(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15),X25),X26)))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X25))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X26)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__infE]) ).

fof(i_0_5860,plain,
    ! [X26,X25,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X25),X26)))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X25))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X26)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_Ole__infE]) ).

fof(i_0_5861,plain,
    ! [X212,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremove1(X5,X12,X212)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremove1(X5,X12,X212)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X212) ) ),
    inference(fof_simplification,[status(thm)],[fact_length__remove1]) ).

fof(i_0_5862,plain,
    ! [X13,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)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13)),X19) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X13),X19) ),
    inference(fof_simplification,[status(thm)],[fact_Int__insert__left__if0]) ).

fof(i_0_5863,plain,
    ! [X25499,X25500] :
      ( ( X25500 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | c_Code__Numeral_Onat__of__aux(X25500,X25499) = X25499 )
      & ( X25500 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | c_Code__Numeral_Onat__of__aux(X25500,X25499) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X25500),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X25499)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__of__aux__code])]) ).

fof(i_0_5864,plain,
    ! [X31296,X31297] : c_Code__Numeral_Onat__of__aux(X31297,X31296) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X31297)),X31296),
    inference(variable_rename,[status(thm)],[fact_nat__of__aux__def]) ).

fof(i_0_5865,plain,
    ! [X28462,X28463] :
      ( ~ c_Wellfounded_Owf(X28463,X28462)
      | c_Wellfounded_Owf(X28463,c_Transitive__Closure_Otrancl(X28463,X28462)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__trancl])]) ).

fof(i_0_5866,plain,
    ! [X28570,X28571,X28572] : hAPP(hAPP(c_Relation_Orel__comp(X28572,X28571,X28571),X28570),c_Relation_OId(X28571)) = X28570,
    inference(variable_rename,[status(thm)],[fact_R__O__Id]) ).

fof(i_0_5867,plain,
    ! [X30194,X30195,X30196,X30197,X30198,X30199] :
      ( hAPP(X30199,X30198) != c_Option_Ooption_ONone(X30197)
      | c_Map_Omap__comp(X30197,X30196,X30195,X30194,X30199,X30198) = c_Option_Ooption_ONone(X30196) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__comp__simps_I1_J])]) ).

fof(i_0_5868,plain,
    ! [X28624,X28625] : c_Transitive__Closure_Otrancl(X28625,X28624) = hAPP(hAPP(c_Relation_Orel__comp(X28625,X28625,X28625),c_Transitive__Closure_Ortrancl(X28625,X28624)),X28624),
    inference(variable_rename,[status(thm)],[fact_trancl__unfold__right]) ).

fof(i_0_5869,plain,
    ! [X28616,X28617] : c_Transitive__Closure_Ortrancl(X28617,c_Transitive__Closure_Otrancl(X28617,X28616)) = c_Transitive__Closure_Ortrancl(X28617,X28616),
    inference(variable_rename,[status(thm)],[fact_trancl__rtrancl__absorb]) ).

fof(i_0_5870,plain,
    ! [X32340] : c_List_Oconcat(X32340,c_List_Olist_ONil(tc_List_Olist(X32340))) = c_List_Olist_ONil(X32340),
    inference(variable_rename,[status(thm)],[fact_concat_Osimps_I1_J]) ).

fof(i_0_5871,plain,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X12),X11) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Min_Oeq__fold_H]) ).

fof(i_0_5872,plain,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X12),X11) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Max_Oeq__fold_H]) ).

fof(i_0_5873,plain,
    ! [X12,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X12),X11) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oeq__fold_H]) ).

fof(i_0_5874,plain,
    ! [X12,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X12),X11) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oeq__fold_H]) ).

fof(i_0_5875,plain,
    ! [X168,X56] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X56) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)
    <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X56)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X168)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X56)))
         => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X168)))
             => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X56) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
            & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X168)))
             => X56 = X168 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_eq__nat__number__of]) ).

fof(i_0_5876,plain,
    ! [X14,X15] :
      ( ( class_Int_Onumber__ring(X15)
        & class_Rings_Olinordered__idom(X15) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X14)),c_Groups_Ozero__class_Ozero(X15)))
         => hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X14)) = hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X14)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X14)),c_Groups_Ozero__class_Ozero(X15)))
         => hAPP(c_Groups_Oabs__class_Oabs(X15),hAPP(c_Int_Onumber__class_Onumber__of(X15),X14)) = hAPP(c_Int_Onumber__class_Onumber__of(X15),X14) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_abs__number__of]) ).

fof(i_0_5877,plain,
    ! [X28706] : hAPP(c_Relation_Oconverse(X28706,X28706),c_Relation_OId(X28706)) = c_Relation_OId(X28706),
    inference(variable_rename,[status(thm)],[fact_converse__Id]) ).

fof(i_0_5878,plain,
    ! [X169,X126] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X169)))
           => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = 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),X169)))
           => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X169))) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_mod__nat__number__of]) ).

fof(i_0_5879,plain,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( X11 != 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),X12),X11)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X12),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X11)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oinsert]) ).

fof(i_0_5880,plain,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( X11 != 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),X12),X11)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X12),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X11)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oinsert]) ).

fof(i_0_5881,plain,
    ! [X24770,X24771] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X24771)),X24770) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24771),X24770)),
    inference(variable_rename,[status(thm)],[fact_mult__Bit0]) ).

fof(i_0_5882,plain,
    ! [X214,X29,X212,X12,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => ( ~ hBOOL(hAPP(X29,X12))
       => c_List_OtakeWhile(X5,X29,hAPP(hAPP(c_List_Oappend(X5),X212),X214)) = c_List_OtakeWhile(X5,X29,X212) ) ),
    inference(fof_simplification,[status(thm)],[fact_takeWhile__append1]) ).

fof(i_0_5883,plain,
    ! [X169,X126] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X169))) ) ),
    inference(fof_simplification,[status(thm)],[fact_div__nat__number__of]) ).

fof(i_0_5884,plain,
    ! [X132,X126] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X132)) = 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),X132)) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X132)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X132))) ) ),
    inference(fof_simplification,[status(thm)],[fact_power__nat__number__of__number__of]) ).

fof(i_0_5885,plain,
    ! [X27,X12,X36,X5] :
      ( c_Partial__Function_Omk__less(X5,X36,X12,X27)
    <=> ( hBOOL(hAPP(hAPP(X36,X12),X27))
        & ~ hBOOL(hAPP(hAPP(X36,X27),X12)) ) ),
    inference(fof_simplification,[status(thm)],[fact_mk__less__def]) ).

fof(i_0_5886,plain,
    ! [X12,X11,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
         => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
           => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X11)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold1__insert]) ).

fof(i_0_5887,plain,
    ! [X24628,X24629] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X24629))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24628)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24629)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24628),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X24629))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__number__of])]) ).

fof(i_0_5888,plain,
    ! [X76,X29] :
      ( ~ hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
     => ( hBOOL(hAPP(X29,X76))
       => ? [X109] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X109),X76))
            & ! [X145] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X145),X109))
               => ~ hBOOL(hAPP(X29,X145)) )
            & hBOOL(hAPP(X29,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X109),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_ex__least__nat__less]) ).

fof(i_0_5889,plain,
    ! [X32480,X32481] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X32481,X32480) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X32481),hAPP(c_Nat_OSuc,X32480))),
    inference(variable_rename,[status(thm)],[fact_greaterThanAtMost__upt]) ).

fof(i_0_5890,plain,
    ! [X33710] :
      ( ( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X33710)))
        | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X33710)) )
      & ( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X33710))
        | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X33710))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__int__code_I3_J])]) ).

fof(i_0_5891,plain,
    ! [X25005] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X25005)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X25005)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X25005))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X25005))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I8_J])]) ).

fof(i_0_5892,plain,
    ! [X25050] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X25050)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X25050)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X25050))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X25050))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I25_J])]) ).

fof(i_0_5893,plain,
    ! [X24798] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X24798)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X24798)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X24798))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X24798))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I4_J])]) ).

fof(i_0_5894,plain,
    ! [X24793] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X24793)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X24793)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X24793))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X24793))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I21_J])]) ).

fof(i_0_5895,plain,
    ! [X13,X11,X6,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X6),X13)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X13) ),
    inference(fof_simplification,[status(thm)],[fact_Int__insert__right__if0]) ).

fof(i_0_5896,plain,
    ! [X31974,X31975,X31976] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X31976,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31975)),X31974)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(c_List_Orotate(X31975,X31976),X31974) = X31974 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__id])]) ).

fof(i_0_5897,plain,
    ! [X31934,X31935,X31936] :
      ( ( hAPP(c_List_Orotate(X31936,X31935),X31934) != c_List_Olist_ONil(X31936)
        | X31934 = c_List_Olist_ONil(X31936) )
      & ( X31934 != c_List_Olist_ONil(X31936)
        | hAPP(c_List_Orotate(X31936,X31935),X31934) = c_List_Olist_ONil(X31936) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__is__Nil__conv])]) ).

fof(i_0_5898,plain,
    ! [X70,X115] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X115),X70))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X70,X115) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X115),X70))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X70,X115) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X70),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X70),c_Groups_Oone__class_Oone(tc_Int_Oint)),X115)) ) ),
    inference(fof_simplification,[status(thm)],[fact_simp__from__to]) ).

fof(i_0_5899,plain,
    ! [X24845,X24846] :
      ( ~ class_Int_Onumber__ring(X24846)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24846),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24846),c_Groups_Oone__class_Oone(X24846)),c_Groups_Oone__class_Oone(X24846))),hAPP(c_Int_Onumber__class_Onumber__of(X24846),X24845)) = hAPP(c_Int_Onumber__class_Onumber__of(X24846),c_Int_OBit0(X24845)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__number__of__Bit0])]) ).

fof(i_0_5900,plain,
    ! [X17,X13,X6,X5] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X13))
       => X6 = X17 )
     => hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X17),X13))) ),
    inference(fof_simplification,[status(thm)],[fact_insertCI]) ).

fof(i_0_5901,plain,
    ! [X24187] : c_Int_OBit1(X24187) = 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)),X24187)),X24187),
    inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).

fof(i_0_5902,plain,
    ! [X33637,X33638,X33639,X33640,X33641,X33642] : hAPP(hAPP(c_Product__Type_Ointernal__split(X33642,X33641,X33640),X33639),hAPP(hAPP(c_Product__Type_OPair(X33642,X33641),X33638),X33637)) = hAPP(hAPP(X33639,X33638),X33637),
    inference(variable_rename,[status(thm)],[fact_internal__split__conv]) ).

fof(i_0_5903,plain,
    ! [X33626,X33627,X33628] : c_Product__Type_Ointernal__split(X33628,X33627,X33626) = c_Product__Type_Oprod_Oprod__case(X33628,X33627,X33626),
    inference(variable_rename,[status(thm)],[fact_internal__split__def]) ).

fof(i_0_5904,plain,
    ! [X34053,X34054,X34055] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X34055),hAPP(c_COMBK(X34055,tc_Nat_Onat),X34054)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X34053)) = c_List_Oreplicate(X34055,X34053,X34054),
    inference(variable_rename,[status(thm)],[fact_map__replicate__trivial]) ).

fof(i_0_5905,plain,
    ! [X11,X21,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
     => hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11))) ),
    inference(fof_simplification,[status(thm)],[fact_ComplI]) ).

fof(i_0_5906,plain,
    ! [X16,X11,X21,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
       => hAPP(c_Set_Ovimage(X16,X5,hAPP(c_COMBK(X5,X16),X21)),X11) = c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X11))
       => hAPP(c_Set_Ovimage(X16,X5,hAPP(c_COMBK(X5,X16),X21)),X11) = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)) ) ),
    inference(fof_simplification,[status(thm)],[fact_vimage__const]) ).

fof(i_0_5907,plain,
    ! [X12,X11,X90,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X90)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X90,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(X2,X12),hAPP(X90,X11)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_folding__one_Oinsert]) ).

fof(i_0_5908,plain,
    ! [X32422,X32423] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(X32423,X32422)) = c_List_Oupt(hAPP(c_Nat_OSuc,X32423),hAPP(c_Nat_OSuc,X32422)),
    inference(variable_rename,[status(thm)],[fact_map__Suc__upt]) ).

fof(i_0_5909,plain,
    ! [X26,X25] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
           => c_Divides_Odivmod__int(X25,X26) = c_Divides_OposDivAlg(X25,X26) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
           => ( ( X25 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
               => c_Divides_Odivmod__int(X25,X26) = 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)) )
              & ( X25 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
               => c_Divides_Odivmod__int(X25,X26) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26))) ) ) ) ) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
           => c_Divides_Odivmod__int(X25,X26) = c_Divides_OnegDivAlg(X25,X26) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
           => c_Divides_Odivmod__int(X25,X26) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26))) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divmod__int__def]) ).

fof(i_0_5910,plain,
    ! [X97,X212,X5,X12,X29] :
      ( ~ hBOOL(hAPP(X29,X12))
     => c_List_OtakeWhile(X5,X29,hAPP(hAPP(c_List_Oappend(X5),X212),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X97))) = c_List_OtakeWhile(X5,X29,X212) ),
    inference(fof_simplification,[status(thm)],[fact_takeWhile__tail]) ).

fof(i_0_5911,plain,
    ! [X28661] : c_Relation_Orefl__on(X28661,c_Orderings_Otop__class_Otop(tc_fun(X28661,tc_HOL_Obool)),c_Relation_OId(X28661)),
    inference(variable_rename,[status(thm)],[fact_refl__Id]) ).

fof(i_0_5912,plain,
    ! [X24641] :
      ( ~ class_Int_Onumber__ring(X24641)
      | hAPP(c_Int_Onumber__class_Onumber__of(X24641),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X24641) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_numeral__1__eq__1])]) ).

fof(i_0_5913,plain,
    ! [X24642] :
      ( ~ class_Int_Onumber__ring(X24642)
      | c_Groups_Oone__class_Oone(X24642) = hAPP(c_Int_Onumber__class_Onumber__of(X24642),c_Int_OBit1(c_Int_OPls)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I110_J])]) ).

fof(i_0_5914,plain,
    ! [X76,X45] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X76)),X45)) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).

fof(i_0_5915,plain,
    ! [X25,X15] :
      ( class_Groups_Oordered__ab__group__add__abs(X15)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(c_Groups_Oabs__class_Oabs(X15),X25)),c_Groups_Ozero__class_Ozero(X15))) ),
    inference(fof_simplification,[status(thm)],[fact_abs__not__less__zero]) ).

fof(i_0_5916,plain,
    ! [X99,X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),X99)),c_Groups_Ozero__class_Ozero(X15))) ),
    inference(fof_simplification,[status(thm)],[fact_of__nat__less__0__iff]) ).

fof(i_0_5917,plain,
    ! [X24761,X24762] :
      ( ( ~ c_Int_Oiszero(X24762,hAPP(c_Int_Onumber__class_Onumber__of(X24762),c_Int_OBit0(X24761)))
        | c_Int_Oiszero(X24762,hAPP(c_Int_Onumber__class_Onumber__of(X24762),X24761))
        | ~ class_Int_Onumber__ring(X24762)
        | ~ class_Int_Oring__char__0(X24762) )
      & ( ~ c_Int_Oiszero(X24762,hAPP(c_Int_Onumber__class_Onumber__of(X24762),X24761))
        | c_Int_Oiszero(X24762,hAPP(c_Int_Onumber__class_Onumber__of(X24762),c_Int_OBit0(X24761)))
        | ~ class_Int_Onumber__ring(X24762)
        | ~ class_Int_Oring__char__0(X24762) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__number__of__Bit0])])]) ).

fof(i_0_5918,plain,
    ! [X169,X126] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X126),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X126),c_Int_OPls))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X169),c_Int_OPls))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X169),c_Int_OPls))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X126),X169)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_add__nat__number__of]) ).

fof(i_0_5919,plain,
    ! [X98,X126] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),X98) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X98) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),X98) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)),X98)) ) ),
    inference(fof_simplification,[status(thm)],[fact_power__nat__number__of]) ).

fof(i_0_5920,plain,
    ! [X24808] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X24808)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X24808)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I3_J]) ).

fof(i_0_5921,plain,
    ! [X123,X103,X100] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X100),X103))
       => c_Random_Ominus__shift(X123,X100,X103) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X123),X100)),X103) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X100),X103))
       => c_Random_Ominus__shift(X123,X100,X103) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X100),X103) ) ),
    inference(fof_simplification,[status(thm)],[fact_minus__shift__def]) ).

fof(i_0_5922,axiom,
    ! [X30,X76,X29] :
      ( hBOOL(hAPP(X29,c_Divides_Odiv__class_Omod(tc_Int_Oint,X76,X30)))
    <=> epred2_3(X29,X30,X76) ),
    inference(apply_def,[status(thm)],[fact_split__zmod,c_0_5241]) ).

fof(i_0_5923,plain,
    ! [X101,X102] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X102),X101))
       => c_List_Oupto(X102,X101) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X102),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X102),c_Groups_Oone__class_Oone(tc_Int_Oint)),X101)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X102),X101))
       => c_List_Oupto(X102,X101) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    inference(fof_simplification,[status(thm)],[fact_upto_Osimps]) ).

fof(i_0_5924,plain,
    ! [X24765,X24766] : c_Int_OBit0(X24766) != c_Int_OBit1(X24765),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I49_J]) ).

fof(i_0_5925,plain,
    ! [X24763,X24764] : c_Int_OBit1(X24764) != c_Int_OBit0(X24763),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I50_J]) ).

fof(i_0_5926,plain,
    ! [X23744,X23745] : c_Divides_Odivmod__nat(X23745,X23744) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23745),X23744)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23745,X23744)),
    inference(variable_rename,[status(thm)],[fact_divmod__nat__div__mod]) ).

fof(i_0_5927,plain,
    ! [X33714] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X33714))),
    inference(variable_rename,[status(thm)],[i_0_5242]) ).

fof(i_0_5928,plain,
    ! [X26991,X26992,X26993,X26994] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X26994,X26993,X26992,c_Code__Numeral_OSuc__code__numeral(X26991)) = hAPP(X26992,X26991),
    inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I5_J]) ).

fof(i_0_5929,plain,
    ! [X32482,X32483] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X32483,X32482) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X32483),X32482)),
    inference(variable_rename,[status(thm)],[fact_greaterThanLessThan__upt]) ).

fof(i_0_5930,plain,
    ! [X212,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => c_List_Oremdups(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = c_List_Oremdups(X5,X212) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => c_List_Oremdups(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Oremdups(X5,X212)) ) ),
    inference(fof_simplification,[status(thm)],[fact_remdups_Osimps_I2_J]) ).

fof(i_0_5931,plain,
    ! [X100,X15] :
      ( class_Rings_Oring__1(X15)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X100),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hAPP(c_Int_Oring__1__class_Oof__int(X15),X100) = hAPP(c_Groups_Ouminus__class_Ouminus(X15),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X100)))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X100),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hAPP(c_Int_Oring__1__class_Oof__int(X15),X100) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),hAPP(c_Int_Onat,X100)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_of__int__of__nat]) ).

fof(i_0_5932,plain,
    ! [X102,X41] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X41),X102))
       => c_Lazy__Sequence_Osmall__lazy_H(X41,X102) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X41),X102))
       => c_Lazy__Sequence_Osmall__lazy_H(X41,X102) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X102),c_Lazy__Sequence_Osmall__lazy_H(X41,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X102),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(fof_simplification,[status(thm)],[fact_small__lazy_H_Osimps]) ).

fof(i_0_5933,plain,
    ! [X28659] : hAPP(c_Relation_ODomain(X28659,X28659),c_Relation_OId(X28659)) = c_Orderings_Otop__class_Otop(tc_fun(X28659,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Domain__Id]) ).

fof(i_0_5934,plain,
    ! [X28660] : hAPP(c_Relation_ORange(X28660,X28660),c_Relation_OId(X28660)) = c_Orderings_Otop__class_Otop(tc_fun(X28660,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Range__Id]) ).

fof(i_0_5935,plain,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X12),c_Big__Operators_Olinorder__class_OMin(X5,X11)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Min_Oinsert]) ).

fof(i_0_5936,plain,
    ! [X12,X11,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( X11 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X12),c_Big__Operators_Olinorder__class_OMax(X5,X11)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Max_Oinsert]) ).

fof(i_0_5937,plain,
    ! [X12,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( X11 != 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),X12),X11)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X12),c_Big__Operators_Olattice__class_OSup__fin(X5,X11)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oinsert]) ).

fof(i_0_5938,plain,
    ! [X12,X11,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => ( X11 != 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),X12),X11)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X12),c_Big__Operators_Olattice__class_OInf__fin(X5,X11)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oinsert]) ).

fof(i_0_5939,plain,
    ! [X28618,X28619] : c_Transitive__Closure_Otrancl(X28619,c_Transitive__Closure_Ortrancl(X28619,X28618)) = c_Transitive__Closure_Ortrancl(X28619,X28618),
    inference(variable_rename,[status(thm)],[fact_rtrancl__trancl__absorb]) ).

fof(i_0_5940,plain,
    ! [X12,X5,X11] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X11))
       => c_List_Osublist(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Olist_ONil(X5)),X11) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Olist_ONil(X5)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X11))
       => c_List_Osublist(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Olist_ONil(X5)),X11) = c_List_Olist_ONil(X5) ) ),
    inference(fof_simplification,[status(thm)],[fact_sublist__singleton]) ).

fof(i_0_5941,plain,
    ! [X34078,X34079,X34080] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X34080),X34079),hAPP(c_List_Oset(X34080),X34078)))
        | hBOOL(hAPP(hAPP(c_List_Omember(X34080),X34078),X34079)) )
      & ( ~ hBOOL(hAPP(hAPP(c_List_Omember(X34080),X34078),X34079))
        | hBOOL(hAPP(hAPP(c_member(X34080),X34079),hAPP(c_List_Oset(X34080),X34078))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__member])]) ).

fof(i_0_5942,plain,
    ! [X34075,X34076,X34077] :
      ( ( ~ hBOOL(hAPP(hAPP(c_List_Omember(X34077),X34076),X34075))
        | hBOOL(hAPP(hAPP(c_member(X34077),X34075),hAPP(c_List_Oset(X34077),X34076))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X34077),X34075),hAPP(c_List_Oset(X34077),X34076)))
        | hBOOL(hAPP(hAPP(c_List_Omember(X34077),X34076),X34075)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_List_Omember__def])]) ).

fof(i_0_5943,plain,
    ! [X169] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X169)))
       => 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),X169)) = 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),X169)))
       => 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),X169)) = 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),X169))) ) ),
    inference(fof_simplification,[status(thm)],[fact_one__mod__nat__number__of]) ).

fof(i_0_5944,plain,
    ! [X28867] : c_Relation_Osingle__valued(X28867,X28867,c_Relation_OId(X28867)),
    inference(variable_rename,[status(thm)],[fact_single__valued__Id]) ).

fof(i_0_5945,plain,
    ! [X27,X12,X5] :
      ( class_Orderings_Opreorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X12),X27))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X27),X12)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).

fof(i_0_5946,plain,
    ! [X12,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),X11)) ) ),
    inference(fof_simplification,[status(thm)],[fact_card_Oinsert]) ).

fof(i_0_5947,axiom,
    ! [X30,X76,X29] :
      ( hBOOL(hAPP(X29,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X76),X30)))
    <=> epred1_3(X29,X30,X76) ),
    inference(apply_def,[status(thm)],[fact_split__zdiv,c_0_5243]) ).

fof(i_0_5948,plain,
    ! [X13,X11,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X13))
       => ( hAPP(hAPP(c_Set_Oinsert(X5),X12),X11) = hAPP(hAPP(c_Set_Oinsert(X5),X12),X13)
        <=> X11 = X13 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_insert__ident]) ).

fof(i_0_5949,plain,
    ! [X12,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(c_Finite__Set_Ocard(X5),X11) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),X11)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__insert__if]) ).

fof(i_0_5950,plain,
    ! [X32462,X32463] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32463),X32462))
      | c_List_Olast(tc_Nat_Onat,c_List_Oupt(X32463,X32462)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X32462),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__upt])]) ).

fof(i_0_5951,plain,
    ! [X25574] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X25574)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X25574,
    inference(variable_rename,[status(thm)],[fact_Suc__code__numeral__minus__one]) ).

fof(i_0_5952,plain,
    ! [X76,X45] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X76))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),hAPP(c_Nat_OSuc,X45))) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).

fof(i_0_5953,plain,
    ! [X32445,X32446] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X32446,X32445))),
    inference(variable_rename,[status(thm)],[fact_distinct__upt]) ).

fof(i_0_5954,plain,
    ! [X28889,X28890] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28890,X28890),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28889) = c_Relation_OId(X28890),
    inference(variable_rename,[status(thm)],[fact_relpow_Osimps_I1_J]) ).

fof(i_0_5955,plain,
    ! [X212,X5,X12,X29] :
      ( ( hBOOL(hAPP(X29,X12))
       => c_List_OtakeWhile(X5,X29,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_OtakeWhile(X5,X29,X212)) )
      & ( ~ hBOOL(hAPP(X29,X12))
       => c_List_OtakeWhile(X5,X29,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = c_List_Olist_ONil(X5) ) ),
    inference(fof_simplification,[status(thm)],[fact_takeWhile_Osimps_I2_J]) ).

fof(i_0_5956,plain,
    ! [X100] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X100)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_simplification,[status(thm)],[fact_int__less__0__conv]) ).

fof(i_0_5957,plain,
    ! [X24987] :
      ( ( c_Int_OMin != c_Int_OBit1(X24987)
        | c_Int_OMin = X24987 )
      & ( c_Int_OMin != X24987
        | c_Int_OMin = c_Int_OBit1(X24987) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I43_J])]) ).

fof(i_0_5958,plain,
    ! [X24986] :
      ( ( c_Int_OBit1(X24986) != c_Int_OMin
        | X24986 = c_Int_OMin )
      & ( X24986 != c_Int_OMin
        | c_Int_OBit1(X24986) = c_Int_OMin ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I47_J])]) ).

fof(i_0_5959,plain,
    ! [X24617] : c_Int_OBit1(X24617) != c_Int_OPls,
    inference(variable_rename,[status(thm)],[fact_rel__simps_I46_J]) ).

fof(i_0_5960,plain,
    ! [X24618] : c_Int_OPls != c_Int_OBit1(X24618),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I39_J]) ).

fof(i_0_5961,plain,
    ! [X126,X15] :
      ( class_Int_Onumber__ring(X15)
     => ( ( 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(c_Nat_Osemiring__1__class_Oof__nat(X15),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(X15),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(c_Nat_Osemiring__1__class_Oof__nat(X15),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = c_Groups_Ozero__class_Ozero(X15) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_of__nat__number__of__lemma]) ).

fof(i_0_5962,plain,
    ! [X12,X11,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X11))
       => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X12),X11)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),X11)) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__insert__disjoint]) ).

fof(i_0_5963,plain,
    ! [X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X12),X27))
        <=> X12 = X27 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).

fof(i_0_5964,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_5965,plain,
    ! [X212,X12,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => c_List_Oinsert(X5,X12,X212) = X212 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
       => c_List_Oinsert(X5,X12,X212) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212) ) ),
    inference(fof_simplification,[status(thm)],[fact_List_Oinsert__def]) ).

fof(i_0_5966,plain,
    ! [X25,X26,X15] :
      ( class_Orderings_Oorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),X25))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26)) ) ),
    inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).

fof(i_0_5967,plain,
    ! [X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X12),X27))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X27),X12))
          | X12 = X27 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).

fof(i_0_5968,plain,
    ! [X14,X22,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X14))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22)) ) ),
    inference(fof_simplification,[status(thm)],[fact_leD]) ).

fof(i_0_5969,plain,
    ! [X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X12),X27))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X27),X12)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).

fof(i_0_5970,plain,
    ! [X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X27),X12)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).

fof(i_0_5971,plain,
    ! [X22,X14,X15] :
      ( class_Orderings_Opreorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),X14)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).

fof(i_0_5972,plain,
    ! [X26,X25,X15] :
      ( class_Orderings_Opreorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),X26))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X26),X25)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).

fof(i_0_5973,plain,
    ! [X22,X14,X15] :
      ( class_Orderings_Opreorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),X14)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).

fof(i_0_5974,plain,
    ! [X22,X14,X15] :
      ( class_Orderings_Opreorder(X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),X14)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).

fof(i_0_5975,plain,
    ! [X169,X126] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X126),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X126),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X169)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X126),X169)) ) ),
    inference(fof_simplification,[status(thm)],[fact_mult__nat__number__of]) ).

fof(i_0_5976,plain,
    ! [X32427,X32428] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32428),X32427))
      | hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(X32428,X32427)) = X32428 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__upt])]) ).

fof(i_0_5977,plain,
    ! [X21,X5] : ~ hBOOL(hAPP(hAPP(c_member(X5),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    inference(fof_simplification,[status(thm)],[fact_empty__iff]) ).

fof(i_0_5978,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_5979,plain,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),hAPP(c_Nat_OSuc,X98)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X98))
       => X99 = hAPP(c_Nat_OSuc,X98) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__SucE]) ).

fof(i_0_5980,plain,
    ! [X32466,X32467] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X32467,X32466) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X32467,hAPP(c_Nat_OSuc,X32466))),
    inference(variable_rename,[status(thm)],[fact_atLeastAtMost__upt]) ).

fof(i_0_5981,plain,
    ! [X76,X45] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45),hAPP(c_Nat_OSuc,X76)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X76),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45),X76)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X76))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45),hAPP(c_Nat_OSuc,X76)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastLessThanSuc]) ).

fof(i_0_5982,plain,
    ! [X212,X5,X12,X29] :
      ( ( hBOOL(hAPP(X29,X12))
       => hAPP(c_List_Ofilter(X5,X29),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),hAPP(c_List_Ofilter(X5,X29),X212)) )
      & ( ~ hBOOL(hAPP(X29,X12))
       => hAPP(c_List_Ofilter(X5,X29),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212)) = hAPP(c_List_Ofilter(X5,X29),X212) ) ),
    inference(fof_simplification,[status(thm)],[fact_filter_Osimps_I2_J]) ).

fof(i_0_5983,plain,
    ! [X98,X99] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),hAPP(c_Nat_OSuc,X98)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
       => X99 = X98 ) ),
    inference(fof_simplification,[status(thm)],[fact_less__SucE]) ).

fof(i_0_5984,plain,
    ! [X99,X98] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X99))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_OSuc,X99)))
       => X99 = X98 ) ),
    inference(fof_simplification,[status(thm)],[fact_less__antisym]) ).

fof(i_0_5985,plain,
    ! [X45,X76] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),X45))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),hAPP(c_Nat_OSuc,X45)))
      <=> X76 = X45 ) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq]) ).

fof(i_0_5986,plain,
    ! [X23728,X23729] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23729,X23728),c_Divides_Odivmod__nat(X23729,X23728))),
    inference(variable_rename,[status(thm)],[fact_divmod__nat__rel__divmod__nat]) ).

fof(i_0_5987,plain,
    ! [X25608] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X25608)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X25608)),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_5988,plain,
    ! [X32489] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X32489) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32489))),
    inference(variable_rename,[status(thm)],[fact_atMost__upto]) ).

fof(i_0_5989,plain,
    ! [X24704] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24704),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24704)),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),X24704),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24704)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X24704)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5244])]) ).

fof(i_0_5990,plain,
    ! [X24634] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24634),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24634)),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),X24634),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24634)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X24634)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5245])]) ).

fof(i_0_5991,plain,
    ! [X24669,X24670] :
      ( ~ class_Int_Onumber__ring(X24670)
      | hAPP(c_Int_Onumber__class_Onumber__of(X24670),c_Int_Opred(X24669)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24670),hAPP(c_Groups_Ouminus__class_Ouminus(X24670),c_Groups_Oone__class_Oone(X24670))),hAPP(c_Int_Onumber__class_Onumber__of(X24670),X24669)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__pred])]) ).

fof(i_0_5992,plain,
    ! [X29,X30,X5] :
      ( class_Orderings_Owellorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),c_Orderings_Oord__class_OLeast(X5,X29)))
       => ~ hBOOL(hAPP(X29,X30)) ) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__Least]) ).

fof(i_0_5993,plain,
    ! [X17,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X17)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X17)) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastatMost__empty__iff2]) ).

fof(i_0_5994,plain,
    ! [X97,X30,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X30,X97)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),X97)) ) ),
    inference(fof_simplification,[status(thm)],[fact_greaterThanAtMost__empty__iff2]) ).

fof(i_0_5995,plain,
    ! [X17,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X17) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X17)) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastatMost__empty__iff]) ).

fof(i_0_5996,plain,
    ! [X97,X30,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X30,X97) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),X97)) ) ),
    inference(fof_simplification,[status(thm)],[fact_greaterThanAtMost__empty__iff]) ).

fof(i_0_5997,plain,
    ! [X23746,X23747] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23747),X23746))
      | c_Divides_Odivmod__nat(X23747,X23746) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23747) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__base])]) ).

fof(i_0_5998,plain,
    ! [X5,X13,X11] :
      ( X11 = X13
     => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X13))
         => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X13),X11)) ) ),
    inference(fof_simplification,[status(thm)],[fact_equalityE]) ).

fof(i_0_5999,plain,
    ! [X98] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X98)),X98)),
    inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).

fof(i_0_6000,plain,
    ! [X100,X103] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X103))
       => c_SMT_Oz3div(X100,X103) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X100),X103) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X103))
       => c_SMT_Oz3div(X100,X103) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X100),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X103))) ) ),
    inference(fof_simplification,[status(thm)],[fact_z3div__def]) ).

fof(i_0_6001,plain,
    ! [X98,X99] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98) = X99 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98),X98) ) ),
    inference(fof_simplification,[status(thm)],[fact_mod__if]) ).

fof(i_0_6002,plain,
    ! [X98,X99] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X99,X98) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98),X98) ),
    inference(fof_simplification,[status(thm)],[fact_mod__geq]) ).

fof(i_0_6003,plain,
    ! [X212,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => c_List_Oinsert(X5,X12,X212) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),X212) ),
    inference(fof_simplification,[status(thm)],[fact_not__in__set__insert]) ).

fof(i_0_6004,plain,
    ! [X27,X12,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X12),X27))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X12),X27))
        <=> X12 = X27 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).

fof(i_0_6005,plain,
    ! [X17,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X17) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X17)) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty__iff]) ).

fof(i_0_6006,plain,
    ! [X17,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),X17)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X17)) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty__iff2]) ).

fof(i_0_6007,plain,
    ! [X24703] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24703),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),X24703)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24703),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),X24703)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X24703)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5246])]) ).

fof(i_0_6008,plain,
    ! [X25564,X25565] :
      ( ( c_Code__Numeral_OSuc__code__numeral(X25565) != c_Code__Numeral_OSuc__code__numeral(X25564)
        | X25565 = X25564 )
      & ( X25565 != X25564
        | c_Code__Numeral_OSuc__code__numeral(X25565) = c_Code__Numeral_OSuc__code__numeral(X25564) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral_Oinject])]) ).

fof(i_0_6009,plain,
    ! [X25557] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X25557)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X25557)),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_6010,plain,
    ! [X24769] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X24769)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24769)),
    inference(variable_rename,[status(thm)],[fact_minus__Bit0]) ).

fof(i_0_6011,plain,
    ! [X76,X5,X12,X29] :
      ( ( hBOOL(hAPP(X29,X12))
       => hAPP(c_List_Ofilter(X5,X29),c_List_Oreplicate(X5,X76,X12)) = c_List_Oreplicate(X5,X76,X12) )
      & ( ~ hBOOL(hAPP(X29,X12))
       => hAPP(c_List_Ofilter(X5,X29),c_List_Oreplicate(X5,X76,X12)) = c_List_Olist_ONil(X5) ) ),
    inference(fof_simplification,[status(thm)],[fact_filter__replicate]) ).

fof(i_0_6012,plain,
    ! [X32539] :
      ( ~ c_List_Onat__list(X32539)
      | c_List_Oembed__list(c_List_Oreturn__list(X32539)) = X32539 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__list__return__embed])]) ).

fof(i_0_6013,plain,
    ! [X24522] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24522)))
        | hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24522)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24522)))
        | hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24522)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X24522)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5247])]) ).

fof(i_0_6014,plain,
    ! [X11,X5] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X11))
    <=> X11 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    inference(fof_simplification,[status(thm)],[fact_all__not__in__conv]) ).

fof(i_0_6015,plain,
    ! [X212,X12,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_List_Oset(X5),X212)))
     => c_List_Oremove1(X5,X12,X212) = X212 ),
    inference(fof_simplification,[status(thm)],[fact_remove1__idem]) ).

fof(i_0_6016,plain,
    ! [X32454,X32455] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X32455,X32454)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X32454),X32455),
    inference(variable_rename,[status(thm)],[fact_length__upt]) ).

fof(i_0_6017,plain,
    ! [X14,X15] :
      ( class_Groups_Osgn__if(X15)
     => ( ( X14 = c_Groups_Ozero__class_Ozero(X15)
         => c_Groups_Osgn__class_Osgn(X15,X14) = c_Groups_Ozero__class_Ozero(X15) )
        & ( X14 != c_Groups_Ozero__class_Ozero(X15)
         => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X14))
             => c_Groups_Osgn__class_Osgn(X15,X14) = c_Groups_Oone__class_Oone(X15) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Ozero__class_Ozero(X15)),X14))
             => c_Groups_Osgn__class_Osgn(X15,X14) = hAPP(c_Groups_Ouminus__class_Ouminus(X15),c_Groups_Oone__class_Oone(X15)) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_sgn__if]) ).

fof(i_0_6018,plain,
    ! [X32439,X32440] :
      ( ( c_List_Oupt(X32440,X32439) != c_List_Olist_ONil(tc_Nat_Onat)
        | X32439 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32439),X32440)) )
      & ( X32439 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oupt(X32440,X32439) = c_List_Olist_ONil(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32439),X32440))
        | c_List_Oupt(X32440,X32439) = 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_6019,plain,
    ! [X32437,X32438] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32438),X32437))
      | c_List_Oupt(X32437,X32438) = c_List_Olist_ONil(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__conv__Nil])]) ).

fof(i_0_6020,plain,
    ! [X100,X103] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X103))
       => c_SMT_Oz3mod(X100,X103) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X100,X103) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X103))
       => c_SMT_Oz3mod(X100,X103) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X100,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X103)) ) ),
    inference(fof_simplification,[status(thm)],[fact_z3mod__def]) ).

fof(i_0_6021,plain,
    ! [X25,X15] :
      ( class_Groups_Oabs__if(X15)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),c_Groups_Ozero__class_Ozero(X15)))
         => hAPP(c_Groups_Oabs__class_Oabs(X15),X25) = hAPP(c_Groups_Ouminus__class_Ouminus(X15),X25) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X25),c_Groups_Ozero__class_Ozero(X15)))
         => hAPP(c_Groups_Oabs__class_Oabs(X15),X25) = X25 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_abs__if]) ).

fof(i_0_6022,plain,
    ! [X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),c_Groups_Oone__class_Oone(X15)),c_Groups_Ozero__class_Ozero(X15))) ),
    inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).

fof(i_0_6023,plain,
    ! [X15] :
      ( class_Rings_Olinordered__semidom(X15)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),c_Groups_Oone__class_Oone(X15)),c_Groups_Ozero__class_Ozero(X15))) ),
    inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).

fof(i_0_6024,plain,
    ! [X98,X99] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X99),X98))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X98)) = X99 ),
    inference(fof_simplification,[status(thm)],[fact_add__diff__inverse]) ).

fof(i_0_6025,plain,
    ! [X32468] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X32468) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X32468)),
    inference(variable_rename,[status(thm)],[fact_atLeast__upt]) ).

fof(i_0_6026,plain,
    ! [X22,X14,X15] :
      ( class_Rings_Olinordered__idom(X15)
     => ( X14 != X22
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),X14)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).

fof(i_0_6027,plain,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
       => ( X14 != X22
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),X14)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).

fof(i_0_6028,plain,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( X14 != X22
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X22),X14)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).

fof(i_0_6029,plain,
    ! [X12,X27,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X27),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X12),X27))
        <=> X12 = X27 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).

fof(i_0_6030,plain,
    ! [X14,X22,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X14))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22)) ) ),
    inference(fof_simplification,[status(thm)],[fact_not__leE]) ).

fof(i_0_6031,plain,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X22))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X14)) ) ),
    inference(fof_simplification,[status(thm)],[fact_leI]) ).

fof(i_0_6032,plain,
    ! [X22,X14,X15] :
      ( class_Orderings_Olinorder(X15)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X14),X22))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15),X22),X14)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).

fof(i_0_6033,plain,
    ! [X32441,X32442] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X32442,X32441)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X32442),X32441),
    inference(variable_rename,[status(thm)],[fact_set__upt]) ).

fof(i_0_6034,plain,
    ! [X32443,X32444] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X32444),X32443) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X32444,X32443)),
    inference(variable_rename,[status(thm)],[fact_atLeastLessThan__upt]) ).

fof(i_0_6035,plain,
    ! [X24619] : c_Int_Osucc(c_Int_Opred(X24619)) = X24619,
    inference(variable_rename,[status(thm)],[fact_succ__pred]) ).

fof(i_0_6036,plain,
    ! [X24588,X24589] :
      ( ~ class_Int_Onumber__ring(X24589)
      | hAPP(c_Int_Onumber__class_Onumber__of(X24589),c_Int_Osucc(X24588)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24589),c_Groups_Oone__class_Oone(X24589)),hAPP(c_Int_Onumber__class_Onumber__of(X24589),X24588)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__succ])]) ).

fof(i_0_6037,plain,
    ! [X6,X5,X11] :
      ( X11 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X11)) ),
    inference(fof_simplification,[status(thm)],[fact_equals0D]) ).

fof(i_0_6038,plain,
    ! [X12] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X12))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12)) ),
    inference(fof_simplification,[status(thm)],[fact_not__neg__eq__ge__0]) ).

fof(i_0_6039,plain,
    ! [X45,X112] :
      ( hAPP(c_Int_Onat,X112) = X45
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X112))
         => X112 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X45) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X112))
         => X45 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__eq__iff]) ).

fof(i_0_6040,plain,
    ! [X112,X45] :
      ( X45 = hAPP(c_Int_Onat,X112)
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X112))
         => X112 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X45) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X112))
         => X45 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__eq__iff2]) ).

fof(i_0_6041,plain,
    ! [X23] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X23)) = X23 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X23)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_simplification,[status(thm)],[fact_int__nat__eq]) ).

fof(i_0_6042,plain,
    ! [X14,X22] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22),X14))
       => c_Nat__Transfer_Otsub(X14,X22) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X14),X22) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22),X14))
       => c_Nat__Transfer_Otsub(X14,X22) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_simplification,[status(thm)],[fact_tsub__def]) ).

fof(i_0_6043,plain,
    ! [X126,X15] :
      ( class_Int_Onumber__ring(X15)
     => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = c_Groups_Ozero__class_Ozero(X15) )
        & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(X15),X126) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_of__nat__number__of__eq]) ).

fof(i_0_6044,plain,
    ! [X34086,X34087] : ~ hBOOL(hAPP(hAPP(c_List_Omember(X34087),c_List_Olist_ONil(X34087)),X34086)),
    inference(variable_rename,[status(thm)],[i_0_5248]) ).

fof(i_0_6045,plain,
    ! [X23854,X23855] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23855,X23854) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X23855,X23854)),
    inference(variable_rename,[status(thm)],[fact_mod__nat__def]) ).

fof(i_0_6046,plain,
    ! [X212,X5,X12,X29] :
      ( ~ hBOOL(hAPP(X29,X12))
     => c_List_Oremove1(X5,X12,hAPP(c_List_Ofilter(X5,X29),X212)) = hAPP(c_List_Ofilter(X5,X29),X212) ),
    inference(fof_simplification,[status(thm)],[fact_remove1__filter__not]) ).

fof(i_0_6047,plain,
    ! [X23852,X23853] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23853),X23852) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X23853,X23852)),
    inference(variable_rename,[status(thm)],[fact_div__nat__def]) ).

fof(i_0_6048,plain,
    ! [X126] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126)))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X126)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126) ) ),
    inference(fof_simplification,[status(thm)],[fact_int__nat__number__of]) ).

fof(i_0_6049,plain,
    ! [X102] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X102),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X102) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X102) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X102),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X102) = X102 ) ),
    inference(fof_simplification,[status(thm)],[fact_zabs__def]) ).

fof(i_0_6050,plain,
    ! [X22,X14] :
      ( X14 != X22
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),X22))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X14)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).

fof(i_0_6051,plain,
    ! [X23730,X23731,X23732] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23732,X23731),X23730))
      | c_Divides_Odivmod__nat(X23732,X23731) = X23730 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__eq])]) ).

fof(i_0_6052,plain,
    ! [X102] :
      ( ( X102 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X102) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X102 != 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)),X102))
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X102) = 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)),X102))
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X102) = 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_6053,plain,
    ! [X32764,X32765] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X32765,X32764)),
    inference(variable_rename,[status(thm)],[fact_sorted__upt]) ).

fof(i_0_6054,plain,
    ! [X27393,X27394] : c_Wellfounded_Owf(X27394,hAPP(c_Wellfounded_Omeasure(X27394),X27393)),
    inference(variable_rename,[status(thm)],[fact_wf__measure]) ).

fof(i_0_6055,plain,
    ! [X14,X15] :
      ( class_Orderings_Opreorder(X15)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15),X14),X14)) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).

fof(i_0_6056,plain,
    ! [X31970] : c_List_Orotate(X31970,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(X31970)),
    inference(variable_rename,[status(thm)],[fact_rotate0]) ).

fof(i_0_6057,plain,
    ! [X98] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).

fof(i_0_6058,plain,
    ! [X98] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_simplification,[status(thm)],[fact_not__less0]) ).

fof(i_0_6059,plain,
    ! [X98] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).

fof(i_0_6060,plain,
    ! [X23743] : c_Divides_Odivmod__nat(X23743,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)),X23743),
    inference(variable_rename,[status(thm)],[fact_divmod__nat__zero]) ).

fof(i_0_6061,plain,
    ! [X98] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X98)),
    inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).

fof(i_0_6062,plain,
    ! [X98] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X98)),
    inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).

fof(i_0_6063,plain,
    ! [X24780,X24781] :
      ( ( c_Int_OBit0(X24781) != c_Int_OBit0(X24780)
        | X24781 = X24780 )
      & ( X24781 != X24780
        | c_Int_OBit0(X24781) = c_Int_OBit0(X24780) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I48_J])]) ).

fof(i_0_6064,plain,
    ! [X2,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X2),X11) = c_Groups_Ozero__class_Ozero(X16) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__infinite]) ).

fof(i_0_6065,plain,
    ! [X1,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__add(X16)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X16),X1),X11) = c_Groups_Ozero__class_Ozero(X16) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum_Oinfinite]) ).

fof(i_0_6066,plain,
    ! [X1,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X1),X11) = c_Groups_Oone__class_Oone(X16) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod_Oinfinite]) ).

fof(i_0_6067,plain,
    ! [X2,X11,X5,X16] :
      ( class_Groups_Ocomm__monoid__mult(X16)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X16),X2),X11) = c_Groups_Oone__class_Oone(X16) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__infinite]) ).

fof(i_0_6068,plain,
    ! [X98] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X98))),
    inference(fof_simplification,[status(thm)],[fact_not__neg__int]) ).

fof(i_0_6069,plain,
    ! [X25566] : c_Code__Numeral_OSuc__code__numeral(X25566) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I3_J]) ).

fof(i_0_6070,plain,
    ! [X25567] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X25567),
    inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I2_J]) ).

fof(i_0_6071,plain,
    ! [X28,X29] :
      ( ~ hBOOL(hAPP(hAPP(c_fimplies,X29),X28))
      | ~ hBOOL(X29)
      | hBOOL(X28) ),
    inference(fof_simplification,[status(thm)],[help_c__fimplies__3]) ).

fof(i_0_6072,plain,
    ! [X11,X5] :
      ( hAPP(c_Finite__Set_Ocard(X5),X11) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X11 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__eq__0__iff]) ).

fof(i_0_6073,plain,
    ! [X28,X29] :
      ( ~ hBOOL(hAPP(hAPP(c_fdisj,X29),X28))
      | hBOOL(X29)
      | hBOOL(X28) ),
    inference(fof_simplification,[status(thm)],[help_c__fdisj__3]) ).

fof(i_0_6074,plain,
    ! [X28,X29] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X29),X28))
      | hBOOL(X29) ),
    inference(fof_simplification,[status(thm)],[help_c__fconj__2]) ).

fof(i_0_6075,plain,
    ! [X28,X29] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X29),X28))
      | hBOOL(X28) ),
    inference(fof_simplification,[status(thm)],[help_c__fconj__3]) ).

fof(i_0_6076,plain,
    ! [X29,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),X29)
    <=> ! [X3] : ~ hBOOL(hAPP(X29,X3)) ),
    inference(fof_simplification,[status(thm)],[fact_empty__Collect__eq]) ).

fof(i_0_6077,plain,
    ! [X29,X5] :
      ( hAPP(c_Set_OCollect(X5),X29) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] : ~ hBOOL(hAPP(X29,X3)) ),
    inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).

fof(i_0_6078,plain,
    ! [X27,X12] :
      ( ~ hBOOL(hAPP(hAPP(c_fequal,X12),X27))
      | X12 = X27 ),
    inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).

fof(i_0_6079,plain,
    ! [X31295] : hAPP(c_Code__Numeral_Onat__of,X31295) = c_Code__Numeral_Onat__of__aux(X31295,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_nat__of__code]) ).

fof(i_0_6080,plain,
    ! [X29,X5] : ~ c_List_Olist__ex1(X5,X29,c_List_Olist_ONil(X5)),
    inference(fof_simplification,[status(thm)],[fact_list__ex1__simps_I1_J]) ).

fof(i_0_6081,plain,
    ! [X29,X5] : ~ c_List_Olist__ex(X5,X29,c_List_Olist_ONil(X5)),
    inference(fof_simplification,[status(thm)],[fact_list__ex__simps_I2_J]) ).

fof(i_0_6082,plain,
    ! [X24633] : c_Int_Opred(X24633) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24633),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[fact_pred__def]) ).

fof(i_0_6083,plain,
    ! [X24552] : c_Int_Osucc(X24552) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24552),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[fact_succ__def]) ).

fof(i_0_6084,plain,
    ! [X32436] : c_List_Oupt(X32436,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_6085,plain,
    ! [X28,X29] :
      ( ~ hBOOL(X29)
      | ~ hBOOL(X28)
      | hBOOL(hAPP(hAPP(c_fconj,X29),X28)) ),
    inference(fof_simplification,[status(thm)],[help_c__fconj__1]) ).

fof(i_0_6086,plain,
    ! [X25008] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X25008) = c_Int_Opred(X25008),
    inference(variable_rename,[status(thm)],[fact_add__Min]) ).

fof(i_0_6087,plain,
    ! [X15] :
      ( class_Int_Onumber__ring(X15)
     => ~ c_Int_Oiszero(X15,hAPP(c_Int_Onumber__class_Onumber__of(X15),c_Int_OMin)) ),
    inference(fof_simplification,[status(thm)],[fact_nonzero__number__of__Min]) ).

fof(i_0_6088,plain,
    ! [X28,X29] :
      ( ~ hBOOL(X29)
      | hBOOL(hAPP(hAPP(c_fdisj,X29),X28)) ),
    inference(fof_simplification,[status(thm)],[help_c__fdisj__1]) ).

fof(i_0_6089,plain,
    ! [X29,X28] :
      ( ~ hBOOL(X28)
      | hBOOL(hAPP(hAPP(c_fdisj,X29),X28)) ),
    inference(fof_simplification,[status(thm)],[help_c__fdisj__2]) ).

fof(i_0_6090,plain,
    ! [X29,X28] :
      ( ~ hBOOL(X28)
      | hBOOL(hAPP(hAPP(c_fimplies,X29),X28)) ),
    inference(fof_simplification,[status(thm)],[help_c__fimplies__2]) ).

fof(i_0_6091,plain,
    ! [X24786] :
      ( ( c_Int_OPls != c_Int_OBit0(X24786)
        | c_Int_OPls = X24786 )
      & ( c_Int_OPls != X24786
        | c_Int_OPls = c_Int_OBit0(X24786) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I38_J])]) ).

fof(i_0_6092,plain,
    ! [X24785] :
      ( ( c_Int_OBit0(X24785) != c_Int_OPls
        | X24785 = c_Int_OPls )
      & ( X24785 != c_Int_OPls
        | c_Int_OBit0(X24785) = c_Int_OPls ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I44_J])]) ).

fof(i_0_6093,plain,
    ! [X24994] : c_Int_OBit0(X24994) != c_Int_OMin,
    inference(variable_rename,[status(thm)],[fact_rel__simps_I45_J]) ).

fof(i_0_6094,plain,
    ! [X24995] : c_Int_OMin != c_Int_OBit0(X24995),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I42_J]) ).

fof(i_0_6095,plain,
    ! [X23] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X23))
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X23)) = X23 ),
    inference(fof_simplification,[status(thm)],[fact_not__neg__nat]) ).

fof(i_0_6096,plain,
    ! [X11,X5] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))
     => hAPP(c_Finite__Set_Ocard(X5),X11) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_simplification,[status(thm)],[fact_card__infinite]) ).

fof(i_0_6097,plain,
    ! [X29] :
      ( ~ hBOOL(hAPP(c_fNot,X29))
      | ~ hBOOL(X29) ),
    inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).

fof(i_0_6098,plain,
    ! [X15] :
      ( class_Rings_Osemiring__1(X15)
     => ~ c_Int_Oiszero(X15,c_Groups_Oone__class_Oone(X15)) ),
    inference(fof_simplification,[status(thm)],[fact_not__iszero__1]) ).

fof(i_0_6099,plain,
    ! [X29] :
      ( hBOOL(X29)
      | hBOOL(hAPP(c_fNot,X29)) ),
    inference(fof_simplification,[status(thm)],[help_c__fNot__2]) ).

fof(i_0_6100,plain,
    ! [X19827,X19828,X19829,X19830,X19831,X19832,X19833,X19834,X19835,X19836,X19837] :
      ( ( hBOOL(hAPP(hAPP(c_member(X19837),esk54_11(X19827,X19828,X19829,X19830,X19831,X19832,X19833,X19834,X19835,X19836,X19837)),X19836))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X19831,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19837,tc_fun(X19831,tc_HOL_Obool)),X19829),hAPP(hAPP(c_COMBB(tc_fun(X19834,tc_fun(X19831,tc_HOL_Obool)),tc_fun(X19831,tc_HOL_Obool),X19837),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19834,tc_fun(X19831,tc_HOL_Obool)),X19828)),X19830))),X19827))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X19834,tc_HOL_Obool)),X19828),hAPP(hAPP(c_Equiv__Relations_Oquotient(X19834),X19833),X19832)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X19837,tc_HOL_Obool)),X19829),hAPP(hAPP(c_Equiv__Relations_Oquotient(X19837),X19836),X19835)))
        | ~ c_Equiv__Relations_Ocongruent2(X19837,X19834,tc_fun(X19831,tc_HOL_Obool),X19835,X19832,X19830)
        | ~ c_Equiv__Relations_Oequiv(X19834,X19833,X19832)
        | ~ c_Equiv__Relations_Oequiv(X19837,X19836,X19835) )
      & ( hBOOL(hAPP(hAPP(c_member(X19834),esk55_11(X19827,X19828,X19829,X19830,X19831,X19832,X19833,X19834,X19835,X19836,X19837)),X19833))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X19831,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19837,tc_fun(X19831,tc_HOL_Obool)),X19829),hAPP(hAPP(c_COMBB(tc_fun(X19834,tc_fun(X19831,tc_HOL_Obool)),tc_fun(X19831,tc_HOL_Obool),X19837),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19834,tc_fun(X19831,tc_HOL_Obool)),X19828)),X19830))),X19827))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X19834,tc_HOL_Obool)),X19828),hAPP(hAPP(c_Equiv__Relations_Oquotient(X19834),X19833),X19832)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X19837,tc_HOL_Obool)),X19829),hAPP(hAPP(c_Equiv__Relations_Oquotient(X19837),X19836),X19835)))
        | ~ c_Equiv__Relations_Ocongruent2(X19837,X19834,tc_fun(X19831,tc_HOL_Obool),X19835,X19832,X19830)
        | ~ c_Equiv__Relations_Oequiv(X19834,X19833,X19832)
        | ~ c_Equiv__Relations_Oequiv(X19837,X19836,X19835) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X19831,tc_HOL_Obool)),hAPP(hAPP(X19830,esk54_11(X19827,X19828,X19829,X19830,X19831,X19832,X19833,X19834,X19835,X19836,X19837)),esk55_11(X19827,X19828,X19829,X19830,X19831,X19832,X19833,X19834,X19835,X19836,X19837))),X19827))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X19831,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19837,tc_fun(X19831,tc_HOL_Obool)),X19829),hAPP(hAPP(c_COMBB(tc_fun(X19834,tc_fun(X19831,tc_HOL_Obool)),tc_fun(X19831,tc_HOL_Obool),X19837),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19834,tc_fun(X19831,tc_HOL_Obool)),X19828)),X19830))),X19827))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X19834,tc_HOL_Obool)),X19828),hAPP(hAPP(c_Equiv__Relations_Oquotient(X19834),X19833),X19832)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X19837,tc_HOL_Obool)),X19829),hAPP(hAPP(c_Equiv__Relations_Oquotient(X19837),X19836),X19835)))
        | ~ c_Equiv__Relations_Ocongruent2(X19837,X19834,tc_fun(X19831,tc_HOL_Obool),X19835,X19832,X19830)
        | ~ c_Equiv__Relations_Oequiv(X19834,X19833,X19832)
        | ~ c_Equiv__Relations_Oequiv(X19837,X19836,X19835) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__type2])])])]) ).

cnf(i_0_6101,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_5249]) ).

cnf(i_0_6102,plain,
    c_Int_Osucc(c_Int_OBit0(X1)) = c_Int_OBit1(X1),
    inference(split_conjunct,[status(thm)],[i_0_5250]) ).

cnf(i_0_6103,plain,
    c_Int_OBit0(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1),
    inference(split_conjunct,[status(thm)],[i_0_5251]) ).

cnf(i_0_6104,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_5252]) ).

fof(i_0_6105,plain,
    ! [X27881,X27882,X27883,X27884,X27885,X27886,X27887] :
      ( ~ class_Rings_Osemiring__0(X27887)
      | ~ c_Fun_Oinj__on(tc_prod(X27886,X27885),X27887,hAPP(c_Product__Type_Oprod_Oprod__case(X27886,X27885,X27887),hAPP(hAPP(c_COMBC(X27886,tc_fun(X27885,X27887),tc_fun(X27885,X27887)),hAPP(hAPP(c_COMBB(tc_fun(X27887,X27887),tc_fun(tc_fun(X27885,X27887),tc_fun(X27885,X27887)),X27886),c_COMBB(X27887,X27887,X27885)),hAPP(hAPP(c_COMBB(X27887,tc_fun(X27887,X27887),X27886),c_Groups_Otimes__class_Otimes(X27887)),X27884))),X27883)),hAPP(hAPP(c_Product__Type_OSigma(X27886,X27885),X27882),hAPP(c_COMBK(tc_fun(X27885,tc_HOL_Obool),X27886),X27881)))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27887),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27886,X27887),X27884),X27882)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27885,X27887),X27883),X27881)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27887,X27887),c_Fun_Oid(X27887)),hAPP(c_Set_OCollect(X27887),hAPP(hAPP(c_COMBB(tc_fun(X27886,tc_HOL_Obool),tc_HOL_Obool,X27887),c_HOL_OEx(X27886)),hAPP(hAPP(c_COMBB(tc_fun(X27886,tc_fun(X27885,tc_HOL_Obool)),tc_fun(X27886,tc_HOL_Obool),X27887),hAPP(c_COMBB(tc_fun(X27885,tc_HOL_Obool),tc_HOL_Obool,X27886),c_HOL_OEx(X27885))),hAPP(hAPP(c_COMBC(X27887,tc_fun(X27886,tc_fun(X27885,tc_HOL_Obool)),tc_fun(X27886,tc_fun(X27885,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27886,tc_fun(tc_fun(X27885,tc_HOL_Obool),tc_fun(X27885,tc_HOL_Obool))),tc_fun(tc_fun(X27886,tc_fun(X27885,tc_HOL_Obool)),tc_fun(X27886,tc_fun(X27885,tc_HOL_Obool))),X27887),c_COMBS(X27886,tc_fun(X27885,tc_HOL_Obool),tc_fun(X27885,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27886,tc_fun(X27885,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X27886,tc_fun(tc_fun(X27885,tc_HOL_Obool),tc_fun(X27885,tc_HOL_Obool))),X27887),hAPP(c_COMBB(tc_fun(X27885,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27885,tc_HOL_Obool),tc_fun(X27885,tc_HOL_Obool)),X27886),c_COMBS(X27885,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27886,tc_fun(X27885,tc_HOL_Obool)),tc_fun(X27886,tc_fun(X27885,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X27887),hAPP(c_COMBB(tc_fun(X27885,tc_HOL_Obool),tc_fun(X27885,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27886),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27885),c_fconj))),hAPP(hAPP(c_COMBC(X27887,tc_fun(X27886,tc_fun(X27885,X27887)),tc_fun(X27886,tc_fun(X27885,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27885,X27887),tc_fun(X27885,tc_HOL_Obool)),tc_fun(tc_fun(X27886,tc_fun(X27885,X27887)),tc_fun(X27886,tc_fun(X27885,tc_HOL_Obool))),X27887),c_COMBB(tc_fun(X27885,X27887),tc_fun(X27885,tc_HOL_Obool),X27886)),hAPP(hAPP(c_COMBB(tc_fun(X27887,tc_HOL_Obool),tc_fun(tc_fun(X27885,X27887),tc_fun(X27885,tc_HOL_Obool)),X27887),c_COMBB(X27887,tc_HOL_Obool,X27885)),c_fequal))),hAPP(hAPP(c_COMBC(X27886,tc_fun(X27885,X27887),tc_fun(X27885,X27887)),hAPP(hAPP(c_COMBB(tc_fun(X27887,X27887),tc_fun(tc_fun(X27885,X27887),tc_fun(X27885,X27887)),X27886),c_COMBB(X27887,X27887,X27885)),hAPP(hAPP(c_COMBB(X27887,tc_fun(X27887,X27887),X27886),c_Groups_Otimes__class_Otimes(X27887)),X27884))),X27883)))))),hAPP(hAPP(c_COMBC(X27886,tc_fun(X27885,tc_HOL_Obool),tc_fun(X27885,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27885,tc_HOL_Obool),tc_fun(X27885,tc_HOL_Obool)),X27886),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27885)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27886),c_fconj),hAPP(hAPP(c_COMBC(X27886,tc_fun(X27886,tc_HOL_Obool),tc_HOL_Obool),c_member(X27886)),X27882)))),hAPP(hAPP(c_COMBC(X27885,tc_fun(X27885,tc_HOL_Obool),tc_HOL_Obool),c_member(X27885)),X27881))))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mult__setsum__if__inj])]) ).

fof(i_0_6106,plain,
    ! [X27264,X27265,X27266,X27267,X27268] : hAPP(hAPP(c_Relation_Orel__comp(X27268,X27267,X27266),X27265),X27264) = hAPP(c_Set_OCollect(tc_prod(X27268,X27266)),hAPP(c_Product__Type_Oprod_Oprod__case(X27268,X27266,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X27266,tc_fun(X27267,tc_HOL_Obool)),tc_fun(X27266,tc_HOL_Obool),X27268),hAPP(c_COMBB(tc_fun(X27267,tc_HOL_Obool),tc_HOL_Obool,X27266),c_HOL_OEx(X27267))),hAPP(hAPP(c_COMBC(X27268,tc_fun(X27266,tc_fun(X27267,tc_HOL_Obool)),tc_fun(X27266,tc_fun(X27267,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27267,tc_HOL_Obool),tc_fun(X27267,tc_HOL_Obool)),tc_fun(tc_fun(X27266,tc_fun(X27267,tc_HOL_Obool)),tc_fun(X27266,tc_fun(X27267,tc_HOL_Obool))),X27268),c_COMBB(tc_fun(X27267,tc_HOL_Obool),tc_fun(X27267,tc_HOL_Obool),X27266)),hAPP(hAPP(c_COMBB(tc_fun(X27267,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27267,tc_HOL_Obool),tc_fun(X27267,tc_HOL_Obool)),X27268),c_COMBS(X27267,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27267,tc_HOL_Obool),tc_fun(X27267,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27268),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27267),c_fconj)),hAPP(hAPP(c_COMBC(X27268,tc_fun(tc_prod(X27268,X27267),tc_HOL_Obool),tc_fun(X27267,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27267,tc_fun(tc_fun(tc_prod(X27268,X27267),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27268,X27267),tc_HOL_Obool),tc_fun(X27267,tc_HOL_Obool)),X27268),c_COMBC(X27267,tc_fun(tc_prod(X27268,X27267),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27267,tc_prod(X27268,X27267)),tc_fun(X27267,tc_fun(tc_fun(tc_prod(X27268,X27267),tc_HOL_Obool),tc_HOL_Obool)),X27268),hAPP(c_COMBB(tc_prod(X27268,X27267),tc_fun(tc_fun(tc_prod(X27268,X27267),tc_HOL_Obool),tc_HOL_Obool),X27267),c_member(tc_prod(X27268,X27267)))),c_Product__Type_OPair(X27268,X27267)))),X27265))))),hAPP(hAPP(c_COMBC(X27266,tc_fun(tc_prod(X27267,X27266),tc_HOL_Obool),tc_fun(X27267,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27267,tc_fun(tc_fun(tc_prod(X27267,X27266),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27267,X27266),tc_HOL_Obool),tc_fun(X27267,tc_HOL_Obool)),X27266),c_COMBC(X27267,tc_fun(tc_prod(X27267,X27266),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27267,tc_prod(X27267,X27266)),tc_fun(X27267,tc_fun(tc_fun(tc_prod(X27267,X27266),tc_HOL_Obool),tc_HOL_Obool)),X27266),hAPP(c_COMBB(tc_prod(X27267,X27266),tc_fun(tc_fun(tc_prod(X27267,X27266),tc_HOL_Obool),tc_HOL_Obool),X27267),c_member(tc_prod(X27267,X27266)))),hAPP(c_COMBC(X27267,X27266,tc_prod(X27267,X27266)),c_Product__Type_OPair(X27267,X27266))))),X27264))))),
    inference(variable_rename,[status(thm)],[fact_rel__comp__def]) ).

fof(i_0_6107,plain,
    ! [X25709,X25710,X25711] :
      ( ~ class_Orderings_Olinorder(X25711)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25711),X25710))
      | X25710 = c_Orderings_Obot__class_Obot(tc_fun(X25711,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25711),X25709))
      | X25709 = c_Orderings_Obot__class_Obot(tc_fun(X25711,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25711),c_Big__Operators_Olattice_OInf__fin(X25711,c_Orderings_Oord__class_Omin(X25711),X25710)),c_Big__Operators_Olattice_OInf__fin(X25711,c_Orderings_Oord__class_Omin(X25711),X25709)) = c_Big__Operators_Olattice_OInf__fin(X25711,c_Orderings_Oord__class_Omin(X25711),hAPP(c_Set_OCollect(X25711),hAPP(hAPP(c_COMBB(tc_fun(X25711,tc_HOL_Obool),tc_HOL_Obool,X25711),c_HOL_OEx(X25711)),hAPP(hAPP(c_COMBB(tc_fun(X25711,tc_fun(X25711,tc_HOL_Obool)),tc_fun(X25711,tc_HOL_Obool),X25711),hAPP(c_COMBB(tc_fun(X25711,tc_HOL_Obool),tc_HOL_Obool,X25711),c_HOL_OEx(X25711))),hAPP(hAPP(c_COMBC(X25711,tc_fun(X25711,tc_fun(X25711,tc_HOL_Obool)),tc_fun(X25711,tc_fun(X25711,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25711,tc_fun(tc_fun(X25711,tc_HOL_Obool),tc_fun(X25711,tc_HOL_Obool))),tc_fun(tc_fun(X25711,tc_fun(X25711,tc_HOL_Obool)),tc_fun(X25711,tc_fun(X25711,tc_HOL_Obool))),X25711),c_COMBS(X25711,tc_fun(X25711,tc_HOL_Obool),tc_fun(X25711,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25711,tc_fun(X25711,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X25711,tc_fun(tc_fun(X25711,tc_HOL_Obool),tc_fun(X25711,tc_HOL_Obool))),X25711),hAPP(c_COMBB(tc_fun(X25711,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X25711,tc_HOL_Obool),tc_fun(X25711,tc_HOL_Obool)),X25711),c_COMBS(X25711,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25711,tc_fun(X25711,tc_HOL_Obool)),tc_fun(X25711,tc_fun(X25711,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X25711),hAPP(c_COMBB(tc_fun(X25711,tc_HOL_Obool),tc_fun(X25711,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X25711),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25711),c_fconj))),hAPP(hAPP(c_COMBC(X25711,tc_fun(X25711,tc_fun(X25711,X25711)),tc_fun(X25711,tc_fun(X25711,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X25711,X25711),tc_fun(X25711,tc_HOL_Obool)),tc_fun(tc_fun(X25711,tc_fun(X25711,X25711)),tc_fun(X25711,tc_fun(X25711,tc_HOL_Obool))),X25711),c_COMBB(tc_fun(X25711,X25711),tc_fun(X25711,tc_HOL_Obool),X25711)),hAPP(hAPP(c_COMBB(tc_fun(X25711,tc_HOL_Obool),tc_fun(tc_fun(X25711,X25711),tc_fun(X25711,tc_HOL_Obool)),X25711),c_COMBB(X25711,tc_HOL_Obool,X25711)),c_fequal))),c_Orderings_Oord__class_Omax(X25711)))))),hAPP(hAPP(c_COMBC(X25711,tc_fun(X25711,tc_HOL_Obool),tc_fun(X25711,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X25711,tc_HOL_Obool),tc_fun(X25711,tc_HOL_Obool)),X25711),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X25711)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25711),c_fconj),hAPP(hAPP(c_COMBC(X25711,tc_fun(X25711,tc_HOL_Obool),tc_HOL_Obool),c_member(X25711)),X25710)))),hAPP(hAPP(c_COMBC(X25711,tc_fun(X25711,tc_HOL_Obool),tc_HOL_Obool),c_member(X25711)),X25709))))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf2__distrib])]) ).

fof(i_0_6108,plain,
    ! [X25935,X25936,X25937] :
      ( ~ class_Orderings_Olinorder(X25937)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25937),X25936))
      | X25936 = c_Orderings_Obot__class_Obot(tc_fun(X25937,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25937),X25935))
      | X25935 = c_Orderings_Obot__class_Obot(tc_fun(X25937,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25937),c_Big__Operators_Olattice_OSup__fin(X25937,c_Orderings_Oord__class_Omax(X25937),X25936)),c_Big__Operators_Olattice_OSup__fin(X25937,c_Orderings_Oord__class_Omax(X25937),X25935)) = c_Big__Operators_Olattice_OSup__fin(X25937,c_Orderings_Oord__class_Omax(X25937),hAPP(c_Set_OCollect(X25937),hAPP(hAPP(c_COMBB(tc_fun(X25937,tc_HOL_Obool),tc_HOL_Obool,X25937),c_HOL_OEx(X25937)),hAPP(hAPP(c_COMBB(tc_fun(X25937,tc_fun(X25937,tc_HOL_Obool)),tc_fun(X25937,tc_HOL_Obool),X25937),hAPP(c_COMBB(tc_fun(X25937,tc_HOL_Obool),tc_HOL_Obool,X25937),c_HOL_OEx(X25937))),hAPP(hAPP(c_COMBC(X25937,tc_fun(X25937,tc_fun(X25937,tc_HOL_Obool)),tc_fun(X25937,tc_fun(X25937,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25937,tc_fun(tc_fun(X25937,tc_HOL_Obool),tc_fun(X25937,tc_HOL_Obool))),tc_fun(tc_fun(X25937,tc_fun(X25937,tc_HOL_Obool)),tc_fun(X25937,tc_fun(X25937,tc_HOL_Obool))),X25937),c_COMBS(X25937,tc_fun(X25937,tc_HOL_Obool),tc_fun(X25937,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25937,tc_fun(X25937,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X25937,tc_fun(tc_fun(X25937,tc_HOL_Obool),tc_fun(X25937,tc_HOL_Obool))),X25937),hAPP(c_COMBB(tc_fun(X25937,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X25937,tc_HOL_Obool),tc_fun(X25937,tc_HOL_Obool)),X25937),c_COMBS(X25937,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25937,tc_fun(X25937,tc_HOL_Obool)),tc_fun(X25937,tc_fun(X25937,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X25937),hAPP(c_COMBB(tc_fun(X25937,tc_HOL_Obool),tc_fun(X25937,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X25937),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25937),c_fconj))),hAPP(hAPP(c_COMBC(X25937,tc_fun(X25937,tc_fun(X25937,X25937)),tc_fun(X25937,tc_fun(X25937,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X25937,X25937),tc_fun(X25937,tc_HOL_Obool)),tc_fun(tc_fun(X25937,tc_fun(X25937,X25937)),tc_fun(X25937,tc_fun(X25937,tc_HOL_Obool))),X25937),c_COMBB(tc_fun(X25937,X25937),tc_fun(X25937,tc_HOL_Obool),X25937)),hAPP(hAPP(c_COMBB(tc_fun(X25937,tc_HOL_Obool),tc_fun(tc_fun(X25937,X25937),tc_fun(X25937,tc_HOL_Obool)),X25937),c_COMBB(X25937,tc_HOL_Obool,X25937)),c_fequal))),c_Orderings_Oord__class_Omin(X25937)))))),hAPP(hAPP(c_COMBC(X25937,tc_fun(X25937,tc_HOL_Obool),tc_fun(X25937,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X25937,tc_HOL_Obool),tc_fun(X25937,tc_HOL_Obool)),X25937),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X25937)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25937),c_fconj),hAPP(hAPP(c_COMBC(X25937,tc_fun(X25937,tc_HOL_Obool),tc_HOL_Obool),c_member(X25937)),X25936)))),hAPP(hAPP(c_COMBC(X25937,tc_fun(X25937,tc_HOL_Obool),tc_HOL_Obool),c_member(X25937)),X25935))))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup2__distrib])]) ).

fof(i_0_6109,plain,
    ! [X21055,X21056,X21057] :
      ( ~ class_Lattices_Odistrib__lattice(X21057)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21057),X21056))
      | X21056 = c_Orderings_Obot__class_Obot(tc_fun(X21057,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21057),X21055))
      | X21055 = c_Orderings_Obot__class_Obot(tc_fun(X21057,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X21057),c_Big__Operators_Olattice__class_OSup__fin(X21057,X21056)),c_Big__Operators_Olattice__class_OSup__fin(X21057,X21055)) = c_Big__Operators_Olattice__class_OSup__fin(X21057,hAPP(c_Set_OCollect(X21057),hAPP(hAPP(c_COMBB(tc_fun(X21057,tc_HOL_Obool),tc_HOL_Obool,X21057),c_HOL_OEx(X21057)),hAPP(hAPP(c_COMBB(tc_fun(X21057,tc_fun(X21057,tc_HOL_Obool)),tc_fun(X21057,tc_HOL_Obool),X21057),hAPP(c_COMBB(tc_fun(X21057,tc_HOL_Obool),tc_HOL_Obool,X21057),c_HOL_OEx(X21057))),hAPP(hAPP(c_COMBC(X21057,tc_fun(X21057,tc_fun(X21057,tc_HOL_Obool)),tc_fun(X21057,tc_fun(X21057,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X21057,tc_fun(tc_fun(X21057,tc_HOL_Obool),tc_fun(X21057,tc_HOL_Obool))),tc_fun(tc_fun(X21057,tc_fun(X21057,tc_HOL_Obool)),tc_fun(X21057,tc_fun(X21057,tc_HOL_Obool))),X21057),c_COMBS(X21057,tc_fun(X21057,tc_HOL_Obool),tc_fun(X21057,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X21057,tc_fun(X21057,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X21057,tc_fun(tc_fun(X21057,tc_HOL_Obool),tc_fun(X21057,tc_HOL_Obool))),X21057),hAPP(c_COMBB(tc_fun(X21057,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X21057,tc_HOL_Obool),tc_fun(X21057,tc_HOL_Obool)),X21057),c_COMBS(X21057,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X21057,tc_fun(X21057,tc_HOL_Obool)),tc_fun(X21057,tc_fun(X21057,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X21057),hAPP(c_COMBB(tc_fun(X21057,tc_HOL_Obool),tc_fun(X21057,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X21057),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X21057),c_fconj))),hAPP(hAPP(c_COMBC(X21057,tc_fun(X21057,tc_fun(X21057,X21057)),tc_fun(X21057,tc_fun(X21057,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X21057,X21057),tc_fun(X21057,tc_HOL_Obool)),tc_fun(tc_fun(X21057,tc_fun(X21057,X21057)),tc_fun(X21057,tc_fun(X21057,tc_HOL_Obool))),X21057),c_COMBB(tc_fun(X21057,X21057),tc_fun(X21057,tc_HOL_Obool),X21057)),hAPP(hAPP(c_COMBB(tc_fun(X21057,tc_HOL_Obool),tc_fun(tc_fun(X21057,X21057),tc_fun(X21057,tc_HOL_Obool)),X21057),c_COMBB(X21057,tc_HOL_Obool,X21057)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X21057)))))),hAPP(hAPP(c_COMBC(X21057,tc_fun(X21057,tc_HOL_Obool),tc_fun(X21057,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X21057,tc_HOL_Obool),tc_fun(X21057,tc_HOL_Obool)),X21057),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X21057)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X21057),c_fconj),hAPP(hAPP(c_COMBC(X21057,tc_fun(X21057,tc_HOL_Obool),tc_HOL_Obool),c_member(X21057)),X21056)))),hAPP(hAPP(c_COMBC(X21057,tc_fun(X21057,tc_HOL_Obool),tc_HOL_Obool),c_member(X21057)),X21055))))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Sup2__distrib])]) ).

fof(i_0_6110,plain,
    ! [X21061,X21062,X21063] :
      ( ~ class_Lattices_Odistrib__lattice(X21063)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21063),X21062))
      | X21062 = c_Orderings_Obot__class_Obot(tc_fun(X21063,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21063),X21061))
      | X21061 = c_Orderings_Obot__class_Obot(tc_fun(X21063,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X21063),c_Big__Operators_Olattice__class_OInf__fin(X21063,X21062)),c_Big__Operators_Olattice__class_OInf__fin(X21063,X21061)) = c_Big__Operators_Olattice__class_OInf__fin(X21063,hAPP(c_Set_OCollect(X21063),hAPP(hAPP(c_COMBB(tc_fun(X21063,tc_HOL_Obool),tc_HOL_Obool,X21063),c_HOL_OEx(X21063)),hAPP(hAPP(c_COMBB(tc_fun(X21063,tc_fun(X21063,tc_HOL_Obool)),tc_fun(X21063,tc_HOL_Obool),X21063),hAPP(c_COMBB(tc_fun(X21063,tc_HOL_Obool),tc_HOL_Obool,X21063),c_HOL_OEx(X21063))),hAPP(hAPP(c_COMBC(X21063,tc_fun(X21063,tc_fun(X21063,tc_HOL_Obool)),tc_fun(X21063,tc_fun(X21063,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X21063,tc_fun(tc_fun(X21063,tc_HOL_Obool),tc_fun(X21063,tc_HOL_Obool))),tc_fun(tc_fun(X21063,tc_fun(X21063,tc_HOL_Obool)),tc_fun(X21063,tc_fun(X21063,tc_HOL_Obool))),X21063),c_COMBS(X21063,tc_fun(X21063,tc_HOL_Obool),tc_fun(X21063,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X21063,tc_fun(X21063,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X21063,tc_fun(tc_fun(X21063,tc_HOL_Obool),tc_fun(X21063,tc_HOL_Obool))),X21063),hAPP(c_COMBB(tc_fun(X21063,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X21063,tc_HOL_Obool),tc_fun(X21063,tc_HOL_Obool)),X21063),c_COMBS(X21063,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X21063,tc_fun(X21063,tc_HOL_Obool)),tc_fun(X21063,tc_fun(X21063,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X21063),hAPP(c_COMBB(tc_fun(X21063,tc_HOL_Obool),tc_fun(X21063,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X21063),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X21063),c_fconj))),hAPP(hAPP(c_COMBC(X21063,tc_fun(X21063,tc_fun(X21063,X21063)),tc_fun(X21063,tc_fun(X21063,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X21063,X21063),tc_fun(X21063,tc_HOL_Obool)),tc_fun(tc_fun(X21063,tc_fun(X21063,X21063)),tc_fun(X21063,tc_fun(X21063,tc_HOL_Obool))),X21063),c_COMBB(tc_fun(X21063,X21063),tc_fun(X21063,tc_HOL_Obool),X21063)),hAPP(hAPP(c_COMBB(tc_fun(X21063,tc_HOL_Obool),tc_fun(tc_fun(X21063,X21063),tc_fun(X21063,tc_HOL_Obool)),X21063),c_COMBB(X21063,tc_HOL_Obool,X21063)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X21063)))))),hAPP(hAPP(c_COMBC(X21063,tc_fun(X21063,tc_HOL_Obool),tc_fun(X21063,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X21063,tc_HOL_Obool),tc_fun(X21063,tc_HOL_Obool)),X21063),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X21063)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X21063),c_fconj),hAPP(hAPP(c_COMBC(X21063,tc_fun(X21063,tc_HOL_Obool),tc_HOL_Obool),c_member(X21063)),X21062)))),hAPP(hAPP(c_COMBC(X21063,tc_fun(X21063,tc_HOL_Obool),tc_HOL_Obool),c_member(X21063)),X21061))))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Inf2__distrib])]) ).

fof(i_0_6111,plain,
    ! [X30366,X30367,X30368] : c_List_Oset__Cons(X30368,X30367,X30366) = hAPP(c_Set_OCollect(tc_List_Olist(X30368)),hAPP(hAPP(c_COMBB(tc_fun(X30368,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X30368)),c_HOL_OEx(X30368)),hAPP(hAPP(c_COMBB(tc_fun(X30368,tc_fun(tc_List_Olist(X30368),tc_HOL_Obool)),tc_fun(X30368,tc_HOL_Obool),tc_List_Olist(X30368)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X30368),tc_HOL_Obool),tc_HOL_Obool,X30368),c_HOL_OEx(tc_List_Olist(X30368)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X30368),tc_fun(X30368,tc_fun(tc_List_Olist(X30368),tc_HOL_Obool)),tc_fun(X30368,tc_fun(tc_List_Olist(X30368),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X30368,tc_fun(tc_fun(tc_List_Olist(X30368),tc_HOL_Obool),tc_fun(tc_List_Olist(X30368),tc_HOL_Obool))),tc_fun(tc_fun(X30368,tc_fun(tc_List_Olist(X30368),tc_HOL_Obool)),tc_fun(X30368,tc_fun(tc_List_Olist(X30368),tc_HOL_Obool))),tc_List_Olist(X30368)),c_COMBS(X30368,tc_fun(tc_List_Olist(X30368),tc_HOL_Obool),tc_fun(tc_List_Olist(X30368),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X30368,tc_fun(tc_List_Olist(X30368),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X30368,tc_fun(tc_fun(tc_List_Olist(X30368),tc_HOL_Obool),tc_fun(tc_List_Olist(X30368),tc_HOL_Obool))),tc_List_Olist(X30368)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X30368),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X30368),tc_HOL_Obool),tc_fun(tc_List_Olist(X30368),tc_HOL_Obool)),X30368),c_COMBS(tc_List_Olist(X30368),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X30368,tc_fun(tc_List_Olist(X30368),tc_HOL_Obool)),tc_fun(X30368,tc_fun(tc_List_Olist(X30368),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X30368)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X30368),tc_HOL_Obool),tc_fun(tc_List_Olist(X30368),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X30368),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X30368)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X30368),tc_fun(X30368,tc_fun(tc_List_Olist(X30368),tc_List_Olist(X30368))),tc_fun(X30368,tc_fun(tc_List_Olist(X30368),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X30368),tc_List_Olist(X30368)),tc_fun(tc_List_Olist(X30368),tc_HOL_Obool)),tc_fun(tc_fun(X30368,tc_fun(tc_List_Olist(X30368),tc_List_Olist(X30368))),tc_fun(X30368,tc_fun(tc_List_Olist(X30368),tc_HOL_Obool))),tc_List_Olist(X30368)),c_COMBB(tc_fun(tc_List_Olist(X30368),tc_List_Olist(X30368)),tc_fun(tc_List_Olist(X30368),tc_HOL_Obool),X30368)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X30368),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X30368),tc_List_Olist(X30368)),tc_fun(tc_List_Olist(X30368),tc_HOL_Obool)),tc_List_Olist(X30368)),c_COMBB(tc_List_Olist(X30368),tc_HOL_Obool,tc_List_Olist(X30368))),c_fequal))),c_List_Olist_OCons(X30368)))))),hAPP(hAPP(c_COMBC(X30368,tc_fun(tc_List_Olist(X30368),tc_HOL_Obool),tc_fun(tc_List_Olist(X30368),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X30368),tc_HOL_Obool),tc_fun(tc_List_Olist(X30368),tc_HOL_Obool)),X30368),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X30368))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X30368),c_fconj),hAPP(hAPP(c_COMBC(X30368,tc_fun(X30368,tc_HOL_Obool),tc_HOL_Obool),c_member(X30368)),X30367)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X30368),tc_fun(tc_List_Olist(X30368),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X30368))),X30366)))))),
    inference(variable_rename,[status(thm)],[fact_set__Cons__def]) ).

fof(i_0_6112,plain,
    ! [X28106,X28107,X28108,X28109,X28110,X28111,X28112,X28113] :
      ( ( X28111 = hAPP(hAPP(c_Product__Type_OPair(X28113,X28112),hAPP(X28108,esk279_8(X28106,X28107,X28108,X28109,X28110,X28111,X28112,X28113))),hAPP(X28107,esk280_8(X28106,X28107,X28108,X28109,X28110,X28111,X28112,X28113)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28113,X28112)),X28111),hAPP(c_Set_Oimage(tc_prod(X28110,X28109),tc_prod(X28113,X28112),c_Product__Type_Omap__pair(X28110,X28113,X28109,X28112,X28108,X28107)),X28106))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28110,X28109)),hAPP(hAPP(c_Product__Type_OPair(X28110,X28109),esk279_8(X28106,X28107,X28108,X28109,X28110,X28111,X28112,X28113)),esk280_8(X28106,X28107,X28108,X28109,X28110,X28111,X28112,X28113))),X28106))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28113,X28112)),X28111),hAPP(c_Set_Oimage(tc_prod(X28110,X28109),tc_prod(X28113,X28112),c_Product__Type_Omap__pair(X28110,X28113,X28109,X28112,X28108,X28107)),X28106))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5253])])])]) ).

cnf(i_0_6113,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_5254]) ).

cnf(i_0_6114,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_5255]) ).

cnf(i_0_6115,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_5256]) ).

fof(i_0_6116,plain,
    ! [X29804,X29805,X29806,X29807,X29808,X29809,X29810,X29811] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29807),esk366_8(X29804,X29805,X29806,X29807,X29808,X29809,X29810,X29811)),X29806))
        | ~ hBOOL(hAPP(hAPP(c_member(X29807),X29804),X29806))
        | hAPP(c_Set_Oimage(X29811,X29810,X29809),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29807,tc_fun(X29811,tc_HOL_Obool)),X29806),X29805)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29807,tc_fun(X29810,tc_HOL_Obool)),X29806),hAPP(hAPP(c_COMBB(tc_fun(X29811,tc_HOL_Obool),tc_fun(X29810,tc_HOL_Obool),X29807),c_Set_Oimage(X29811,X29810,X29809)),X29805))
        | ~ c_Fun_Oinj__on(X29811,X29810,X29809,X29808) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29811,tc_HOL_Obool)),hAPP(X29805,esk366_8(X29804,X29805,X29806,X29807,X29808,X29809,X29810,X29811))),X29808))
        | ~ hBOOL(hAPP(hAPP(c_member(X29807),X29804),X29806))
        | hAPP(c_Set_Oimage(X29811,X29810,X29809),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29807,tc_fun(X29811,tc_HOL_Obool)),X29806),X29805)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29807,tc_fun(X29810,tc_HOL_Obool)),X29806),hAPP(hAPP(c_COMBB(tc_fun(X29811,tc_HOL_Obool),tc_fun(X29810,tc_HOL_Obool),X29807),c_Set_Oimage(X29811,X29810,X29809)),X29805))
        | ~ c_Fun_Oinj__on(X29811,X29810,X29809,X29808) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__INT])])])]) ).

fof(i_0_6117,plain,
    ! [X19916,X19917,X19918,X19919,X19920,X19921] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19921,tc_fun(X19920,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X19921,tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_fun(X19920,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19920,tc_fun(tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_fun(X19920,tc_HOL_Obool)),X19921),c_COMBC(X19920,tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19920,tc_prod(X19921,X19920)),tc_fun(X19920,tc_fun(tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_HOL_Obool)),X19921),hAPP(c_COMBB(tc_prod(X19921,X19920),tc_fun(tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_HOL_Obool),X19920),c_member(tc_prod(X19921,X19920)))),c_Product__Type_OPair(X19921,X19920)))),X19919)),hAPP(hAPP(c_COMBC(X19921,tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_fun(X19920,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19920,tc_fun(tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_fun(X19920,tc_HOL_Obool)),X19921),c_COMBC(X19920,tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19920,tc_prod(X19921,X19920)),tc_fun(X19920,tc_fun(tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_HOL_Obool)),X19921),hAPP(c_COMBB(tc_prod(X19921,X19920),tc_fun(tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_HOL_Obool),X19920),c_member(tc_prod(X19921,X19920)))),c_Product__Type_OPair(X19921,X19920)))),X19918)),X19917),X19916))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X19921,X19920)),hAPP(hAPP(c_Product__Type_OPair(X19921,X19920),X19917),X19916)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool)),X19919),X19918))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X19921,X19920)),hAPP(hAPP(c_Product__Type_OPair(X19921,X19920),X19917),X19916)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool)),X19919),X19918)))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19921,tc_fun(X19920,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X19921,tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_fun(X19920,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19920,tc_fun(tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_fun(X19920,tc_HOL_Obool)),X19921),c_COMBC(X19920,tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19920,tc_prod(X19921,X19920)),tc_fun(X19920,tc_fun(tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_HOL_Obool)),X19921),hAPP(c_COMBB(tc_prod(X19921,X19920),tc_fun(tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_HOL_Obool),X19920),c_member(tc_prod(X19921,X19920)))),c_Product__Type_OPair(X19921,X19920)))),X19919)),hAPP(hAPP(c_COMBC(X19921,tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_fun(X19920,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19920,tc_fun(tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_fun(X19920,tc_HOL_Obool)),X19921),c_COMBC(X19920,tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19920,tc_prod(X19921,X19920)),tc_fun(X19920,tc_fun(tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_HOL_Obool)),X19921),hAPP(c_COMBB(tc_prod(X19921,X19920),tc_fun(tc_fun(tc_prod(X19921,X19920),tc_HOL_Obool),tc_HOL_Obool),X19920),c_member(tc_prod(X19921,X19920)))),c_Product__Type_OPair(X19921,X19920)))),X19918)),X19917),X19916)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq2])]) ).

fof(i_0_6118,plain,
    ! [X19967,X19968,X19969,X19970,X19971,X19972] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19972,tc_fun(X19971,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X19972,tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_fun(X19971,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19971,tc_fun(tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_fun(X19971,tc_HOL_Obool)),X19972),c_COMBC(X19971,tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19971,tc_prod(X19972,X19971)),tc_fun(X19971,tc_fun(tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_HOL_Obool)),X19972),hAPP(c_COMBB(tc_prod(X19972,X19971),tc_fun(tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_HOL_Obool),X19971),c_member(tc_prod(X19972,X19971)))),c_Product__Type_OPair(X19972,X19971)))),X19970)),hAPP(hAPP(c_COMBC(X19972,tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_fun(X19971,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19971,tc_fun(tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_fun(X19971,tc_HOL_Obool)),X19972),c_COMBC(X19971,tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19971,tc_prod(X19972,X19971)),tc_fun(X19971,tc_fun(tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_HOL_Obool)),X19972),hAPP(c_COMBB(tc_prod(X19972,X19971),tc_fun(tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_HOL_Obool),X19971),c_member(tc_prod(X19972,X19971)))),c_Product__Type_OPair(X19972,X19971)))),X19969)),X19968),X19967))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X19972,X19971)),hAPP(hAPP(c_Product__Type_OPair(X19972,X19971),X19968),X19967)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool)),X19970),X19969))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X19972,X19971)),hAPP(hAPP(c_Product__Type_OPair(X19972,X19971),X19968),X19967)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool)),X19970),X19969)))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19972,tc_fun(X19971,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X19972,tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_fun(X19971,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19971,tc_fun(tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_fun(X19971,tc_HOL_Obool)),X19972),c_COMBC(X19971,tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19971,tc_prod(X19972,X19971)),tc_fun(X19971,tc_fun(tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_HOL_Obool)),X19972),hAPP(c_COMBB(tc_prod(X19972,X19971),tc_fun(tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_HOL_Obool),X19971),c_member(tc_prod(X19972,X19971)))),c_Product__Type_OPair(X19972,X19971)))),X19970)),hAPP(hAPP(c_COMBC(X19972,tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_fun(X19971,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19971,tc_fun(tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_fun(X19971,tc_HOL_Obool)),X19972),c_COMBC(X19971,tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19971,tc_prod(X19972,X19971)),tc_fun(X19971,tc_fun(tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_HOL_Obool)),X19972),hAPP(c_COMBB(tc_prod(X19972,X19971),tc_fun(tc_fun(tc_prod(X19972,X19971),tc_HOL_Obool),tc_HOL_Obool),X19971),c_member(tc_prod(X19972,X19971)))),c_Product__Type_OPair(X19972,X19971)))),X19969)),X19968),X19967)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Un__eq2])]) ).

fof(i_0_6119,plain,
    ! [X30529,X30530] : c_List_Olenlex(X30530,X30529) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X30530),tc_List_Olist(X30530))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X30530),tc_List_Olist(X30530),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X30530),tc_fun(tc_List_Olist(X30530),tc_HOL_Obool),tc_fun(tc_List_Olist(X30530),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X30530),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X30530),tc_HOL_Obool),tc_fun(tc_List_Olist(X30530),tc_HOL_Obool)),tc_List_Olist(X30530)),c_COMBS(tc_List_Olist(X30530),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X30530),tc_HOL_Obool),tc_fun(tc_List_Olist(X30530),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X30530)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X30530)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X30530),tc_fun(tc_List_Olist(X30530),tc_Nat_Onat),tc_fun(tc_List_Olist(X30530),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X30530),tc_Nat_Onat),tc_fun(tc_List_Olist(X30530),tc_HOL_Obool)),tc_List_Olist(X30530)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X30530))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X30530)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X30530))))),c_Nat_Osize__class_Osize(tc_List_Olist(X30530)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X30530),tc_fun(tc_List_Olist(X30530),tc_HOL_Obool),tc_fun(tc_List_Olist(X30530),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X30530),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X30530),tc_HOL_Obool),tc_fun(tc_List_Olist(X30530),tc_HOL_Obool)),tc_List_Olist(X30530)),c_COMBS(tc_List_Olist(X30530),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X30530),tc_HOL_Obool),tc_fun(tc_List_Olist(X30530),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X30530)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X30530)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X30530),tc_fun(tc_List_Olist(X30530),tc_Nat_Onat),tc_fun(tc_List_Olist(X30530),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X30530),tc_Nat_Onat),tc_fun(tc_List_Olist(X30530),tc_HOL_Obool)),tc_List_Olist(X30530)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X30530))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X30530)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X30530))))),c_Nat_Osize__class_Osize(tc_List_Olist(X30530)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X30530),tc_fun(tc_prod(tc_List_Olist(X30530),tc_List_Olist(X30530)),tc_HOL_Obool),tc_fun(tc_List_Olist(X30530),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X30530),tc_fun(tc_fun(tc_prod(tc_List_Olist(X30530),tc_List_Olist(X30530)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X30530),tc_List_Olist(X30530)),tc_HOL_Obool),tc_fun(tc_List_Olist(X30530),tc_HOL_Obool)),tc_List_Olist(X30530)),c_COMBC(tc_List_Olist(X30530),tc_fun(tc_prod(tc_List_Olist(X30530),tc_List_Olist(X30530)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X30530),tc_prod(tc_List_Olist(X30530),tc_List_Olist(X30530))),tc_fun(tc_List_Olist(X30530),tc_fun(tc_fun(tc_prod(tc_List_Olist(X30530),tc_List_Olist(X30530)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X30530)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X30530),tc_List_Olist(X30530)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X30530),tc_List_Olist(X30530)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X30530)),c_member(tc_prod(tc_List_Olist(X30530),tc_List_Olist(X30530))))),c_Product__Type_OPair(tc_List_Olist(X30530),tc_List_Olist(X30530))))),c_List_Olex(X30530,X30529)))))),
    inference(variable_rename,[status(thm)],[fact_lenlex__conv]) ).

fof(i_0_6120,plain,
    ! [X33402,X33403,X33404,X33405,X33406,X33407,X33408,X33409] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33409),esk478_8(X33402,X33403,X33404,X33405,X33406,X33407,X33408,X33409)),hAPP(c_List_Oset(X33409),X33408)))
        | hAPP(c_List_Ofoldl(X33407,X33409,hAPP(c_COMBC(X33409,X33407,X33407),X33405),hAPP(X33404,X33402)),X33408) = hAPP(X33404,hAPP(c_List_Ofoldl(X33406,X33409,hAPP(c_COMBC(X33409,X33406,X33406),X33403),X33402),X33408)) )
      & ( hAPP(c_Fun_Ocomp(X33407,X33407,X33406,hAPP(X33405,esk478_8(X33402,X33403,X33404,X33405,X33406,X33407,X33408,X33409))),X33404) != hAPP(c_Fun_Ocomp(X33406,X33407,X33406,X33404),hAPP(X33403,esk478_8(X33402,X33403,X33404,X33405,X33406,X33407,X33408,X33409)))
        | hAPP(c_List_Ofoldl(X33407,X33409,hAPP(c_COMBC(X33409,X33407,X33407),X33405),hAPP(X33404,X33402)),X33408) = hAPP(X33404,hAPP(c_List_Ofoldl(X33406,X33409,hAPP(c_COMBC(X33409,X33406,X33406),X33403),X33402),X33408)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__apply])])])]) ).

cnf(i_0_6121,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_5257]) ).

cnf(i_0_6122,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_5258]) ).

cnf(i_0_6123,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_5259]) ).

fof(i_0_6124,plain,
    ! [X29367,X29368,X29369,X29370,X29371,X29372] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29372,tc_fun(X29371,tc_fun(X29370,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X29372,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X29371,X29370),tc_HOL_Obool),tc_fun(X29371,tc_fun(X29370,tc_HOL_Obool)),X29372),hAPP(c_COMBC(X29371,tc_fun(tc_prod(X29371,X29370),tc_HOL_Obool),tc_fun(X29370,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29370,tc_fun(tc_fun(tc_prod(X29371,X29370),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29371,X29370),tc_HOL_Obool),tc_fun(X29370,tc_HOL_Obool)),X29371),c_COMBC(X29370,tc_fun(tc_prod(X29371,X29370),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29370,tc_prod(X29371,X29370)),tc_fun(X29370,tc_fun(tc_fun(tc_prod(X29371,X29370),tc_HOL_Obool),tc_HOL_Obool)),X29371),hAPP(c_COMBB(tc_prod(X29371,X29370),tc_fun(tc_fun(tc_prod(X29371,X29370),tc_HOL_Obool),tc_HOL_Obool),X29370),c_member(tc_prod(X29371,X29370)))),c_Product__Type_OPair(X29371,X29370))))),X29369)),X29368),X29367))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29371,X29370)),hAPP(hAPP(c_Product__Type_OPair(X29371,X29370),X29368),X29367)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29372,tc_fun(tc_prod(X29371,X29370),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X29372,tc_HOL_Obool))),X29369))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29371,X29370)),hAPP(hAPP(c_Product__Type_OPair(X29371,X29370),X29368),X29367)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29372,tc_fun(tc_prod(X29371,X29370),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X29372,tc_HOL_Obool))),X29369)))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29372,tc_fun(X29371,tc_fun(X29370,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X29372,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X29371,X29370),tc_HOL_Obool),tc_fun(X29371,tc_fun(X29370,tc_HOL_Obool)),X29372),hAPP(c_COMBC(X29371,tc_fun(tc_prod(X29371,X29370),tc_HOL_Obool),tc_fun(X29370,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29370,tc_fun(tc_fun(tc_prod(X29371,X29370),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29371,X29370),tc_HOL_Obool),tc_fun(X29370,tc_HOL_Obool)),X29371),c_COMBC(X29370,tc_fun(tc_prod(X29371,X29370),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29370,tc_prod(X29371,X29370)),tc_fun(X29370,tc_fun(tc_fun(tc_prod(X29371,X29370),tc_HOL_Obool),tc_HOL_Obool)),X29371),hAPP(c_COMBB(tc_prod(X29371,X29370),tc_fun(tc_fun(tc_prod(X29371,X29370),tc_HOL_Obool),tc_HOL_Obool),X29370),c_member(tc_prod(X29371,X29370)))),c_Product__Type_OPair(X29371,X29370))))),X29369)),X29368),X29367)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__INT__eq2])]) ).

fof(i_0_6125,plain,
    ! [X19922,X19923,X19924,X19925,X19926,X19927] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19927,tc_fun(X19926,tc_fun(X19925,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X19927,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X19926,X19925),tc_HOL_Obool),tc_fun(X19926,tc_fun(X19925,tc_HOL_Obool)),X19927),hAPP(c_COMBC(X19926,tc_fun(tc_prod(X19926,X19925),tc_HOL_Obool),tc_fun(X19925,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19925,tc_fun(tc_fun(tc_prod(X19926,X19925),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X19926,X19925),tc_HOL_Obool),tc_fun(X19925,tc_HOL_Obool)),X19926),c_COMBC(X19925,tc_fun(tc_prod(X19926,X19925),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19925,tc_prod(X19926,X19925)),tc_fun(X19925,tc_fun(tc_fun(tc_prod(X19926,X19925),tc_HOL_Obool),tc_HOL_Obool)),X19926),hAPP(c_COMBB(tc_prod(X19926,X19925),tc_fun(tc_fun(tc_prod(X19926,X19925),tc_HOL_Obool),tc_HOL_Obool),X19925),c_member(tc_prod(X19926,X19925)))),c_Product__Type_OPair(X19926,X19925))))),X19924)),X19923),X19922))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X19926,X19925)),hAPP(hAPP(c_Product__Type_OPair(X19926,X19925),X19923),X19922)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19927,tc_fun(tc_prod(X19926,X19925),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X19927,tc_HOL_Obool))),X19924))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X19926,X19925)),hAPP(hAPP(c_Product__Type_OPair(X19926,X19925),X19923),X19922)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19927,tc_fun(tc_prod(X19926,X19925),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X19927,tc_HOL_Obool))),X19924)))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19927,tc_fun(X19926,tc_fun(X19925,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X19927,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X19926,X19925),tc_HOL_Obool),tc_fun(X19926,tc_fun(X19925,tc_HOL_Obool)),X19927),hAPP(c_COMBC(X19926,tc_fun(tc_prod(X19926,X19925),tc_HOL_Obool),tc_fun(X19925,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19925,tc_fun(tc_fun(tc_prod(X19926,X19925),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X19926,X19925),tc_HOL_Obool),tc_fun(X19925,tc_HOL_Obool)),X19926),c_COMBC(X19925,tc_fun(tc_prod(X19926,X19925),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19925,tc_prod(X19926,X19925)),tc_fun(X19925,tc_fun(tc_fun(tc_prod(X19926,X19925),tc_HOL_Obool),tc_HOL_Obool)),X19926),hAPP(c_COMBB(tc_prod(X19926,X19925),tc_fun(tc_fun(tc_prod(X19926,X19925),tc_HOL_Obool),tc_HOL_Obool),X19925),c_member(tc_prod(X19926,X19925)))),c_Product__Type_OPair(X19926,X19925))))),X19924)),X19923),X19922)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq2])]) ).

fof(i_0_6126,plain,
    ! [X27354,X27355,X27356,X27357,X27358,X27359,X27360] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X27360,X27359,X27358,hAPP(hAPP(c_COMBC(X27360,tc_fun(tc_prod(X27360,X27359),tc_HOL_Obool),tc_fun(X27359,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27359,tc_fun(tc_fun(tc_prod(X27360,X27359),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27360,X27359),tc_HOL_Obool),tc_fun(X27359,tc_HOL_Obool)),X27360),c_COMBC(X27359,tc_fun(tc_prod(X27360,X27359),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27359,tc_prod(X27360,X27359)),tc_fun(X27359,tc_fun(tc_fun(tc_prod(X27360,X27359),tc_HOL_Obool),tc_HOL_Obool)),X27360),hAPP(c_COMBB(tc_prod(X27360,X27359),tc_fun(tc_fun(tc_prod(X27360,X27359),tc_HOL_Obool),tc_HOL_Obool),X27359),c_member(tc_prod(X27360,X27359)))),c_Product__Type_OPair(X27360,X27359)))),X27357),hAPP(hAPP(c_COMBC(X27359,tc_fun(tc_prod(X27359,X27358),tc_HOL_Obool),tc_fun(X27358,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27358,tc_fun(tc_fun(tc_prod(X27359,X27358),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27359,X27358),tc_HOL_Obool),tc_fun(X27358,tc_HOL_Obool)),X27359),c_COMBC(X27358,tc_fun(tc_prod(X27359,X27358),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27358,tc_prod(X27359,X27358)),tc_fun(X27358,tc_fun(tc_fun(tc_prod(X27359,X27358),tc_HOL_Obool),tc_HOL_Obool)),X27359),hAPP(c_COMBB(tc_prod(X27359,X27358),tc_fun(tc_fun(tc_prod(X27359,X27358),tc_HOL_Obool),tc_HOL_Obool),X27358),c_member(tc_prod(X27359,X27358)))),c_Product__Type_OPair(X27359,X27358)))),X27356)),X27355),X27354))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X27360,X27358)),hAPP(hAPP(c_Product__Type_OPair(X27360,X27358),X27355),X27354)),hAPP(hAPP(c_Relation_Orel__comp(X27360,X27359,X27358),X27357),X27356))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27360,X27358)),hAPP(hAPP(c_Product__Type_OPair(X27360,X27358),X27355),X27354)),hAPP(hAPP(c_Relation_Orel__comp(X27360,X27359,X27358),X27357),X27356)))
        | hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X27360,X27359,X27358,hAPP(hAPP(c_COMBC(X27360,tc_fun(tc_prod(X27360,X27359),tc_HOL_Obool),tc_fun(X27359,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27359,tc_fun(tc_fun(tc_prod(X27360,X27359),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27360,X27359),tc_HOL_Obool),tc_fun(X27359,tc_HOL_Obool)),X27360),c_COMBC(X27359,tc_fun(tc_prod(X27360,X27359),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27359,tc_prod(X27360,X27359)),tc_fun(X27359,tc_fun(tc_fun(tc_prod(X27360,X27359),tc_HOL_Obool),tc_HOL_Obool)),X27360),hAPP(c_COMBB(tc_prod(X27360,X27359),tc_fun(tc_fun(tc_prod(X27360,X27359),tc_HOL_Obool),tc_HOL_Obool),X27359),c_member(tc_prod(X27360,X27359)))),c_Product__Type_OPair(X27360,X27359)))),X27357),hAPP(hAPP(c_COMBC(X27359,tc_fun(tc_prod(X27359,X27358),tc_HOL_Obool),tc_fun(X27358,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27358,tc_fun(tc_fun(tc_prod(X27359,X27358),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27359,X27358),tc_HOL_Obool),tc_fun(X27358,tc_HOL_Obool)),X27359),c_COMBC(X27358,tc_fun(tc_prod(X27359,X27358),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27358,tc_prod(X27359,X27358)),tc_fun(X27358,tc_fun(tc_fun(tc_prod(X27359,X27358),tc_HOL_Obool),tc_HOL_Obool)),X27359),hAPP(c_COMBB(tc_prod(X27359,X27358),tc_fun(tc_fun(tc_prod(X27359,X27358),tc_HOL_Obool),tc_HOL_Obool),X27358),c_member(tc_prod(X27359,X27358)))),c_Product__Type_OPair(X27359,X27358)))),X27356)),X27355),X27354)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__comp__rel__comp__eq])]) ).

cnf(i_0_6127,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_5260]) ).

cnf(i_0_6128,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_5261]) ).

fof(i_0_6129,plain,
    ! [X18330,X18331,X18332] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18332,tc_HOL_Obool)),X18331),hAPP(X18330,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X18332,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X18332,tc_HOL_Obool),tc_fun(X18332,tc_HOL_Obool),tc_fun(X18332,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18332,tc_HOL_Obool),tc_fun(tc_fun(X18332,tc_HOL_Obool),tc_fun(X18332,tc_HOL_Obool)),tc_fun(X18332,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18332,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X18332,tc_HOL_Obool),tc_fun(X18332,tc_HOL_Obool),tc_fun(X18332,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18332,tc_HOL_Obool),tc_fun(tc_fun(X18332,tc_HOL_Obool),tc_fun(X18332,tc_HOL_Obool)),tc_fun(X18332,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18332,tc_HOL_Obool))),X18330)),X18331))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X18332,tc_HOL_Obool),X18330))))))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(X18332,tc_HOL_Obool),tc_fun(X18332,tc_HOL_Obool),X18330)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18332,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X18332,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X18332,tc_HOL_Obool),tc_fun(X18332,tc_HOL_Obool),tc_fun(X18332,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18332,tc_HOL_Obool),tc_fun(tc_fun(X18332,tc_HOL_Obool),tc_fun(X18332,tc_HOL_Obool)),tc_fun(X18332,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18332,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X18332,tc_HOL_Obool),tc_fun(X18332,tc_HOL_Obool),tc_fun(X18332,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18332,tc_HOL_Obool),tc_fun(tc_fun(X18332,tc_HOL_Obool),tc_fun(X18332,tc_HOL_Obool)),tc_fun(X18332,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18332,tc_HOL_Obool))),X18330)),X18331))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X18332,tc_HOL_Obool),X18330)))),hAPP(X18330,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X18332,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X18332,tc_HOL_Obool),tc_fun(X18332,tc_HOL_Obool),tc_fun(X18332,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18332,tc_HOL_Obool),tc_fun(tc_fun(X18332,tc_HOL_Obool),tc_fun(X18332,tc_HOL_Obool)),tc_fun(X18332,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18332,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X18332,tc_HOL_Obool),tc_fun(X18332,tc_HOL_Obool),tc_fun(X18332,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18332,tc_HOL_Obool),tc_fun(tc_fun(X18332,tc_HOL_Obool),tc_fun(X18332,tc_HOL_Obool)),tc_fun(X18332,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18332,tc_HOL_Obool))),X18330)),X18331))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X18332,tc_HOL_Obool),X18330)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coinduct3__lemma])]) ).

fof(i_0_6130,plain,
    ! [X20074,X20075,X20076,X20077,X20078,X20079,X20080] :
      ( ( hBOOL(hAPP(hAPP(c_member(X20080),esk64_7(X20074,X20075,X20076,X20077,X20078,X20079,X20080)),X20079))
        | X20075 = X20074
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X20080,tc_HOL_Obool)),X20074),hAPP(hAPP(c_Equiv__Relations_Oquotient(X20080),X20079),X20078)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X20080,tc_HOL_Obool)),X20075),hAPP(hAPP(c_Equiv__Relations_Oquotient(X20080),X20079),X20078)))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20080,tc_fun(X20077,tc_HOL_Obool)),X20075),X20076) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20080,tc_fun(X20077,tc_HOL_Obool)),X20074),X20076)
        | ~ c_Equiv__Relations_Ocongruent(X20080,tc_fun(X20077,tc_HOL_Obool),X20078,X20076)
        | ~ c_Equiv__Relations_Oequiv(X20080,X20079,X20078) )
      & ( hBOOL(hAPP(hAPP(c_member(X20080),esk65_7(X20074,X20075,X20076,X20077,X20078,X20079,X20080)),X20079))
        | X20075 = X20074
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X20080,tc_HOL_Obool)),X20074),hAPP(hAPP(c_Equiv__Relations_Oquotient(X20080),X20079),X20078)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X20080,tc_HOL_Obool)),X20075),hAPP(hAPP(c_Equiv__Relations_Oquotient(X20080),X20079),X20078)))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20080,tc_fun(X20077,tc_HOL_Obool)),X20075),X20076) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20080,tc_fun(X20077,tc_HOL_Obool)),X20074),X20076)
        | ~ c_Equiv__Relations_Ocongruent(X20080,tc_fun(X20077,tc_HOL_Obool),X20078,X20076)
        | ~ c_Equiv__Relations_Oequiv(X20080,X20079,X20078) )
      & ( hAPP(X20076,esk64_7(X20074,X20075,X20076,X20077,X20078,X20079,X20080)) = hAPP(X20076,esk65_7(X20074,X20075,X20076,X20077,X20078,X20079,X20080))
        | X20075 = X20074
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X20080,tc_HOL_Obool)),X20074),hAPP(hAPP(c_Equiv__Relations_Oquotient(X20080),X20079),X20078)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X20080,tc_HOL_Obool)),X20075),hAPP(hAPP(c_Equiv__Relations_Oquotient(X20080),X20079),X20078)))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20080,tc_fun(X20077,tc_HOL_Obool)),X20075),X20076) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20080,tc_fun(X20077,tc_HOL_Obool)),X20074),X20076)
        | ~ c_Equiv__Relations_Ocongruent(X20080,tc_fun(X20077,tc_HOL_Obool),X20078,X20076)
        | ~ c_Equiv__Relations_Oequiv(X20080,X20079,X20078) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20080,X20080)),hAPP(hAPP(c_Product__Type_OPair(X20080,X20080),esk64_7(X20074,X20075,X20076,X20077,X20078,X20079,X20080)),esk65_7(X20074,X20075,X20076,X20077,X20078,X20079,X20080))),X20078))
        | X20075 = X20074
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X20080,tc_HOL_Obool)),X20074),hAPP(hAPP(c_Equiv__Relations_Oquotient(X20080),X20079),X20078)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X20080,tc_HOL_Obool)),X20075),hAPP(hAPP(c_Equiv__Relations_Oquotient(X20080),X20079),X20078)))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20080,tc_fun(X20077,tc_HOL_Obool)),X20075),X20076) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20080,tc_fun(X20077,tc_HOL_Obool)),X20074),X20076)
        | ~ c_Equiv__Relations_Ocongruent(X20080,tc_fun(X20077,tc_HOL_Obool),X20078,X20076)
        | ~ c_Equiv__Relations_Oequiv(X20080,X20079,X20078) ) ),
    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_6131,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_5260]) ).

cnf(i_0_6132,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_5262]) ).

fof(i_0_6133,plain,
    ! [X21075,X21076,X21077,X21078] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21078),hAPP(c_Set_OCollect(X21078),X21077)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X21076),hAPP(c_Set_OCollect(X21076),hAPP(hAPP(c_COMBB(tc_fun(X21078,tc_HOL_Obool),tc_HOL_Obool,X21076),c_HOL_OEx(X21078)),hAPP(hAPP(c_COMBC(X21076,tc_fun(X21078,tc_HOL_Obool),tc_fun(X21078,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21078,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X21078,tc_HOL_Obool),tc_fun(X21078,tc_HOL_Obool)),X21076),c_COMBS(X21078,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21078,tc_HOL_Obool),tc_fun(X21078,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X21076),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X21078),c_fconj)),hAPP(hAPP(c_COMBC(X21076,tc_fun(X21078,X21076),tc_fun(X21078,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21076,tc_HOL_Obool),tc_fun(tc_fun(X21078,X21076),tc_fun(X21078,tc_HOL_Obool)),X21076),c_COMBB(X21076,tc_HOL_Obool,X21078)),c_fequal)),X21075)))),X21077))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__image__set])]) ).

fof(i_0_6134,plain,
    ! [X28398,X28399,X28400,X28401,X28402,X28403,X28404,X28405] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28404),esk324_8(X28398,X28399,X28400,X28401,X28402,X28403,X28404,X28405)),X28401))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28403,X28405),X28398),X28400) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28404,X28405),X28399),X28401)
        | X28400 != hAPP(c_Set_Oimage(X28404,X28403,X28402),X28401)
        | ~ c_Fun_Oinj__on(X28404,X28403,X28402,X28401)
        | ~ class_Groups_Ocomm__monoid__add(X28405) )
      & ( hAPP(X28399,esk324_8(X28398,X28399,X28400,X28401,X28402,X28403,X28404,X28405)) != hAPP(X28398,hAPP(X28402,esk324_8(X28398,X28399,X28400,X28401,X28402,X28403,X28404,X28405)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28403,X28405),X28398),X28400) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28404,X28405),X28399),X28401)
        | X28400 != hAPP(c_Set_Oimage(X28404,X28403,X28402),X28401)
        | ~ c_Fun_Oinj__on(X28404,X28403,X28402,X28401)
        | ~ class_Groups_Ocomm__monoid__add(X28405) ) ),
    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_6135,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_5263]) ).

cnf(i_0_6136,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_5264]) ).

cnf(i_0_6137,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_5265]) ).

fof(i_0_6138,plain,
    ! [X33937,X33938,X33939,X33940,X33941] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X33941,X33940,hAPP(hAPP(c_COMBC(X33941,tc_fun(tc_prod(X33941,X33940),tc_HOL_Obool),tc_fun(X33940,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33940,tc_fun(tc_fun(tc_prod(X33941,X33940),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X33941,X33940),tc_HOL_Obool),tc_fun(X33940,tc_HOL_Obool)),X33941),c_COMBC(X33940,tc_fun(tc_prod(X33941,X33940),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33940,tc_prod(X33941,X33940)),tc_fun(X33940,tc_fun(tc_fun(tc_prod(X33941,X33940),tc_HOL_Obool),tc_HOL_Obool)),X33941),hAPP(c_COMBB(tc_prod(X33941,X33940),tc_fun(tc_fun(tc_prod(X33941,X33940),tc_HOL_Obool),tc_HOL_Obool),X33940),c_member(tc_prod(X33941,X33940)))),c_Product__Type_OPair(X33941,X33940)))),X33939)),X33938),X33937))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X33940,X33941)),hAPP(hAPP(c_Product__Type_OPair(X33940,X33941),X33938),X33937)),hAPP(c_Relation_Oconverse(X33941,X33940),X33939))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33940,X33941)),hAPP(hAPP(c_Product__Type_OPair(X33940,X33941),X33938),X33937)),hAPP(c_Relation_Oconverse(X33941,X33940),X33939)))
        | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X33941,X33940,hAPP(hAPP(c_COMBC(X33941,tc_fun(tc_prod(X33941,X33940),tc_HOL_Obool),tc_fun(X33940,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33940,tc_fun(tc_fun(tc_prod(X33941,X33940),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X33941,X33940),tc_HOL_Obool),tc_fun(X33940,tc_HOL_Obool)),X33941),c_COMBC(X33940,tc_fun(tc_prod(X33941,X33940),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33940,tc_prod(X33941,X33940)),tc_fun(X33940,tc_fun(tc_fun(tc_prod(X33941,X33940),tc_HOL_Obool),tc_HOL_Obool)),X33941),hAPP(c_COMBB(tc_prod(X33941,X33940),tc_fun(tc_fun(tc_prod(X33941,X33940),tc_HOL_Obool),tc_HOL_Obool),X33940),c_member(tc_prod(X33941,X33940)))),c_Product__Type_OPair(X33941,X33940)))),X33939)),X33938),X33937)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__converse__eq])]) ).

fof(i_0_6139,plain,
    ! [X26049,X26050,X26051,X26052,X26053,X26054,X26055,X26056] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26055),esk186_8(X26049,X26050,X26051,X26052,X26053,X26054,X26055,X26056)),X26052))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26054,X26056),X26049),X26051) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26055,X26056),X26050),X26052)
        | X26051 != hAPP(c_Set_Oimage(X26055,X26054,X26053),X26052)
        | ~ c_Fun_Oinj__on(X26055,X26054,X26053,X26052)
        | ~ class_Groups_Ocomm__monoid__mult(X26056) )
      & ( hAPP(X26050,esk186_8(X26049,X26050,X26051,X26052,X26053,X26054,X26055,X26056)) != hAPP(hAPP(c_Fun_Ocomp(X26054,X26056,X26055,X26049),X26053),esk186_8(X26049,X26050,X26051,X26052,X26053,X26054,X26055,X26056))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26054,X26056),X26049),X26051) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26055,X26056),X26050),X26052)
        | X26051 != hAPP(c_Set_Oimage(X26055,X26054,X26053),X26052)
        | ~ c_Fun_Oinj__on(X26055,X26054,X26053,X26052)
        | ~ class_Groups_Ocomm__monoid__mult(X26056) ) ),
    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_6140,plain,
    ! [X28451,X28452,X28453,X28454,X28455,X28456,X28457,X28458] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28457),X28455),esk325_8(X28451,X28452,X28453,X28454,X28455,X28456,X28457,X28458)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28457,X28458),X28452),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X28457,X28456),X28454)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28457,X28458),X28451),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X28457,X28455),X28453))
        | X28454 != X28453
        | X28456 != X28455
        | ~ class_Groups_Ocomm__monoid__add(X28458)
        | ~ class_Orderings_Oord(X28457) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X28457),esk325_8(X28451,X28452,X28453,X28454,X28455,X28456,X28457,X28458)),X28453))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28457,X28458),X28452),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X28457,X28456),X28454)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28457,X28458),X28451),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X28457,X28455),X28453))
        | X28454 != X28453
        | X28456 != X28455
        | ~ class_Groups_Ocomm__monoid__add(X28458)
        | ~ class_Orderings_Oord(X28457) )
      & ( hAPP(X28452,esk325_8(X28451,X28452,X28453,X28454,X28455,X28456,X28457,X28458)) != hAPP(X28451,esk325_8(X28451,X28452,X28453,X28454,X28455,X28456,X28457,X28458))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28457,X28458),X28452),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X28457,X28456),X28454)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28457,X28458),X28451),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X28457,X28455),X28453))
        | X28454 != X28453
        | X28456 != X28455
        | ~ class_Groups_Ocomm__monoid__add(X28458)
        | ~ class_Orderings_Oord(X28457) ) ),
    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_6141,plain,
    ! [X33745,X33746,X33747] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X33747,X33746),X33745) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X33747,tc_Lazy__Sequence_Olazy__sequence(X33747)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X33747,tc_Lazy__Sequence_Olazy__sequence(X33747),tc_Nat_Onat),hAPP(hAPP(c_COMBC(X33747,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33747),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33747),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33747),tc_Nat_Onat)),X33747),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X33747),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33747),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33747),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),X33747),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X33747)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(X33747,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33747),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33747),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33747),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33747),tc_Nat_Onat)),X33747),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(X33747))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),X33747),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X33746))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X33747,X33746))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(X33747),X33745)),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence__size__code]) ).

fof(i_0_6142,plain,
    ! [X25607] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25607) = 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,X25607)),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_6143,plain,
    ! [X24093,X24094] : c_FunDef_Orp__inv__image(X24094,X24093) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X24094,X24094),tc_HOL_Obool),tc_fun(tc_prod(X24094,X24094),tc_HOL_Obool),tc_fun(tc_fun(X24093,X24094),tc_prod(tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool),tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X24094,X24094),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X24094,X24094),tc_HOL_Obool),tc_fun(tc_fun(X24093,X24094),tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X24094,X24094),tc_HOL_Obool),tc_fun(tc_fun(X24093,X24094),tc_prod(tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool),tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X24093,X24094),tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool)),tc_fun(tc_fun(X24093,X24094),tc_prod(tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool),tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X24094,X24094),tc_HOL_Obool),tc_fun(tc_fun(X24093,X24094),tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X24094,X24094),tc_HOL_Obool),tc_fun(tc_fun(X24093,X24094),tc_prod(tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool),tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool))))),tc_fun(tc_prod(X24094,X24094),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X24093,X24094),tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool)),tc_fun(tc_fun(X24093,X24094),tc_prod(tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool),tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool))),tc_fun(tc_prod(X24094,X24094),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X24093,X24094),tc_fun(tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool),tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X24093,X24094),tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool)),tc_fun(tc_fun(X24093,X24094),tc_prod(tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool),tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool)))),tc_fun(tc_prod(X24094,X24094),tc_HOL_Obool)),c_COMBS(tc_fun(X24093,X24094),tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool),tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X24093,X24094),tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool)),tc_fun(tc_fun(X24093,X24094),tc_fun(tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool),tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool)))),tc_fun(tc_prod(X24094,X24094),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool),tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool))),tc_fun(X24093,X24094)),c_Product__Type_OPair(tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool),tc_fun(tc_prod(X24093,X24093),tc_HOL_Obool)))),c_Relation_Oinv__image(X24094,X24093))))),c_Relation_Oinv__image(X24094,X24093))),
    inference(variable_rename,[status(thm)],[fact_rp__inv__image__def]) ).

fof(i_0_6144,plain,
    ! [X18304,X18305,X18306,X18307] :
      ( ~ c_Orderings_Oorder__class_Omono(tc_fun(X18307,tc_HOL_Obool),tc_fun(X18307,tc_HOL_Obool),X18306)
      | ~ hBOOL(hAPP(hAPP(c_member(X18307),X18305),X18304))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18307,tc_HOL_Obool)),X18304),hAPP(X18306,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X18307,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X18307,tc_HOL_Obool),tc_fun(X18307,tc_HOL_Obool),tc_fun(X18307,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18307,tc_HOL_Obool),tc_fun(tc_fun(X18307,tc_HOL_Obool),tc_fun(X18307,tc_HOL_Obool)),tc_fun(X18307,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18307,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X18307,tc_HOL_Obool),tc_fun(X18307,tc_HOL_Obool),tc_fun(X18307,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18307,tc_HOL_Obool),tc_fun(tc_fun(X18307,tc_HOL_Obool),tc_fun(X18307,tc_HOL_Obool)),tc_fun(X18307,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18307,tc_HOL_Obool))),X18306)),X18304))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X18307,tc_HOL_Obool),X18306))))))
      | hBOOL(hAPP(hAPP(c_member(X18307),X18305),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X18307,tc_HOL_Obool),X18306))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coinduct3])]) ).

fof(i_0_6145,plain,
    ! [X18308,X18309,X18310,X18311,X18312] :
      ( X18312 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X18311,tc_HOL_Obool),X18310)
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(X18311,tc_HOL_Obool),tc_fun(X18311,tc_HOL_Obool),X18310)
      | ~ hBOOL(hAPP(hAPP(c_member(X18311),X18309),X18308))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18311,tc_HOL_Obool)),X18308),hAPP(X18310,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X18311,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X18311,tc_HOL_Obool),tc_fun(X18311,tc_HOL_Obool),tc_fun(X18311,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18311,tc_HOL_Obool),tc_fun(tc_fun(X18311,tc_HOL_Obool),tc_fun(X18311,tc_HOL_Obool)),tc_fun(X18311,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18311,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X18311,tc_HOL_Obool),tc_fun(X18311,tc_HOL_Obool),tc_fun(X18311,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18311,tc_HOL_Obool),tc_fun(tc_fun(X18311,tc_HOL_Obool),tc_fun(X18311,tc_HOL_Obool)),tc_fun(X18311,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18311,tc_HOL_Obool))),X18310)),X18308))),X18312)))))
      | hBOOL(hAPP(hAPP(c_member(X18311),X18309),X18312)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_def__coinduct3])]) ).

cnf(i_0_6146,plain,
    c_Map_Omap__add(X1,X2,X3,hAPP(c_Map_Omap__of(X1,X2),X4)) = c_List_Ofoldr(tc_prod(X1,X2),tc_fun(X1,tc_Option_Ooption(X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))))),X1),c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))),X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),X1),c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),X1,tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)))))),c_Option_Ooption_OSome(X2))),X4,X3),
    inference(split_conjunct,[status(thm)],[i_0_5266]) ).

cnf(i_0_6147,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_5267]) ).

fof(i_0_6148,plain,
    ! [X23989,X23990,X23991,X23992] : hAPP(hAPP(c_Relation_Oinv__image(X23992,X23991),X23990),X23989) = hAPP(c_Set_OCollect(tc_prod(X23991,X23991)),hAPP(c_Product__Type_Oprod_Oprod__case(X23991,X23991,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X23991,tc_fun(tc_prod(X23992,X23992),tc_HOL_Obool),tc_fun(X23991,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23991,tc_fun(tc_fun(tc_prod(X23992,X23992),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23992,X23992),tc_HOL_Obool),tc_fun(X23991,tc_HOL_Obool)),X23991),c_COMBC(X23991,tc_fun(tc_prod(X23992,X23992),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23991,tc_prod(X23992,X23992)),tc_fun(X23991,tc_fun(tc_fun(tc_prod(X23992,X23992),tc_HOL_Obool),tc_HOL_Obool)),X23991),hAPP(c_COMBB(tc_prod(X23992,X23992),tc_fun(tc_fun(tc_prod(X23992,X23992),tc_HOL_Obool),tc_HOL_Obool),X23991),c_member(tc_prod(X23992,X23992)))),hAPP(hAPP(c_COMBC(X23991,tc_fun(X23991,X23992),tc_fun(X23991,tc_prod(X23992,X23992))),hAPP(hAPP(c_COMBB(tc_fun(X23992,tc_prod(X23992,X23992)),tc_fun(tc_fun(X23991,X23992),tc_fun(X23991,tc_prod(X23992,X23992))),X23991),c_COMBB(X23992,tc_prod(X23992,X23992),X23991)),hAPP(hAPP(c_COMBB(X23992,tc_fun(X23992,tc_prod(X23992,X23992)),X23991),c_Product__Type_OPair(X23992,X23992)),X23989))),X23989)))),X23990))),
    inference(variable_rename,[status(thm)],[fact_inv__image__def]) ).

fof(i_0_6149,plain,
    ! [X30925,X30926,X30927,X30928] : hAPP(c_List_Oset(tc_prod(X30928,X30927)),hAPP(hAPP(c_List_Ozip(X30928,X30927),X30926),X30925)) = hAPP(c_Set_OCollect(tc_prod(X30928,X30927)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X30928,X30927)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X30928,X30927),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(X30928,X30927)),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(X30928,X30927)),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(X30928,X30927),tc_fun(tc_Nat_Onat,tc_prod(X30928,X30927)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X30928,X30927),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X30928,X30927)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X30928,X30927)),c_COMBB(tc_prod(X30928,X30927),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X30927,tc_prod(X30928,X30927)),hAPP(hAPP(c_COMBB(X30928,tc_fun(X30927,tc_prod(X30928,X30927)),tc_Nat_Onat),c_Product__Type_OPair(X30928,X30927)),hAPP(c_List_Onth(X30928),X30926))),hAPP(c_List_Onth(X30927),X30925)))))),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(X30928)),X30926)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30927)),X30925)))))),
    inference(variable_rename,[status(thm)],[fact_set__zip]) ).

fof(i_0_6150,plain,
    ! [X19963,X19964,X19965,X19966] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19966,tc_fun(X19965,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X19966,tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_fun(X19965,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19965,tc_fun(tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_fun(X19965,tc_HOL_Obool)),X19966),c_COMBC(X19965,tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19965,tc_prod(X19966,X19965)),tc_fun(X19965,tc_fun(tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_HOL_Obool)),X19966),hAPP(c_COMBB(tc_prod(X19966,X19965),tc_fun(tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_HOL_Obool),X19965),c_member(tc_prod(X19966,X19965)))),c_Product__Type_OPair(X19966,X19965)))),X19964)),hAPP(hAPP(c_COMBC(X19966,tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_fun(X19965,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19965,tc_fun(tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_fun(X19965,tc_HOL_Obool)),X19966),c_COMBC(X19965,tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19965,tc_prod(X19966,X19965)),tc_fun(X19965,tc_fun(tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_HOL_Obool)),X19966),hAPP(c_COMBB(tc_prod(X19966,X19965),tc_fun(tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_HOL_Obool),X19965),c_member(tc_prod(X19966,X19965)))),c_Product__Type_OPair(X19966,X19965)))),X19963)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool)),X19964),X19963)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool)),X19964),X19963))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19966,tc_fun(X19965,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X19966,tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_fun(X19965,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19965,tc_fun(tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_fun(X19965,tc_HOL_Obool)),X19966),c_COMBC(X19965,tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19965,tc_prod(X19966,X19965)),tc_fun(X19965,tc_fun(tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_HOL_Obool)),X19966),hAPP(c_COMBB(tc_prod(X19966,X19965),tc_fun(tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_HOL_Obool),X19965),c_member(tc_prod(X19966,X19965)))),c_Product__Type_OPair(X19966,X19965)))),X19964)),hAPP(hAPP(c_COMBC(X19966,tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_fun(X19965,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19965,tc_fun(tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_fun(X19965,tc_HOL_Obool)),X19966),c_COMBC(X19965,tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19965,tc_prod(X19966,X19965)),tc_fun(X19965,tc_fun(tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_HOL_Obool)),X19966),hAPP(c_COMBB(tc_prod(X19966,X19965),tc_fun(tc_fun(tc_prod(X19966,X19965),tc_HOL_Obool),tc_HOL_Obool),X19965),c_member(tc_prod(X19966,X19965)))),c_Product__Type_OPair(X19966,X19965)))),X19963))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])]) ).

fof(i_0_6151,plain,
    ! [X21094,X21095] : hAPP(c_Set_OPow(X21095),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21095,tc_HOL_Obool)),X21094)) = hAPP(c_Set_OCollect(tc_fun(X21095,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X21095,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X21095,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X21095,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X21095,tc_HOL_Obool),tc_fun(tc_fun(X21095,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X21095,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X21095,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X21095,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X21095,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X21095,tc_HOL_Obool)),c_COMBS(tc_fun(X21095,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X21095,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X21095,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X21095,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X21095,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X21095,tc_HOL_Obool),tc_fun(tc_fun(X21095,tc_HOL_Obool),tc_fun(X21095,tc_HOL_Obool)),tc_fun(tc_fun(X21095,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X21095,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X21095,tc_HOL_Obool),tc_fun(X21095,tc_HOL_Obool)),tc_fun(tc_fun(X21095,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X21095,tc_HOL_Obool)),c_COMBB(tc_fun(X21095,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X21095,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X21095,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X21095,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X21095,tc_HOL_Obool)),hAPP(c_member(tc_fun(X21095,tc_HOL_Obool)),X21094)),c_Set_OPow(X21095))))),
    inference(variable_rename,[status(thm)],[fact_Pow__Compl]) ).

fof(i_0_6152,plain,
    ! [X32082,X32083,X32084,X32085,X32086] : c_Map_Omap__upds(X32086,X32085,X32084,X32083,X32082) = hAPP(c_List_Ofoldl(tc_fun(X32086,tc_Option_Ooption(X32085)),tc_prod(X32086,X32085),hAPP(hAPP(c_COMBB(tc_fun(X32086,tc_fun(X32085,tc_fun(X32086,tc_Option_Ooption(X32085)))),tc_fun(tc_prod(X32086,X32085),tc_fun(X32086,tc_Option_Ooption(X32085))),tc_fun(X32086,tc_Option_Ooption(X32085))),c_Product__Type_Oprod_Oprod__case(X32086,X32085,tc_fun(X32086,tc_Option_Ooption(X32085)))),hAPP(hAPP(c_COMBC(tc_fun(X32086,tc_Option_Ooption(X32085)),tc_fun(X32085,tc_Option_Ooption(X32085)),tc_fun(X32086,tc_fun(X32085,tc_fun(X32086,tc_Option_Ooption(X32085))))),hAPP(hAPP(c_COMBB(tc_fun(X32086,tc_fun(tc_fun(X32085,tc_Option_Ooption(X32085)),tc_fun(X32085,tc_fun(X32086,tc_Option_Ooption(X32085))))),tc_fun(tc_fun(X32085,tc_Option_Ooption(X32085)),tc_fun(X32086,tc_fun(X32085,tc_fun(X32086,tc_Option_Ooption(X32085))))),tc_fun(X32086,tc_Option_Ooption(X32085))),c_COMBC(X32086,tc_fun(X32085,tc_Option_Ooption(X32085)),tc_fun(X32085,tc_fun(X32086,tc_Option_Ooption(X32085))))),hAPP(hAPP(c_COMBB(tc_fun(X32086,tc_fun(tc_Option_Ooption(X32085),tc_fun(X32086,tc_Option_Ooption(X32085)))),tc_fun(X32086,tc_fun(tc_fun(X32085,tc_Option_Ooption(X32085)),tc_fun(X32085,tc_fun(X32086,tc_Option_Ooption(X32085))))),tc_fun(X32086,tc_Option_Ooption(X32085))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X32085),tc_fun(X32086,tc_Option_Ooption(X32085))),tc_fun(tc_fun(X32085,tc_Option_Ooption(X32085)),tc_fun(X32085,tc_fun(X32086,tc_Option_Ooption(X32085)))),X32086),c_COMBB(tc_Option_Ooption(X32085),tc_fun(X32086,tc_Option_Ooption(X32085)),X32085))),c_Fun_Ofun__upd(X32086,tc_Option_Ooption(X32085))))),c_Option_Ooption_OSome(X32085))),X32084),hAPP(hAPP(c_List_Ozip(X32086,X32085),X32083),X32082)),
    inference(variable_rename,[status(thm)],[fact_map__upds__fold__map__upd]) ).

fof(i_0_6153,plain,
    ! [X19840,X19841,X19842,X19843,X19844,X19845,X19846] :
      ( ( hBOOL(hAPP(hAPP(c_member(X19846),esk56_7(X19840,X19841,X19842,X19843,X19844,X19845,X19846)),X19845))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X19843,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19846,tc_fun(X19843,tc_HOL_Obool)),X19841),X19842)),X19840))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X19846,tc_HOL_Obool)),X19841),hAPP(hAPP(c_Equiv__Relations_Oquotient(X19846),X19845),X19844)))
        | ~ c_Equiv__Relations_Ocongruent(X19846,tc_fun(X19843,tc_HOL_Obool),X19844,X19842)
        | ~ c_Equiv__Relations_Oequiv(X19846,X19845,X19844) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X19843,tc_HOL_Obool)),hAPP(X19842,esk56_7(X19840,X19841,X19842,X19843,X19844,X19845,X19846))),X19840))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X19843,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19846,tc_fun(X19843,tc_HOL_Obool)),X19841),X19842)),X19840))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X19846,tc_HOL_Obool)),X19841),hAPP(hAPP(c_Equiv__Relations_Oquotient(X19846),X19845),X19844)))
        | ~ c_Equiv__Relations_Ocongruent(X19846,tc_fun(X19843,tc_HOL_Obool),X19844,X19842)
        | ~ c_Equiv__Relations_Oequiv(X19846,X19845,X19844) ) ),
    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_6154,plain,
    ! [X34152,X34153,X34154,X34155,X34156,X34157,X34158] :
      ( ( hBOOL(hAPP(hAPP(c_member(X34158),esk530_7(X34152,X34153,X34154,X34155,X34156,X34157,X34158)),X34157))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X34158,tc_fun(X34153,tc_fun(X34152,tc_HOL_Obool))),X34157),X34156),X34155),X34154)) )
      & ( ~ hBOOL(hAPP(hAPP(hAPP(X34156,esk530_7(X34152,X34153,X34154,X34155,X34156,X34157,X34158)),X34155),X34154))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X34158,tc_fun(X34153,tc_fun(X34152,tc_HOL_Obool))),X34157),X34156),X34155),X34154)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF2__I])])])]) ).

fof(i_0_6155,plain,
    ! [X29586,X29587,X29588,X29589,X29590,X29591,X29592,X29593,X29594,X29595,X29596,X29597,X29598,X29599,X29600] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29592,tc_fun(X29591,tc_fun(X29590,tc_HOL_Obool))),X29589),X29588),X29587),X29586))
        | ~ hBOOL(hAPP(hAPP(c_member(X29592),X29593),X29589))
        | hBOOL(hAPP(hAPP(hAPP(X29588,X29593),X29587),X29586)) )
      & ( hBOOL(hAPP(hAPP(c_member(X29600),esk359_7(X29594,X29595,X29596,X29597,X29598,X29599,X29600)),X29597))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29600,tc_fun(X29599,tc_fun(X29598,tc_HOL_Obool))),X29597),X29596),X29595),X29594)) )
      & ( ~ hBOOL(hAPP(hAPP(hAPP(X29596,esk359_7(X29594,X29595,X29596,X29597,X29598,X29599,X29600)),X29595),X29594))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29600,tc_fun(X29599,tc_fun(X29598,tc_HOL_Obool))),X29597),X29596),X29595),X29594)) ) ),
    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_6156,plain,
    ! [X25706,X25707,X25708] :
      ( ~ class_Orderings_Olinorder(X25708)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25708),X25707))
      | X25707 = c_Orderings_Obot__class_Obot(tc_fun(X25708,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25708),X25706),c_Big__Operators_Olattice_OInf__fin(X25708,c_Orderings_Oord__class_Omin(X25708),X25707)) = c_Big__Operators_Olattice_OInf__fin(X25708,c_Orderings_Oord__class_Omin(X25708),hAPP(c_Set_OCollect(X25708),hAPP(hAPP(c_COMBB(tc_fun(X25708,tc_HOL_Obool),tc_HOL_Obool,X25708),c_HOL_OEx(X25708)),hAPP(hAPP(c_COMBC(X25708,tc_fun(X25708,tc_HOL_Obool),tc_fun(X25708,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25708,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X25708,tc_HOL_Obool),tc_fun(X25708,tc_HOL_Obool)),X25708),c_COMBS(X25708,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25708,tc_HOL_Obool),tc_fun(X25708,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X25708),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25708),c_fconj)),hAPP(hAPP(c_COMBC(X25708,tc_fun(X25708,X25708),tc_fun(X25708,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25708,tc_HOL_Obool),tc_fun(tc_fun(X25708,X25708),tc_fun(X25708,tc_HOL_Obool)),X25708),c_COMBB(X25708,tc_HOL_Obool,X25708)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X25708),X25706))))),hAPP(hAPP(c_COMBC(X25708,tc_fun(X25708,tc_HOL_Obool),tc_HOL_Obool),c_member(X25708)),X25707))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf1__distrib])]) ).

fof(i_0_6157,plain,
    ! [X26006,X26007,X26008] :
      ( ~ class_Orderings_Olinorder(X26008)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26008),X26007))
      | X26007 = c_Orderings_Obot__class_Obot(tc_fun(X26008,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X26008),X26006),c_Big__Operators_Olattice_OSup__fin(X26008,c_Orderings_Oord__class_Omax(X26008),X26007)) = c_Big__Operators_Olattice_OSup__fin(X26008,c_Orderings_Oord__class_Omax(X26008),hAPP(c_Set_OCollect(X26008),hAPP(hAPP(c_COMBB(tc_fun(X26008,tc_HOL_Obool),tc_HOL_Obool,X26008),c_HOL_OEx(X26008)),hAPP(hAPP(c_COMBC(X26008,tc_fun(X26008,tc_HOL_Obool),tc_fun(X26008,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26008,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X26008,tc_HOL_Obool),tc_fun(X26008,tc_HOL_Obool)),X26008),c_COMBS(X26008,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26008,tc_HOL_Obool),tc_fun(X26008,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X26008),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X26008),c_fconj)),hAPP(hAPP(c_COMBC(X26008,tc_fun(X26008,X26008),tc_fun(X26008,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26008,tc_HOL_Obool),tc_fun(tc_fun(X26008,X26008),tc_fun(X26008,tc_HOL_Obool)),X26008),c_COMBB(X26008,tc_HOL_Obool,X26008)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X26008),X26006))))),hAPP(hAPP(c_COMBC(X26008,tc_fun(X26008,tc_HOL_Obool),tc_HOL_Obool),c_member(X26008)),X26007))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup1__distrib])]) ).

fof(i_0_6158,plain,
    ! [X22001,X22002,X22003] :
      ( ~ class_Groups_Olinordered__ab__semigroup__add(X22003)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22003),X22002))
      | X22002 = c_Orderings_Obot__class_Obot(tc_fun(X22003,tc_HOL_Obool))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22003),X22001),c_Big__Operators_Olinorder__class_OMin(X22003,X22002)) = c_Big__Operators_Olinorder__class_OMin(X22003,hAPP(c_Set_OCollect(X22003),hAPP(hAPP(c_COMBB(tc_fun(X22003,tc_HOL_Obool),tc_HOL_Obool,X22003),c_HOL_OEx(X22003)),hAPP(hAPP(c_COMBC(X22003,tc_fun(X22003,tc_HOL_Obool),tc_fun(X22003,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22003,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X22003,tc_HOL_Obool),tc_fun(X22003,tc_HOL_Obool)),X22003),c_COMBS(X22003,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22003,tc_HOL_Obool),tc_fun(X22003,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X22003),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X22003),c_fconj)),hAPP(hAPP(c_COMBC(X22003,tc_fun(X22003,X22003),tc_fun(X22003,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22003,tc_HOL_Obool),tc_fun(tc_fun(X22003,X22003),tc_fun(X22003,tc_HOL_Obool)),X22003),c_COMBB(X22003,tc_HOL_Obool,X22003)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X22003),X22001))))),hAPP(hAPP(c_COMBC(X22003,tc_fun(X22003,tc_HOL_Obool),tc_HOL_Obool),c_member(X22003)),X22002))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__Min__commute])]) ).

fof(i_0_6159,plain,
    ! [X21998,X21999,X22000] :
      ( ~ class_Groups_Olinordered__ab__semigroup__add(X22000)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22000),X21999))
      | X21999 = c_Orderings_Obot__class_Obot(tc_fun(X22000,tc_HOL_Obool))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22000),X21998),c_Big__Operators_Olinorder__class_OMax(X22000,X21999)) = c_Big__Operators_Olinorder__class_OMax(X22000,hAPP(c_Set_OCollect(X22000),hAPP(hAPP(c_COMBB(tc_fun(X22000,tc_HOL_Obool),tc_HOL_Obool,X22000),c_HOL_OEx(X22000)),hAPP(hAPP(c_COMBC(X22000,tc_fun(X22000,tc_HOL_Obool),tc_fun(X22000,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22000,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X22000,tc_HOL_Obool),tc_fun(X22000,tc_HOL_Obool)),X22000),c_COMBS(X22000,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22000,tc_HOL_Obool),tc_fun(X22000,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X22000),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X22000),c_fconj)),hAPP(hAPP(c_COMBC(X22000,tc_fun(X22000,X22000),tc_fun(X22000,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22000,tc_HOL_Obool),tc_fun(tc_fun(X22000,X22000),tc_fun(X22000,tc_HOL_Obool)),X22000),c_COMBB(X22000,tc_HOL_Obool,X22000)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X22000),X21998))))),hAPP(hAPP(c_COMBC(X22000,tc_fun(X22000,tc_HOL_Obool),tc_HOL_Obool),c_member(X22000)),X21999))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__Max__commute])]) ).

fof(i_0_6160,plain,
    ! [X21052,X21053,X21054] :
      ( ~ class_Lattices_Odistrib__lattice(X21054)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21054),X21053))
      | X21053 = c_Orderings_Obot__class_Obot(tc_fun(X21054,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X21054),X21052),c_Big__Operators_Olattice__class_OSup__fin(X21054,X21053)) = c_Big__Operators_Olattice__class_OSup__fin(X21054,hAPP(c_Set_OCollect(X21054),hAPP(hAPP(c_COMBB(tc_fun(X21054,tc_HOL_Obool),tc_HOL_Obool,X21054),c_HOL_OEx(X21054)),hAPP(hAPP(c_COMBC(X21054,tc_fun(X21054,tc_HOL_Obool),tc_fun(X21054,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21054,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X21054,tc_HOL_Obool),tc_fun(X21054,tc_HOL_Obool)),X21054),c_COMBS(X21054,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21054,tc_HOL_Obool),tc_fun(X21054,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X21054),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X21054),c_fconj)),hAPP(hAPP(c_COMBC(X21054,tc_fun(X21054,X21054),tc_fun(X21054,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21054,tc_HOL_Obool),tc_fun(tc_fun(X21054,X21054),tc_fun(X21054,tc_HOL_Obool)),X21054),c_COMBB(X21054,tc_HOL_Obool,X21054)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X21054),X21052))))),hAPP(hAPP(c_COMBC(X21054,tc_fun(X21054,tc_HOL_Obool),tc_HOL_Obool),c_member(X21054)),X21053))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Sup1__distrib])]) ).

fof(i_0_6161,plain,
    ! [X21058,X21059,X21060] :
      ( ~ class_Lattices_Odistrib__lattice(X21060)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21060),X21059))
      | X21059 = c_Orderings_Obot__class_Obot(tc_fun(X21060,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X21060),X21058),c_Big__Operators_Olattice__class_OInf__fin(X21060,X21059)) = c_Big__Operators_Olattice__class_OInf__fin(X21060,hAPP(c_Set_OCollect(X21060),hAPP(hAPP(c_COMBB(tc_fun(X21060,tc_HOL_Obool),tc_HOL_Obool,X21060),c_HOL_OEx(X21060)),hAPP(hAPP(c_COMBC(X21060,tc_fun(X21060,tc_HOL_Obool),tc_fun(X21060,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21060,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X21060,tc_HOL_Obool),tc_fun(X21060,tc_HOL_Obool)),X21060),c_COMBS(X21060,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21060,tc_HOL_Obool),tc_fun(X21060,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X21060),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X21060),c_fconj)),hAPP(hAPP(c_COMBC(X21060,tc_fun(X21060,X21060),tc_fun(X21060,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21060,tc_HOL_Obool),tc_fun(tc_fun(X21060,X21060),tc_fun(X21060,tc_HOL_Obool)),X21060),c_COMBB(X21060,tc_HOL_Obool,X21060)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X21060),X21058))))),hAPP(hAPP(c_COMBC(X21060,tc_fun(X21060,tc_HOL_Obool),tc_HOL_Obool),c_member(X21060)),X21059))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Inf1__distrib])]) ).

fof(i_0_6162,plain,
    ! [X31468,X31469,X31470,X31471,X31472] :
      ( ( X31472 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X31471,X31470,X31469),X31472),X31468) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31470),X31471),c_List_Olist_ONil(X31470)),X31468) )
      & ( X31472 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X31471,X31470,X31469),X31472),X31468) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X31470),X31471),tc_prod(X31470,X31471),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31470),X31471),c_List_Olist_ONil(X31470)),X31468),hAPP(c_Product__Type_Oprod_Oprod__case(X31470,X31471,tc_prod(tc_List_Olist(X31470),X31471)),hAPP(hAPP(c_COMBC(X31470,tc_fun(X31471,tc_prod(tc_List_Olist(X31470),X31471)),tc_fun(X31471,tc_prod(tc_List_Olist(X31470),X31471))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X31470),X31471),tc_prod(tc_List_Olist(X31470),X31471)),tc_fun(tc_fun(X31471,tc_prod(tc_List_Olist(X31470),X31471)),tc_fun(X31471,tc_prod(tc_List_Olist(X31470),X31471))),X31470),c_COMBB(tc_prod(tc_List_Olist(X31470),X31471),tc_prod(tc_List_Olist(X31470),X31471),X31471)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X31470),tc_fun(X31471,tc_prod(tc_List_Olist(X31470),X31471))),tc_fun(tc_prod(tc_List_Olist(X31470),X31471),tc_prod(tc_List_Olist(X31470),X31471)),X31470),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X31470),X31471,tc_prod(tc_List_Olist(X31470),X31471))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X31470),tc_List_Olist(X31470)),tc_fun(tc_List_Olist(X31470),tc_fun(X31471,tc_prod(tc_List_Olist(X31470),X31471))),X31470),hAPP(c_COMBB(tc_List_Olist(X31470),tc_fun(X31471,tc_prod(tc_List_Olist(X31470),X31471)),tc_List_Olist(X31470)),c_Product__Type_OPair(tc_List_Olist(X31470),X31471))),c_List_Olist_OCons(X31470))))),hAPP(c_Lazy__Sequence_Oanamorph(X31471,X31470,X31469),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X31472),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(X31469,X31468)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_anamorph_Osimps])]) ).

fof(i_0_6163,plain,
    ! [X30727,X30728,X30729,X30730,X30731,X30732,X30733,X30734,X30735] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30730)),X30729) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30730)),X30728)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30730),tc_List_Olist(X30730))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30730),tc_List_Olist(X30730)),X30729),X30728)),c_List_Olistrel(X30730,X30727))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30730,X30730)),X30731),hAPP(c_List_Oset(tc_prod(X30730,X30730)),hAPP(hAPP(c_List_Ozip(X30730,X30730),X30729),X30728))))
        | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X30730,X30730,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X30730,tc_fun(tc_prod(X30730,X30730),tc_HOL_Obool),tc_fun(X30730,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30730,tc_fun(tc_fun(tc_prod(X30730,X30730),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X30730,X30730),tc_HOL_Obool),tc_fun(X30730,tc_HOL_Obool)),X30730),c_COMBC(X30730,tc_fun(tc_prod(X30730,X30730),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30730,tc_prod(X30730,X30730)),tc_fun(X30730,tc_fun(tc_fun(tc_prod(X30730,X30730),tc_HOL_Obool),tc_HOL_Obool)),X30730),hAPP(c_COMBB(tc_prod(X30730,X30730),tc_fun(tc_fun(tc_prod(X30730,X30730),tc_HOL_Obool),tc_HOL_Obool),X30730),c_member(tc_prod(X30730,X30730)))),c_Product__Type_OPair(X30730,X30730)))),X30727)),X30731))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30730),tc_List_Olist(X30730))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30730),tc_List_Olist(X30730)),X30729),X30728)),c_List_Olistrel(X30730,X30727))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30735,X30735)),esk401_4(X30732,X30733,X30734,X30735)),hAPP(c_List_Oset(tc_prod(X30735,X30735)),hAPP(hAPP(c_List_Ozip(X30735,X30735),X30734),X30733))))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30735)),X30734) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30735)),X30733)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30735),tc_List_Olist(X30735))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30735),tc_List_Olist(X30735)),X30734),X30733)),c_List_Olistrel(X30735,X30732))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X30735,X30735,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X30735,tc_fun(tc_prod(X30735,X30735),tc_HOL_Obool),tc_fun(X30735,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30735,tc_fun(tc_fun(tc_prod(X30735,X30735),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X30735,X30735),tc_HOL_Obool),tc_fun(X30735,tc_HOL_Obool)),X30735),c_COMBC(X30735,tc_fun(tc_prod(X30735,X30735),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30735,tc_prod(X30735,X30735)),tc_fun(X30735,tc_fun(tc_fun(tc_prod(X30735,X30735),tc_HOL_Obool),tc_HOL_Obool)),X30735),hAPP(c_COMBB(tc_prod(X30735,X30735),tc_fun(tc_fun(tc_prod(X30735,X30735),tc_HOL_Obool),tc_HOL_Obool),X30735),c_member(tc_prod(X30735,X30735)))),c_Product__Type_OPair(X30735,X30735)))),X30732)),esk401_4(X30732,X30733,X30734,X30735)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30735)),X30734) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30735)),X30733)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30735),tc_List_Olist(X30735))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30735),tc_List_Olist(X30735)),X30734),X30733)),c_List_Olistrel(X30735,X30732))) ) ),
    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_6164,plain,
    ! [X27644,X27645,X27646,X27647] :
      ( ( ~ hBOOL(hAPP(c_Predicate_ODomainP(X27647,X27646,hAPP(hAPP(c_COMBC(X27647,tc_fun(tc_prod(X27647,X27646),tc_HOL_Obool),tc_fun(X27646,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27646,tc_fun(tc_fun(tc_prod(X27647,X27646),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27647,X27646),tc_HOL_Obool),tc_fun(X27646,tc_HOL_Obool)),X27647),c_COMBC(X27646,tc_fun(tc_prod(X27647,X27646),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27646,tc_prod(X27647,X27646)),tc_fun(X27646,tc_fun(tc_fun(tc_prod(X27647,X27646),tc_HOL_Obool),tc_HOL_Obool)),X27647),hAPP(c_COMBB(tc_prod(X27647,X27646),tc_fun(tc_fun(tc_prod(X27647,X27646),tc_HOL_Obool),tc_HOL_Obool),X27646),c_member(tc_prod(X27647,X27646)))),c_Product__Type_OPair(X27647,X27646)))),X27645)),X27644))
        | hBOOL(hAPP(hAPP(c_member(X27647),X27644),hAPP(c_Relation_ODomain(X27647,X27646),X27645))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27647),X27644),hAPP(c_Relation_ODomain(X27647,X27646),X27645)))
        | hBOOL(hAPP(c_Predicate_ODomainP(X27647,X27646,hAPP(hAPP(c_COMBC(X27647,tc_fun(tc_prod(X27647,X27646),tc_HOL_Obool),tc_fun(X27646,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27646,tc_fun(tc_fun(tc_prod(X27647,X27646),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27647,X27646),tc_HOL_Obool),tc_fun(X27646,tc_HOL_Obool)),X27647),c_COMBC(X27646,tc_fun(tc_prod(X27647,X27646),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27646,tc_prod(X27647,X27646)),tc_fun(X27646,tc_fun(tc_fun(tc_prod(X27647,X27646),tc_HOL_Obool),tc_HOL_Obool)),X27647),hAPP(c_COMBB(tc_prod(X27647,X27646),tc_fun(tc_fun(tc_prod(X27647,X27646),tc_HOL_Obool),tc_HOL_Obool),X27646),c_member(tc_prod(X27647,X27646)))),c_Product__Type_OPair(X27647,X27646)))),X27645)),X27644)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP__Domain__eq])]) ).

fof(i_0_6165,plain,
    ! [X27560,X27561,X27562,X27563] :
      ( ( ~ hBOOL(hAPP(c_Predicate_ORangeP(X27563,X27562,hAPP(hAPP(c_COMBC(X27563,tc_fun(tc_prod(X27563,X27562),tc_HOL_Obool),tc_fun(X27562,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27562,tc_fun(tc_fun(tc_prod(X27563,X27562),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27563,X27562),tc_HOL_Obool),tc_fun(X27562,tc_HOL_Obool)),X27563),c_COMBC(X27562,tc_fun(tc_prod(X27563,X27562),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27562,tc_prod(X27563,X27562)),tc_fun(X27562,tc_fun(tc_fun(tc_prod(X27563,X27562),tc_HOL_Obool),tc_HOL_Obool)),X27563),hAPP(c_COMBB(tc_prod(X27563,X27562),tc_fun(tc_fun(tc_prod(X27563,X27562),tc_HOL_Obool),tc_HOL_Obool),X27562),c_member(tc_prod(X27563,X27562)))),c_Product__Type_OPair(X27563,X27562)))),X27561)),X27560))
        | hBOOL(hAPP(hAPP(c_member(X27562),X27560),hAPP(c_Relation_ORange(X27563,X27562),X27561))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27562),X27560),hAPP(c_Relation_ORange(X27563,X27562),X27561)))
        | hBOOL(hAPP(c_Predicate_ORangeP(X27563,X27562,hAPP(hAPP(c_COMBC(X27563,tc_fun(tc_prod(X27563,X27562),tc_HOL_Obool),tc_fun(X27562,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27562,tc_fun(tc_fun(tc_prod(X27563,X27562),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27563,X27562),tc_HOL_Obool),tc_fun(X27562,tc_HOL_Obool)),X27563),c_COMBC(X27562,tc_fun(tc_prod(X27563,X27562),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27562,tc_prod(X27563,X27562)),tc_fun(X27562,tc_fun(tc_fun(tc_prod(X27563,X27562),tc_HOL_Obool),tc_HOL_Obool)),X27563),hAPP(c_COMBB(tc_prod(X27563,X27562),tc_fun(tc_fun(tc_prod(X27563,X27562),tc_HOL_Obool),tc_HOL_Obool),X27562),c_member(tc_prod(X27563,X27562)))),c_Product__Type_OPair(X27563,X27562)))),X27561)),X27560)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP__Range__eq])]) ).

fof(i_0_6166,plain,
    ! [X27261,X27262,X27263] :
      ( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X27263,hAPP(hAPP(c_COMBC(X27263,tc_fun(tc_prod(X27263,X27263),tc_HOL_Obool),tc_fun(X27263,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27263,tc_fun(tc_fun(tc_prod(X27263,X27263),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27263,X27263),tc_HOL_Obool),tc_fun(X27263,tc_HOL_Obool)),X27263),c_COMBC(X27263,tc_fun(tc_prod(X27263,X27263),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27263,tc_prod(X27263,X27263)),tc_fun(X27263,tc_fun(tc_fun(tc_prod(X27263,X27263),tc_HOL_Obool),tc_HOL_Obool)),X27263),hAPP(c_COMBB(tc_prod(X27263,X27263),tc_fun(tc_fun(tc_prod(X27263,X27263),tc_HOL_Obool),tc_HOL_Obool),X27263),c_member(tc_prod(X27263,X27263)))),c_Product__Type_OPair(X27263,X27263)))),X27262)),X27261))
        | hBOOL(hAPP(hAPP(c_member(X27263),X27261),c_Wellfounded_Oacc(X27263,X27262))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27263),X27261),c_Wellfounded_Oacc(X27263,X27262)))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X27263,hAPP(hAPP(c_COMBC(X27263,tc_fun(tc_prod(X27263,X27263),tc_HOL_Obool),tc_fun(X27263,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27263,tc_fun(tc_fun(tc_prod(X27263,X27263),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27263,X27263),tc_HOL_Obool),tc_fun(X27263,tc_HOL_Obool)),X27263),c_COMBC(X27263,tc_fun(tc_prod(X27263,X27263),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27263,tc_prod(X27263,X27263)),tc_fun(X27263,tc_fun(tc_fun(tc_prod(X27263,X27263),tc_HOL_Obool),tc_HOL_Obool)),X27263),hAPP(c_COMBB(tc_prod(X27263,X27263),tc_fun(tc_fun(tc_prod(X27263,X27263),tc_HOL_Obool),tc_HOL_Obool),X27263),c_member(tc_prod(X27263,X27263)))),c_Product__Type_OPair(X27263,X27263)))),X27262)),X27261)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__acc__eq])]) ).

fof(i_0_6167,plain,
    ! [X18645,X18646,X18647,X18648,X18649,X18650,X18651,X18654,X18655,X18656,X18657,X18658,X18659,X18660,X18661,X18662] :
      ( ( hAPP(hAPP(X18649,X18646),X18645) = hAPP(hAPP(X18649,esk29_7(X18645,X18646,X18647,X18648,X18649,X18650,X18651)),esk30_7(X18645,X18646,X18647,X18648,X18649,X18650,X18651))
        | X18647 = c_Orderings_Obot__class_Obot(tc_fun(X18651,tc_HOL_Obool))
        | ~ c_Nitpick_Ofold__graph_H(X18651,X18650,X18649,X18648,X18647,hAPP(hAPP(X18649,X18646),X18645)) )
      & ( hBOOL(hAPP(hAPP(c_member(X18651),esk29_7(X18645,X18646,X18647,X18648,X18649,X18650,X18651)),X18647))
        | X18647 = c_Orderings_Obot__class_Obot(tc_fun(X18651,tc_HOL_Obool))
        | ~ c_Nitpick_Ofold__graph_H(X18651,X18650,X18649,X18648,X18647,hAPP(hAPP(X18649,X18646),X18645)) )
      & ( c_Nitpick_Ofold__graph_H(X18651,X18650,X18649,X18648,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18651,tc_HOL_Obool)),X18647),hAPP(hAPP(c_Set_Oinsert(X18651),esk29_7(X18645,X18646,X18647,X18648,X18649,X18650,X18651)),c_Orderings_Obot__class_Obot(tc_fun(X18651,tc_HOL_Obool)))),esk30_7(X18645,X18646,X18647,X18648,X18649,X18650,X18651))
        | X18647 = c_Orderings_Obot__class_Obot(tc_fun(X18651,tc_HOL_Obool))
        | ~ c_Nitpick_Ofold__graph_H(X18651,X18650,X18649,X18648,X18647,hAPP(hAPP(X18649,X18646),X18645)) )
      & ( hAPP(hAPP(X18649,X18646),X18645) = hAPP(hAPP(X18649,esk29_7(X18645,X18646,X18647,X18648,X18649,X18650,X18651)),esk30_7(X18645,X18646,X18647,X18648,X18649,X18650,X18651))
        | hAPP(hAPP(X18649,X18646),X18645) = X18648
        | ~ c_Nitpick_Ofold__graph_H(X18651,X18650,X18649,X18648,X18647,hAPP(hAPP(X18649,X18646),X18645)) )
      & ( hBOOL(hAPP(hAPP(c_member(X18651),esk29_7(X18645,X18646,X18647,X18648,X18649,X18650,X18651)),X18647))
        | hAPP(hAPP(X18649,X18646),X18645) = X18648
        | ~ c_Nitpick_Ofold__graph_H(X18651,X18650,X18649,X18648,X18647,hAPP(hAPP(X18649,X18646),X18645)) )
      & ( c_Nitpick_Ofold__graph_H(X18651,X18650,X18649,X18648,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18651,tc_HOL_Obool)),X18647),hAPP(hAPP(c_Set_Oinsert(X18651),esk29_7(X18645,X18646,X18647,X18648,X18649,X18650,X18651)),c_Orderings_Obot__class_Obot(tc_fun(X18651,tc_HOL_Obool)))),esk30_7(X18645,X18646,X18647,X18648,X18649,X18650,X18651))
        | hAPP(hAPP(X18649,X18646),X18645) = X18648
        | ~ c_Nitpick_Ofold__graph_H(X18651,X18650,X18649,X18648,X18647,hAPP(hAPP(X18649,X18646),X18645)) )
      & ( X18656 != c_Orderings_Obot__class_Obot(tc_fun(X18660,tc_HOL_Obool))
        | hAPP(hAPP(X18658,X18655),X18654) != X18657
        | c_Nitpick_Ofold__graph_H(X18660,X18659,X18658,X18657,X18656,hAPP(hAPP(X18658,X18655),X18654)) )
      & ( hAPP(hAPP(X18658,X18655),X18654) != hAPP(hAPP(X18658,X18661),X18662)
        | ~ hBOOL(hAPP(hAPP(c_member(X18660),X18661),X18656))
        | ~ c_Nitpick_Ofold__graph_H(X18660,X18659,X18658,X18657,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18660,tc_HOL_Obool)),X18656),hAPP(hAPP(c_Set_Oinsert(X18660),X18661),c_Orderings_Obot__class_Obot(tc_fun(X18660,tc_HOL_Obool)))),X18662)
        | c_Nitpick_Ofold__graph_H(X18660,X18659,X18658,X18657,X18656,hAPP(hAPP(X18658,X18655),X18654)) ) ),
    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_6168,plain,
    ! [X34144,X34145,X34146,X34147,X34148,X34149,X34150] :
      ( ( hBOOL(hAPP(hAPP(c_member(X34150),esk529_7(X34144,X34145,X34146,X34147,X34148,X34149,X34150)),X34147))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X34150,tc_fun(X34149,tc_fun(X34148,tc_HOL_Obool))),X34147),X34146),X34145),X34144)) )
      & ( hBOOL(hAPP(hAPP(hAPP(X34146,esk529_7(X34144,X34145,X34146,X34147,X34148,X34149,X34150)),X34145),X34144))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X34150,tc_fun(X34149,tc_fun(X34148,tc_HOL_Obool))),X34147),X34146),X34145),X34144)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5268])])])]) ).

fof(i_0_6169,plain,
    ! [X20139,X20140,X20141,X20142,X20143,X20144,X20145,X20147,X20148,X20149,X20150,X20151,X20152,X20153,X20154] :
      ( ( hBOOL(hAPP(hAPP(c_member(X20145),esk69_7(X20139,X20140,X20141,X20142,X20143,X20144,X20145)),X20142))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20145,tc_fun(X20144,tc_fun(X20143,tc_HOL_Obool))),X20142),X20141),X20140),X20139)) )
      & ( hBOOL(hAPP(hAPP(hAPP(X20141,esk69_7(X20139,X20140,X20141,X20142,X20143,X20144,X20145)),X20140),X20139))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20145,tc_fun(X20144,tc_fun(X20143,tc_HOL_Obool))),X20142),X20141),X20140),X20139)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X20153),X20154),X20150))
        | ~ hBOOL(hAPP(hAPP(hAPP(X20149,X20154),X20148),X20147))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20153,tc_fun(X20152,tc_fun(X20151,tc_HOL_Obool))),X20150),X20149),X20148),X20147)) ) ),
    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_6170,plain,
    ! [X32625,X32626,X32627,X32628] : c_List_Opartition(X32628,X32627,hAPP(hAPP(c_List_Olist_OCons(X32628),X32626),X32625)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X32628),tc_List_Olist(X32628),tc_prod(tc_List_Olist(X32628),tc_List_Olist(X32628))),hAPP(hAPP(c_COMBS(tc_List_Olist(X32628),tc_fun(tc_List_Olist(X32628),tc_prod(tc_List_Olist(X32628),tc_List_Olist(X32628))),tc_fun(tc_List_Olist(X32628),tc_prod(tc_List_Olist(X32628),tc_List_Olist(X32628)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32628),tc_fun(tc_prod(tc_List_Olist(X32628),tc_List_Olist(X32628)),tc_prod(tc_List_Olist(X32628),tc_List_Olist(X32628)))),tc_fun(tc_fun(tc_List_Olist(X32628),tc_prod(tc_List_Olist(X32628),tc_List_Olist(X32628))),tc_fun(tc_List_Olist(X32628),tc_prod(tc_List_Olist(X32628),tc_List_Olist(X32628)))),tc_List_Olist(X32628)),c_COMBS(tc_List_Olist(X32628),tc_prod(tc_List_Olist(X32628),tc_List_Olist(X32628)),tc_prod(tc_List_Olist(X32628),tc_List_Olist(X32628)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32628),tc_prod(tc_List_Olist(X32628),tc_List_Olist(X32628))),tc_fun(tc_List_Olist(X32628),tc_fun(tc_prod(tc_List_Olist(X32628),tc_List_Olist(X32628)),tc_prod(tc_List_Olist(X32628),tc_List_Olist(X32628)))),tc_List_Olist(X32628)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X32628),tc_List_Olist(X32628)),tc_fun(tc_prod(tc_List_Olist(X32628),tc_List_Olist(X32628)),tc_prod(tc_List_Olist(X32628),tc_List_Olist(X32628))),tc_List_Olist(X32628)),hAPP(c_If(tc_prod(tc_List_Olist(X32628),tc_List_Olist(X32628))),hAPP(X32627,X32626)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X32628),tc_fun(tc_List_Olist(X32628),tc_prod(tc_List_Olist(X32628),tc_List_Olist(X32628))),tc_List_Olist(X32628)),c_Product__Type_OPair(tc_List_Olist(X32628),tc_List_Olist(X32628))),hAPP(c_List_Olist_OCons(X32628),X32626))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X32628),tc_fun(tc_List_Olist(X32628),tc_List_Olist(X32628)),tc_fun(tc_List_Olist(X32628),tc_prod(tc_List_Olist(X32628),tc_List_Olist(X32628)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32628),tc_prod(tc_List_Olist(X32628),tc_List_Olist(X32628))),tc_fun(tc_fun(tc_List_Olist(X32628),tc_List_Olist(X32628)),tc_fun(tc_List_Olist(X32628),tc_prod(tc_List_Olist(X32628),tc_List_Olist(X32628)))),tc_List_Olist(X32628)),c_COMBB(tc_List_Olist(X32628),tc_prod(tc_List_Olist(X32628),tc_List_Olist(X32628)),tc_List_Olist(X32628))),c_Product__Type_OPair(tc_List_Olist(X32628),tc_List_Olist(X32628)))),hAPP(c_List_Olist_OCons(X32628),X32626)))),c_List_Opartition(X32628,X32627,X32625)),
    inference(variable_rename,[status(thm)],[fact_partition_Osimps_I2_J]) ).

fof(i_0_6171,plain,
    ! [X30510,X30511,X30512] : hAPP(c_List_Olexn(X30512,X30511),hAPP(c_Nat_OSuc,X30510)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X30512),tc_List_Olist(X30512)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X30512,tc_List_Olist(X30512)),tc_prod(X30512,tc_List_Olist(X30512))),tc_prod(tc_List_Olist(X30512),tc_List_Olist(X30512)),c_Product__Type_Omap__pair(tc_prod(X30512,tc_List_Olist(X30512)),tc_List_Olist(X30512),tc_prod(X30512,tc_List_Olist(X30512)),tc_List_Olist(X30512),hAPP(c_Product__Type_Oprod_Oprod__case(X30512,tc_List_Olist(X30512),tc_List_Olist(X30512)),c_List_Olist_OCons(X30512)),hAPP(c_Product__Type_Oprod_Oprod__case(X30512,tc_List_Olist(X30512),tc_List_Olist(X30512)),c_List_Olist_OCons(X30512)))),c_Wellfounded_Olex__prod(X30512,tc_List_Olist(X30512),X30511,hAPP(c_List_Olexn(X30512,X30511),X30510)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X30512),tc_List_Olist(X30512))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X30512),tc_List_Olist(X30512),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X30512),tc_fun(tc_List_Olist(X30512),tc_HOL_Obool),tc_fun(tc_List_Olist(X30512),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X30512),tc_HOL_Obool),tc_fun(tc_List_Olist(X30512),tc_HOL_Obool)),tc_List_Olist(X30512)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X30512))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X30512)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X30512),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X30512)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X30512)))),hAPP(c_Nat_OSuc,X30510))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X30512),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X30512)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X30512)))),hAPP(c_Nat_OSuc,X30510)))))),
    inference(variable_rename,[status(thm)],[fact_lexn_Osimps_I2_J]) ).

cnf(i_0_6172,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_5269]) ).

cnf(i_0_6173,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_5269]) ).

cnf(i_0_6174,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_5270]) ).

fof(i_0_6175,plain,
    ! [X31032,X31033,X31034] : hAPP(c_List_Oset(X31034),c_List_Osublist(X31034,X31033,X31032)) = hAPP(c_Set_OCollect(X31034),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X31034),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X31034,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)),X31034),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)),X31034),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X31034,tc_fun(tc_Nat_Onat,X31034),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31034,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X31034),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X31034),c_COMBB(X31034,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X31034),X31033))))),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(X31034)),X31033)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X31032))))),
    inference(variable_rename,[status(thm)],[fact_set__sublist]) ).

cnf(i_0_6176,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_5271]) ).

cnf(i_0_6177,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_5272]) ).

cnf(i_0_6178,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_5273]) ).

fof(i_0_6179,plain,
    ! [X26843,X26844,X26845,X26846,X26847,X26848] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26846),esk243_6(X26843,X26844,X26845,X26846,X26847,X26848)),X26845))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26848,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X26846,tc_HOL_Obool),tc_Nat_Onat,X26848),c_Finite__Set_Ocard(X26846)),hAPP(hAPP(c_COMBB(tc_fun(X26846,tc_HOL_Obool),tc_fun(X26846,tc_HOL_Obool),X26848),c_Set_OCollect(X26846)),hAPP(hAPP(c_COMBB(tc_fun(X26846,tc_HOL_Obool),tc_fun(X26846,tc_HOL_Obool),X26848),hAPP(c_COMBS(X26846,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X26846),c_fconj),hAPP(hAPP(c_COMBC(X26846,tc_fun(X26846,tc_HOL_Obool),tc_HOL_Obool),c_member(X26846)),X26845)))),X26844)))),X26847) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26846,tc_Nat_Onat),X26843),X26845)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26846),X26845))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26848),X26847)) )
      & ( hAPP(c_Finite__Set_Ocard(X26848),hAPP(c_Set_OCollect(X26848),hAPP(hAPP(c_COMBS(X26848,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X26848),c_fconj),hAPP(hAPP(c_COMBC(X26848,tc_fun(X26848,tc_HOL_Obool),tc_HOL_Obool),c_member(X26848)),X26847))),hAPP(hAPP(c_COMBC(X26848,X26846,tc_HOL_Obool),X26844),esk243_6(X26843,X26844,X26845,X26846,X26847,X26848))))) != hAPP(X26843,esk243_6(X26843,X26844,X26845,X26846,X26847,X26848))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26848,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X26846,tc_HOL_Obool),tc_Nat_Onat,X26848),c_Finite__Set_Ocard(X26846)),hAPP(hAPP(c_COMBB(tc_fun(X26846,tc_HOL_Obool),tc_fun(X26846,tc_HOL_Obool),X26848),c_Set_OCollect(X26846)),hAPP(hAPP(c_COMBB(tc_fun(X26846,tc_HOL_Obool),tc_fun(X26846,tc_HOL_Obool),X26848),hAPP(c_COMBS(X26846,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X26846),c_fconj),hAPP(hAPP(c_COMBC(X26846,tc_fun(X26846,tc_HOL_Obool),tc_HOL_Obool),c_member(X26846)),X26845)))),X26844)))),X26847) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26846,tc_Nat_Onat),X26843),X26845)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26846),X26845))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26848),X26847)) ) ),
    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_6180,plain,
    ! [X31010,X31011] : hAPP(c_List_Oset(X31011),X31010) = hAPP(c_Set_OCollect(X31011),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X31011),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X31011,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)),X31011),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)),X31011),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X31011,tc_fun(tc_Nat_Onat,X31011),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31011,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X31011),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X31011),c_COMBB(X31011,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X31011),X31010))))),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(X31011)),X31010))))),
    inference(variable_rename,[status(thm)],[fact_set__conv__nth]) ).

fof(i_0_6181,plain,
    ! [X27874,X27875,X27876,X27877] : hAPP(hAPP(c_Product__Type_OSigma(X27877,X27876),X27875),X27874) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27877,tc_fun(tc_prod(X27877,X27876),tc_HOL_Obool)),X27875),hAPP(hAPP(c_COMBS(X27877,tc_fun(X27876,tc_fun(tc_prod(X27877,X27876),tc_HOL_Obool)),tc_fun(tc_prod(X27877,X27876),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27876,tc_HOL_Obool),tc_fun(tc_fun(X27876,tc_fun(tc_prod(X27877,X27876),tc_HOL_Obool)),tc_fun(tc_prod(X27877,X27876),tc_HOL_Obool)),X27877),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27876,tc_fun(tc_prod(X27877,X27876),tc_HOL_Obool))),X27874)),hAPP(hAPP(c_COMBC(X27877,tc_fun(tc_prod(X27877,X27876),tc_HOL_Obool),tc_fun(X27876,tc_fun(tc_prod(X27877,X27876),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27876,tc_fun(tc_fun(tc_prod(X27877,X27876),tc_HOL_Obool),tc_fun(tc_prod(X27877,X27876),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X27877,X27876),tc_HOL_Obool),tc_fun(X27876,tc_fun(tc_prod(X27877,X27876),tc_HOL_Obool))),X27877),c_COMBC(X27876,tc_fun(tc_prod(X27877,X27876),tc_HOL_Obool),tc_fun(tc_prod(X27877,X27876),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27876,tc_prod(X27877,X27876)),tc_fun(X27876,tc_fun(tc_fun(tc_prod(X27877,X27876),tc_HOL_Obool),tc_fun(tc_prod(X27877,X27876),tc_HOL_Obool))),X27877),hAPP(c_COMBB(tc_prod(X27877,X27876),tc_fun(tc_fun(tc_prod(X27877,X27876),tc_HOL_Obool),tc_fun(tc_prod(X27877,X27876),tc_HOL_Obool)),X27876),c_Set_Oinsert(tc_prod(X27877,X27876)))),c_Product__Type_OPair(X27877,X27876)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27877,X27876),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_Sigma__def]) ).

cnf(i_0_6182,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_5274]) ).

fof(i_0_6183,plain,
    ! [X26766,X26767,X26768,X26769,X26770,X26771] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26769),esk238_6(X26766,X26767,X26768,X26769,X26770,X26771)),X26768))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26771,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X26769,tc_HOL_Obool),tc_Nat_Onat,X26771),c_Finite__Set_Ocard(X26769)),hAPP(hAPP(c_COMBB(tc_fun(X26769,tc_HOL_Obool),tc_fun(X26769,tc_HOL_Obool),X26771),c_Set_OCollect(X26769)),hAPP(hAPP(c_COMBB(tc_fun(X26769,tc_HOL_Obool),tc_fun(X26769,tc_HOL_Obool),X26771),hAPP(c_COMBS(X26769,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X26769),c_fconj),hAPP(hAPP(c_COMBC(X26769,tc_fun(X26769,tc_HOL_Obool),tc_HOL_Obool),c_member(X26769)),X26768)))),X26767)))),X26770) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26766),hAPP(c_Finite__Set_Ocard(X26769),X26768))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26769),X26768))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26771),X26770)) )
      & ( hAPP(c_Finite__Set_Ocard(X26771),hAPP(c_Set_OCollect(X26771),hAPP(hAPP(c_COMBS(X26771,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X26771),c_fconj),hAPP(hAPP(c_COMBC(X26771,tc_fun(X26771,tc_HOL_Obool),tc_HOL_Obool),c_member(X26771)),X26770))),hAPP(hAPP(c_COMBC(X26771,X26769,tc_HOL_Obool),X26767),esk238_6(X26766,X26767,X26768,X26769,X26770,X26771))))) != X26766
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26771,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X26769,tc_HOL_Obool),tc_Nat_Onat,X26771),c_Finite__Set_Ocard(X26769)),hAPP(hAPP(c_COMBB(tc_fun(X26769,tc_HOL_Obool),tc_fun(X26769,tc_HOL_Obool),X26771),c_Set_OCollect(X26769)),hAPP(hAPP(c_COMBB(tc_fun(X26769,tc_HOL_Obool),tc_fun(X26769,tc_HOL_Obool),X26771),hAPP(c_COMBS(X26769,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X26769),c_fconj),hAPP(hAPP(c_COMBC(X26769,tc_fun(X26769,tc_HOL_Obool),tc_HOL_Obool),c_member(X26769)),X26768)))),X26767)))),X26770) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26766),hAPP(c_Finite__Set_Ocard(X26769),X26768))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26769),X26768))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26771),X26770)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__multicount])])])]) ).

fof(i_0_6184,plain,
    ! [X26549,X26550,X26551,X26552,X26553,X26554,X26555] :
      ( ~ class_Groups_Ocomm__monoid__add(X26555)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26554),X26553))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26552),X26551))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26554,X26555),hAPP(hAPP(c_COMBS(X26554,tc_fun(X26552,tc_HOL_Obool),X26555),hAPP(hAPP(c_COMBB(tc_fun(X26552,X26555),tc_fun(tc_fun(X26552,tc_HOL_Obool),X26555),X26554),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26552,X26555)),X26550)),hAPP(hAPP(c_COMBB(tc_fun(X26552,tc_HOL_Obool),tc_fun(X26552,tc_HOL_Obool),X26554),c_Set_OCollect(X26552)),hAPP(hAPP(c_COMBB(tc_fun(X26552,tc_HOL_Obool),tc_fun(X26552,tc_HOL_Obool),X26554),hAPP(c_COMBS(X26552,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X26552),c_fconj),hAPP(hAPP(c_COMBC(X26552,tc_fun(X26552,tc_HOL_Obool),tc_HOL_Obool),c_member(X26552)),X26551)))),X26549)))),X26553) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26552,X26555),hAPP(hAPP(c_COMBS(X26552,tc_fun(X26554,tc_HOL_Obool),X26555),hAPP(hAPP(c_COMBB(tc_fun(X26554,X26555),tc_fun(tc_fun(X26554,tc_HOL_Obool),X26555),X26552),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26554,X26555)),hAPP(c_COMBC(X26554,X26552,X26555),X26550))),hAPP(hAPP(c_COMBB(tc_fun(X26554,tc_HOL_Obool),tc_fun(X26554,tc_HOL_Obool),X26552),c_Set_OCollect(X26554)),hAPP(hAPP(c_COMBB(tc_fun(X26554,tc_HOL_Obool),tc_fun(X26554,tc_HOL_Obool),X26552),hAPP(c_COMBS(X26554,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X26554),c_fconj),hAPP(hAPP(c_COMBC(X26554,tc_fun(X26554,tc_HOL_Obool),tc_HOL_Obool),c_member(X26554)),X26553)))),hAPP(c_COMBC(X26554,X26552,tc_HOL_Obool),X26549))))),X26551) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__setsum__restrict])]) ).

fof(i_0_6185,plain,
    ! [X28697,X28698,X28699,X28700,X28701] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28701,X28701)),hAPP(hAPP(c_Product__Type_OPair(X28701,X28701),hAPP(X28700,hAPP(c_Nat_OSuc,esk327_5(X28697,X28698,X28699,X28700,X28701)))),hAPP(X28700,esk327_5(X28697,X28698,X28699,X28700,X28701)))),c_Transitive__Closure_Ortrancl(X28701,X28699)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28701,X28701)),hAPP(hAPP(c_Product__Type_OPair(X28701,X28701),hAPP(X28700,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28698),X28697))),hAPP(X28700,X28698))),c_Transitive__Closure_Ortrancl(X28701,X28699))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sequence__trans])])]) ).

fof(i_0_6186,plain,
    ! [X24095,X24096,X24097,X24098,X24099,X24100] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X24100,X24099)),hAPP(hAPP(c_Product__Type_OPair(X24100,X24099),esk141_6(X24095,X24096,X24097,X24098,X24099,X24100)),esk142_6(X24095,X24096,X24097,X24098,X24099,X24100))),hAPP(X24096,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X24100,X24099),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(X24100,X24099),tc_HOL_Obool),X24096)),hAPP(c_Set_OCollect(tc_prod(X24100,X24099)),hAPP(c_Product__Type_Oprod_Oprod__case(X24100,X24099,tc_HOL_Obool),X24095))))))
        | hBOOL(hAPP(hAPP(X24095,X24098),X24097))
        | ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(X24100,X24099),tc_HOL_Obool),tc_fun(tc_prod(X24100,X24099),tc_HOL_Obool),X24096)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24100,X24099)),hAPP(hAPP(c_Product__Type_OPair(X24100,X24099),X24098),X24097)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(X24100,X24099),tc_HOL_Obool),X24096))) )
      & ( ~ hBOOL(hAPP(hAPP(X24095,esk141_6(X24095,X24096,X24097,X24098,X24099,X24100)),esk142_6(X24095,X24096,X24097,X24098,X24099,X24100)))
        | hBOOL(hAPP(hAPP(X24095,X24098),X24097))
        | ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(X24100,X24099),tc_HOL_Obool),tc_fun(tc_prod(X24100,X24099),tc_HOL_Obool),X24096)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24100,X24099)),hAPP(hAPP(c_Product__Type_OPair(X24100,X24099),X24098),X24097)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(X24100,X24099),tc_HOL_Obool),X24096))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lfp__induct2])])])]) ).

fof(i_0_6187,plain,
    ! [X30028,X30029,X30030,X30031,X30032,X30033] :
      ( ( X30031 = hAPP(hAPP(c_Product__Type_OPair(X30033,X30032),esk390_6(X30028,X30029,X30030,X30031,X30032,X30033)),esk392_6(X30028,X30029,X30030,X30031,X30032,X30033))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30033,X30032)),X30031),hAPP(hAPP(c_Relation_Orel__comp(X30033,X30030,X30032),X30029),X30028))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30033,X30030)),hAPP(hAPP(c_Product__Type_OPair(X30033,X30030),esk390_6(X30028,X30029,X30030,X30031,X30032,X30033)),esk391_6(X30028,X30029,X30030,X30031,X30032,X30033))),X30029))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30033,X30032)),X30031),hAPP(hAPP(c_Relation_Orel__comp(X30033,X30030,X30032),X30029),X30028))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30030,X30032)),hAPP(hAPP(c_Product__Type_OPair(X30030,X30032),esk391_6(X30028,X30029,X30030,X30031,X30032,X30033)),esk392_6(X30028,X30029,X30030,X30031,X30032,X30033))),X30028))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30033,X30032)),X30031),hAPP(hAPP(c_Relation_Orel__comp(X30033,X30030,X30032),X30029),X30028))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5275])])])]) ).

fof(i_0_6188,plain,
    ! [X23893,X23894] : c_Divides_Odivmod__int__rel(X23894,X23893) = 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,X23894))),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),X23893)))))),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)),X23893))),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)),X23893))))),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)),X23893)))),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),X23893))),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_6189,plain,
    ! [X26454,X26455,X26456,X26457,X26458,X26459,X26460] :
      ( ~ class_Rings_Osemiring__0(X26460)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26460),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26459,X26460),X26458),X26457)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26456,X26460),X26455),X26454)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26459,X26460),hAPP(hAPP(c_COMBC(X26459,tc_fun(X26456,tc_HOL_Obool),X26460),hAPP(hAPP(c_COMBB(tc_fun(X26456,X26460),tc_fun(tc_fun(X26456,tc_HOL_Obool),X26460),X26459),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26456,X26460)),hAPP(hAPP(c_COMBC(X26459,tc_fun(X26456,X26460),tc_fun(X26456,X26460)),hAPP(hAPP(c_COMBB(tc_fun(X26460,X26460),tc_fun(tc_fun(X26456,X26460),tc_fun(X26456,X26460)),X26459),c_COMBB(X26460,X26460,X26456)),hAPP(hAPP(c_COMBB(X26460,tc_fun(X26460,X26460),X26459),c_Groups_Otimes__class_Otimes(X26460)),X26458))),X26455))),X26454)),X26457) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__product])]) ).

fof(i_0_6190,plain,
    ! [X27893,X27894,X27895,X27896,X27897,X27898] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27897),esk272_6(X27893,X27894,X27895,X27896,X27897,X27898)),X27896))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27898,X27897,c_Groups_Otimes__class_Otimes(X27898)),hAPP(hAPP(c_COMBS(X27897,tc_fun(X27895,tc_HOL_Obool),X27898),hAPP(hAPP(c_COMBC(X27897,X27898,tc_fun(tc_fun(X27895,tc_HOL_Obool),X27898)),hAPP(hAPP(c_COMBB(tc_fun(X27895,X27898),tc_fun(X27898,tc_fun(tc_fun(X27895,tc_HOL_Obool),X27898)),X27897),c_Finite__Set_Ofold__image(X27898,X27895,c_Groups_Otimes__class_Otimes(X27898))),X27893)),c_Groups_Oone__class_Oone(X27898))),X27894)),c_Groups_Oone__class_Oone(X27898)),X27896) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27898,tc_prod(X27897,X27895),c_Groups_Otimes__class_Otimes(X27898)),hAPP(c_Product__Type_Oprod_Oprod__case(X27897,X27895,X27898),X27893)),c_Groups_Oone__class_Oone(X27898)),hAPP(hAPP(c_Product__Type_OSigma(X27897,X27895),X27896),X27894))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27897),X27896))
        | ~ class_Groups_Ocomm__monoid__mult(X27898) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27895),hAPP(X27894,esk272_6(X27893,X27894,X27895,X27896,X27897,X27898))))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27898,X27897,c_Groups_Otimes__class_Otimes(X27898)),hAPP(hAPP(c_COMBS(X27897,tc_fun(X27895,tc_HOL_Obool),X27898),hAPP(hAPP(c_COMBC(X27897,X27898,tc_fun(tc_fun(X27895,tc_HOL_Obool),X27898)),hAPP(hAPP(c_COMBB(tc_fun(X27895,X27898),tc_fun(X27898,tc_fun(tc_fun(X27895,tc_HOL_Obool),X27898)),X27897),c_Finite__Set_Ofold__image(X27898,X27895,c_Groups_Otimes__class_Otimes(X27898))),X27893)),c_Groups_Oone__class_Oone(X27898))),X27894)),c_Groups_Oone__class_Oone(X27898)),X27896) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27898,tc_prod(X27897,X27895),c_Groups_Otimes__class_Otimes(X27898)),hAPP(c_Product__Type_Oprod_Oprod__case(X27897,X27895,X27898),X27893)),c_Groups_Oone__class_Oone(X27898)),hAPP(hAPP(c_Product__Type_OSigma(X27897,X27895),X27896),X27894))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27897),X27896))
        | ~ class_Groups_Ocomm__monoid__mult(X27898) ) ),
    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_6191,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_5276]) ).

fof(i_0_6192,plain,
    ! [X30476,X30477,X30478] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30478),X30477))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X30478)),hAPP(c_Set_OCollect(tc_List_Olist(X30478)),hAPP(hAPP(c_COMBS(tc_List_Olist(X30478),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X30478)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X30478),tc_fun(X30478,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X30478,tc_HOL_Obool),tc_fun(tc_fun(X30478,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X30478)),c_Orderings_Oord__class_Oless__eq(tc_fun(X30478,tc_HOL_Obool))),c_List_Oset(X30478))),X30477))),hAPP(hAPP(c_COMBC(tc_List_Olist(X30478),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X30478)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X30478)))),X30476))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__lists__length__le])]) ).

fof(i_0_6193,plain,
    ! [X30533,X30534,X30535] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30535),X30534))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X30535)),hAPP(c_Set_OCollect(tc_List_Olist(X30535)),hAPP(hAPP(c_COMBS(tc_List_Olist(X30535),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X30535)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X30535),tc_fun(X30535,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X30535,tc_HOL_Obool),tc_fun(tc_fun(X30535,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X30535)),c_Orderings_Oord__class_Oless__eq(tc_fun(X30535,tc_HOL_Obool))),c_List_Oset(X30535))),X30534))),hAPP(hAPP(c_COMBC(tc_List_Olist(X30535),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X30535)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X30535)))),X30533))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__lists__length__eq])]) ).

cnf(i_0_6194,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_5269]) ).

fof(i_0_6195,plain,
    ! [X21176,X21177,X21178,X21179,X21180,X21181,X21182,X21183] :
      ( ( hBOOL(hAPP(hAPP(c_member(X21182),esk99_7(X21176,X21177,X21178,X21179,X21180,X21181,X21182)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21182,tc_HOL_Obool)),X21177),X21176)))
        | hAPP(X21178,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21182,tc_HOL_Obool)),X21177),X21176)) = hAPP(hAPP(X21181,hAPP(X21178,X21177)),hAPP(X21178,X21176))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21182),X21176))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21182),X21177))
        | ~ c_Finite__Set_Ofolding__image__simple(X21183,X21182,X21181,X21180,X21179,X21178) )
      & ( hAPP(X21179,esk99_7(X21176,X21177,X21178,X21179,X21180,X21181,X21182)) != X21180
        | hAPP(X21178,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21182,tc_HOL_Obool)),X21177),X21176)) = hAPP(hAPP(X21181,hAPP(X21178,X21177)),hAPP(X21178,X21176))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21182),X21176))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21182),X21177))
        | ~ c_Finite__Set_Ofolding__image__simple(X21183,X21182,X21181,X21180,X21179,X21178) ) ),
    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_6196,plain,
    ! [X25616] : hAPP(c_Int_Onat,X25616) = 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,X25616)),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_6197,plain,
    ! [X33467,X33468,X33469,X33470,X33471,X33474,X33475,X33476,X33477,X33478,X33479,X33480,X33481] :
      ( ( X33467 = hAPP(hAPP(c_List_Oappend(X33471),esk488_5(X33467,X33468,X33469,X33470,X33471)),hAPP(hAPP(c_List_Olist_OCons(X33471),X33470),esk489_5(X33467,X33468,X33469,X33470,X33471)))
        | hAPP(hAPP(c_List_Olist_OCons(X33471),X33470),X33469) != hAPP(c_List_Ofilter(X33471,X33468),X33467) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X33471),X33474),hAPP(c_List_Oset(X33471),esk488_5(X33467,X33468,X33469,X33470,X33471))))
        | ~ hBOOL(hAPP(X33468,X33474))
        | hAPP(hAPP(c_List_Olist_OCons(X33471),X33470),X33469) != hAPP(c_List_Ofilter(X33471,X33468),X33467) )
      & ( hBOOL(hAPP(X33468,X33470))
        | hAPP(hAPP(c_List_Olist_OCons(X33471),X33470),X33469) != hAPP(c_List_Ofilter(X33471,X33468),X33467) )
      & ( X33469 = hAPP(c_List_Ofilter(X33471,X33468),esk489_5(X33467,X33468,X33469,X33470,X33471))
        | hAPP(hAPP(c_List_Olist_OCons(X33471),X33470),X33469) != hAPP(c_List_Ofilter(X33471,X33468),X33467) )
      & ( hBOOL(hAPP(hAPP(c_member(X33479),esk490_7(X33475,X33476,X33477,X33478,X33479,X33480,X33481)),hAPP(c_List_Oset(X33479),X33480)))
        | X33475 != hAPP(hAPP(c_List_Oappend(X33479),X33480),hAPP(hAPP(c_List_Olist_OCons(X33479),X33478),X33481))
        | ~ hBOOL(hAPP(X33476,X33478))
        | X33477 != hAPP(c_List_Ofilter(X33479,X33476),X33481)
        | hAPP(hAPP(c_List_Olist_OCons(X33479),X33478),X33477) = hAPP(c_List_Ofilter(X33479,X33476),X33475) )
      & ( hBOOL(hAPP(X33476,esk490_7(X33475,X33476,X33477,X33478,X33479,X33480,X33481)))
        | X33475 != hAPP(hAPP(c_List_Oappend(X33479),X33480),hAPP(hAPP(c_List_Olist_OCons(X33479),X33478),X33481))
        | ~ hBOOL(hAPP(X33476,X33478))
        | X33477 != hAPP(c_List_Ofilter(X33479,X33476),X33481)
        | hAPP(hAPP(c_List_Olist_OCons(X33479),X33478),X33477) = hAPP(c_List_Ofilter(X33479,X33476),X33475) ) ),
    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_5277])])])])])]) ).

fof(i_0_6198,plain,
    ! [X33451,X33452,X33453,X33454,X33455,X33458,X33459,X33460,X33461,X33462,X33463,X33464,X33465] :
      ( ( X33453 = hAPP(hAPP(c_List_Oappend(X33455),esk485_5(X33451,X33452,X33453,X33454,X33455)),hAPP(hAPP(c_List_Olist_OCons(X33455),X33452),esk486_5(X33451,X33452,X33453,X33454,X33455)))
        | hAPP(c_List_Ofilter(X33455,X33454),X33453) != hAPP(hAPP(c_List_Olist_OCons(X33455),X33452),X33451) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X33455),X33458),hAPP(c_List_Oset(X33455),esk485_5(X33451,X33452,X33453,X33454,X33455))))
        | ~ hBOOL(hAPP(X33454,X33458))
        | hAPP(c_List_Ofilter(X33455,X33454),X33453) != hAPP(hAPP(c_List_Olist_OCons(X33455),X33452),X33451) )
      & ( hBOOL(hAPP(X33454,X33452))
        | hAPP(c_List_Ofilter(X33455,X33454),X33453) != hAPP(hAPP(c_List_Olist_OCons(X33455),X33452),X33451) )
      & ( X33451 = hAPP(c_List_Ofilter(X33455,X33454),esk486_5(X33451,X33452,X33453,X33454,X33455))
        | hAPP(c_List_Ofilter(X33455,X33454),X33453) != hAPP(hAPP(c_List_Olist_OCons(X33455),X33452),X33451) )
      & ( hBOOL(hAPP(hAPP(c_member(X33463),esk487_7(X33459,X33460,X33461,X33462,X33463,X33464,X33465)),hAPP(c_List_Oset(X33463),X33464)))
        | X33461 != hAPP(hAPP(c_List_Oappend(X33463),X33464),hAPP(hAPP(c_List_Olist_OCons(X33463),X33460),X33465))
        | ~ hBOOL(hAPP(X33462,X33460))
        | X33459 != hAPP(c_List_Ofilter(X33463,X33462),X33465)
        | hAPP(c_List_Ofilter(X33463,X33462),X33461) = hAPP(hAPP(c_List_Olist_OCons(X33463),X33460),X33459) )
      & ( hBOOL(hAPP(X33462,esk487_7(X33459,X33460,X33461,X33462,X33463,X33464,X33465)))
        | X33461 != hAPP(hAPP(c_List_Oappend(X33463),X33464),hAPP(hAPP(c_List_Olist_OCons(X33463),X33460),X33465))
        | ~ hBOOL(hAPP(X33462,X33460))
        | X33459 != hAPP(c_List_Ofilter(X33463,X33462),X33465)
        | hAPP(c_List_Ofilter(X33463,X33462),X33461) = hAPP(hAPP(c_List_Olist_OCons(X33463),X33460),X33459) ) ),
    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_5278])])])])])]) ).

fof(i_0_6199,plain,
    ! [X29012,X29013,X29014,X29015] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29015),esk351_4(X29012,X29013,X29014,X29015)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29012),hAPP(X29013,X29014)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29013,X29015)),X29012))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29015),X29014))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29015),esk350_4(X29012,X29013,X29014,X29015))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk351_4(X29012,X29013,X29014,X29015)),X29014))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29012),hAPP(X29013,X29014)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29013,X29015)),X29012))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29015),X29014))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29015),esk350_4(X29012,X29013,X29014,X29015))) )
      & ( hAPP(X29013,esk351_4(X29012,X29013,X29014,X29015)) = X29012
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29012),hAPP(X29013,X29014)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29013,X29015)),X29012))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29015),X29014))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29015),esk350_4(X29012,X29013,X29014,X29015))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29015),esk351_4(X29012,X29013,X29014,X29015)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29012),hAPP(X29013,X29014)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29013,X29015)),X29012))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29015),X29014))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk350_4(X29012,X29013,X29014,X29015)),X29014)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk351_4(X29012,X29013,X29014,X29015)),X29014))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29012),hAPP(X29013,X29014)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29013,X29015)),X29012))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29015),X29014))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk350_4(X29012,X29013,X29014,X29015)),X29014)) )
      & ( hAPP(X29013,esk351_4(X29012,X29013,X29014,X29015)) = X29012
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29012),hAPP(X29013,X29014)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29013,X29015)),X29012))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29015),X29014))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk350_4(X29012,X29013,X29014,X29015)),X29014)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29015),esk351_4(X29012,X29013,X29014,X29015)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29012),hAPP(X29013,X29014)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29013,X29015)),X29012))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29015),X29014))
        | ~ 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(X29013,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk350_4(X29012,X29013,X29014,X29015)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X29013,esk350_4(X29012,X29013,X29014,X29015))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk351_4(X29012,X29013,X29014,X29015)),X29014))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29012),hAPP(X29013,X29014)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29013,X29015)),X29012))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29015),X29014))
        | ~ 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(X29013,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk350_4(X29012,X29013,X29014,X29015)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X29013,esk350_4(X29012,X29013,X29014,X29015))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
      & ( hAPP(X29013,esk351_4(X29012,X29013,X29014,X29015)) = X29012
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29012),hAPP(X29013,X29014)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29013,X29015)),X29012))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29015),X29014))
        | ~ 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(X29013,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk350_4(X29012,X29013,X29014,X29015)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X29013,esk350_4(X29012,X29013,X29014,X29015))))),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_6200,plain,
    ! [X28340,X28341,X28342,X28343,X28344,X28345] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28345),esk312_6(X28340,X28341,X28342,X28343,X28344,X28345)),X28344))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28345,X28342),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28345,X28342),X28344),X28341)),hAPP(hAPP(c_Product__Type_OSigma(X28345,X28342),X28343),X28340)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28345,tc_HOL_Obool)),X28344),X28343)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28342,tc_HOL_Obool)),hAPP(X28341,esk312_6(X28340,X28341,X28342,X28343,X28344,X28345))),hAPP(X28340,esk312_6(X28340,X28341,X28342,X28343,X28344,X28345))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28345,X28342),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28345,X28342),X28344),X28341)),hAPP(hAPP(c_Product__Type_OSigma(X28345,X28342),X28343),X28340)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28345,tc_HOL_Obool)),X28344),X28343)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sigma__mono])])])]) ).

fof(i_0_6201,plain,
    ! [X28270,X28271,X28272,X28273,X28274,X28275] :
      ( ( X28275 = hAPP(hAPP(c_Product__Type_OPair(X28274,X28273),esk304_6(X28270,X28271,X28272,X28273,X28274,X28275)),esk305_6(X28270,X28271,X28272,X28273,X28274,X28275))
        | hBOOL(hAPP(hAPP(c_member(X28272),X28271),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28274,X28273,tc_fun(X28272,tc_HOL_Obool)),X28270),X28275))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28272),X28271),hAPP(hAPP(X28270,esk304_6(X28270,X28271,X28272,X28273,X28274,X28275)),esk305_6(X28270,X28271,X28272,X28273,X28274,X28275))))
        | hBOOL(hAPP(hAPP(c_member(X28272),X28271),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28274,X28273,tc_fun(X28272,tc_HOL_Obool)),X28270),X28275))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__splitI2])])])]) ).

cnf(i_0_6202,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_5279]) ).

cnf(i_0_6203,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_5280]) ).

fof(i_0_6204,plain,
    ! [X28821,X28822,X28823] : hAPP(c_Relation_Oconverse(X28823,X28822),X28821) = hAPP(c_Set_OCollect(tc_prod(X28822,X28823)),hAPP(c_Product__Type_Oprod_Oprod__case(X28822,X28823,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28822,tc_fun(tc_prod(X28823,X28822),tc_HOL_Obool),tc_fun(X28823,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28823,tc_fun(tc_fun(tc_prod(X28823,X28822),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28823,X28822),tc_HOL_Obool),tc_fun(X28823,tc_HOL_Obool)),X28822),c_COMBC(X28823,tc_fun(tc_prod(X28823,X28822),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28823,tc_prod(X28823,X28822)),tc_fun(X28823,tc_fun(tc_fun(tc_prod(X28823,X28822),tc_HOL_Obool),tc_HOL_Obool)),X28822),hAPP(c_COMBB(tc_prod(X28823,X28822),tc_fun(tc_fun(tc_prod(X28823,X28822),tc_HOL_Obool),tc_HOL_Obool),X28823),c_member(tc_prod(X28823,X28822)))),hAPP(c_COMBC(X28823,X28822,tc_prod(X28823,X28822)),c_Product__Type_OPair(X28823,X28822))))),X28821))),
    inference(variable_rename,[status(thm)],[fact_converse__def]) ).

fof(i_0_6205,plain,
    ! [X30472,X30473,X30474,X30475] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30474),X30473))
        | c_Nitpick_Osetsum_H(X30474,X30475,X30472,X30473) = hAPP(c_List_Omonoid__add__class_Olistsum(X30475),hAPP(hAPP(c_List_Omap(X30474,X30475),X30472),c_Hilbert__Choice_OEps(tc_List_Olist(X30474),hAPP(hAPP(c_COMBS(tc_List_Olist(X30474),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X30474)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X30474),tc_fun(X30474,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X30474,tc_HOL_Obool),tc_fun(tc_fun(X30474,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X30474)),c_fequal),c_List_Oset(X30474))),X30473))),c_List_Odistinct(X30474)))))
        | ~ class_Groups_Ocomm__monoid__add(X30475) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X30474),X30473))
        | c_Nitpick_Osetsum_H(X30474,X30475,X30472,X30473) = c_Groups_Ozero__class_Ozero(X30475)
        | ~ class_Groups_Ocomm__monoid__add(X30475) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5281])])]) ).

cnf(i_0_6206,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_5282]) ).

cnf(i_0_6207,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_5283]) ).

cnf(i_0_6208,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_5284]) ).

cnf(i_0_6209,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_5285]) ).

fof(i_0_6210,plain,
    ! [X22518,X22519] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22519))
      | 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)),X22519))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X22518))))) = 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)),X22519))),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,X22518))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__less__Suc])]) ).

fof(i_0_6211,plain,
    ! [X26617,X26618,X26619,X26620,X26621,X26622] :
      ( ~ class_Groups_Ocomm__monoid__add(X26622)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26621),X26620))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26621,X26622),X26619),X26620) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26618,X26622),hAPP(hAPP(c_COMBB(tc_fun(X26621,tc_HOL_Obool),X26622,X26618),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26621,X26622),X26619)),hAPP(hAPP(c_COMBB(tc_fun(X26621,tc_HOL_Obool),tc_fun(X26621,tc_HOL_Obool),X26618),c_Set_OCollect(X26621)),hAPP(hAPP(c_COMBB(tc_fun(X26621,tc_HOL_Obool),tc_fun(X26621,tc_HOL_Obool),X26618),hAPP(c_COMBS(X26621,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X26621),c_fconj),hAPP(hAPP(c_COMBC(X26621,tc_fun(X26621,tc_HOL_Obool),tc_HOL_Obool),c_member(X26621)),X26620)))),hAPP(c_COMBC(X26621,X26618,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X26618,tc_fun(X26618,tc_HOL_Obool),X26621),c_fequal),X26617)))))),hAPP(c_Set_Oimage(X26621,X26618,X26617),X26620)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__image__gen])]) ).

fof(i_0_6212,plain,
    ! [X28216,X28217,X28218,X28219,X28220,X28221,X28222,X28223] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28218,X28218)),X28219),X28216))
        | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28218,X28218,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28218,tc_fun(X28218,tc_HOL_Obool),tc_fun(X28218,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X28218,tc_HOL_Obool),tc_fun(X28218,tc_HOL_Obool)),X28218),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X28218)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28218),c_fconj),hAPP(hAPP(c_COMBC(X28218,tc_fun(X28218,tc_HOL_Obool),tc_HOL_Obool),c_member(X28218)),X28217)))),hAPP(hAPP(c_COMBC(X28218,tc_fun(X28218,tc_HOL_Obool),tc_HOL_Obool),c_member(X28218)),X28217))),X28219))
        | ~ c_Relation_Orefl__on(X28218,X28217,X28216) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28218),X28220),X28217))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28218,X28218)),hAPP(hAPP(c_Product__Type_OPair(X28218,X28218),X28220),X28220)),X28216))
        | ~ c_Relation_Orefl__on(X28218,X28217,X28216) )
      & ( hBOOL(hAPP(hAPP(c_member(X28223),esk293_3(X28221,X28222,X28223)),X28222))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28223,X28223)),esk292_3(X28221,X28222,X28223)),X28221))
        | c_Relation_Orefl__on(X28223,X28222,X28221) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28223,X28223)),hAPP(hAPP(c_Product__Type_OPair(X28223,X28223),esk293_3(X28221,X28222,X28223)),esk293_3(X28221,X28222,X28223))),X28221))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28223,X28223)),esk292_3(X28221,X28222,X28223)),X28221))
        | c_Relation_Orefl__on(X28223,X28222,X28221) )
      & ( hBOOL(hAPP(hAPP(c_member(X28223),esk293_3(X28221,X28222,X28223)),X28222))
        | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28223,X28223,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28223,tc_fun(X28223,tc_HOL_Obool),tc_fun(X28223,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X28223,tc_HOL_Obool),tc_fun(X28223,tc_HOL_Obool)),X28223),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X28223)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28223),c_fconj),hAPP(hAPP(c_COMBC(X28223,tc_fun(X28223,tc_HOL_Obool),tc_HOL_Obool),c_member(X28223)),X28222)))),hAPP(hAPP(c_COMBC(X28223,tc_fun(X28223,tc_HOL_Obool),tc_HOL_Obool),c_member(X28223)),X28222))),esk292_3(X28221,X28222,X28223)))
        | c_Relation_Orefl__on(X28223,X28222,X28221) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28223,X28223)),hAPP(hAPP(c_Product__Type_OPair(X28223,X28223),esk293_3(X28221,X28222,X28223)),esk293_3(X28221,X28222,X28223))),X28221))
        | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28223,X28223,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28223,tc_fun(X28223,tc_HOL_Obool),tc_fun(X28223,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X28223,tc_HOL_Obool),tc_fun(X28223,tc_HOL_Obool)),X28223),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X28223)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28223),c_fconj),hAPP(hAPP(c_COMBC(X28223,tc_fun(X28223,tc_HOL_Obool),tc_HOL_Obool),c_member(X28223)),X28222)))),hAPP(hAPP(c_COMBC(X28223,tc_fun(X28223,tc_HOL_Obool),tc_HOL_Obool),c_member(X28223)),X28222))),esk292_3(X28221,X28222,X28223)))
        | c_Relation_Orefl__on(X28223,X28222,X28221) ) ),
    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_6213,plain,
    ! [X34202,X34203,X34204,X34205] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X34205),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
        | c_Random__Sequence_ORandom(X34204,X34203,X34205,X34202) = 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(X34204)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X34204)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X34205),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
        | c_Random__Sequence_ORandom(X34204,X34203,X34205,X34202) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X34204,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(X34204)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X34203,X34202)),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(X34204)))),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(X34204)))),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(X34204)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X34204,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(X34204)))),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(X34204)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(X34204,X34203,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X34205),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X34202))),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(X34204)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X34204))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X34204)))),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(X34204)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X34204,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(X34204)))),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(X34204)))),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(X34204))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X34204)))),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(X34204)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X34204)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X34204))))),tc_prod(X34204,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X34204)),hAPP(hAPP(c_COMBB(X34204,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X34204)))),tc_prod(X34204,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X34204)),c_Product__Type_Ofst(X34204,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5286])]) ).

cnf(i_0_6214,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_5287]) ).

cnf(i_0_6215,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_5288]) ).

cnf(i_0_6216,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_5289]) ).

fof(i_0_6217,plain,
    ! [X31492,X31493,X31494,X31495,X31496] : hAPP(hAPP(c_List_Ozip(X31496,X31495),X31494),hAPP(hAPP(c_List_Olist_OCons(X31495),X31493),X31492)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X31496,X31495)),X31496,c_List_Olist_ONil(tc_prod(X31496,X31495)),hAPP(hAPP(c_COMBC(X31496,tc_fun(tc_List_Olist(X31496),tc_List_Olist(tc_prod(X31496,X31495))),tc_fun(tc_List_Olist(X31496),tc_List_Olist(tc_prod(X31496,X31495)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X31496,X31495)),tc_List_Olist(tc_prod(X31496,X31495))),tc_fun(tc_fun(tc_List_Olist(X31496),tc_List_Olist(tc_prod(X31496,X31495))),tc_fun(tc_List_Olist(X31496),tc_List_Olist(tc_prod(X31496,X31495)))),X31496),c_COMBB(tc_List_Olist(tc_prod(X31496,X31495)),tc_List_Olist(tc_prod(X31496,X31495)),tc_List_Olist(X31496))),hAPP(hAPP(c_COMBB(tc_prod(X31496,X31495),tc_fun(tc_List_Olist(tc_prod(X31496,X31495)),tc_List_Olist(tc_prod(X31496,X31495))),X31496),c_List_Olist_OCons(tc_prod(X31496,X31495))),hAPP(hAPP(c_COMBC(X31496,X31495,tc_prod(X31496,X31495)),c_Product__Type_OPair(X31496,X31495)),X31493)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X31496),tc_List_Olist(X31495),tc_List_Olist(tc_prod(X31496,X31495))),c_List_Ozip(X31496,X31495)),X31492))),X31494),
    inference(variable_rename,[status(thm)],[fact_zip__Cons]) ).

fof(i_0_6218,plain,
    ! [X23243,X23244,X23245,X23246] :
      ( ( ~ c_Wellfounded_Omax__extp(X23246,hAPP(hAPP(c_COMBC(X23246,tc_fun(tc_prod(X23246,X23246),tc_HOL_Obool),tc_fun(X23246,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23246,tc_fun(tc_fun(tc_prod(X23246,X23246),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23246,X23246),tc_HOL_Obool),tc_fun(X23246,tc_HOL_Obool)),X23246),c_COMBC(X23246,tc_fun(tc_prod(X23246,X23246),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23246,tc_prod(X23246,X23246)),tc_fun(X23246,tc_fun(tc_fun(tc_prod(X23246,X23246),tc_HOL_Obool),tc_HOL_Obool)),X23246),hAPP(c_COMBB(tc_prod(X23246,X23246),tc_fun(tc_fun(tc_prod(X23246,X23246),tc_HOL_Obool),tc_HOL_Obool),X23246),c_member(tc_prod(X23246,X23246)))),c_Product__Type_OPair(X23246,X23246)))),X23245),X23244,X23243)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X23246,tc_HOL_Obool),tc_fun(X23246,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X23246,tc_HOL_Obool),tc_fun(X23246,tc_HOL_Obool)),X23244),X23243)),c_Wellfounded_Omax__ext(X23246,X23245))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X23246,tc_HOL_Obool),tc_fun(X23246,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X23246,tc_HOL_Obool),tc_fun(X23246,tc_HOL_Obool)),X23244),X23243)),c_Wellfounded_Omax__ext(X23246,X23245)))
        | c_Wellfounded_Omax__extp(X23246,hAPP(hAPP(c_COMBC(X23246,tc_fun(tc_prod(X23246,X23246),tc_HOL_Obool),tc_fun(X23246,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23246,tc_fun(tc_fun(tc_prod(X23246,X23246),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23246,X23246),tc_HOL_Obool),tc_fun(X23246,tc_HOL_Obool)),X23246),c_COMBC(X23246,tc_fun(tc_prod(X23246,X23246),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23246,tc_prod(X23246,X23246)),tc_fun(X23246,tc_fun(tc_fun(tc_prod(X23246,X23246),tc_HOL_Obool),tc_HOL_Obool)),X23246),hAPP(c_COMBB(tc_prod(X23246,X23246),tc_fun(tc_fun(tc_prod(X23246,X23246),tc_HOL_Obool),tc_HOL_Obool),X23246),c_member(tc_prod(X23246,X23246)))),c_Product__Type_OPair(X23246,X23246)))),X23245),X23244,X23243) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__extp__max__ext__eq])]) ).

fof(i_0_6219,plain,
    ! [X30711,X30712,X30713,X30714] :
      ( ( ~ c_List_Olistrelp(X30714,hAPP(hAPP(c_COMBC(X30714,tc_fun(tc_prod(X30714,X30714),tc_HOL_Obool),tc_fun(X30714,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30714,tc_fun(tc_fun(tc_prod(X30714,X30714),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X30714,X30714),tc_HOL_Obool),tc_fun(X30714,tc_HOL_Obool)),X30714),c_COMBC(X30714,tc_fun(tc_prod(X30714,X30714),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30714,tc_prod(X30714,X30714)),tc_fun(X30714,tc_fun(tc_fun(tc_prod(X30714,X30714),tc_HOL_Obool),tc_HOL_Obool)),X30714),hAPP(c_COMBB(tc_prod(X30714,X30714),tc_fun(tc_fun(tc_prod(X30714,X30714),tc_HOL_Obool),tc_HOL_Obool),X30714),c_member(tc_prod(X30714,X30714)))),c_Product__Type_OPair(X30714,X30714)))),X30713),X30712,X30711)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30714),tc_List_Olist(X30714))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30714),tc_List_Olist(X30714)),X30712),X30711)),c_List_Olistrel(X30714,X30713))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30714),tc_List_Olist(X30714))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30714),tc_List_Olist(X30714)),X30712),X30711)),c_List_Olistrel(X30714,X30713)))
        | c_List_Olistrelp(X30714,hAPP(hAPP(c_COMBC(X30714,tc_fun(tc_prod(X30714,X30714),tc_HOL_Obool),tc_fun(X30714,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30714,tc_fun(tc_fun(tc_prod(X30714,X30714),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X30714,X30714),tc_HOL_Obool),tc_fun(X30714,tc_HOL_Obool)),X30714),c_COMBC(X30714,tc_fun(tc_prod(X30714,X30714),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30714,tc_prod(X30714,X30714)),tc_fun(X30714,tc_fun(tc_fun(tc_prod(X30714,X30714),tc_HOL_Obool),tc_HOL_Obool)),X30714),hAPP(c_COMBB(tc_prod(X30714,X30714),tc_fun(tc_fun(tc_prod(X30714,X30714),tc_HOL_Obool),tc_HOL_Obool),X30714),c_member(tc_prod(X30714,X30714)))),c_Product__Type_OPair(X30714,X30714)))),X30713),X30712,X30711) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp__listrel__eq])]) ).

fof(i_0_6220,plain,
    ! [X27866,X27867,X27868,X27869,X27870,X27871,X27872,X27873] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X27873,X27872),tc_fun(tc_prod(X27871,X27870),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27873,X27872),X27869),hAPP(c_COMBK(tc_fun(X27872,tc_HOL_Obool),X27873),X27868))),hAPP(c_Product__Type_Oprod_Oprod__case(X27873,X27872,tc_fun(tc_prod(X27871,X27870),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X27873,tc_fun(X27872,tc_fun(X27871,tc_fun(X27870,tc_HOL_Obool))),tc_fun(X27872,tc_fun(tc_prod(X27871,X27870),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27871,tc_fun(X27870,tc_HOL_Obool)),tc_fun(tc_prod(X27871,X27870),tc_HOL_Obool)),tc_fun(tc_fun(X27872,tc_fun(X27871,tc_fun(X27870,tc_HOL_Obool))),tc_fun(X27872,tc_fun(tc_prod(X27871,X27870),tc_HOL_Obool))),X27873),c_COMBB(tc_fun(X27871,tc_fun(X27870,tc_HOL_Obool)),tc_fun(tc_prod(X27871,X27870),tc_HOL_Obool),X27872)),hAPP(hAPP(c_COMBB(tc_fun(X27871,tc_HOL_Obool),tc_fun(tc_fun(X27871,tc_fun(X27870,tc_HOL_Obool)),tc_fun(tc_prod(X27871,X27870),tc_HOL_Obool)),X27873),c_Product__Type_OSigma(X27871,X27870)),X27867))),hAPP(hAPP(c_COMBB(tc_fun(X27870,tc_HOL_Obool),tc_fun(X27871,tc_fun(X27870,tc_HOL_Obool)),X27872),c_COMBK(tc_fun(X27870,tc_HOL_Obool),X27871)),X27866)))) = hAPP(hAPP(c_Product__Type_OSigma(X27871,X27870),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27873,tc_fun(X27871,tc_HOL_Obool)),X27869),X27867)),hAPP(c_COMBK(tc_fun(X27870,tc_HOL_Obool),X27871),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27872,tc_fun(X27870,tc_HOL_Obool)),X27868),X27866))),
    inference(variable_rename,[status(thm)],[fact_UN__Times__distrib]) ).

fof(i_0_6221,plain,
    ! [X20208,X20209] :
      ( ( ~ c_Equiv__Relations_Oequiv(X20209,c_Orderings_Otop__class_Otop(tc_fun(X20209,tc_HOL_Obool)),X20208)
        | c_Equiv__Relations_Oequivp(X20209,hAPP(hAPP(c_COMBC(X20209,tc_fun(tc_prod(X20209,X20209),tc_HOL_Obool),tc_fun(X20209,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20209,tc_fun(tc_fun(tc_prod(X20209,X20209),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X20209,X20209),tc_HOL_Obool),tc_fun(X20209,tc_HOL_Obool)),X20209),c_COMBC(X20209,tc_fun(tc_prod(X20209,X20209),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20209,tc_prod(X20209,X20209)),tc_fun(X20209,tc_fun(tc_fun(tc_prod(X20209,X20209),tc_HOL_Obool),tc_HOL_Obool)),X20209),hAPP(c_COMBB(tc_prod(X20209,X20209),tc_fun(tc_fun(tc_prod(X20209,X20209),tc_HOL_Obool),tc_HOL_Obool),X20209),c_member(tc_prod(X20209,X20209)))),c_Product__Type_OPair(X20209,X20209)))),X20208)) )
      & ( ~ c_Equiv__Relations_Oequivp(X20209,hAPP(hAPP(c_COMBC(X20209,tc_fun(tc_prod(X20209,X20209),tc_HOL_Obool),tc_fun(X20209,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20209,tc_fun(tc_fun(tc_prod(X20209,X20209),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X20209,X20209),tc_HOL_Obool),tc_fun(X20209,tc_HOL_Obool)),X20209),c_COMBC(X20209,tc_fun(tc_prod(X20209,X20209),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20209,tc_prod(X20209,X20209)),tc_fun(X20209,tc_fun(tc_fun(tc_prod(X20209,X20209),tc_HOL_Obool),tc_HOL_Obool)),X20209),hAPP(c_COMBB(tc_prod(X20209,X20209),tc_fun(tc_fun(tc_prod(X20209,X20209),tc_HOL_Obool),tc_HOL_Obool),X20209),c_member(tc_prod(X20209,X20209)))),c_Product__Type_OPair(X20209,X20209)))),X20208))
        | c_Equiv__Relations_Oequiv(X20209,c_Orderings_Otop__class_Otop(tc_fun(X20209,tc_HOL_Obool)),X20208) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__equiv])]) ).

fof(i_0_6222,plain,
    ! [X28194,X28195] :
      ( ( ~ c_Wellfounded_OwfP(X28195,hAPP(hAPP(c_COMBC(X28195,tc_fun(tc_prod(X28195,X28195),tc_HOL_Obool),tc_fun(X28195,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28195,tc_fun(tc_fun(tc_prod(X28195,X28195),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28195,X28195),tc_HOL_Obool),tc_fun(X28195,tc_HOL_Obool)),X28195),c_COMBC(X28195,tc_fun(tc_prod(X28195,X28195),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28195,tc_prod(X28195,X28195)),tc_fun(X28195,tc_fun(tc_fun(tc_prod(X28195,X28195),tc_HOL_Obool),tc_HOL_Obool)),X28195),hAPP(c_COMBB(tc_prod(X28195,X28195),tc_fun(tc_fun(tc_prod(X28195,X28195),tc_HOL_Obool),tc_HOL_Obool),X28195),c_member(tc_prod(X28195,X28195)))),c_Product__Type_OPair(X28195,X28195)))),X28194))
        | c_Wellfounded_Owf(X28195,X28194) )
      & ( ~ c_Wellfounded_Owf(X28195,X28194)
        | c_Wellfounded_OwfP(X28195,hAPP(hAPP(c_COMBC(X28195,tc_fun(tc_prod(X28195,X28195),tc_HOL_Obool),tc_fun(X28195,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28195,tc_fun(tc_fun(tc_prod(X28195,X28195),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28195,X28195),tc_HOL_Obool),tc_fun(X28195,tc_HOL_Obool)),X28195),c_COMBC(X28195,tc_fun(tc_prod(X28195,X28195),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28195,tc_prod(X28195,X28195)),tc_fun(X28195,tc_fun(tc_fun(tc_prod(X28195,X28195),tc_HOL_Obool),tc_HOL_Obool)),X28195),hAPP(c_COMBB(tc_prod(X28195,X28195),tc_fun(tc_fun(tc_prod(X28195,X28195),tc_HOL_Obool),tc_HOL_Obool),X28195),c_member(tc_prod(X28195,X28195)))),c_Product__Type_OPair(X28195,X28195)))),X28194)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__wf__eq])]) ).

fof(i_0_6223,plain,
    ! [X19912,X19913,X19914,X19915] :
      ( ( hAPP(hAPP(c_COMBC(X19915,tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_fun(X19914,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19914,tc_fun(tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_fun(X19914,tc_HOL_Obool)),X19915),c_COMBC(X19914,tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19914,tc_prod(X19915,X19914)),tc_fun(X19914,tc_fun(tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_HOL_Obool)),X19915),hAPP(c_COMBB(tc_prod(X19915,X19914),tc_fun(tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_HOL_Obool),X19914),c_member(tc_prod(X19915,X19914)))),c_Product__Type_OPair(X19915,X19914)))),X19913) != hAPP(hAPP(c_COMBC(X19915,tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_fun(X19914,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19914,tc_fun(tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_fun(X19914,tc_HOL_Obool)),X19915),c_COMBC(X19914,tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19914,tc_prod(X19915,X19914)),tc_fun(X19914,tc_fun(tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_HOL_Obool)),X19915),hAPP(c_COMBB(tc_prod(X19915,X19914),tc_fun(tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_HOL_Obool),X19914),c_member(tc_prod(X19915,X19914)))),c_Product__Type_OPair(X19915,X19914)))),X19912)
        | X19913 = X19912 )
      & ( X19913 != X19912
        | hAPP(hAPP(c_COMBC(X19915,tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_fun(X19914,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19914,tc_fun(tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_fun(X19914,tc_HOL_Obool)),X19915),c_COMBC(X19914,tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19914,tc_prod(X19915,X19914)),tc_fun(X19914,tc_fun(tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_HOL_Obool)),X19915),hAPP(c_COMBB(tc_prod(X19915,X19914),tc_fun(tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_HOL_Obool),X19914),c_member(tc_prod(X19915,X19914)))),c_Product__Type_OPair(X19915,X19914)))),X19913) = hAPP(hAPP(c_COMBC(X19915,tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_fun(X19914,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19914,tc_fun(tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_fun(X19914,tc_HOL_Obool)),X19915),c_COMBC(X19914,tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19914,tc_prod(X19915,X19914)),tc_fun(X19914,tc_fun(tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_HOL_Obool)),X19915),hAPP(c_COMBB(tc_prod(X19915,X19914),tc_fun(tc_fun(tc_prod(X19915,X19914),tc_HOL_Obool),tc_HOL_Obool),X19914),c_member(tc_prod(X19915,X19914)))),c_Product__Type_OPair(X19915,X19914)))),X19912) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])]) ).

fof(i_0_6224,plain,
    ! [X28278,X28279,X28280,X28281,X28282,X28283] :
      ( ( X28278 = hAPP(hAPP(c_Product__Type_OPair(X28281,X28280),esk306_6(X28278,X28279,X28280,X28281,X28282,X28283)),esk307_6(X28278,X28279,X28280,X28281,X28282,X28283))
        | ~ hBOOL(hAPP(hAPP(c_member(X28283),X28282),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28281,X28280,tc_fun(X28283,tc_HOL_Obool)),X28279),X28278))) )
      & ( hBOOL(hAPP(hAPP(c_member(X28283),X28282),hAPP(hAPP(X28279,esk306_6(X28278,X28279,X28280,X28281,X28282,X28283)),esk307_6(X28278,X28279,X28280,X28281,X28282,X28283))))
        | ~ hBOOL(hAPP(hAPP(c_member(X28283),X28282),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28281,X28280,tc_fun(X28283,tc_HOL_Obool)),X28279),X28278))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5290])])])]) ).

fof(i_0_6225,plain,
    ! [X30785,X30786,X30787,X30788,X30789,X30790,X30791,X30792] : hAPP(hAPP(c_List_Omap(tc_prod(X30792,X30791),X30790),X30789),hAPP(hAPP(c_List_Ozip(X30792,X30791),X30788),hAPP(hAPP(c_List_Omap(X30787,X30791),X30786),X30785))) = hAPP(hAPP(c_List_Omap(tc_prod(X30792,X30787),X30790),hAPP(c_Product__Type_Oprod_Oprod__case(X30792,X30787,X30790),hAPP(hAPP(c_COMBB(tc_fun(X30787,tc_prod(X30792,X30791)),tc_fun(X30787,X30790),X30792),hAPP(c_COMBB(tc_prod(X30792,X30791),X30790,X30787),X30789)),hAPP(hAPP(c_COMBC(X30792,tc_fun(X30787,X30791),tc_fun(X30787,tc_prod(X30792,X30791))),hAPP(hAPP(c_COMBB(tc_fun(X30791,tc_prod(X30792,X30791)),tc_fun(tc_fun(X30787,X30791),tc_fun(X30787,tc_prod(X30792,X30791))),X30792),c_COMBB(X30791,tc_prod(X30792,X30791),X30787)),c_Product__Type_OPair(X30792,X30791))),X30786)))),hAPP(hAPP(c_List_Ozip(X30792,X30787),X30788),X30785)),
    inference(variable_rename,[status(thm)],[fact_map__zip__map2]) ).

fof(i_0_6226,plain,
    ! [X29213,X29214,X29215,X29216,X29217,X29218,X29219] :
      ( ( X29214 = hAPP(hAPP(X29217,X29213),esk352_7(X29213,X29214,X29215,X29216,X29217,X29218,X29219))
        | ~ hBOOL(hAPP(hAPP(c_member(X29219),X29213),X29215))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X29219,X29218,X29217,X29216,X29215),X29214))
        | ~ c_Finite__Set_Ofun__left__comm(X29219,X29218,X29217) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X29219,X29218,X29217,X29216,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29219,tc_HOL_Obool)),X29215),hAPP(hAPP(c_Set_Oinsert(X29219),X29213),c_Orderings_Obot__class_Obot(tc_fun(X29219,tc_HOL_Obool))))),esk352_7(X29213,X29214,X29215,X29216,X29217,X29218,X29219)))
        | ~ hBOOL(hAPP(hAPP(c_member(X29219),X29213),X29215))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X29219,X29218,X29217,X29216,X29215),X29214))
        | ~ c_Finite__Set_Ofun__left__comm(X29219,X29218,X29217) ) ),
    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_6227,plain,
    ! [X29847,X29848,X29849,X29850,X29851,X29852,X29853] :
      ( ( X29847 = hAPP(hAPP(X29851,X29849),esk376_7(X29847,X29848,X29849,X29850,X29851,X29852,X29853))
        | hBOOL(hAPP(hAPP(c_member(X29853),X29849),X29848))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X29853,X29852,X29851,X29850,hAPP(hAPP(c_Set_Oinsert(X29853),X29849),X29848)),X29847))
        | ~ c_Finite__Set_Ofun__left__comm(X29853,X29852,X29851) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X29853,X29852,X29851,X29850,X29848),esk376_7(X29847,X29848,X29849,X29850,X29851,X29852,X29853)))
        | hBOOL(hAPP(hAPP(c_member(X29853),X29849),X29848))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X29853,X29852,X29851,X29850,hAPP(hAPP(c_Set_Oinsert(X29853),X29849),X29848)),X29847))
        | ~ c_Finite__Set_Ofun__left__comm(X29853,X29852,X29851) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5291])])])]) ).

fof(i_0_6228,plain,
    ! [X30130,X30131,X30132,X30133,X30134] : hAPP(c_Map_Omap__of(X30134,X30133),hAPP(hAPP(c_List_Omap(tc_prod(X30134,X30132),tc_prod(X30134,X30133)),hAPP(c_Product__Type_Oprod_Oprod__case(X30134,X30132,tc_prod(X30134,X30133)),hAPP(hAPP(c_COMBC(X30134,tc_fun(X30132,X30133),tc_fun(X30132,tc_prod(X30134,X30133))),hAPP(hAPP(c_COMBB(tc_fun(X30133,tc_prod(X30134,X30133)),tc_fun(tc_fun(X30132,X30133),tc_fun(X30132,tc_prod(X30134,X30133))),X30134),c_COMBB(X30133,tc_prod(X30134,X30133),X30132)),c_Product__Type_OPair(X30134,X30133))),X30131))),X30130)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(X30132),tc_Option_Ooption(X30133),X30134,hAPP(c_Option_Omap(X30132,X30133),X30131)),hAPP(c_Map_Omap__of(X30134,X30132),X30130)),
    inference(variable_rename,[status(thm)],[fact_map__of__map]) ).

fof(i_0_6229,plain,
    ! [X31474,X31475,X31476,X31477,X31478] : hAPP(hAPP(c_List_Ozip(X31478,X31477),hAPP(hAPP(c_List_Olist_OCons(X31478),X31476),X31475)),X31474) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X31478,X31477)),X31477,c_List_Olist_ONil(tc_prod(X31478,X31477)),hAPP(hAPP(c_COMBC(X31477,tc_fun(tc_List_Olist(X31477),tc_List_Olist(tc_prod(X31478,X31477))),tc_fun(tc_List_Olist(X31477),tc_List_Olist(tc_prod(X31478,X31477)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X31478,X31477)),tc_List_Olist(tc_prod(X31478,X31477))),tc_fun(tc_fun(tc_List_Olist(X31477),tc_List_Olist(tc_prod(X31478,X31477))),tc_fun(tc_List_Olist(X31477),tc_List_Olist(tc_prod(X31478,X31477)))),X31477),c_COMBB(tc_List_Olist(tc_prod(X31478,X31477)),tc_List_Olist(tc_prod(X31478,X31477)),tc_List_Olist(X31477))),hAPP(hAPP(c_COMBB(tc_prod(X31478,X31477),tc_fun(tc_List_Olist(tc_prod(X31478,X31477)),tc_List_Olist(tc_prod(X31478,X31477))),X31477),c_List_Olist_OCons(tc_prod(X31478,X31477))),hAPP(c_Product__Type_OPair(X31478,X31477),X31476)))),hAPP(c_List_Ozip(X31478,X31477),X31475))),X31474),
    inference(variable_rename,[status(thm)],[fact_zip__Cons1]) ).

cnf(i_0_6230,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_5292]) ).

cnf(i_0_6231,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_5282]) ).

cnf(i_0_6232,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_5282]) ).

cnf(i_0_6233,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_5293]) ).

fof(i_0_6234,plain,
    ! [X28200,X28201,X28202,X28203] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28203),esk291_4(X28200,X28201,X28202,X28203)),X28202))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28201),hAPP(c_Set_Oimage(X28203,X28201,X28200),X28202)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X28203),X28202)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28203),hAPP(c_Set_OCollect(X28203),hAPP(hAPP(c_COMBS(X28203,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28203),c_fconj),hAPP(hAPP(c_COMBC(X28203,tc_fun(X28203,tc_HOL_Obool),tc_HOL_Obool),c_member(X28203)),X28202))),hAPP(hAPP(c_COMBC(X28203,X28201,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X28201,tc_fun(X28201,tc_HOL_Obool),X28203),c_fequal),X28200)),hAPP(X28200,esk291_4(X28200,X28201,X28202,X28203)))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28201),hAPP(c_Set_Oimage(X28203,X28201,X28200),X28202)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X28203),X28202)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5294])])])]) ).

fof(i_0_6235,plain,
    ! [X27483,X27484,X27485,X27486] :
      ( ( hBOOL(hAPP(X27486,esk262_4(X27483,X27484,X27485,X27486)))
        | c_Wellfounded_Owf(X27483,hAPP(c_Set_OCollect(tc_prod(X27483,X27483)),hAPP(c_Product__Type_Oprod_Oprod__case(X27483,X27483,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X27483,tc_HOL_Obool),tc_fun(X27483,tc_HOL_Obool),X27483),hAPP(c_COMBS(X27483,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27483),c_fconj),X27486))),hAPP(hAPP(c_COMBC(X27483,tc_fun(X27483,X27483),tc_fun(X27483,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27483,tc_HOL_Obool),tc_fun(tc_fun(X27483,X27483),tc_fun(X27483,tc_HOL_Obool)),X27483),c_COMBB(X27483,tc_HOL_Obool,X27483)),c_fequal)),X27484))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X27485,hAPP(X27484,esk262_4(X27483,X27484,X27485,X27486)))),hAPP(X27485,esk262_4(X27483,X27484,X27485,X27486))))
        | c_Wellfounded_Owf(X27483,hAPP(c_Set_OCollect(tc_prod(X27483,X27483)),hAPP(c_Product__Type_Oprod_Oprod__case(X27483,X27483,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X27483,tc_HOL_Obool),tc_fun(X27483,tc_HOL_Obool),X27483),hAPP(c_COMBS(X27483,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27483),c_fconj),X27486))),hAPP(hAPP(c_COMBC(X27483,tc_fun(X27483,X27483),tc_fun(X27483,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27483,tc_HOL_Obool),tc_fun(tc_fun(X27483,X27483),tc_fun(X27483,tc_HOL_Obool)),X27483),c_COMBB(X27483,tc_HOL_Obool,X27483)),c_fequal)),X27484))))) ) ),
    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_6236,plain,
    ! [X27351,X27352,X27353] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27353,X27353),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27353,X27353,X27353),X27352),X27351)),X27352))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X27353,tc_HOL_Obool),tc_fun(X27353,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X27353,tc_HOL_Obool),tc_fun(X27353,tc_HOL_Obool),tc_fun(X27353,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X27353,X27352)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X27353,tc_HOL_Obool),tc_fun(X27353,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X27353,X27351)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X27353,tc_HOL_Obool),tc_fun(X27353,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X27353,tc_HOL_Obool),tc_fun(X27353,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X27353,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X27353,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X27353,tc_HOL_Obool),tc_fun(X27353,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(X27353,X27352))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ext__compat])]) ).

fof(i_0_6237,plain,
    ! [X27348,X27349,X27350] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27350,X27350),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27350,X27350,X27350),X27349),X27348)),X27349))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X27350,tc_HOL_Obool),tc_fun(X27350,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X27350,tc_HOL_Obool),tc_fun(X27350,tc_HOL_Obool),tc_fun(X27350,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X27350,X27349)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X27350,tc_HOL_Obool),tc_fun(X27350,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X27350,X27348)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X27350,tc_HOL_Obool),tc_fun(X27350,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X27350,tc_HOL_Obool),tc_fun(X27350,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X27350,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X27350,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X27350,tc_HOL_Obool),tc_fun(X27350,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(X27350,X27349))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__compat])]) ).

cnf(i_0_6238,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)))),esk451_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5295]) ).

cnf(i_0_6239,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)))),esk450_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_5296]) ).

fof(i_0_6240,plain,
    ! [X26607,X26608,X26609,X26610,X26611] :
      ( ~ class_Groups_Ocomm__monoid__add(X26611)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26610),X26609))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26610,X26611),X26608),hAPP(c_Set_OCollect(X26610),hAPP(hAPP(c_COMBS(X26610,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X26610),c_fconj),hAPP(hAPP(c_COMBC(X26610,tc_fun(X26610,tc_HOL_Obool),tc_HOL_Obool),c_member(X26610)),X26609))),hAPP(hAPP(c_COMBC(X26610,tc_fun(X26610,tc_HOL_Obool),tc_HOL_Obool),c_member(X26610)),X26607)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26610,X26611),hAPP(hAPP(c_COMBC(X26610,X26611,X26611),hAPP(hAPP(c_COMBS(X26610,X26611,tc_fun(X26611,X26611)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26611,tc_fun(X26611,X26611)),X26610),c_If(X26611)),hAPP(hAPP(c_COMBC(X26610,tc_fun(X26610,tc_HOL_Obool),tc_HOL_Obool),c_member(X26610)),X26607))),X26608)),c_Groups_Ozero__class_Ozero(X26611))),X26609) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set_H])]) ).

cnf(i_0_6241,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_5297]) ).

cnf(i_0_6242,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_5298]) ).

cnf(i_0_6243,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_5299]) ).

fof(i_0_6244,plain,
    ! [X30855,X30856,X30857,X30858,X30859,X30860,X30861,X30862] : hAPP(hAPP(c_List_Ozip(X30862,X30861),hAPP(hAPP(c_List_Omap(X30860,X30862),X30859),X30858)),hAPP(hAPP(c_List_Omap(X30857,X30861),X30856),X30855)) = hAPP(hAPP(c_List_Omap(tc_prod(X30860,X30857),tc_prod(X30862,X30861)),hAPP(c_Product__Type_Oprod_Oprod__case(X30860,X30857,tc_prod(X30862,X30861)),hAPP(hAPP(c_COMBC(X30860,tc_fun(X30857,X30861),tc_fun(X30857,tc_prod(X30862,X30861))),hAPP(hAPP(c_COMBB(tc_fun(X30861,tc_prod(X30862,X30861)),tc_fun(tc_fun(X30857,X30861),tc_fun(X30857,tc_prod(X30862,X30861))),X30860),c_COMBB(X30861,tc_prod(X30862,X30861),X30857)),hAPP(hAPP(c_COMBB(X30862,tc_fun(X30861,tc_prod(X30862,X30861)),X30860),c_Product__Type_OPair(X30862,X30861)),X30859))),X30856))),hAPP(hAPP(c_List_Ozip(X30860,X30857),X30858),X30855)),
    inference(variable_rename,[status(thm)],[fact_zip__map__map]) ).

cnf(i_0_6245,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_5300]) ).

cnf(i_0_6246,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_5301]) ).

fof(i_0_6247,plain,
    ! [X23892] : c_Wellfounded_Ofinite__psubset(X23892) = hAPP(c_Set_OCollect(tc_prod(tc_fun(X23892,tc_HOL_Obool),tc_fun(X23892,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X23892,tc_HOL_Obool),tc_fun(X23892,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X23892,tc_HOL_Obool),tc_fun(tc_fun(X23892,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X23892,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X23892,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X23892,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X23892,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X23892,tc_HOL_Obool)),c_COMBS(tc_fun(X23892,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X23892,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X23892,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X23892,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X23892,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X23892,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X23892)))),
    inference(variable_rename,[status(thm)],[fact_finite__psubset__def]) ).

cnf(i_0_6248,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_5302]) ).

cnf(i_0_6249,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_5303]) ).

fof(i_0_6250,plain,
    ! [X30536,X30537] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30537),X30536))
        | c_Nitpick_Ocard_H(X30537,X30536) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30537)),c_Hilbert__Choice_OEps(tc_List_Olist(X30537),hAPP(hAPP(c_COMBS(tc_List_Olist(X30537),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X30537)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X30537),tc_fun(X30537,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X30537,tc_HOL_Obool),tc_fun(tc_fun(X30537,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X30537)),c_fequal),c_List_Oset(X30537))),X30536))),c_List_Odistinct(X30537)))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X30537),X30536))
        | c_Nitpick_Ocard_H(X30537,X30536) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5304])]) ).

fof(i_0_6251,plain,
    ! [X22514,X22515] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22515))
      | 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)),X22515))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X22514)))) = 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)),X22515))),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,X22514))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5305])]) ).

fof(i_0_6252,plain,
    ! [X27989,X27990,X27991,X27992,X27993,X27994,X27995,X27996,X27997] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27997,X27996)),hAPP(hAPP(c_Product__Type_OPair(X27997,X27996),X27995),X27994)),X27993))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X27992,X27991)),hAPP(hAPP(c_Product__Type_OPair(X27992,X27991),hAPP(X27990,X27995)),hAPP(X27989,X27994))),hAPP(c_Set_Oimage(tc_prod(X27997,X27996),tc_prod(X27992,X27991),c_Product__Type_Omap__pair(X27997,X27992,X27996,X27991,X27990,X27989)),X27993))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__imageI])]) ).

cnf(i_0_6253,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_5306]) ).

cnf(i_0_6254,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_5307]) ).

fof(i_0_6255,plain,
    ! [X33784,X33785,X33786,X33787,X33788,X33789,X33790] : c_New__Random__Sequence_Oneg__decr__bind(X33790,X33789,X33788,X33787,X33786,X33785,X33784) = c_New__DSequence_Oneg__decr__bind(X33790,X33789,hAPP(hAPP(hAPP(X33788,X33786),X33785),X33784),hAPP(hAPP(c_COMBC(X33790,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(X33789)))),hAPP(hAPP(c_COMBC(X33790,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(X33789))))),hAPP(hAPP(c_COMBC(X33790,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(X33789)))))),X33787),X33786)),X33785)),X33784)),
    inference(variable_rename,[status(thm)],[fact_New__Random__Sequence_Oneg__decr__bind__def]) ).

fof(i_0_6256,plain,
    ! [X29517,X29518,X29519,X29520] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29520,tc_fun(X29519,tc_HOL_Obool)),X29518),X29517) = hAPP(c_Set_OCollect(X29519),hAPP(hAPP(c_COMBB(tc_fun(X29520,tc_HOL_Obool),tc_HOL_Obool,X29519),c_HOL_OAll(X29520)),hAPP(hAPP(c_COMBB(tc_fun(X29520,tc_HOL_Obool),tc_fun(X29520,tc_HOL_Obool),X29519),hAPP(c_COMBS(X29520,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29520),c_fimplies),hAPP(hAPP(c_COMBC(X29520,tc_fun(X29520,tc_HOL_Obool),tc_HOL_Obool),c_member(X29520)),X29518)))),hAPP(hAPP(c_COMBC(X29519,tc_fun(X29520,tc_fun(X29519,tc_HOL_Obool)),tc_fun(X29520,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29519,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X29520,tc_fun(X29519,tc_HOL_Obool)),tc_fun(X29520,tc_HOL_Obool)),X29519),c_COMBB(tc_fun(X29519,tc_HOL_Obool),tc_HOL_Obool,X29520)),c_member(X29519))),X29517)))),
    inference(variable_rename,[status(thm)],[fact_INTER__def]) ).

fof(i_0_6257,plain,
    ! [X28240,X28241,X28242,X28243,X28244,X28245,X28246,X28247,X28248] :
      ( ( ~ c_Equiv__Relations_Ocongruent(X28243,X28242,X28241,X28240)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28243,X28243)),X28244),X28241))
        | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28243,X28243,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28243,tc_fun(X28243,X28242),tc_fun(X28243,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28242,tc_HOL_Obool),tc_fun(tc_fun(X28243,X28242),tc_fun(X28243,tc_HOL_Obool)),X28243),c_COMBB(X28242,tc_HOL_Obool,X28243)),hAPP(hAPP(c_COMBB(X28242,tc_fun(X28242,tc_HOL_Obool),X28243),c_fequal),X28240))),X28240)),X28244)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28248,X28248)),esk296_4(X28245,X28246,X28247,X28248)),X28246))
        | c_Equiv__Relations_Ocongruent(X28248,X28247,X28246,X28245) )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28248,X28248,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28248,tc_fun(X28248,X28247),tc_fun(X28248,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28247,tc_HOL_Obool),tc_fun(tc_fun(X28248,X28247),tc_fun(X28248,tc_HOL_Obool)),X28248),c_COMBB(X28247,tc_HOL_Obool,X28248)),hAPP(hAPP(c_COMBB(X28247,tc_fun(X28247,tc_HOL_Obool),X28248),c_fequal),X28245))),X28245)),esk296_4(X28245,X28246,X28247,X28248)))
        | c_Equiv__Relations_Ocongruent(X28248,X28247,X28246,X28245) ) ),
    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_6258,plain,
    ! [X21069,X21070,X21071,X21072,X21073] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21070),hAPP(c_Set_OCollect(X21070),hAPP(hAPP(c_COMBB(tc_fun(X21072,tc_HOL_Obool),tc_HOL_Obool,X21070),c_HOL_OEx(X21072)),hAPP(hAPP(c_COMBB(tc_fun(X21072,tc_HOL_Obool),tc_fun(X21072,tc_HOL_Obool),X21070),hAPP(c_COMBS(X21072,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X21072),c_fconj),X21071))),X21069)))))
        | ~ hBOOL(hAPP(X21071,X21073))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X21070),hAPP(c_Set_OCollect(X21070),hAPP(hAPP(c_COMBC(X21070,X21072,tc_HOL_Obool),X21069),X21073))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21072),hAPP(c_Set_OCollect(X21072),X21071))) )
      & ( hBOOL(hAPP(X21071,esk86_4(X21069,X21070,X21071,X21072)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X21070),hAPP(c_Set_OCollect(X21070),hAPP(hAPP(c_COMBB(tc_fun(X21072,tc_HOL_Obool),tc_HOL_Obool,X21070),c_HOL_OEx(X21072)),hAPP(hAPP(c_COMBB(tc_fun(X21072,tc_HOL_Obool),tc_fun(X21072,tc_HOL_Obool),X21070),hAPP(c_COMBS(X21072,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X21072),c_fconj),X21071))),X21069)))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21072),hAPP(c_Set_OCollect(X21072),X21071))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21070),hAPP(c_Set_OCollect(X21070),hAPP(hAPP(c_COMBC(X21070,X21072,tc_HOL_Obool),X21069),esk86_4(X21069,X21070,X21071,X21072)))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X21070),hAPP(c_Set_OCollect(X21070),hAPP(hAPP(c_COMBB(tc_fun(X21072,tc_HOL_Obool),tc_HOL_Obool,X21070),c_HOL_OEx(X21072)),hAPP(hAPP(c_COMBB(tc_fun(X21072,tc_HOL_Obool),tc_fun(X21072,tc_HOL_Obool),X21070),hAPP(c_COMBS(X21072,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X21072),c_fconj),X21071))),X21069)))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21072),hAPP(c_Set_OCollect(X21072),X21071))) ) ),
    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_6259,plain,
    ! [X27959,X27960,X27961,X27962,X27963,X27964] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27963),esk274_6(X27959,X27960,X27961,X27962,X27963,X27964)),X27962))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27963,X27964),hAPP(hAPP(c_COMBS(X27963,tc_fun(X27961,tc_HOL_Obool),X27964),hAPP(hAPP(c_COMBB(tc_fun(X27961,X27964),tc_fun(tc_fun(X27961,tc_HOL_Obool),X27964),X27963),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27961,X27964)),X27959)),X27960)),X27962) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X27963,X27961),X27964),hAPP(c_Product__Type_Oprod_Oprod__case(X27963,X27961,X27964),X27959)),hAPP(hAPP(c_Product__Type_OSigma(X27963,X27961),X27962),X27960))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27963),X27962))
        | ~ class_Groups_Ocomm__monoid__add(X27964) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27961),hAPP(X27960,esk274_6(X27959,X27960,X27961,X27962,X27963,X27964))))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27963,X27964),hAPP(hAPP(c_COMBS(X27963,tc_fun(X27961,tc_HOL_Obool),X27964),hAPP(hAPP(c_COMBB(tc_fun(X27961,X27964),tc_fun(tc_fun(X27961,tc_HOL_Obool),X27964),X27963),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27961,X27964)),X27959)),X27960)),X27962) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X27963,X27961),X27964),hAPP(c_Product__Type_Oprod_Oprod__case(X27963,X27961,X27964),X27959)),hAPP(hAPP(c_Product__Type_OSigma(X27963,X27961),X27962),X27960))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27963),X27962))
        | ~ class_Groups_Ocomm__monoid__add(X27964) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Sigma])])])]) ).

fof(i_0_6260,plain,
    ! [X27952,X27953,X27954,X27955,X27956,X27957] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27956),esk273_6(X27952,X27953,X27954,X27955,X27956,X27957)),X27955))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27956,X27957),hAPP(hAPP(c_COMBS(X27956,tc_fun(X27954,tc_HOL_Obool),X27957),hAPP(hAPP(c_COMBB(tc_fun(X27954,X27957),tc_fun(tc_fun(X27954,tc_HOL_Obool),X27957),X27956),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27954,X27957)),X27952)),X27953)),X27955) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X27956,X27954),X27957),hAPP(c_Product__Type_Oprod_Oprod__case(X27956,X27954,X27957),X27952)),hAPP(hAPP(c_Product__Type_OSigma(X27956,X27954),X27955),X27953))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27956),X27955))
        | ~ class_Groups_Ocomm__monoid__mult(X27957) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27954),hAPP(X27953,esk273_6(X27952,X27953,X27954,X27955,X27956,X27957))))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27956,X27957),hAPP(hAPP(c_COMBS(X27956,tc_fun(X27954,tc_HOL_Obool),X27957),hAPP(hAPP(c_COMBB(tc_fun(X27954,X27957),tc_fun(tc_fun(X27954,tc_HOL_Obool),X27957),X27956),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27954,X27957)),X27952)),X27953)),X27955) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X27956,X27954),X27957),hAPP(c_Product__Type_Oprod_Oprod__case(X27956,X27954,X27957),X27952)),hAPP(hAPP(c_Product__Type_OSigma(X27956,X27954),X27955),X27953))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27956),X27955))
        | ~ class_Groups_Ocomm__monoid__mult(X27957) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Sigma])])])]) ).

fof(i_0_6261,plain,
    ! [X26612,X26613,X26614,X26615,X26616] :
      ( ~ class_Groups_Ocomm__monoid__add(X26616)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26615),X26614))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26615,X26616),X26613),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26615,tc_HOL_Obool)),X26614),X26612)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26615,X26616),hAPP(hAPP(c_COMBC(X26615,X26616,X26616),hAPP(hAPP(c_COMBS(X26615,X26616,tc_fun(X26616,X26616)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26616,tc_fun(X26616,X26616)),X26615),c_If(X26616)),hAPP(hAPP(c_COMBC(X26615,tc_fun(X26615,tc_HOL_Obool),tc_HOL_Obool),c_member(X26615)),X26612))),X26613)),c_Groups_Ozero__class_Ozero(X26616))),X26614) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set])]) ).

fof(i_0_6262,plain,
    ! [X20607,X20608,X20609,X20610,X20611,X20612] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20612),X20609),X20610))
        | hAPP(c_Set_Ovimage(X20608,X20612,hAPP(hAPP(c_COMBC(X20608,X20612,X20612),hAPP(hAPP(c_COMBC(X20608,X20612,tc_fun(X20612,X20612)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20612,tc_fun(X20612,X20612)),X20608),c_If(X20612)),hAPP(hAPP(c_COMBC(X20608,tc_fun(X20608,tc_HOL_Obool),tc_HOL_Obool),c_member(X20608)),X20607))),X20611)),X20609)),X20610) = c_Orderings_Otop__class_Otop(tc_fun(X20608,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(X20612),X20611),X20610)) )
      & ( hBOOL(hAPP(hAPP(c_member(X20612),X20609),X20610))
        | hAPP(c_Set_Ovimage(X20608,X20612,hAPP(hAPP(c_COMBC(X20608,X20612,X20612),hAPP(hAPP(c_COMBC(X20608,X20612,tc_fun(X20612,X20612)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20612,tc_fun(X20612,X20612)),X20608),c_If(X20612)),hAPP(hAPP(c_COMBC(X20608,tc_fun(X20608,tc_HOL_Obool),tc_HOL_Obool),c_member(X20608)),X20607))),X20611)),X20609)),X20610) = X20607
        | ~ hBOOL(hAPP(hAPP(c_member(X20612),X20611),X20610)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X20612),X20609),X20610))
        | hAPP(c_Set_Ovimage(X20608,X20612,hAPP(hAPP(c_COMBC(X20608,X20612,X20612),hAPP(hAPP(c_COMBC(X20608,X20612,tc_fun(X20612,X20612)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20612,tc_fun(X20612,X20612)),X20608),c_If(X20612)),hAPP(hAPP(c_COMBC(X20608,tc_fun(X20608,tc_HOL_Obool),tc_HOL_Obool),c_member(X20608)),X20607))),X20611)),X20609)),X20610) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20608,tc_HOL_Obool)),X20607)
        | hBOOL(hAPP(hAPP(c_member(X20612),X20611),X20610)) )
      & ( hBOOL(hAPP(hAPP(c_member(X20612),X20609),X20610))
        | hAPP(c_Set_Ovimage(X20608,X20612,hAPP(hAPP(c_COMBC(X20608,X20612,X20612),hAPP(hAPP(c_COMBC(X20608,X20612,tc_fun(X20612,X20612)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20612,tc_fun(X20612,X20612)),X20608),c_If(X20612)),hAPP(hAPP(c_COMBC(X20608,tc_fun(X20608,tc_HOL_Obool),tc_HOL_Obool),c_member(X20608)),X20607))),X20611)),X20609)),X20610) = c_Orderings_Obot__class_Obot(tc_fun(X20608,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(X20612),X20611),X20610)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5308])])]) ).

fof(i_0_6263,plain,
    ! [X26367,X26368,X26369,X26370] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26370,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26370,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk218_4(X26367,X26368,X26369,X26370))),X26369)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26370,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),esk218_4(X26367,X26368,X26369,X26370)),X26368))),X26367)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26370,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26370,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X26369)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26370,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X26367))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__finite2__subset])])]) ).

cnf(i_0_6264,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_5309]) ).

fof(i_0_6265,plain,
    ! [X33717,X33718,X33719,X33720,X33721,X33722,X33723] : c_New__Random__Sequence_Opos__decr__bind(X33723,X33722,X33721,X33720,X33719,X33718,X33717) = c_New__DSequence_Opos__decr__bind(X33723,X33722,hAPP(hAPP(hAPP(X33721,X33719),X33718),X33717),hAPP(hAPP(c_COMBC(X33723,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X33722))),hAPP(hAPP(c_COMBC(X33723,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(X33722)))),hAPP(hAPP(c_COMBC(X33723,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(X33722))))),X33720),X33719)),X33718)),X33717)),
    inference(variable_rename,[status(thm)],[fact_New__Random__Sequence_Opos__decr__bind__def]) ).

cnf(i_0_6266,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_5310]) ).

cnf(i_0_6267,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_5311]) ).

cnf(i_0_6268,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_5312]) ).

cnf(i_0_6269,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_5313]) ).

cnf(i_0_6270,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_5314]) ).

fof(i_0_6271,plain,
    ! [X27653,X27654,X27655,X27656,X27657,X27658] : hAPP(c_Set_Oimage(X27658,tc_prod(X27657,X27656),hAPP(hAPP(c_COMBS(X27658,X27656,tc_prod(X27657,X27656)),hAPP(hAPP(c_COMBB(X27657,tc_fun(X27656,tc_prod(X27657,X27656)),X27658),c_Product__Type_OPair(X27657,X27656)),X27655)),X27654)),X27653) = hAPP(hAPP(c_Product__Type_OSigma(X27657,X27656),hAPP(c_Set_Oimage(X27658,X27657,X27655),X27653)),hAPP(hAPP(c_COMBB(tc_fun(X27658,tc_HOL_Obool),tc_fun(X27656,tc_HOL_Obool),X27657),c_Set_Oimage(X27658,X27656,X27654)),hAPP(hAPP(c_COMBC(X27657,tc_fun(X27658,tc_HOL_Obool),tc_fun(X27658,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27658,tc_HOL_Obool),tc_fun(tc_fun(X27658,tc_HOL_Obool),tc_fun(X27658,tc_HOL_Obool)),X27657),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27658,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27657,tc_HOL_Obool),tc_fun(X27658,tc_HOL_Obool),X27657),c_Set_Ovimage(X27658,X27657,X27655)),hAPP(hAPP(c_COMBC(X27657,tc_fun(X27657,tc_HOL_Obool),tc_fun(X27657,tc_HOL_Obool)),c_Set_Oinsert(X27657)),c_Orderings_Obot__class_Obot(tc_fun(X27657,tc_HOL_Obool)))))),X27653))),
    inference(variable_rename,[status(thm)],[fact_image__split__eq__Sigma]) ).

cnf(i_0_6272,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_5315]) ).

fof(i_0_6273,plain,
    ! [X33819,X33820] :
      ( ~ class_Lazy__Sequence_Osmall__lazy(X33820)
      | c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X33820),X33819) = c_Lazy__Sequence_Oappend(tc_List_Olist(X33820),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(X33820)),c_List_Olist_ONil(X33820)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X33820))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33819)),hAPP(c_Lazy__Sequence_Obind(tc_prod(X33820,tc_List_Olist(X33820)),tc_List_Olist(X33820),c_Lazy__Sequence_Oproduct(X33820,tc_List_Olist(X33820),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X33820,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X33819),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X33820),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X33819),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(X33820,tc_List_Olist(X33820),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X33820))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X33820),tc_List_Olist(X33820)),tc_fun(tc_List_Olist(X33820),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X33820))),X33820),hAPP(c_COMBB(tc_List_Olist(X33820),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X33820)),tc_List_Olist(X33820)),c_Lazy__Sequence_Osingle(tc_List_Olist(X33820)))),c_List_Olist_OCons(X33820))))),c_Lazy__Sequence_Oempty(tc_List_Olist(X33820)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_small__lazy__list_Osimps])]) ).

fof(i_0_6274,plain,
    ! [X29703,X29704] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29704)
      | c_Complete__Lattice_OSup__class_OSup(X29704,X29703) = c_Complete__Lattice_OInf__class_OInf(X29704,hAPP(c_Set_OCollect(X29704),hAPP(hAPP(c_COMBB(tc_fun(X29704,tc_HOL_Obool),tc_HOL_Obool,X29704),c_HOL_OAll(X29704)),hAPP(hAPP(c_COMBB(tc_fun(X29704,tc_HOL_Obool),tc_fun(X29704,tc_HOL_Obool),X29704),hAPP(c_COMBS(X29704,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29704),c_fimplies),hAPP(hAPP(c_COMBC(X29704,tc_fun(X29704,tc_HOL_Obool),tc_HOL_Obool),c_member(X29704)),X29703)))),hAPP(c_COMBC(X29704,X29704,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X29704)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__Inf])]) ).

fof(i_0_6275,plain,
    ! [X26856,X26857,X26858,X26859,X26860,X26861] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26860),esk245_6(X26856,X26857,X26858,X26859,X26860,X26861)),X26859))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26860,X26861),X26858),X26859) != X26857
        | ~ hBOOL(hAPP(hAPP(c_member(X26860),X26856),X26859))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26861),hAPP(X26858,X26856)),X26857))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26860),X26859))
        | ~ class_Groups_Oordered__ab__group__add(X26861) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26861),c_Groups_Ozero__class_Ozero(X26861)),hAPP(X26858,esk245_6(X26856,X26857,X26858,X26859,X26860,X26861))))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26860,X26861),X26858),X26859) != X26857
        | ~ hBOOL(hAPP(hAPP(c_member(X26860),X26856),X26859))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26861),hAPP(X26858,X26856)),X26857))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26860),X26859))
        | ~ class_Groups_Oordered__ab__group__add(X26861) ) ),
    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_6276,plain,
    ! [X22971,X22972,X22973,X22974,X22975,X22976] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X22975),X22973),X22974))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22975,X22976),hAPP(hAPP(c_COMBC(X22975,X22976,X22976),hAPP(hAPP(c_COMBS(X22975,X22976,tc_fun(X22976,X22976)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X22976,tc_fun(X22976,X22976)),X22975),c_If(X22976)),hAPP(hAPP(c_COMBC(X22975,X22975,tc_HOL_Obool),c_fequal),X22973))),X22972)),X22971)),X22974) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22976),hAPP(X22972,X22973)),hAPP(hAPP(c_Power_Opower__class_Opower(X22976),X22971),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X22975),X22974)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22975),X22974))
        | ~ class_Groups_Ocomm__monoid__mult(X22976) )
      & ( hBOOL(hAPP(hAPP(c_member(X22975),X22973),X22974))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22975,X22976),hAPP(hAPP(c_COMBC(X22975,X22976,X22976),hAPP(hAPP(c_COMBS(X22975,X22976,tc_fun(X22976,X22976)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X22976,tc_fun(X22976,X22976)),X22975),c_If(X22976)),hAPP(hAPP(c_COMBC(X22975,X22975,tc_HOL_Obool),c_fequal),X22973))),X22972)),X22971)),X22974) = hAPP(hAPP(c_Power_Opower__class_Opower(X22976),X22971),hAPP(c_Finite__Set_Ocard(X22975),X22974))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22975),X22974))
        | ~ class_Groups_Ocomm__monoid__mult(X22976) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5316])])]) ).

fof(i_0_6277,plain,
    ! [X26539,X26540,X26541,X26542,X26543] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26542),X26540),X26541))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26542,X26543),hAPP(hAPP(c_COMBC(X26542,X26543,X26543),hAPP(hAPP(c_COMBS(X26542,X26543,tc_fun(X26543,X26543)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26543,tc_fun(X26543,X26543)),X26542),c_If(X26543)),hAPP(hAPP(c_COMBC(X26542,X26542,tc_HOL_Obool),c_fequal),X26540))),X26539)),c_Groups_Ozero__class_Ozero(X26543))),X26541) = hAPP(X26539,X26540)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26542),X26541))
        | ~ class_Groups_Ocomm__monoid__add(X26543) )
      & ( hBOOL(hAPP(hAPP(c_member(X26542),X26540),X26541))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26542,X26543),hAPP(hAPP(c_COMBC(X26542,X26543,X26543),hAPP(hAPP(c_COMBS(X26542,X26543,tc_fun(X26543,X26543)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26543,tc_fun(X26543,X26543)),X26542),c_If(X26543)),hAPP(hAPP(c_COMBC(X26542,X26542,tc_HOL_Obool),c_fequal),X26540))),X26539)),c_Groups_Ozero__class_Ozero(X26543))),X26541) = c_Groups_Ozero__class_Ozero(X26543)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26542),X26541))
        | ~ class_Groups_Ocomm__monoid__add(X26543) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5317])])]) ).

fof(i_0_6278,plain,
    ! [X23152,X23153,X23154,X23155,X23156] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X23155),X23153),X23154))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23155,X23156),hAPP(hAPP(c_COMBC(X23155,X23156,X23156),hAPP(hAPP(c_COMBS(X23155,X23156,tc_fun(X23156,X23156)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X23156,tc_fun(X23156,X23156)),X23155),c_If(X23156)),hAPP(hAPP(c_COMBC(X23155,X23155,tc_HOL_Obool),c_fequal),X23153))),X23152)),c_Groups_Oone__class_Oone(X23156))),X23154) = hAPP(X23152,X23153)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23155),X23154))
        | ~ class_Groups_Ocomm__monoid__mult(X23156) )
      & ( hBOOL(hAPP(hAPP(c_member(X23155),X23153),X23154))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23155,X23156),hAPP(hAPP(c_COMBC(X23155,X23156,X23156),hAPP(hAPP(c_COMBS(X23155,X23156,tc_fun(X23156,X23156)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X23156,tc_fun(X23156,X23156)),X23155),c_If(X23156)),hAPP(hAPP(c_COMBC(X23155,X23155,tc_HOL_Obool),c_fequal),X23153))),X23152)),c_Groups_Oone__class_Oone(X23156))),X23154) = c_Groups_Oone__class_Oone(X23156)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23155),X23154))
        | ~ class_Groups_Ocomm__monoid__mult(X23156) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5318])])]) ).

fof(i_0_6279,plain,
    ! [X17735,X17736,X17737,X17738,X17739] :
      ( ~ class_Orderings_Oorder(X17739)
      | ~ c_Orderings_Oorder__class_Omono(X17739,tc_fun(X17738,tc_HOL_Obool),X17737)
      | c_Orderings_Oorder__class_Omono(X17739,tc_fun(X17738,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X17739,tc_fun(X17738,tc_HOL_Obool),tc_fun(X17738,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17738,tc_HOL_Obool),tc_fun(tc_fun(X17738,tc_HOL_Obool),tc_fun(X17738,tc_HOL_Obool)),X17739),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17738,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X17739,tc_fun(X17738,tc_HOL_Obool),tc_fun(X17738,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17738,tc_HOL_Obool),tc_fun(tc_fun(X17738,tc_HOL_Obool),tc_fun(X17738,tc_HOL_Obool)),X17739),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17738,tc_HOL_Obool))),X17737)),X17736))),X17735)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coinduct3__mono__lemma])]) ).

fof(i_0_6280,plain,
    ! [X29705,X29706] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29706)
      | c_Complete__Lattice_OInf__class_OInf(X29706,X29705) = c_Complete__Lattice_OSup__class_OSup(X29706,hAPP(c_Set_OCollect(X29706),hAPP(hAPP(c_COMBB(tc_fun(X29706,tc_HOL_Obool),tc_HOL_Obool,X29706),c_HOL_OAll(X29706)),hAPP(hAPP(c_COMBB(tc_fun(X29706,tc_HOL_Obool),tc_fun(X29706,tc_HOL_Obool),X29706),hAPP(c_COMBS(X29706,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29706),c_fimplies),hAPP(hAPP(c_COMBC(X29706,tc_fun(X29706,tc_HOL_Obool),tc_HOL_Obool),c_member(X29706)),X29705)))),c_Orderings_Oord__class_Oless__eq(X29706))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__Sup])]) ).

fof(i_0_6281,plain,
    ! [X19750,X19751,X19752,X19753,X19754,X19755,X19756] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19756,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19755,tc_fun(X19756,tc_HOL_Obool)),X19754),X19753)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19752,tc_fun(X19756,tc_HOL_Obool)),X19751),X19750)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19755,tc_fun(X19756,tc_HOL_Obool)),X19754),hAPP(hAPP(c_COMBB(tc_fun(X19752,tc_fun(X19756,tc_HOL_Obool)),tc_fun(X19756,tc_HOL_Obool),X19755),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19752,tc_fun(X19756,tc_HOL_Obool)),X19751)),hAPP(hAPP(c_COMBC(X19755,tc_fun(X19752,tc_fun(X19756,tc_HOL_Obool)),tc_fun(X19752,tc_fun(X19756,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X19756,tc_HOL_Obool),tc_fun(X19756,tc_HOL_Obool)),tc_fun(tc_fun(X19752,tc_fun(X19756,tc_HOL_Obool)),tc_fun(X19752,tc_fun(X19756,tc_HOL_Obool))),X19755),c_COMBB(tc_fun(X19756,tc_HOL_Obool),tc_fun(X19756,tc_HOL_Obool),X19752)),hAPP(hAPP(c_COMBB(tc_fun(X19756,tc_HOL_Obool),tc_fun(tc_fun(X19756,tc_HOL_Obool),tc_fun(X19756,tc_HOL_Obool)),X19755),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19756,tc_HOL_Obool))),X19753))),X19750))),
    inference(variable_rename,[status(thm)],[fact_Int__UN__distrib2]) ).

fof(i_0_6282,plain,
    ! [X29474,X29475,X29476,X29477,X29478,X29479,X29480] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29480,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29479,tc_fun(X29480,tc_HOL_Obool)),X29478),X29477)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29476,tc_fun(X29480,tc_HOL_Obool)),X29475),X29474)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29479,tc_fun(X29480,tc_HOL_Obool)),X29478),hAPP(hAPP(c_COMBB(tc_fun(X29476,tc_fun(X29480,tc_HOL_Obool)),tc_fun(X29480,tc_HOL_Obool),X29479),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29476,tc_fun(X29480,tc_HOL_Obool)),X29475)),hAPP(hAPP(c_COMBC(X29479,tc_fun(X29476,tc_fun(X29480,tc_HOL_Obool)),tc_fun(X29476,tc_fun(X29480,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29480,tc_HOL_Obool),tc_fun(X29480,tc_HOL_Obool)),tc_fun(tc_fun(X29476,tc_fun(X29480,tc_HOL_Obool)),tc_fun(X29476,tc_fun(X29480,tc_HOL_Obool))),X29479),c_COMBB(tc_fun(X29480,tc_HOL_Obool),tc_fun(X29480,tc_HOL_Obool),X29476)),hAPP(hAPP(c_COMBB(tc_fun(X29480,tc_HOL_Obool),tc_fun(tc_fun(X29480,tc_HOL_Obool),tc_fun(X29480,tc_HOL_Obool)),X29479),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29480,tc_HOL_Obool))),X29477))),X29474))),
    inference(variable_rename,[status(thm)],[fact_Un__INT__distrib2]) ).

cnf(i_0_6283,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_5319]) ).

cnf(i_0_6284,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_5320]) ).

cnf(i_0_6285,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_5321]) ).

cnf(i_0_6286,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_5322]) ).

fof(i_0_6287,plain,
    ! [X33804,X33805,X33806,X33807,X33808,X33809,X33810] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X33810,X33809,X33808,X33807),X33806),X33805),X33804) = c_New__DSequence_Oneg__bind(X33810,X33809,hAPP(hAPP(hAPP(X33808,X33806),X33805),X33804),hAPP(hAPP(c_COMBC(X33810,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(X33809)))),hAPP(hAPP(c_COMBC(X33810,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(X33809))))),hAPP(hAPP(c_COMBC(X33810,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(X33809)))))),X33807),X33806)),X33805)),X33804)),
    inference(variable_rename,[status(thm)],[fact_neg__bind__def]) ).

fof(i_0_6288,plain,
    ! [X31743,X31744,X31745,X31746,X31747] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31747),tc_List_Olist(X31747))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31747),tc_List_Olist(X31747)),hAPP(hAPP(c_List_Oappend(X31747),X31746),X31745)),hAPP(hAPP(c_List_Oappend(X31747),X31746),X31744))),c_List_Olexord(X31747,X31743)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X31747,X31747)),hAPP(hAPP(c_Product__Type_OPair(X31747,X31747),esk432_5(X31743,X31744,X31745,X31746,X31747)),esk432_5(X31743,X31744,X31745,X31746,X31747))),X31743))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31747),tc_List_Olist(X31747))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31747),tc_List_Olist(X31747)),X31745),X31744)),c_List_Olexord(X31747,X31743))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5323])])]) ).

fof(i_0_6289,plain,
    ! [X29725,X29726] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X29726,tc_HOL_Obool),X29725) = hAPP(c_Set_OCollect(X29726),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29726,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X29726),c_HOL_OAll(tc_fun(X29726,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29726,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X29726,tc_HOL_Obool),tc_HOL_Obool),X29726),hAPP(c_COMBS(tc_fun(X29726,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(X29726,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(X29726,tc_HOL_Obool),tc_fun(tc_fun(X29726,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X29726,tc_HOL_Obool))),X29725)))),c_member(X29726)))),
    inference(variable_rename,[status(thm)],[fact_Inter__eq]) ).

fof(i_0_6290,plain,
    ! [X28974,X28975,X28976,X28977,X28978] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28978,X28978)),hAPP(hAPP(c_Product__Type_OPair(X28978,X28978),X28977),esk342_5(X28974,X28975,X28976,X28977,X28978))),c_Transitive__Closure_Ortrancl(X28978,X28975)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28978,X28978)),hAPP(hAPP(c_Product__Type_OPair(X28978,X28978),X28977),X28976)),c_Transitive__Closure_Ortrancl(X28978,X28975)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28978,X28978)),hAPP(hAPP(c_Product__Type_OPair(X28978,X28978),X28977),X28976)),c_Transitive__Closure_Ortrancl(X28978,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28978,X28978),tc_HOL_Obool)),X28975),X28974)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28978,X28978)),hAPP(hAPP(c_Product__Type_OPair(X28978,X28978),esk342_5(X28974,X28975,X28976,X28977,X28978)),esk343_5(X28974,X28975,X28976,X28977,X28978))),X28974))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28978,X28978)),hAPP(hAPP(c_Product__Type_OPair(X28978,X28978),X28977),X28976)),c_Transitive__Closure_Ortrancl(X28978,X28975)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28978,X28978)),hAPP(hAPP(c_Product__Type_OPair(X28978,X28978),X28977),X28976)),c_Transitive__Closure_Ortrancl(X28978,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28978,X28978),tc_HOL_Obool)),X28975),X28974)))) )
      & ( esk342_5(X28974,X28975,X28976,X28977,X28978) != esk343_5(X28974,X28975,X28976,X28977,X28978)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28978,X28978)),hAPP(hAPP(c_Product__Type_OPair(X28978,X28978),X28977),X28976)),c_Transitive__Closure_Ortrancl(X28978,X28975)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28978,X28978)),hAPP(hAPP(c_Product__Type_OPair(X28978,X28978),X28977),X28976)),c_Transitive__Closure_Ortrancl(X28978,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28978,X28978),tc_HOL_Obool)),X28975),X28974)))) ) ),
    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_6291,plain,
    ! [X28967,X28968,X28969,X28970,X28971] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28971,X28971)),hAPP(hAPP(c_Product__Type_OPair(X28971,X28971),esk340_5(X28967,X28968,X28969,X28970,X28971)),X28969)),c_Transitive__Closure_Ortrancl(X28971,X28968)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28971,X28971)),hAPP(hAPP(c_Product__Type_OPair(X28971,X28971),X28970),X28969)),c_Transitive__Closure_Ortrancl(X28971,X28968)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28971,X28971)),hAPP(hAPP(c_Product__Type_OPair(X28971,X28971),X28970),X28969)),c_Transitive__Closure_Ortrancl(X28971,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28971,X28971),tc_HOL_Obool)),X28968),X28967)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28971,X28971)),hAPP(hAPP(c_Product__Type_OPair(X28971,X28971),esk341_5(X28967,X28968,X28969,X28970,X28971)),esk340_5(X28967,X28968,X28969,X28970,X28971))),X28967))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28971,X28971)),hAPP(hAPP(c_Product__Type_OPair(X28971,X28971),X28970),X28969)),c_Transitive__Closure_Ortrancl(X28971,X28968)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28971,X28971)),hAPP(hAPP(c_Product__Type_OPair(X28971,X28971),X28970),X28969)),c_Transitive__Closure_Ortrancl(X28971,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28971,X28971),tc_HOL_Obool)),X28968),X28967)))) )
      & ( esk341_5(X28967,X28968,X28969,X28970,X28971) != esk340_5(X28967,X28968,X28969,X28970,X28971)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28971,X28971)),hAPP(hAPP(c_Product__Type_OPair(X28971,X28971),X28970),X28969)),c_Transitive__Closure_Ortrancl(X28971,X28968)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28971,X28971)),hAPP(hAPP(c_Product__Type_OPair(X28971,X28971),X28970),X28969)),c_Transitive__Closure_Ortrancl(X28971,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28971,X28971),tc_HOL_Obool)),X28968),X28967)))) ) ),
    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_6292,plain,
    ! [X30843,X30844,X30845,X30846,X30847,X30848] : hAPP(hAPP(c_List_Ozip(X30848,X30847),X30846),hAPP(hAPP(c_List_Omap(X30845,X30847),X30844),X30843)) = hAPP(hAPP(c_List_Omap(tc_prod(X30848,X30845),tc_prod(X30848,X30847)),hAPP(c_Product__Type_Oprod_Oprod__case(X30848,X30845,tc_prod(X30848,X30847)),hAPP(hAPP(c_COMBC(X30848,tc_fun(X30845,X30847),tc_fun(X30845,tc_prod(X30848,X30847))),hAPP(hAPP(c_COMBB(tc_fun(X30847,tc_prod(X30848,X30847)),tc_fun(tc_fun(X30845,X30847),tc_fun(X30845,tc_prod(X30848,X30847))),X30848),c_COMBB(X30847,tc_prod(X30848,X30847),X30845)),c_Product__Type_OPair(X30848,X30847))),X30844))),hAPP(hAPP(c_List_Ozip(X30848,X30845),X30846),X30843)),
    inference(variable_rename,[status(thm)],[fact_zip__map2]) ).

cnf(i_0_6293,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_5324]) ).

cnf(i_0_6294,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_5302]) ).

cnf(i_0_6295,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_5303]) ).

fof(i_0_6296,plain,
    ! [X28162,X28163,X28164] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk286_3(X28162,X28163,X28164)),X28164))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28162),hAPP(X28163,X28164)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X28163,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X28162))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk285_3(X28162,X28163,X28164)),X28164)) )
      & ( hAPP(X28163,esk286_3(X28162,X28163,X28164)) = X28162
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28162),hAPP(X28163,X28164)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X28163,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X28162))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk285_3(X28162,X28163,X28164)),X28164)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk286_3(X28162,X28163,X28164)),X28164))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28162),hAPP(X28163,X28164)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X28163,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X28162))
        | ~ 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(X28163,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk285_3(X28162,X28163,X28164)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X28163,esk285_3(X28162,X28163,X28164))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
      & ( hAPP(X28163,esk286_3(X28162,X28163,X28164)) = X28162
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28162),hAPP(X28163,X28164)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X28163,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X28162))
        | ~ 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(X28163,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk285_3(X28162,X28163,X28164)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X28163,esk285_3(X28162,X28163,X28164))))),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_6297,plain,
    ! [X28124,X28125,X28126] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk283_3(X28124,X28125,X28126)),X28126))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28124),hAPP(X28125,X28126)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X28125,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X28124))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk282_3(X28124,X28125,X28126)),X28126)) )
      & ( hAPP(X28125,esk283_3(X28124,X28125,X28126)) = X28124
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28124),hAPP(X28125,X28126)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X28125,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X28124))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk282_3(X28124,X28125,X28126)),X28126)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk283_3(X28124,X28125,X28126)),X28126))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28124),hAPP(X28125,X28126)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X28125,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X28124))
        | ~ 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(X28125,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk282_3(X28124,X28125,X28126)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X28125,esk282_3(X28124,X28125,X28126))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
      & ( hAPP(X28125,esk283_3(X28124,X28125,X28126)) = X28124
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28124),hAPP(X28125,X28126)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X28125,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X28124))
        | ~ 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(X28125,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk282_3(X28124,X28125,X28126)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X28125,esk282_3(X28124,X28125,X28126))))),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_6298,plain,
    ! [X28960,X28961,X28962,X28963,X28964] :
      ( ( X28961 = hAPP(c_Nat_OSuc,esk339_5(X28960,X28961,X28962,X28963,X28964))
        | X28961 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28964,X28964)),hAPP(hAPP(c_Product__Type_OPair(X28964,X28964),X28963),X28962)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28964,X28964),tc_HOL_Obool),X28961),X28960))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28964,X28964)),hAPP(hAPP(c_Product__Type_OPair(X28964,X28964),X28963),esk338_5(X28960,X28961,X28962,X28963,X28964))),X28960))
        | X28961 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28964,X28964)),hAPP(hAPP(c_Product__Type_OPair(X28964,X28964),X28963),X28962)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28964,X28964),tc_HOL_Obool),X28961),X28960))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28964,X28964)),hAPP(hAPP(c_Product__Type_OPair(X28964,X28964),esk338_5(X28960,X28961,X28962,X28963,X28964)),X28962)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28964,X28964),tc_HOL_Obool),esk339_5(X28960,X28961,X28962,X28963,X28964)),X28960)))
        | X28961 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28964,X28964)),hAPP(hAPP(c_Product__Type_OPair(X28964,X28964),X28963),X28962)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28964,X28964),tc_HOL_Obool),X28961),X28960))) )
      & ( X28961 = hAPP(c_Nat_OSuc,esk339_5(X28960,X28961,X28962,X28963,X28964))
        | X28963 = X28962
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28964,X28964)),hAPP(hAPP(c_Product__Type_OPair(X28964,X28964),X28963),X28962)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28964,X28964),tc_HOL_Obool),X28961),X28960))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28964,X28964)),hAPP(hAPP(c_Product__Type_OPair(X28964,X28964),X28963),esk338_5(X28960,X28961,X28962,X28963,X28964))),X28960))
        | X28963 = X28962
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28964,X28964)),hAPP(hAPP(c_Product__Type_OPair(X28964,X28964),X28963),X28962)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28964,X28964),tc_HOL_Obool),X28961),X28960))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28964,X28964)),hAPP(hAPP(c_Product__Type_OPair(X28964,X28964),esk338_5(X28960,X28961,X28962,X28963,X28964)),X28962)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28964,X28964),tc_HOL_Obool),esk339_5(X28960,X28961,X28962,X28963,X28964)),X28960)))
        | X28963 = X28962
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28964,X28964)),hAPP(hAPP(c_Product__Type_OPair(X28964,X28964),X28963),X28962)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28964,X28964),tc_HOL_Obool),X28961),X28960))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5325])])])]) ).

fof(i_0_6299,plain,
    ! [X30060,X30061,X30062,X30063] :
      ( ~ class_Smallcheck_Osmall(X30063)
      | ~ class_Smallcheck_Osmall(X30062)
      | hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(X30062,X30063)),X30061),X30060) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(X30062),hAPP(hAPP(c_COMBC(X30062,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(X30063,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X30062),c_Smallcheck_Osmall__class_Osmall(X30063)),hAPP(hAPP(c_COMBB(tc_fun(X30063,tc_prod(X30062,X30063)),tc_fun(X30063,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X30062),hAPP(c_COMBB(tc_prod(X30062,X30063),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),X30063),X30061)),c_Product__Type_OPair(X30062,X30063)))),X30060)),X30060) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_small__prod__def])]) ).

cnf(i_0_6300,plain,
    ( hAPP(X1,esk397_7(X2,X3,X4,X1,X5,X6,X7)) = hAPP(c_Option_Ooption_OSome(X6),X2)
    | c_Map_Omap__comp(X7,X6,X5,X1,X4,X3) != hAPP(c_Option_Ooption_OSome(X6),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5326]) ).

cnf(i_0_6301,plain,
    c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X2),X1,c_Option_Ooption_ONone(X2),X4),hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_5327]) ).

cnf(i_0_6302,plain,
    ( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),esk397_7(X4,X2,X1,X5,X6,X7,X3))
    | c_Map_Omap__comp(X3,X7,X6,X5,X1,X2) != hAPP(c_Option_Ooption_OSome(X7),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_5326]) ).

fof(i_0_6303,plain,
    ! [X19366,X19367,X19368,X19369] :
      ( ~ c_Fun_Oinj__on(X19369,X19368,X19367,c_Orderings_Otop__class_Otop(tc_fun(X19369,tc_HOL_Obool)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19369,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X19369,X19368,X19367),hAPP(hAPP(c_Set_Oinsert(X19368),X19366),c_Orderings_Obot__class_Obot(tc_fun(X19368,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X19369),c_HOL_OThe(X19369,hAPP(hAPP(c_COMBC(X19369,X19368,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X19368,tc_fun(X19368,tc_HOL_Obool),X19369),c_fequal),X19367)),X19366))),c_Orderings_Obot__class_Obot(tc_fun(X19369,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__vimage__singleton])]) ).

fof(i_0_6304,plain,
    ! [X33736,X33737,X33738,X33739,X33740,X33741,X33742] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X33742,X33741,X33740,X33739),X33738),X33737),X33736) = c_New__DSequence_Opos__bind(X33742,X33741,hAPP(hAPP(hAPP(X33740,X33738),X33737),X33736),hAPP(hAPP(c_COMBC(X33742,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X33741))),hAPP(hAPP(c_COMBC(X33742,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(X33741)))),hAPP(hAPP(c_COMBC(X33742,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(X33741))))),X33739),X33738)),X33737)),X33736)),
    inference(variable_rename,[status(thm)],[fact_pos__bind__def]) ).

fof(i_0_6305,plain,
    ! [X23983,X23984,X23985,X23986] : c_Nitpick_Oprod(X23986,X23985,X23984,X23983) = hAPP(c_Set_OCollect(tc_prod(X23986,X23985)),hAPP(c_Product__Type_Oprod_Oprod__case(X23986,X23985,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X23986,tc_fun(X23985,tc_HOL_Obool),tc_fun(X23985,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X23985,tc_HOL_Obool),tc_fun(X23985,tc_HOL_Obool)),X23986),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X23985)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X23986),c_fconj),hAPP(hAPP(c_COMBC(X23986,tc_fun(X23986,tc_HOL_Obool),tc_HOL_Obool),c_member(X23986)),X23984)))),hAPP(hAPP(c_COMBC(X23985,tc_fun(X23985,tc_HOL_Obool),tc_HOL_Obool),c_member(X23985)),X23983)))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Oprod__def]) ).

cnf(i_0_6306,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_5328]) ).

fof(i_0_6307,plain,
    ! [X28035,X28036,X28037,X28038,X28039,X28040,X28041,X28042,X28043,X28044,X28045] : hAPP(c_Product__Type_Omap__pair(X28045,X28044,X28043,X28042,X28041,X28040),hAPP(c_Product__Type_Omap__pair(X28039,X28045,X28038,X28043,X28037,X28036),X28035)) = hAPP(c_Product__Type_Omap__pair(X28039,X28044,X28038,X28042,hAPP(c_Fun_Ocomp(X28045,X28044,X28039,X28041),X28037),hAPP(c_Fun_Ocomp(X28043,X28042,X28038,X28040),X28036)),X28035),
    inference(variable_rename,[status(thm)],[fact_map__pair_Ocompositionality]) ).

fof(i_0_6308,plain,
    ! [X25603,X25604,X25605,X25606] :
      ( ( ~ 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),X25606),X25605)),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),X25604),X25603)),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),X25606),X25603)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25604),X25605))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25606),X25603)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25604),X25605)))
        | 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),X25606),X25605)),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),X25604),X25603)),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_6309,plain,
    ! [X25586,X25587,X25588,X25589] :
      ( ( ~ 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),X25589),X25588)),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),X25587),X25586)),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),X25589),X25586)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25587),X25588))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25589),X25586)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25587),X25588)))
        | 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),X25589),X25588)),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),X25587),X25586)),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_6310,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_5329]) ).

cnf(i_0_6311,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_5330]) ).

fof(i_0_6312,plain,
    ! [X26785,X26786,X26787,X26788,X26789,X26790] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26789),esk241_6(X26785,X26786,X26787,X26788,X26789,X26790)),X26788))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26785,X26790),X26786),hAPP(c_Set_Oimage(X26789,X26785,X26787),X26788)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26789,X26790),hAPP(c_Fun_Ocomp(X26785,X26790,X26789,X26786),X26787)),X26788)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26789),X26788))
        | ~ class_Groups_Ocomm__monoid__add(X26790) )
      & ( hBOOL(hAPP(hAPP(c_member(X26789),esk242_6(X26785,X26786,X26787,X26788,X26789,X26790)),X26788))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26785,X26790),X26786),hAPP(c_Set_Oimage(X26789,X26785,X26787),X26788)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26789,X26790),hAPP(c_Fun_Ocomp(X26785,X26790,X26789,X26786),X26787)),X26788)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26789),X26788))
        | ~ class_Groups_Ocomm__monoid__add(X26790) )
      & ( esk241_6(X26785,X26786,X26787,X26788,X26789,X26790) != esk242_6(X26785,X26786,X26787,X26788,X26789,X26790)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26785,X26790),X26786),hAPP(c_Set_Oimage(X26789,X26785,X26787),X26788)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26789,X26790),hAPP(c_Fun_Ocomp(X26785,X26790,X26789,X26786),X26787)),X26788)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26789),X26788))
        | ~ class_Groups_Ocomm__monoid__add(X26790) )
      & ( hAPP(X26787,esk241_6(X26785,X26786,X26787,X26788,X26789,X26790)) = hAPP(X26787,esk242_6(X26785,X26786,X26787,X26788,X26789,X26790))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26785,X26790),X26786),hAPP(c_Set_Oimage(X26789,X26785,X26787),X26788)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26789,X26790),hAPP(c_Fun_Ocomp(X26785,X26790,X26789,X26786),X26787)),X26788)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26789),X26788))
        | ~ class_Groups_Ocomm__monoid__add(X26790) )
      & ( hAPP(X26786,hAPP(X26787,esk241_6(X26785,X26786,X26787,X26788,X26789,X26790))) != c_Groups_Ozero__class_Ozero(X26790)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26785,X26790),X26786),hAPP(c_Set_Oimage(X26789,X26785,X26787),X26788)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26789,X26790),hAPP(c_Fun_Ocomp(X26785,X26790,X26789,X26786),X26787)),X26788)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26789),X26788))
        | ~ class_Groups_Ocomm__monoid__add(X26790) ) ),
    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_6313,plain,
    ! [X17779,X17780,X17781,X17782,X17783,X17784] : hAPP(c_Set_Oimage(X17784,X17783,hAPP(hAPP(c_COMBS(X17784,X17783,X17783),hAPP(hAPP(c_COMBS(X17784,X17783,tc_fun(X17783,X17783)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17783,tc_fun(X17783,X17783)),X17784),c_If(X17783)),X17782)),X17781)),X17780)),X17779) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17783,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17784,X17783,X17781),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17784,tc_HOL_Obool)),X17779),hAPP(c_Set_OCollect(X17784),X17782)))),hAPP(c_Set_Oimage(X17784,X17783,X17780),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17784,tc_HOL_Obool)),X17779),hAPP(c_Set_OCollect(X17784),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X17784),c_fNot),X17782))))),
    inference(variable_rename,[status(thm)],[fact_if__image__distrib]) ).

cnf(i_0_6314,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_5331]) ).

cnf(i_0_6315,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_5332]) ).

fof(i_0_6316,plain,
    ! [X25582,X25583,X25584,X25585] : 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),X25585),X25584)),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),X25583),X25582)),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),X25585),X25583)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25584),X25582))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25585),X25582)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25584),X25583)))),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_6317,plain,
    ! [X28379,X28380,X28381,X28382,X28383,X28384] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28383),esk320_6(X28379,X28380,X28381,X28382,X28383,X28384)),X28382))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28384,X28383,c_Groups_Otimes__class_Otimes(X28384)),X28381),X28379),X28382) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28384,X28383,c_Groups_Otimes__class_Otimes(X28384)),X28380),X28379),X28382)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28383),X28382))
        | ~ class_Groups_Oab__semigroup__mult(X28384) )
      & ( hAPP(X28381,esk320_6(X28379,X28380,X28381,X28382,X28383,X28384)) != hAPP(X28380,esk320_6(X28379,X28380,X28381,X28382,X28383,X28384))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28384,X28383,c_Groups_Otimes__class_Otimes(X28384)),X28381),X28379),X28382) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28384,X28383,c_Groups_Otimes__class_Otimes(X28384)),X28380),X28379),X28382)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28383),X28382))
        | ~ class_Groups_Oab__semigroup__mult(X28384) ) ),
    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_6318,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_5333]) ).

cnf(i_0_6319,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_5333]) ).

fof(i_0_6320,plain,
    ! [X28094,X28095,X28096,X28097] :
      ( ~ c_Wellfounded_Owf(X28097,X28096)
      | ~ c_Fun_Oinj__on(X28097,X28095,X28094,c_Orderings_Otop__class_Otop(tc_fun(X28097,tc_HOL_Obool)))
      | c_Wellfounded_Owf(X28095,hAPP(c_Set_Oimage(tc_prod(X28097,X28097),tc_prod(X28095,X28095),c_Product__Type_Omap__pair(X28097,X28095,X28097,X28095,X28094,X28094)),X28096)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__map__pair__image])]) ).

fof(i_0_6321,plain,
    ! [X29840,X29841,X29842,X29843,X29844,X29845] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29844),esk375_6(X29840,X29841,X29842,X29843,X29844,X29845)),X29845))
        | c_Fun_Oinj__on(X29843,X29842,X29841,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29844,tc_fun(X29843,tc_HOL_Obool)),X29845),X29840))
        | X29845 = c_Orderings_Obot__class_Obot(tc_fun(X29844,tc_HOL_Obool)) )
      & ( ~ c_Fun_Oinj__on(X29843,X29842,X29841,hAPP(X29840,esk375_6(X29840,X29841,X29842,X29843,X29844,X29845)))
        | c_Fun_Oinj__on(X29843,X29842,X29841,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29844,tc_fun(X29843,tc_HOL_Obool)),X29845),X29840))
        | X29845 = c_Orderings_Obot__class_Obot(tc_fun(X29844,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_6322,plain,
    ! [X31315,X31316,X31317,X31318,X31319] :
      ( ( hBOOL(hAPP(hAPP(c_member(X31318),esk421_5(X31315,X31316,X31317,X31318,X31319)),hAPP(c_List_Oset(X31318),X31317)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31319),hAPP(c_List_Omonoid__add__class_Olistsum(X31319),hAPP(hAPP(c_List_Omap(X31318,X31319),X31316),X31317))),hAPP(c_List_Omonoid__add__class_Olistsum(X31319),hAPP(hAPP(c_List_Omap(X31318,X31319),X31315),X31317))))
        | ~ class_Groups_Omonoid__add(X31319)
        | ~ class_Groups_Oordered__ab__semigroup__add(X31319) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31319),hAPP(X31316,esk421_5(X31315,X31316,X31317,X31318,X31319))),hAPP(X31315,esk421_5(X31315,X31316,X31317,X31318,X31319))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31319),hAPP(c_List_Omonoid__add__class_Olistsum(X31319),hAPP(hAPP(c_List_Omap(X31318,X31319),X31316),X31317))),hAPP(c_List_Omonoid__add__class_Olistsum(X31319),hAPP(hAPP(c_List_Omap(X31318,X31319),X31315),X31317))))
        | ~ class_Groups_Omonoid__add(X31319)
        | ~ class_Groups_Oordered__ab__semigroup__add(X31319) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__mono])])])]) ).

fof(i_0_6323,plain,
    ! [X33430,X33431,X33432,X33433,X33434] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk481_5(X33430,X33431,X33432,X33433,X33434)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33434)),X33433)))
        | c_List_Olist__all2(X33434,X33432,X33430,X33433,X33431)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33434)),X33433) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33432)),X33431) )
      & ( ~ hBOOL(hAPP(hAPP(X33430,hAPP(hAPP(c_List_Onth(X33434),X33433),esk481_5(X33430,X33431,X33432,X33433,X33434))),hAPP(hAPP(c_List_Onth(X33432),X33431),esk481_5(X33430,X33431,X33432,X33433,X33434))))
        | c_List_Olist__all2(X33434,X33432,X33430,X33433,X33431)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33434)),X33433) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33432)),X33431) ) ),
    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_6324,plain,
    ! [X33193,X33194,X33195,X33196,X33197,X33198,X33199,X33200,X33201,X33202,X33203] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33197)),X33194) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33196)),X33193)
        | ~ c_List_Olist__all2(X33197,X33196,X33195,X33194,X33193) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33198),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33197)),X33194)))
        | hBOOL(hAPP(hAPP(X33195,hAPP(hAPP(c_List_Onth(X33197),X33194),X33198)),hAPP(hAPP(c_List_Onth(X33196),X33193),X33198)))
        | ~ c_List_Olist__all2(X33197,X33196,X33195,X33194,X33193) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk472_5(X33199,X33200,X33201,X33202,X33203)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33203)),X33200)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33203)),X33200) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33202)),X33199)
        | c_List_Olist__all2(X33203,X33202,X33201,X33200,X33199) )
      & ( ~ hBOOL(hAPP(hAPP(X33201,hAPP(hAPP(c_List_Onth(X33203),X33200),esk472_5(X33199,X33200,X33201,X33202,X33203))),hAPP(hAPP(c_List_Onth(X33202),X33199),esk472_5(X33199,X33200,X33201,X33202,X33203))))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33203)),X33200) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33202)),X33199)
        | c_List_Olist__all2(X33203,X33202,X33201,X33200,X33199) ) ),
    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_6325,plain,
    ! [X26952,X26953,X26954,X26955,X26956] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26955),esk249_5(X26952,X26953,X26954,X26955,X26956)),X26954))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26956),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26955,X26956),X26953),X26954)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26955,X26956),X26952),X26954)))
        | X26954 = c_Orderings_Obot__class_Obot(tc_fun(X26955,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26955),X26954))
        | ~ class_Groups_Ocomm__monoid__add(X26956)
        | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X26956) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26956),hAPP(X26953,esk249_5(X26952,X26953,X26954,X26955,X26956))),hAPP(X26952,esk249_5(X26952,X26953,X26954,X26955,X26956))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26956),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26955,X26956),X26953),X26954)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26955,X26956),X26952),X26954)))
        | X26954 = c_Orderings_Obot__class_Obot(tc_fun(X26955,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26955),X26954))
        | ~ class_Groups_Ocomm__monoid__add(X26956)
        | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X26956) ) ),
    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_6326,plain,
    ! [X26655,X26656,X26657,X26658,X26659,X26660] :
      ( ~ class_Groups_Ocomm__monoid__add(X26660)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26659),X26658))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26659,X26660),hAPP(hAPP(c_COMBS(X26659,X26660,X26660),hAPP(hAPP(c_COMBS(X26659,X26660,tc_fun(X26660,X26660)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26660,tc_fun(X26660,X26660)),X26659),c_If(X26660)),X26657)),X26656)),X26655)),X26658) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26660),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26659,X26660),X26656),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26659,tc_HOL_Obool)),X26658),hAPP(c_Set_OCollect(X26659),X26657)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26659,X26660),X26655),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26659,tc_HOL_Obool)),X26658),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26659,tc_HOL_Obool)),hAPP(c_Set_OCollect(X26659),X26657))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__cases])]) ).

cnf(i_0_6327,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_5319]) ).

cnf(i_0_6328,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_5320]) ).

fof(i_0_6329,plain,
    ! [X21169,X21170,X21171,X21172,X21173] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X21173,X21172,X21171)
      | hAPP(X21170,hAPP(hAPP(X21172,esk97_5(X21169,X21170,X21171,X21172,X21173)),esk98_5(X21169,X21170,X21171,X21172,X21173))) != hAPP(hAPP(X21172,hAPP(X21170,esk97_5(X21169,X21170,X21171,X21172,X21173))),hAPP(X21170,esk98_5(X21169,X21170,X21171,X21172,X21173)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21173),X21169))
      | X21169 = c_Orderings_Obot__class_Obot(tc_fun(X21173,tc_HOL_Obool))
      | hAPP(X21170,hAPP(X21171,X21169)) = hAPP(X21171,hAPP(c_Set_Oimage(X21173,X21173,X21170),X21169)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ohom__commute])])]) ).

cnf(i_0_6330,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk452_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_5334]) ).

cnf(i_0_6331,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk452_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_5334]) ).

cnf(i_0_6332,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),esk452_3(X3,X1,X2))) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_5334]) ).

cnf(i_0_6333,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),esk452_3(X3,X1,X2))) != X3
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_5334]) ).

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(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_5335]) ).

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),esk157_3(X1,X2,X3)),esk158_3(X1,X2,X3))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk158_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(X1,esk157_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)))),esk158_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_5336]) ).

fof(i_0_6336,plain,
    ! [X26544,X26545,X26546,X26547,X26548] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26547),X26545),X26546))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26547,X26548),hAPP(hAPP(c_COMBC(X26547,X26548,X26548),hAPP(hAPP(c_COMBS(X26547,X26548,tc_fun(X26548,X26548)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26548,tc_fun(X26548,X26548)),X26547),c_If(X26548)),hAPP(c_fequal,X26545))),X26544)),c_Groups_Ozero__class_Ozero(X26548))),X26546) = hAPP(X26544,X26545)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26547),X26546))
        | ~ class_Groups_Ocomm__monoid__add(X26548) )
      & ( hBOOL(hAPP(hAPP(c_member(X26547),X26545),X26546))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26547,X26548),hAPP(hAPP(c_COMBC(X26547,X26548,X26548),hAPP(hAPP(c_COMBS(X26547,X26548,tc_fun(X26548,X26548)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26548,tc_fun(X26548,X26548)),X26547),c_If(X26548)),hAPP(c_fequal,X26545))),X26544)),c_Groups_Ozero__class_Ozero(X26548))),X26546) = c_Groups_Ozero__class_Ozero(X26548)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26547),X26546))
        | ~ class_Groups_Ocomm__monoid__add(X26548) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5337])])]) ).

fof(i_0_6337,plain,
    ! [X23147,X23148,X23149,X23150,X23151] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X23150),X23148),X23149))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23150,X23151),hAPP(hAPP(c_COMBC(X23150,X23151,X23151),hAPP(hAPP(c_COMBS(X23150,X23151,tc_fun(X23151,X23151)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X23151,tc_fun(X23151,X23151)),X23150),c_If(X23151)),hAPP(c_fequal,X23148))),X23147)),c_Groups_Oone__class_Oone(X23151))),X23149) = hAPP(X23147,X23148)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23150),X23149))
        | ~ class_Groups_Ocomm__monoid__mult(X23151) )
      & ( hBOOL(hAPP(hAPP(c_member(X23150),X23148),X23149))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23150,X23151),hAPP(hAPP(c_COMBC(X23150,X23151,X23151),hAPP(hAPP(c_COMBS(X23150,X23151,tc_fun(X23151,X23151)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X23151,tc_fun(X23151,X23151)),X23150),c_If(X23151)),hAPP(c_fequal,X23148))),X23147)),c_Groups_Oone__class_Oone(X23151))),X23149) = c_Groups_Oone__class_Oone(X23151)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23150),X23149))
        | ~ class_Groups_Ocomm__monoid__mult(X23151) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5338])])]) ).

fof(i_0_6338,plain,
    ! [X30538,X30539,X30540] : hAPP(c_List_Oset(tc_List_Olist(X30540)),c_Enum_On__lists(X30540,X30539,X30538)) = hAPP(c_Set_OCollect(tc_List_Olist(X30540)),hAPP(hAPP(c_COMBS(tc_List_Olist(X30540),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X30540)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X30540),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X30540)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X30540)))),X30539))),hAPP(hAPP(c_COMBC(tc_List_Olist(X30540),tc_fun(X30540,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X30540,tc_HOL_Obool),tc_fun(tc_fun(X30540,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X30540)),c_Orderings_Oord__class_Oless__eq(tc_fun(X30540,tc_HOL_Obool))),c_List_Oset(X30540))),hAPP(c_List_Oset(X30540),X30538)))),
    inference(variable_rename,[status(thm)],[fact_set__n__lists]) ).

fof(i_0_6339,plain,
    ! [X28056,X28057,X28058,X28059,X28060,X28061,X28062,X28063,X28064,X28065] : hAPP(c_Fun_Ocomp(tc_prod(X28065,X28064),tc_prod(X28063,X28062),tc_prod(X28061,X28060),c_Product__Type_Omap__pair(X28065,X28063,X28064,X28062,X28059,X28058)),c_Product__Type_Omap__pair(X28061,X28065,X28060,X28064,X28057,X28056)) = c_Product__Type_Omap__pair(X28061,X28063,X28060,X28062,hAPP(c_Fun_Ocomp(X28065,X28063,X28061,X28059),X28057),hAPP(c_Fun_Ocomp(X28064,X28062,X28060,X28058),X28056)),
    inference(variable_rename,[status(thm)],[fact_map__pair_Ocomp]) ).

fof(i_0_6340,plain,
    ! [X28046,X28047,X28048,X28049,X28050,X28051,X28052,X28053,X28054,X28055] : c_Product__Type_Omap__pair(X28055,X28054,X28053,X28052,hAPP(c_Fun_Ocomp(X28051,X28054,X28055,X28050),X28049),hAPP(c_Fun_Ocomp(X28048,X28052,X28053,X28047),X28046)) = hAPP(c_Fun_Ocomp(tc_prod(X28051,X28048),tc_prod(X28054,X28052),tc_prod(X28055,X28053),c_Product__Type_Omap__pair(X28051,X28054,X28048,X28052,X28050,X28047)),c_Product__Type_Omap__pair(X28055,X28051,X28053,X28048,X28049,X28046)),
    inference(variable_rename,[status(thm)],[fact_map__pair__compose]) ).

fof(i_0_6341,plain,
    ! [X31035,X31036,X31037,X31038,X31039,X31040,X31041,X31042,X31043] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31038)),X31037) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31038)),X31036)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31038),tc_List_Olist(X31038))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31038),tc_List_Olist(X31038)),X31037),X31036)),c_List_Olistrel(X31038,X31035))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31039),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31038)),X31037)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X31038,X31038)),hAPP(hAPP(c_Product__Type_OPair(X31038,X31038),hAPP(hAPP(c_List_Onth(X31038),X31037),X31039)),hAPP(hAPP(c_List_Onth(X31038),X31036),X31039))),X31035))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31038),tc_List_Olist(X31038))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31038),tc_List_Olist(X31038)),X31037),X31036)),c_List_Olistrel(X31038,X31035))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk417_4(X31040,X31041,X31042,X31043)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31043)),X31042)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31043)),X31042) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31043)),X31041)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31043),tc_List_Olist(X31043))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31043),tc_List_Olist(X31043)),X31042),X31041)),c_List_Olistrel(X31043,X31040))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31043,X31043)),hAPP(hAPP(c_Product__Type_OPair(X31043,X31043),hAPP(hAPP(c_List_Onth(X31043),X31042),esk417_4(X31040,X31041,X31042,X31043))),hAPP(hAPP(c_List_Onth(X31043),X31041),esk417_4(X31040,X31041,X31042,X31043)))),X31040))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31043)),X31042) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31043)),X31041)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31043),tc_List_Olist(X31043))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31043),tc_List_Olist(X31043)),X31042),X31041)),c_List_Olistrel(X31043,X31040))) ) ),
    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_6342,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk148_3(X1,X2,X3)),esk149_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk149_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(X1,esk148_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)))),esk149_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_5339]) ).

fof(i_0_6343,plain,
    ! [X30737,X30738,X30739,X30740,X30741] :
      ( ( X30740 = hAPP(hAPP(c_List_Olist_OCons(X30741),esk402_5(X30737,X30738,X30739,X30740,X30741)),esk403_5(X30737,X30738,X30739,X30740,X30741))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30741),tc_List_Olist(X30741))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30741),tc_List_Olist(X30741)),X30740),hAPP(hAPP(c_List_Olist_OCons(X30741),X30739),X30738))),c_List_Olistrel(X30741,X30737))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30741,X30741)),hAPP(hAPP(c_Product__Type_OPair(X30741,X30741),esk402_5(X30737,X30738,X30739,X30740,X30741)),X30739)),X30737))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30741),tc_List_Olist(X30741))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30741),tc_List_Olist(X30741)),X30740),hAPP(hAPP(c_List_Olist_OCons(X30741),X30739),X30738))),c_List_Olistrel(X30741,X30737))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30741),tc_List_Olist(X30741))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30741),tc_List_Olist(X30741)),esk403_5(X30737,X30738,X30739,X30740,X30741)),X30738)),c_List_Olistrel(X30741,X30737)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30741),tc_List_Olist(X30741))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30741),tc_List_Olist(X30741)),X30740),hAPP(hAPP(c_List_Olist_OCons(X30741),X30739),X30738))),c_List_Olistrel(X30741,X30737))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5340])])])]) ).

cnf(i_0_6344,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_5335]) ).

fof(i_0_6345,plain,
    ! [X28993,X28994,X28995,X28996,X28997] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28997,X28997)),hAPP(hAPP(c_Product__Type_OPair(X28997,X28997),X28996),esk346_5(X28993,X28994,X28995,X28996,X28997))),X28993))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28997,X28997)),hAPP(hAPP(c_Product__Type_OPair(X28997,X28997),X28996),X28995)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28997,X28997),tc_HOL_Obool),hAPP(c_Nat_OSuc,X28994)),X28993))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28997,X28997)),hAPP(hAPP(c_Product__Type_OPair(X28997,X28997),esk346_5(X28993,X28994,X28995,X28996,X28997)),X28995)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28997,X28997),tc_HOL_Obool),X28994),X28993)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28997,X28997)),hAPP(hAPP(c_Product__Type_OPair(X28997,X28997),X28996),X28995)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28997,X28997),tc_HOL_Obool),hAPP(c_Nat_OSuc,X28994)),X28993))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5341])])])]) ).

fof(i_0_6346,plain,
    ! [X28981,X28982,X28983,X28984,X28985] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28985,X28985)),hAPP(hAPP(c_Product__Type_OPair(X28985,X28985),X28984),esk344_5(X28981,X28982,X28983,X28984,X28985))),X28981))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28985,X28985)),hAPP(hAPP(c_Product__Type_OPair(X28985,X28985),X28984),X28983)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28985,X28985),tc_HOL_Obool),hAPP(c_Nat_OSuc,X28982)),X28981))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28985,X28985)),hAPP(hAPP(c_Product__Type_OPair(X28985,X28985),esk344_5(X28981,X28982,X28983,X28984,X28985)),X28983)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28985,X28985),tc_HOL_Obool),X28982),X28981)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28985,X28985)),hAPP(hAPP(c_Product__Type_OPair(X28985,X28985),X28984),X28983)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28985,X28985),tc_HOL_Obool),hAPP(c_Nat_OSuc,X28982)),X28981))) ) ),
    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_6347,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_5342]) ).

fof(i_0_6348,plain,
    ! [X28953,X28954,X28955,X28956,X28957] :
      ( ( X28954 = hAPP(c_Nat_OSuc,esk337_5(X28953,X28954,X28955,X28956,X28957))
        | X28954 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28957,X28957)),hAPP(hAPP(c_Product__Type_OPair(X28957,X28957),X28956),X28955)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28957,X28957),tc_HOL_Obool),X28954),X28953))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28957,X28957)),hAPP(hAPP(c_Product__Type_OPair(X28957,X28957),X28956),esk336_5(X28953,X28954,X28955,X28956,X28957))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28957,X28957),tc_HOL_Obool),esk337_5(X28953,X28954,X28955,X28956,X28957)),X28953)))
        | X28954 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28957,X28957)),hAPP(hAPP(c_Product__Type_OPair(X28957,X28957),X28956),X28955)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28957,X28957),tc_HOL_Obool),X28954),X28953))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28957,X28957)),hAPP(hAPP(c_Product__Type_OPair(X28957,X28957),esk336_5(X28953,X28954,X28955,X28956,X28957)),X28955)),X28953))
        | X28954 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28957,X28957)),hAPP(hAPP(c_Product__Type_OPair(X28957,X28957),X28956),X28955)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28957,X28957),tc_HOL_Obool),X28954),X28953))) )
      & ( X28954 = hAPP(c_Nat_OSuc,esk337_5(X28953,X28954,X28955,X28956,X28957))
        | X28956 = X28955
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28957,X28957)),hAPP(hAPP(c_Product__Type_OPair(X28957,X28957),X28956),X28955)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28957,X28957),tc_HOL_Obool),X28954),X28953))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28957,X28957)),hAPP(hAPP(c_Product__Type_OPair(X28957,X28957),X28956),esk336_5(X28953,X28954,X28955,X28956,X28957))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28957,X28957),tc_HOL_Obool),esk337_5(X28953,X28954,X28955,X28956,X28957)),X28953)))
        | X28956 = X28955
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28957,X28957)),hAPP(hAPP(c_Product__Type_OPair(X28957,X28957),X28956),X28955)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28957,X28957),tc_HOL_Obool),X28954),X28953))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28957,X28957)),hAPP(hAPP(c_Product__Type_OPair(X28957,X28957),esk336_5(X28953,X28954,X28955,X28956,X28957)),X28955)),X28953))
        | X28956 = X28955
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28957,X28957)),hAPP(hAPP(c_Product__Type_OPair(X28957,X28957),X28956),X28955)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28957,X28957),tc_HOL_Obool),X28954),X28953))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5343])])])]) ).

fof(i_0_6349,plain,
    ! [X28987,X28988,X28989,X28990,X28991] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28991,X28991)),hAPP(hAPP(c_Product__Type_OPair(X28991,X28991),X28990),esk345_5(X28987,X28988,X28989,X28990,X28991))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28991,X28991),tc_HOL_Obool),X28988),X28987)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28991,X28991)),hAPP(hAPP(c_Product__Type_OPair(X28991,X28991),X28990),X28989)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28991,X28991),tc_HOL_Obool),hAPP(c_Nat_OSuc,X28988)),X28987))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28991,X28991)),hAPP(hAPP(c_Product__Type_OPair(X28991,X28991),esk345_5(X28987,X28988,X28989,X28990,X28991)),X28989)),X28987))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28991,X28991)),hAPP(hAPP(c_Product__Type_OPair(X28991,X28991),X28990),X28989)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28991,X28991),tc_HOL_Obool),hAPP(c_Nat_OSuc,X28988)),X28987))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5344])])])]) ).

cnf(i_0_6350,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_5345]) ).

cnf(i_0_6351,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_5346]) ).

cnf(i_0_6352,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_5347]) ).

cnf(i_0_6353,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_5348]) ).

cnf(i_0_6354,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_5349]) ).

cnf(i_0_6355,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_5350]) ).

cnf(i_0_6356,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_5351]) ).

cnf(i_0_6357,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_5352]) ).

cnf(i_0_6358,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_5353]) ).

cnf(i_0_6359,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_5354]) ).

fof(i_0_6360,plain,
    ! [X19363,X19364,X19365] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X19365),X19364),X19363) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19365,tc_fun(tc_fun(X19365,tc_HOL_Obool),tc_HOL_Obool)),X19364),hAPP(hAPP(c_COMBC(X19365,tc_fun(tc_fun(X19365,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X19365,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19365,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X19365,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X19365,tc_HOL_Obool),tc_HOL_Obool)),X19365),c_Set_Oinsert(tc_fun(X19365,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X19365,tc_HOL_Obool),tc_fun(X19365,tc_HOL_Obool),X19365),c_Relation_OImage(X19365,X19365,X19363)),hAPP(hAPP(c_COMBC(X19365,tc_fun(X19365,tc_HOL_Obool),tc_fun(X19365,tc_HOL_Obool)),c_Set_Oinsert(X19365)),c_Orderings_Obot__class_Obot(tc_fun(X19365,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X19365,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_quotient__def]) ).

cnf(i_0_6361,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_5355]) ).

cnf(i_0_6362,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_5356]) ).

cnf(i_0_6363,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_5357]) ).

cnf(i_0_6364,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_5358]) ).

cnf(i_0_6365,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_5359]) ).

cnf(i_0_6366,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_5360]) ).

cnf(i_0_6367,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_5361]) ).

cnf(i_0_6368,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_5362]) ).

cnf(i_0_6369,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_5363]) ).

cnf(i_0_6370,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_6371,plain,
    ! [X20210,X20211,X20212,X20213,X20214] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X20212,X20214)),hAPP(hAPP(c_Product__Type_OPair(X20212,X20214),esk70_5(X20210,X20211,X20212,X20213,X20214)),X20213)),X20211))
        | ~ hBOOL(hAPP(hAPP(c_member(X20214),X20213),hAPP(c_Relation_OImage(X20212,X20214,X20211),X20210))) )
      & ( hBOOL(hAPP(hAPP(c_member(X20212),esk70_5(X20210,X20211,X20212,X20213,X20214)),X20210))
        | ~ hBOOL(hAPP(hAPP(c_member(X20214),X20213),hAPP(c_Relation_OImage(X20212,X20214,X20211),X20210))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5364])])])]) ).

fof(i_0_6372,plain,
    ! [X20001,X20002,X20003,X20004,X20005,X20007,X20008,X20009,X20010,X20011,X20012] :
      ( ( hBOOL(hAPP(hAPP(c_member(X20003),esk62_5(X20001,X20002,X20003,X20004,X20005)),X20001))
        | ~ hBOOL(hAPP(hAPP(c_member(X20005),X20004),hAPP(c_Relation_OImage(X20003,X20005,X20002),X20001))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X20003,X20005)),hAPP(hAPP(c_Product__Type_OPair(X20003,X20005),esk62_5(X20001,X20002,X20003,X20004,X20005)),X20004)),X20002))
        | ~ hBOOL(hAPP(hAPP(c_member(X20005),X20004),hAPP(c_Relation_OImage(X20003,X20005,X20002),X20001))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X20009),X20012),X20007))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20009,X20011)),hAPP(hAPP(c_Product__Type_OPair(X20009,X20011),X20012),X20010)),X20008))
        | hBOOL(hAPP(hAPP(c_member(X20011),X20010),hAPP(c_Relation_OImage(X20009,X20011,X20008),X20007))) ) ),
    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_6373,plain,
    ! [X21046,X21047,X21048,X21049] :
      ( ~ c_Finite__Set_Ofolding__one(X21049,X21048,X21047)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21049),X21046))
      | X21046 = c_Orderings_Obot__class_Obot(tc_fun(X21049,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X21049),hAPP(hAPP(X21048,esk84_4(X21046,X21047,X21048,X21049)),esk85_4(X21046,X21047,X21048,X21049))),hAPP(hAPP(c_Set_Oinsert(X21049),esk84_4(X21046,X21047,X21048,X21049)),hAPP(hAPP(c_Set_Oinsert(X21049),esk85_4(X21046,X21047,X21048,X21049)),c_Orderings_Obot__class_Obot(tc_fun(X21049,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X21049),hAPP(X21047,X21046)),X21046)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oclosed])])]) ).

cnf(i_0_6374,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_5365]) ).

cnf(i_0_6375,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_5366]) ).

cnf(i_0_6376,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_5292]) ).

fof(i_0_6377,plain,
    ! [X30469,X30470,X30471] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30471),hAPP(hAPP(c_List_Omap(tc_prod(X30471,X30470),X30471),c_Product__Type_Ofst(X30471,X30470)),X30469)))
      | hAPP(c_List_Oset(tc_prod(X30471,X30470)),X30469) = hAPP(c_Set_OCollect(tc_prod(X30471,X30470)),hAPP(c_Product__Type_Oprod_Oprod__case(X30471,X30470,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X30471,tc_fun(X30470,tc_Option_Ooption(X30470)),tc_fun(X30470,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X30470),tc_HOL_Obool),tc_fun(tc_fun(X30470,tc_Option_Ooption(X30470)),tc_fun(X30470,tc_HOL_Obool)),X30471),c_COMBB(tc_Option_Ooption(X30470),tc_HOL_Obool,X30470)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X30470),tc_fun(tc_Option_Ooption(X30470),tc_HOL_Obool),X30471),c_fequal),hAPP(c_Map_Omap__of(X30471,X30470),X30469)))),c_Option_Ooption_OSome(X30470)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__map__of__compr])]) ).

fof(i_0_6378,plain,
    ! [X18852,X18853,X18854,X18855] :
      ( ~ c_Fun_Oinj__on(X18855,tc_fun(tc_fun(X18855,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X18855,tc_fun(tc_prod(X18855,X18855),tc_HOL_Obool),tc_fun(tc_fun(X18855,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18855,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X18855,X18855),tc_HOL_Obool),tc_fun(tc_fun(X18855,tc_HOL_Obool),tc_HOL_Obool)),X18855),c_Equiv__Relations_Oquotient(X18855)),hAPP(hAPP(c_COMBC(X18855,tc_fun(X18855,tc_HOL_Obool),tc_fun(X18855,tc_HOL_Obool)),c_Set_Oinsert(X18855)),c_Orderings_Obot__class_Obot(tc_fun(X18855,tc_HOL_Obool))))),X18854),X18853)
      | ~ hBOOL(hAPP(hAPP(c_member(X18855),X18852),X18853))
      | hAPP(hAPP(c_Equiv__Relations_Oquotient(X18855),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18855,tc_HOL_Obool)),X18853),hAPP(hAPP(c_Set_Oinsert(X18855),X18852),c_Orderings_Obot__class_Obot(tc_fun(X18855,tc_HOL_Obool))))),X18854) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X18855,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X18855),X18853),X18854)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X18855),hAPP(hAPP(c_Set_Oinsert(X18855),X18852),c_Orderings_Obot__class_Obot(tc_fun(X18855,tc_HOL_Obool)))),X18854)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__diff1])]) ).

fof(i_0_6379,plain,
    ! [X29460,X29461,X29462,X29463] : hAPP(c_Set_OCollect(X29463),hAPP(hAPP(c_COMBB(tc_fun(X29462,tc_HOL_Obool),tc_HOL_Obool,X29463),c_HOL_OAll(X29462)),hAPP(hAPP(c_COMBB(tc_fun(X29462,tc_HOL_Obool),tc_fun(X29462,tc_HOL_Obool),X29463),hAPP(c_COMBS(X29462,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29462),c_fimplies),hAPP(hAPP(c_COMBC(X29462,tc_fun(X29462,tc_HOL_Obool),tc_HOL_Obool),c_member(X29462)),X29461)))),X29460))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29462,tc_fun(X29463,tc_HOL_Obool)),X29461),hAPP(hAPP(c_COMBB(tc_fun(X29463,tc_HOL_Obool),tc_fun(X29463,tc_HOL_Obool),X29462),c_Set_OCollect(X29463)),hAPP(c_COMBC(X29463,X29462,tc_HOL_Obool),X29460))),
    inference(variable_rename,[status(thm)],[fact_Collect__ball__eq]) ).

fof(i_0_6380,plain,
    ! [X31703,X31704,X31705,X31706] : c_List_Osublist(X31706,hAPP(hAPP(c_List_Oappend(X31706),X31705),X31704),X31703) = hAPP(hAPP(c_List_Oappend(X31706),c_List_Osublist(X31706,X31705,X31703)),c_List_Osublist(X31706,X31704,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(X31706)),X31705)))),X31703)))),
    inference(variable_rename,[status(thm)],[fact_sublist__append]) ).

fof(i_0_6381,plain,
    ! [X33411,X33412,X33413,X33414,X33415] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33415)),hAPP(hAPP(c_List_Otake(X33415),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33415)),X33414)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33413)),X33412))),X33414)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33413)),hAPP(hAPP(c_List_Otake(X33413),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33415)),X33414)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33413)),X33412))),X33412))
        | hBOOL(hAPP(X33411,hAPP(hAPP(c_List_Ozip(X33415,X33413),X33414),X33412))) )
      & ( ~ hBOOL(hAPP(X33411,hAPP(hAPP(c_List_Ozip(X33415,X33413),hAPP(hAPP(c_List_Otake(X33415),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33415)),X33414)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33413)),X33412))),X33414)),hAPP(hAPP(c_List_Otake(X33413),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33415)),X33414)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33413)),X33412))),X33412))))
        | hBOOL(hAPP(X33411,hAPP(hAPP(c_List_Ozip(X33415,X33413),X33414),X33412))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__obtain__same__length])])]) ).

cnf(i_0_6382,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_5367]) ).

cnf(i_0_6383,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_5368]) ).

cnf(i_0_6384,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_5369]) ).

cnf(i_0_6385,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_5370]) ).

cnf(i_0_6386,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_5371]) ).

cnf(i_0_6387,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_5372]) ).

fof(i_0_6388,plain,
    ! [X32410,X32411,X32412,X32413,X32414] : hAPP(hAPP(c_List_Omap(X32414,X32413),X32412),hAPP(c_List_Ofilter(X32414,X32411),X32410)) = c_List_Omap__filter(X32414,X32413,hAPP(hAPP(c_COMBC(X32414,tc_Option_Ooption(X32413),tc_Option_Ooption(X32413)),hAPP(hAPP(c_COMBS(X32414,tc_Option_Ooption(X32413),tc_fun(tc_Option_Ooption(X32413),tc_Option_Ooption(X32413))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X32413),tc_fun(tc_Option_Ooption(X32413),tc_Option_Ooption(X32413))),X32414),c_If(tc_Option_Ooption(X32413))),X32411)),hAPP(hAPP(c_COMBB(X32413,tc_Option_Ooption(X32413),X32414),c_Option_Ooption_OSome(X32413)),X32412))),c_Option_Ooption_ONone(X32413)),X32410),
    inference(variable_rename,[status(thm)],[fact_map__filter__map__filter]) ).

fof(i_0_6389,plain,
    ! [X21249,X21250,X21251] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21251),X21250))
      | ~ c_Fun_Oinj__on(X21251,tc_fun(tc_fun(X21251,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X21251,tc_fun(tc_prod(X21251,X21251),tc_HOL_Obool),tc_fun(tc_fun(X21251,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21251,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X21251,X21251),tc_HOL_Obool),tc_fun(tc_fun(X21251,tc_HOL_Obool),tc_HOL_Obool)),X21251),c_Equiv__Relations_Oquotient(X21251)),hAPP(hAPP(c_COMBC(X21251,tc_fun(X21251,tc_HOL_Obool),tc_fun(X21251,tc_HOL_Obool)),c_Set_Oinsert(X21251)),c_Orderings_Obot__class_Obot(tc_fun(X21251,tc_HOL_Obool))))),X21249),X21250)
      | hAPP(c_Finite__Set_Ocard(tc_fun(X21251,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X21251),X21250),X21249)) = hAPP(c_Finite__Set_Ocard(X21251),X21250) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__quotient__disjoint])]) ).

fof(i_0_6390,plain,
    ! [X19001,X19002,X19003,X19004,X19005] : c_Map_Odom(X19005,X19004,hAPP(hAPP(c_COMBS(X19005,tc_Option_Ooption(X19004),tc_Option_Ooption(X19004)),hAPP(hAPP(c_COMBS(X19005,tc_Option_Ooption(X19004),tc_fun(tc_Option_Ooption(X19004),tc_Option_Ooption(X19004))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X19004),tc_fun(tc_Option_Ooption(X19004),tc_Option_Ooption(X19004))),X19005),c_If(tc_Option_Ooption(X19004))),X19003)),X19002)),X19001)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19005,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19005,tc_HOL_Obool)),c_Map_Odom(X19005,X19004,X19002)),hAPP(c_Set_OCollect(X19005),X19003))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19005,tc_HOL_Obool)),c_Map_Odom(X19005,X19004,X19001)),hAPP(c_Set_OCollect(X19005),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X19005),c_fNot),X19003)))),
    inference(variable_rename,[status(thm)],[fact_dom__if]) ).

fof(i_0_6391,plain,
    ! [X32322,X32323,X32324,X32325] : c_List_Omap__filter(X32325,X32324,X32323,X32322) = hAPP(hAPP(c_List_Omap(X32325,X32324),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X32324),X32324,X32325,c_Option_Othe(X32324)),X32323)),hAPP(c_List_Ofilter(X32325,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32325),c_fNot),hAPP(hAPP(c_COMBC(X32325,tc_Option_Ooption(X32324),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X32324),tc_fun(tc_Option_Ooption(X32324),tc_HOL_Obool),X32325),c_fequal),X32323)),c_Option_Ooption_ONone(X32324)))),X32322)),
    inference(variable_rename,[status(thm)],[fact_map__filter__def]) ).

fof(i_0_6392,plain,
    ! [X26690,X26691,X26692,X26693] :
      ( ~ class_Rings_Ocomm__semiring__1(X26693)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26693),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26693),c_Groups_Oone__class_Oone(X26693)),c_Groups_Oone__class_Oone(X26693))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26693),hAPP(hAPP(c_COMBB(X26693,X26693,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X26693),X26692)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X26693,X26693),hAPP(hAPP(c_COMBB(X26693,tc_fun(X26693,X26693),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X26693)),c_Nat_Osemiring__1__class_Oof__nat(X26693))),X26691))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26690))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26693),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26693),X26690)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26693),X26692),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26693),X26692),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26693),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26693),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26690),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X26691)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__series__general])]) ).

cnf(i_0_6393,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_5373]) ).

fof(i_0_6394,plain,
    ! [X27475,X27476] :
      ( ( c_Wellfounded_Owf(X27476,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X27476,X27476),tc_HOL_Obool),tc_fun(tc_prod(X27476,X27476),tc_HOL_Obool)),X27475))
        | ~ c_FunDef_Oreduction__pair(X27476,X27475) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27476,X27476),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27476,X27476,X27476),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X27476,X27476),tc_HOL_Obool),tc_fun(tc_prod(X27476,X27476),tc_HOL_Obool)),X27475)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X27476,X27476),tc_HOL_Obool),tc_fun(tc_prod(X27476,X27476),tc_HOL_Obool)),X27475))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X27476,X27476),tc_HOL_Obool),tc_fun(tc_prod(X27476,X27476),tc_HOL_Obool)),X27475)))
        | ~ c_FunDef_Oreduction__pair(X27476,X27475) )
      & ( ~ c_Wellfounded_Owf(X27476,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X27476,X27476),tc_HOL_Obool),tc_fun(tc_prod(X27476,X27476),tc_HOL_Obool)),X27475))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27476,X27476),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27476,X27476,X27476),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X27476,X27476),tc_HOL_Obool),tc_fun(tc_prod(X27476,X27476),tc_HOL_Obool)),X27475)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X27476,X27476),tc_HOL_Obool),tc_fun(tc_prod(X27476,X27476),tc_HOL_Obool)),X27475))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X27476,X27476),tc_HOL_Obool),tc_fun(tc_prod(X27476,X27476),tc_HOL_Obool)),X27475)))
        | c_FunDef_Oreduction__pair(X27476,X27475) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduction__pair__def])])]) ).

cnf(i_0_6395,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_5374]) ).

cnf(i_0_6396,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_5375]) ).

cnf(i_0_6397,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_5376]) ).

fof(i_0_6398,plain,
    ! [X19685,X19686,X19687,X19688,X19689,X19690,X19691,X19692,X19693,X19694,X19695] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19689,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19688,tc_fun(X19689,tc_HOL_Obool)),X19687),X19686)),X19685))
        | ~ hBOOL(hAPP(hAPP(c_member(X19688),X19690),X19687))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19689,tc_HOL_Obool)),hAPP(X19686,X19690)),X19685)) )
      & ( hBOOL(hAPP(hAPP(c_member(X19694),esk53_5(X19691,X19692,X19693,X19694,X19695)),X19693))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19695,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19694,tc_fun(X19695,tc_HOL_Obool)),X19693),X19692)),X19691)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19695,tc_HOL_Obool)),hAPP(X19692,esk53_5(X19691,X19692,X19693,X19694,X19695))),X19691))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19695,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19694,tc_fun(X19695,tc_HOL_Obool)),X19693),X19692)),X19691)) ) ),
    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_6399,plain,
    ! [X26700,X26701,X26702,X26703,X26704] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26703),esk230_5(X26700,X26701,X26702,X26703,X26704)),X26702))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26704),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26703,X26704),X26701),X26702)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26704),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26704),hAPP(c_Finite__Set_Ocard(X26703),X26702))),X26700)))
        | ~ class_Groups_Oordered__ab__semigroup__add(X26704)
        | ~ class_Rings_Osemiring__1(X26704) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26704),hAPP(X26701,esk230_5(X26700,X26701,X26702,X26703,X26704))),X26700))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26704),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26703,X26704),X26701),X26702)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26704),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26704),hAPP(c_Finite__Set_Ocard(X26703),X26702))),X26700)))
        | ~ class_Groups_Oordered__ab__semigroup__add(X26704)
        | ~ class_Rings_Osemiring__1(X26704) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__bounded])])])]) ).

cnf(i_0_6400,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_5377]) ).

fof(i_0_6401,plain,
    ! [X28078,X28079,X28080,X28081,X28082,X28083] : c_Product__Type_Omap__pair(X28083,X28082,X28081,X28080,X28079,X28078) = hAPP(c_Product__Type_Oprod_Oprod__case(X28083,X28081,tc_prod(X28082,X28080)),hAPP(hAPP(c_COMBC(X28083,tc_fun(X28081,X28080),tc_fun(X28081,tc_prod(X28082,X28080))),hAPP(hAPP(c_COMBB(tc_fun(X28080,tc_prod(X28082,X28080)),tc_fun(tc_fun(X28081,X28080),tc_fun(X28081,tc_prod(X28082,X28080))),X28083),c_COMBB(X28080,tc_prod(X28082,X28080),X28081)),hAPP(hAPP(c_COMBB(X28082,tc_fun(X28080,tc_prod(X28082,X28080)),X28083),c_Product__Type_OPair(X28082,X28080)),X28079))),X28078)),
    inference(variable_rename,[status(thm)],[fact_map__pair__def]) ).

fof(i_0_6402,plain,
    ! [X17761,X17762,X17763,X17764,X17765] :
      ( ( hBOOL(hAPP(hAPP(c_member(X17765),esk22_5(X17761,X17762,X17763,X17764,X17765)),X17764))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17763,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17765,X17763,X17762),X17764)),X17761)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17763),hAPP(X17762,esk22_5(X17761,X17762,X17763,X17764,X17765))),X17761))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17763,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17765,X17763,X17762),X17764)),X17761)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__subsetI])])])]) ).

fof(i_0_6403,plain,
    ! [X26995,X26996,X26997] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26997))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26996),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),X26996),X26995))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26997))),X26995)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_decr__lemma])]) ).

fof(i_0_6404,plain,
    ! [X19628,X19629,X19630,X19631,X19632,X19633] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19632),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19631,X19632),X19630),X19629)),X19628))
        | ~ hBOOL(hAPP(hAPP(c_member(X19631),X19633),X19630))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19632),hAPP(X19629,X19633)),X19628))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X19632) )
      & ( hBOOL(hAPP(hAPP(c_member(X19631),esk48_5(X19628,X19629,X19630,X19631,X19632)),X19630))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19632),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19631,X19632),X19630),X19629)),X19628))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X19632) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19632),hAPP(X19629,esk48_5(X19628,X19629,X19630,X19631,X19632))),X19628))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19632),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19631,X19632),X19630),X19629)),X19628))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X19632) ) ),
    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_6405,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_5333]) ).

cnf(i_0_6406,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_6407,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_6408,plain,
    ! [X33743,X33744] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X33744)),X33743) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X33744,tc_Lazy__Sequence_Olazy__sequence(X33744)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X33744,tc_Lazy__Sequence_Olazy__sequence(X33744),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33744),tc_Nat_Onat),X33744),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X33744),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(X33744)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X33744)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(c_Lazy__Sequence_Oyield(X33744),X33743)),
    inference(variable_rename,[status(thm)],[fact_size__code]) ).

fof(i_0_6409,plain,
    ! [X31051,X31052,X31053,X31054,X31056,X31057,X31058,X31059,X31060] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk418_4(X31051,X31052,X31053,X31054)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31054)),X31053)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31054)),X31052))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31054)),X31053)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31054)),X31052)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31054),tc_List_Olist(X31054))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31054),tc_List_Olist(X31054)),X31053),X31052)),c_List_Olexord(X31054,X31051))) )
      & ( hAPP(hAPP(c_List_Otake(X31054),esk418_4(X31051,X31052,X31053,X31054)),X31053) = hAPP(hAPP(c_List_Otake(X31054),esk418_4(X31051,X31052,X31053,X31054)),X31052)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31054)),X31053)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31054)),X31052)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31054),tc_List_Olist(X31054))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31054),tc_List_Olist(X31054)),X31053),X31052)),c_List_Olexord(X31054,X31051))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X31054,X31054)),hAPP(hAPP(c_Product__Type_OPair(X31054,X31054),hAPP(hAPP(c_List_Onth(X31054),X31053),esk418_4(X31051,X31052,X31053,X31054))),hAPP(hAPP(c_List_Onth(X31054),X31052),esk418_4(X31051,X31052,X31053,X31054)))),X31051))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31054)),X31053)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31054)),X31052)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31054),tc_List_Olist(X31054))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31054),tc_List_Olist(X31054)),X31053),X31052)),c_List_Olexord(X31054,X31051))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk418_4(X31051,X31052,X31053,X31054)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31054)),X31053)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31054)),X31052))))
        | hAPP(hAPP(c_List_Otake(X31054),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31054)),X31053)),X31052) = X31053
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31054),tc_List_Olist(X31054))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31054),tc_List_Olist(X31054)),X31053),X31052)),c_List_Olexord(X31054,X31051))) )
      & ( hAPP(hAPP(c_List_Otake(X31054),esk418_4(X31051,X31052,X31053,X31054)),X31053) = hAPP(hAPP(c_List_Otake(X31054),esk418_4(X31051,X31052,X31053,X31054)),X31052)
        | hAPP(hAPP(c_List_Otake(X31054),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31054)),X31053)),X31052) = X31053
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31054),tc_List_Olist(X31054))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31054),tc_List_Olist(X31054)),X31053),X31052)),c_List_Olexord(X31054,X31051))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X31054,X31054)),hAPP(hAPP(c_Product__Type_OPair(X31054,X31054),hAPP(hAPP(c_List_Onth(X31054),X31053),esk418_4(X31051,X31052,X31053,X31054))),hAPP(hAPP(c_List_Onth(X31054),X31052),esk418_4(X31051,X31052,X31053,X31054)))),X31051))
        | hAPP(hAPP(c_List_Otake(X31054),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31054)),X31053)),X31052) = X31053
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31054),tc_List_Olist(X31054))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31054),tc_List_Olist(X31054)),X31053),X31052)),c_List_Olexord(X31054,X31051))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31059)),X31058)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31059)),X31057)))
        | hAPP(hAPP(c_List_Otake(X31059),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31059)),X31058)),X31057) != X31058
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31059),tc_List_Olist(X31059))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31059),tc_List_Olist(X31059)),X31058),X31057)),c_List_Olexord(X31059,X31056))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31060),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31059)),X31058)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31059)),X31057))))
        | hAPP(hAPP(c_List_Otake(X31059),X31060),X31058) != hAPP(hAPP(c_List_Otake(X31059),X31060),X31057)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31059,X31059)),hAPP(hAPP(c_Product__Type_OPair(X31059,X31059),hAPP(hAPP(c_List_Onth(X31059),X31058),X31060)),hAPP(hAPP(c_List_Onth(X31059),X31057),X31060))),X31056))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31059),tc_List_Olist(X31059))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31059),tc_List_Olist(X31059)),X31058),X31057)),c_List_Olexord(X31059,X31056))) ) ),
    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_6410,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_5378]) ).

fof(i_0_6411,plain,
    ! [X27834,X27835,X27836,X27837] : hAPP(c_Set_OCollect(tc_prod(X27837,X27836)),hAPP(c_Product__Type_Oprod_Oprod__case(X27837,X27836,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X27837,tc_fun(X27836,tc_HOL_Obool),tc_fun(X27836,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27836,tc_HOL_Obool),tc_fun(X27836,tc_HOL_Obool)),X27837),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27836)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27837),c_fconj),X27835))),X27834))) = hAPP(hAPP(c_Product__Type_OSigma(X27837,X27836),hAPP(c_Set_OCollect(X27837),X27835)),hAPP(hAPP(c_COMBB(tc_fun(X27836,tc_HOL_Obool),tc_fun(X27836,tc_HOL_Obool),X27837),c_Set_OCollect(X27836)),X27834)),
    inference(variable_rename,[status(thm)],[fact_SetCompr__Sigma__eq]) ).

fof(i_0_6412,plain,
    ! [X22516,X22517] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22517))
      | 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)),X22517))),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,X22516))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__less])]) ).

fof(i_0_6413,plain,
    ! [X28320,X28321,X28322,X28323] : c_Hilbert__Choice_OEps(tc_prod(X28323,X28322),hAPP(c_Product__Type_Oprod_Oprod__case(X28323,X28322,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28323,tc_fun(X28322,tc_HOL_Obool),tc_fun(X28322,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X28322,tc_HOL_Obool),tc_fun(X28322,tc_HOL_Obool)),X28323),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X28322)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28323),c_fconj),hAPP(c_fequal,X28321)))),hAPP(c_fequal,X28320)))) = hAPP(hAPP(c_Product__Type_OPair(X28323,X28322),X28321),X28320),
    inference(variable_rename,[status(thm)],[fact_Eps__split__eq]) ).

fof(i_0_6414,plain,
    ! [X23846,X23847,X23848,X23849] : c_HOL_OThe(tc_prod(X23849,X23848),hAPP(c_Product__Type_Oprod_Oprod__case(X23849,X23848,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X23849,tc_fun(X23848,tc_HOL_Obool),tc_fun(X23848,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X23848,tc_HOL_Obool),tc_fun(X23848,tc_HOL_Obool)),X23849),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X23848)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X23849),c_fconj),hAPP(c_fequal,X23847)))),hAPP(c_fequal,X23846)))) = hAPP(hAPP(c_Product__Type_OPair(X23849,X23848),X23847),X23846),
    inference(variable_rename,[status(thm)],[fact_The__split__eq]) ).

cnf(i_0_6415,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_5367]) ).

fof(i_0_6416,plain,
    ! [X26471,X26472,X26473,X26474,X26475,X26476] :
      ( ~ class_Groups_Ocomm__monoid__add(X26476)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26475,X26476),hAPP(hAPP(c_COMBC(X26475,tc_fun(X26474,tc_HOL_Obool),X26476),hAPP(hAPP(c_COMBB(tc_fun(X26474,X26476),tc_fun(tc_fun(X26474,tc_HOL_Obool),X26476),X26475),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26474,X26476)),X26473)),X26472)),X26471) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26474,X26476),hAPP(hAPP(c_COMBC(X26474,tc_fun(X26475,tc_HOL_Obool),X26476),hAPP(hAPP(c_COMBB(tc_fun(X26475,X26476),tc_fun(tc_fun(X26475,tc_HOL_Obool),X26476),X26474),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26475,X26476)),hAPP(c_COMBC(X26475,X26474,X26476),X26473))),X26471)),X26472) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__commute])]) ).

fof(i_0_6417,plain,
    ! [X27838,X27839,X27840,X27841] : hAPP(c_Set_OCollect(tc_prod(X27841,X27840)),hAPP(c_Product__Type_Oprod_Oprod__case(X27841,X27840,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X27841,tc_fun(X27840,tc_HOL_Obool),tc_fun(X27840,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27840,tc_HOL_Obool),tc_fun(X27840,tc_HOL_Obool)),X27841),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27840)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27841),c_fconj),X27839))),X27838))) = hAPP(hAPP(c_Product__Type_OSigma(X27841,X27840),hAPP(c_Set_OCollect(X27841),X27839)),hAPP(c_COMBK(tc_fun(X27840,tc_HOL_Obool),X27841),hAPP(c_Set_OCollect(X27840),X27838))),
    inference(variable_rename,[status(thm)],[fact_Collect__split]) ).

fof(i_0_6418,plain,
    ! [X21155,X21156,X21157,X21158] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21158),X21157))
      | hAPP(c_Set_Oimage(X21158,X21156,X21155),X21157) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X21156,tc_HOL_Obool),X21158,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21156,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X21158,tc_fun(X21156,tc_HOL_Obool),tc_fun(X21156,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X21156,tc_fun(tc_fun(X21156,tc_HOL_Obool),tc_fun(X21156,tc_HOL_Obool)),X21158),c_Set_Oinsert(X21156)),X21155)),c_Orderings_Obot__class_Obot(tc_fun(X21156,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X21156,tc_HOL_Obool))),X21157) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eq__fold__image])]) ).

cnf(i_0_6419,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_5379]) ).

fof(i_0_6420,plain,
    ! [X21162,X21163,X21164,X21165] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21165),X21164))
      | ~ hBOOL(hAPP(hAPP(c_member(X21165),X21163),X21164))
      | ~ hBOOL(hAPP(hAPP(c_member(X21165),X21162),X21164))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21165),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21165,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21165,tc_HOL_Obool)),X21164),hAPP(hAPP(c_Set_Oinsert(X21165),X21163),c_Orderings_Obot__class_Obot(tc_fun(X21165,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X21165),X21162),c_Orderings_Obot__class_Obot(tc_fun(X21165,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X21165),X21164))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff2__less])]) ).

cnf(i_0_6421,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_5380]) ).

fof(i_0_6422,plain,
    ! [X23841,X23842] : c_Relation_OId__on(X23842,X23841) = hAPP(c_Product__Type_Oprod_Oprod__case(X23842,X23842,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X23842,tc_HOL_Obool,tc_fun(X23842,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23842,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X23842,tc_HOL_Obool)),X23842),c_COMBC(X23842,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23842,tc_HOL_Obool),tc_fun(X23842,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X23842),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X23842),c_fconj)),c_fequal))),X23841)),
    inference(variable_rename,[status(thm)],[fact_Id__on__def_H]) ).

fof(i_0_6423,plain,
    ! [X23982] : c_Int_Oint__ge__less__than(X23982) = 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),X23982)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[fact_int__ge__less__than__def]) ).

fof(i_0_6424,plain,
    ! [X28414,X28415,X28416,X28417,X28418,X28419,X28420,X28421,X28422] : hAPP(hAPP(c_Product__Type_Oscomp(X28422,X28421,X28420,X28419),hAPP(hAPP(c_Product__Type_Oscomp(X28422,X28418,X28417,tc_prod(X28421,X28420)),X28416),X28415)),X28414) = hAPP(hAPP(c_Product__Type_Oscomp(X28422,X28418,X28417,X28419),X28416),hAPP(hAPP(c_COMBC(X28418,tc_fun(X28421,tc_fun(X28420,X28419)),tc_fun(X28417,X28419)),hAPP(hAPP(c_COMBB(tc_fun(X28417,tc_prod(X28421,X28420)),tc_fun(tc_fun(X28421,tc_fun(X28420,X28419)),tc_fun(X28417,X28419)),X28418),c_Product__Type_Oscomp(X28417,X28421,X28420,X28419)),X28415)),X28414)),
    inference(variable_rename,[status(thm)],[fact_scomp__scomp]) ).

fof(i_0_6425,plain,
    ! [X24500,X24501,X24502,X24503] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X24503),X24502))
      | ~ 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)),X24501),X24503)),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)),X24500),X24502)),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)),X24501),X24500)),X24502)),c_FunDef_Omax__weak)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wmax__insertI])]) ).

fof(i_0_6426,plain,
    ! [X24484,X24485,X24486,X24487] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X24487),X24486))
      | ~ 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)),X24485),X24487)),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)),X24484),X24486)),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)),X24485),X24484)),X24486)),c_FunDef_Omax__strict)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smax__insertI])]) ).

cnf(i_0_6427,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_5352]) ).

cnf(i_0_6428,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_5353]) ).

fof(i_0_6429,plain,
    ! [X32748,X32749,X32750,X32751,X32752] :
      ( ~ class_Orderings_Olinorder(X32752)
      | c_List_Olinorder__class_Osorted(X32752,hAPP(hAPP(c_List_Omap(X32751,X32752),X32750),hAPP(c_List_Ofilter(X32751,hAPP(hAPP(c_COMBC(X32751,X32752,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X32752,tc_fun(X32752,tc_HOL_Obool),X32751),c_fequal),X32750)),hAPP(X32749,X32748))),X32748))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__map__same])]) ).

fof(i_0_6430,plain,
    ! [X30880,X30881,X30882,X30883,X30884] :
      ( ( X30881 = hAPP(hAPP(c_List_Olist_OCons(X30884),esk406_5(X30880,X30881,X30882,X30883,X30884)),esk407_5(X30880,X30881,X30882,X30883,X30884))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30884),tc_List_Olist(X30884))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30884),tc_List_Olist(X30884)),hAPP(hAPP(c_List_Olist_OCons(X30884),X30883),X30882)),X30881)),c_List_Olistrel(X30884,X30880))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30884,X30884)),hAPP(hAPP(c_Product__Type_OPair(X30884,X30884),X30883),esk406_5(X30880,X30881,X30882,X30883,X30884))),X30880))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30884),tc_List_Olist(X30884))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30884),tc_List_Olist(X30884)),hAPP(hAPP(c_List_Olist_OCons(X30884),X30883),X30882)),X30881)),c_List_Olistrel(X30884,X30880))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30884),tc_List_Olist(X30884))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30884),tc_List_Olist(X30884)),X30882),esk407_5(X30880,X30881,X30882,X30883,X30884))),c_List_Olistrel(X30884,X30880)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30884),tc_List_Olist(X30884))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30884),tc_List_Olist(X30884)),hAPP(hAPP(c_List_Olist_OCons(X30884),X30883),X30882)),X30881)),c_List_Olistrel(X30884,X30880))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5381])])])]) ).

cnf(i_0_6431,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_5382]) ).

cnf(i_0_6432,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_5383]) ).

fof(i_0_6433,plain,
    ! [X28363,X28364,X28365,X28366,X28367,X28369,X28370,X28371,X28372,X28374] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X28366),X28365))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28366,tc_HOL_Obool),tc_fun(X28366,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28366,tc_HOL_Obool),tc_fun(X28366,tc_HOL_Obool)),X28365),X28364)),c_Wellfounded_Omax__ext(X28366,X28363))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X28366),X28364))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28366,tc_HOL_Obool),tc_fun(X28366,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28366,tc_HOL_Obool),tc_fun(X28366,tc_HOL_Obool)),X28365),X28364)),c_Wellfounded_Omax__ext(X28366,X28363))) )
      & ( X28364 != c_Orderings_Obot__class_Obot(tc_fun(X28366,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28366,tc_HOL_Obool),tc_fun(X28366,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28366,tc_HOL_Obool),tc_fun(X28366,tc_HOL_Obool)),X28365),X28364)),c_Wellfounded_Omax__ext(X28366,X28363))) )
      & ( hBOOL(hAPP(hAPP(c_member(X28366),esk317_5(X28363,X28364,X28365,X28366,X28367)),X28364))
        | ~ hBOOL(hAPP(hAPP(c_member(X28366),X28367),X28365))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28366,tc_HOL_Obool),tc_fun(X28366,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28366,tc_HOL_Obool),tc_fun(X28366,tc_HOL_Obool)),X28365),X28364)),c_Wellfounded_Omax__ext(X28366,X28363))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28366,X28366)),hAPP(hAPP(c_Product__Type_OPair(X28366,X28366),X28367),esk317_5(X28363,X28364,X28365,X28366,X28367))),X28363))
        | ~ hBOOL(hAPP(hAPP(c_member(X28366),X28367),X28365))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28366,tc_HOL_Obool),tc_fun(X28366,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28366,tc_HOL_Obool),tc_fun(X28366,tc_HOL_Obool)),X28365),X28364)),c_Wellfounded_Omax__ext(X28366,X28363))) )
      & ( hBOOL(hAPP(hAPP(c_member(X28372),esk318_4(X28369,X28370,X28371,X28372)),X28371))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28372),X28371))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28372),X28370))
        | X28370 = c_Orderings_Obot__class_Obot(tc_fun(X28372,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28372,tc_HOL_Obool),tc_fun(X28372,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28372,tc_HOL_Obool),tc_fun(X28372,tc_HOL_Obool)),X28371),X28370)),c_Wellfounded_Omax__ext(X28372,X28369))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28372),X28374),X28370))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28372,X28372)),hAPP(hAPP(c_Product__Type_OPair(X28372,X28372),esk318_4(X28369,X28370,X28371,X28372)),X28374)),X28369))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28372),X28371))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28372),X28370))
        | X28370 = c_Orderings_Obot__class_Obot(tc_fun(X28372,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28372,tc_HOL_Obool),tc_fun(X28372,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28372,tc_HOL_Obool),tc_fun(X28372,tc_HOL_Obool)),X28371),X28370)),c_Wellfounded_Omax__ext(X28372,X28369))) ) ),
    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_6434,plain,
    ! [X27457,X27458,X27459] :
      ( ( ~ c_Wellfounded_Owf(X27459,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27459,X27459),tc_HOL_Obool)),X27458),X27457))
        | c_Wellfounded_Owf(X27459,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27459,X27459),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27459,X27459),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27459,X27459,X27459),X27458),X27458)),hAPP(hAPP(c_Relation_Orel__comp(X27459,X27459,X27459),X27457),X27458))),X27457)) )
      & ( ~ c_Wellfounded_Owf(X27459,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27459,X27459),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27459,X27459),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27459,X27459,X27459),X27458),X27458)),hAPP(hAPP(c_Relation_Orel__comp(X27459,X27459,X27459),X27457),X27458))),X27457))
        | c_Wellfounded_Owf(X27459,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27459,X27459),tc_HOL_Obool)),X27458),X27457)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__union__merge])]) ).

fof(i_0_6435,plain,
    ! [X28084,X28085,X28086,X28087,X28088,X28089,X28090,X28091,X28092,X28093] :
      ( hAPP(c_Set_Oimage(X28093,X28092,X28091),X28090) != X28089
      | hAPP(c_Set_Oimage(X28088,X28087,X28086),X28085) != X28084
      | hAPP(c_Set_Oimage(tc_prod(X28093,X28088),tc_prod(X28092,X28087),c_Product__Type_Omap__pair(X28093,X28092,X28088,X28087,X28091,X28086)),hAPP(hAPP(c_Product__Type_OSigma(X28093,X28088),X28090),hAPP(c_COMBK(tc_fun(X28088,tc_HOL_Obool),X28093),X28085))) = hAPP(hAPP(c_Product__Type_OSigma(X28092,X28087),X28089),hAPP(c_COMBK(tc_fun(X28087,tc_HOL_Obool),X28092),X28084)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__surj__on])]) ).

fof(i_0_6436,plain,
    ! [X24504,X24505,X24506,X24507] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X24507),X24506))
      | ~ 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)),X24507),X24505)),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)),X24506),X24504)),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)),X24506),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X24505),X24504))),c_FunDef_Omin__weak)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wmin__insertI])]) ).

fof(i_0_6437,plain,
    ! [X24480,X24481,X24482,X24483] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X24483),X24482))
      | ~ 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)),X24483),X24481)),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)),X24482),X24480)),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)),X24482),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X24481),X24480))),c_FunDef_Omin__strict)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smin__insertI])]) ).

fof(i_0_6438,plain,
    ! [X19866,X19867,X19868,X19869,X19870,X19873,X19874,X19875,X19876,X19877,X19878,X19879] :
      ( ( hAPP(hAPP(c_Set_Oinsert(X19870),X19868),X19867) = hAPP(hAPP(c_Set_Oinsert(X19870),esk59_5(X19866,X19867,X19868,X19869,X19870)),esk60_5(X19866,X19867,X19868,X19869,X19870))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X19870,X19869,hAPP(hAPP(c_Set_Oinsert(X19870),X19868),X19867)),X19866)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19870,X19870,X19869,esk59_5(X19866,X19867,X19868,X19869,X19870),esk60_5(X19866,X19867,X19868,X19869,X19870)),X19866))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X19870,X19869,hAPP(hAPP(c_Set_Oinsert(X19870),X19868),X19867)),X19866)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X19870),esk59_5(X19866,X19867,X19868,X19869,X19870)),esk60_5(X19866,X19867,X19868,X19869,X19870)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X19870,X19869,hAPP(hAPP(c_Set_Oinsert(X19870),X19868),X19867)),X19866)) )
      & ( hAPP(hAPP(c_Set_Oinsert(X19877),X19875),X19874) != hAPP(hAPP(c_Set_Oinsert(X19877),X19878),X19879)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19877,X19877,X19876,X19878,X19879),X19873))
        | hBOOL(hAPP(hAPP(c_member(X19877),X19878),X19879))
        | hBOOL(hAPP(c_Finite__Set_Ofold1Set(X19877,X19876,hAPP(hAPP(c_Set_Oinsert(X19877),X19875),X19874)),X19873)) ) ),
    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_5384])])])])])]) ).

fof(i_0_6439,plain,
    ! [X19859,X19860,X19861,X19862,X19863] :
      ( ( hAPP(hAPP(c_Set_Oinsert(X19863),X19861),X19860) = hAPP(hAPP(c_Set_Oinsert(X19863),esk57_5(X19859,X19860,X19861,X19862,X19863)),esk58_5(X19859,X19860,X19861,X19862,X19863))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X19863,X19862,hAPP(hAPP(c_Set_Oinsert(X19863),X19861),X19860)),X19859)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19863,X19863,X19862,esk57_5(X19859,X19860,X19861,X19862,X19863),esk58_5(X19859,X19860,X19861,X19862,X19863)),X19859))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X19863,X19862,hAPP(hAPP(c_Set_Oinsert(X19863),X19861),X19860)),X19859)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X19863),esk57_5(X19859,X19860,X19861,X19862,X19863)),esk58_5(X19859,X19860,X19861,X19862,X19863)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X19863,X19862,hAPP(hAPP(c_Set_Oinsert(X19863),X19861),X19860)),X19859)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__fold1SetE])])])]) ).

fof(i_0_6440,plain,
    ! [X31215,X31216,X31217,X31218,X31221,X31222,X31223,X31224,X31225,X31226] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X31218,X31218)),hAPP(hAPP(c_Product__Type_OPair(X31218,X31218),hAPP(hAPP(c_List_Onth(X31218),X31217),esk420_4(X31215,X31216,X31217,X31218))),esk419_4(X31215,X31216,X31217,X31218))),X31215))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31218),tc_List_Olist(X31218))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31218),tc_List_Olist(X31218)),X31217),X31216)),c_List_Olistrel1(X31218,X31215))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk420_4(X31215,X31216,X31217,X31218)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31218)),X31217)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31218),tc_List_Olist(X31218))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31218),tc_List_Olist(X31218)),X31217),X31216)),c_List_Olistrel1(X31218,X31215))) )
      & ( X31216 = hAPP(hAPP(c_List_Olist__update(X31218,X31217),esk420_4(X31215,X31216,X31217,X31218)),esk419_4(X31215,X31216,X31217,X31218))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31218),tc_List_Olist(X31218))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31218),tc_List_Olist(X31218)),X31217),X31216)),c_List_Olistrel1(X31218,X31215))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31224,X31224)),hAPP(hAPP(c_Product__Type_OPair(X31224,X31224),hAPP(hAPP(c_List_Onth(X31224),X31223),X31226)),X31225)),X31221))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31226),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31224)),X31223)))
        | X31222 != hAPP(hAPP(c_List_Olist__update(X31224,X31223),X31226),X31225)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31224),tc_List_Olist(X31224))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31224),tc_List_Olist(X31224)),X31223),X31222)),c_List_Olistrel1(X31224,X31221))) ) ),
    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_6441,plain,
    ! [X27983,X27984,X27985,X27986,X27987,X27988] :
      ( hAPP(c_Set_Oimage(X27988,X27987,X27986),c_Orderings_Otop__class_Otop(tc_fun(X27988,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X27987,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(X27985,X27984,X27983),c_Orderings_Otop__class_Otop(tc_fun(X27985,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X27984,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(tc_prod(X27988,X27985),tc_prod(X27987,X27984),c_Product__Type_Omap__pair(X27988,X27987,X27985,X27984,X27986,X27983)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X27988,X27985),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X27987,X27984),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__surj])]) ).

fof(i_0_6442,plain,
    ! [X29121,X29122,X29123] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29123),X29122))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29123,tc_HOL_Obool)),X29121),X29122) = hAPP(hAPP(c_Finite__Set_Ofold(X29123,tc_fun(X29123,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X29123,tc_HOL_Obool),tc_fun(tc_fun(X29123,tc_HOL_Obool),tc_fun(X29123,tc_HOL_Obool)),X29123),hAPP(c_COMBC(tc_fun(X29123,tc_HOL_Obool),tc_fun(X29123,tc_HOL_Obool),tc_fun(X29123,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X29123,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X29123,tc_fun(X29123,tc_HOL_Obool),tc_fun(X29123,tc_HOL_Obool)),c_Set_Oinsert(X29123)),c_Orderings_Obot__class_Obot(tc_fun(X29123,tc_HOL_Obool))))),X29121),X29122) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__fold__remove])]) ).

fof(i_0_6443,plain,
    ! [X30071,X30072,X30073,X30074,X30075,X30076,X30077] :
      ( ~ c_Fun_Oinj__on(X30077,X30076,X30075,c_Orderings_Otop__class_Otop(tc_fun(X30077,tc_HOL_Obool)))
      | hAPP(hAPP(c_Map_Omap__of(X30077,X30074),X30073),X30072) != hAPP(c_Option_Ooption_OSome(X30074),X30071)
      | hAPP(hAPP(c_Map_Omap__of(X30076,X30074),hAPP(hAPP(c_List_Omap(tc_prod(X30077,X30074),tc_prod(X30076,X30074)),hAPP(c_Product__Type_Oprod_Oprod__case(X30077,X30074,tc_prod(X30076,X30074)),hAPP(hAPP(c_COMBB(X30076,tc_fun(X30074,tc_prod(X30076,X30074)),X30077),c_Product__Type_OPair(X30076,X30074)),X30075))),X30073)),hAPP(X30075,X30072)) = hAPP(c_Option_Ooption_OSome(X30074),X30071) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__mapk__SomeI])]) ).

cnf(i_0_6444,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_5368]) ).

cnf(i_0_6445,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_5369]) ).

cnf(i_0_6446,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_5385]) ).

cnf(i_0_6447,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_5386]) ).

cnf(i_0_6448,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_5387]) ).

fof(i_0_6449,plain,
    ! [X28009,X28010,X28011,X28012,X28013,X28014,X28015] : hAPP(c_Product__Type_Ofst(X28015,X28014),hAPP(c_Product__Type_Omap__pair(X28013,X28015,X28012,X28014,X28011,X28010),X28009)) = hAPP(X28011,hAPP(c_Product__Type_Ofst(X28013,X28012),X28009)),
    inference(variable_rename,[status(thm)],[fact_fst__map__pair]) ).

fof(i_0_6450,plain,
    ! [X28016,X28017,X28018,X28019,X28020,X28021,X28022] : hAPP(c_Product__Type_Osnd(X28022,X28021),hAPP(c_Product__Type_Omap__pair(X28020,X28022,X28019,X28021,X28018,X28017),X28016)) = hAPP(X28017,hAPP(c_Product__Type_Osnd(X28020,X28019),X28016)),
    inference(variable_rename,[status(thm)],[fact_snd__prod__fun]) ).

cnf(i_0_6451,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_5388]) ).

cnf(i_0_6452,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_5389]) ).

fof(i_0_6453,plain,
    ! [X32146,X32147,X32148,X32149] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32149,X32149)),hAPP(hAPP(c_Product__Type_OPair(X32149,X32149),esk438_4(X32146,X32147,X32148,X32149)),esk439_4(X32146,X32147,X32148,X32149))),X32148))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32149),tc_List_Olist(X32149))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32149),tc_List_Olist(X32149)),X32147),X32146)),c_List_Olexord(X32149,X32148)))
        | X32147 = X32146
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32149),tc_List_Olist(X32149))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32149),tc_List_Olist(X32149)),X32146),X32147)),c_List_Olexord(X32149,X32148))) )
      & ( esk438_4(X32146,X32147,X32148,X32149) != esk439_4(X32146,X32147,X32148,X32149)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32149),tc_List_Olist(X32149))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32149),tc_List_Olist(X32149)),X32147),X32146)),c_List_Olexord(X32149,X32148)))
        | X32147 = X32146
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32149),tc_List_Olist(X32149))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32149),tc_List_Olist(X32149)),X32146),X32147)),c_List_Olexord(X32149,X32148))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32149,X32149)),hAPP(hAPP(c_Product__Type_OPair(X32149,X32149),esk439_4(X32146,X32147,X32148,X32149)),esk438_4(X32146,X32147,X32148,X32149))),X32148))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32149),tc_List_Olist(X32149))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32149),tc_List_Olist(X32149)),X32147),X32146)),c_List_Olexord(X32149,X32148)))
        | X32147 = X32146
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32149),tc_List_Olist(X32149))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32149),tc_List_Olist(X32149)),X32146),X32147)),c_List_Olexord(X32149,X32148))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__linear])])])]) ).

fof(i_0_6454,plain,
    ! [X25597,X25598,X25599,X25600] : 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),X25600),X25599)),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),X25598),X25597)),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),X25600),X25598)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25599),X25597))),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_6455,plain,
    ! [X20226,X20227] : c_Relation_OId__on(X20227,X20226) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20227,tc_fun(tc_prod(X20227,X20227),tc_HOL_Obool)),X20226),hAPP(hAPP(c_COMBC(X20227,tc_fun(tc_prod(X20227,X20227),tc_HOL_Obool),tc_fun(tc_prod(X20227,X20227),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(X20227,X20227),tc_fun(tc_fun(tc_prod(X20227,X20227),tc_HOL_Obool),tc_fun(tc_prod(X20227,X20227),tc_HOL_Obool)),X20227),c_Set_Oinsert(tc_prod(X20227,X20227))),hAPP(hAPP(c_COMBS(X20227,X20227,tc_prod(X20227,X20227)),c_Product__Type_OPair(X20227,X20227)),c_COMBI(X20227)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X20227,X20227),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_Id__on__def]) ).

fof(i_0_6456,plain,
    ! [X30064,X30065,X30066,X30067] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),esk393_4(X30064,X30065,X30066,X30067)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk394_4(X30064,X30065,X30066,X30067)),esk395_4(X30064,X30065,X30066,X30067)))))
        | hBOOL(hAPP(hAPP(hAPP(X30064,X30067),X30066),X30065))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X30067),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X30066),X30065)))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk394_4(X30064,X30065,X30066,X30067)),esk395_4(X30064,X30065,X30066,X30067)))
        | hAPP(esk393_4(X30064,X30065,X30066,X30067),esk395_4(X30064,X30065,X30066,X30067)) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
        | hBOOL(hAPP(hAPP(hAPP(X30064,esk393_4(X30064,X30065,X30066,X30067)),esk394_4(X30064,X30065,X30066,X30067)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk395_4(X30064,X30065,X30066,X30067)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(hAPP(X30064,X30067),X30066),X30065))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X30067),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X30066),X30065)))) )
      & ( ~ hBOOL(hAPP(hAPP(hAPP(X30064,esk393_4(X30064,X30065,X30066,X30067)),esk394_4(X30064,X30065,X30066,X30067)),esk395_4(X30064,X30065,X30066,X30067)))
        | hBOOL(hAPP(hAPP(hAPP(X30064,X30067),X30066),X30065))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X30067),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X30066),X30065)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5390])])])]) ).

cnf(i_0_6457,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_5391]) ).

fof(i_0_6458,plain,
    ! [X33897,X33898,X33899] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X33899,X33899,hAPP(hAPP(c_COMBB(tc_fun(X33899,tc_HOL_Obool),tc_fun(X33899,tc_HOL_Obool),X33899),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33899),c_fNot)),c_fequal)),X33898),X33897))
        | X33898 != X33897 )
      & ( X33898 = X33897
        | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X33899,X33899,hAPP(hAPP(c_COMBB(tc_fun(X33899,tc_HOL_Obool),tc_fun(X33899,tc_HOL_Obool),X33899),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33899),c_fNot)),c_fequal)),X33898),X33897)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__noteq])]) ).

cnf(i_0_6459,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_5392]) ).

cnf(i_0_6460,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_5393]) ).

fof(i_0_6461,plain,
    ! [X30793,X30794,X30795,X30796,X30797,X30798,X30799,X30800] : hAPP(hAPP(c_List_Omap(tc_prod(X30800,X30799),X30798),X30797),hAPP(hAPP(c_List_Ozip(X30800,X30799),hAPP(hAPP(c_List_Omap(X30796,X30800),X30795),X30794)),X30793)) = hAPP(hAPP(c_List_Omap(tc_prod(X30796,X30799),X30798),hAPP(c_Product__Type_Oprod_Oprod__case(X30796,X30799,X30798),hAPP(hAPP(c_COMBB(tc_fun(X30799,tc_prod(X30800,X30799)),tc_fun(X30799,X30798),X30796),hAPP(c_COMBB(tc_prod(X30800,X30799),X30798,X30799),X30797)),hAPP(hAPP(c_COMBB(X30800,tc_fun(X30799,tc_prod(X30800,X30799)),X30796),c_Product__Type_OPair(X30800,X30799)),X30795)))),hAPP(hAPP(c_List_Ozip(X30796,X30799),X30794),X30793)),
    inference(variable_rename,[status(thm)],[fact_map__zip__map]) ).

fof(i_0_6462,plain,
    ! [X18663,X18664,X18665,X18666] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18665,X18666)),X18664),X18663))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18665,X18666)),X18664),X18663))
        | ~ class_Orderings_Oorder(X18666)
        | ~ class_Enum_Oenum(X18665) )
      & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X18665),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X18665),c_fNot),hAPP(hAPP(c_COMBS(X18665,X18666,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X18666,tc_fun(X18666,tc_HOL_Obool),X18665),c_fequal),X18664)),X18663))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18665,X18666)),X18664),X18663))
        | ~ class_Orderings_Oorder(X18666)
        | ~ class_Enum_Oenum(X18665) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18665,X18666)),X18664),X18663))
        | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X18665),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X18665),c_fNot),hAPP(hAPP(c_COMBS(X18665,X18666,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X18666,tc_fun(X18666,tc_HOL_Obool),X18665),c_fequal),X18664)),X18663))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18665,X18666)),X18664),X18663))
        | ~ class_Orderings_Oorder(X18666)
        | ~ class_Enum_Oenum(X18665) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__fun_I2_J])])]) ).

fof(i_0_6463,plain,
    ! [X31731,X31732,X31733,X31734] : c_List_Osublist(X31734,hAPP(hAPP(c_List_Olist_OCons(X31734),X31733),X31732),X31731) = hAPP(hAPP(c_List_Oappend(X31734),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X31734)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31731)),hAPP(hAPP(c_List_Olist_OCons(X31734),X31733),c_List_Olist_ONil(X31734))),c_List_Olist_ONil(X31734))),c_List_Osublist(X31734,X31732,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)),X31731)))),
    inference(variable_rename,[status(thm)],[fact_sublist__Cons]) ).

cnf(i_0_6464,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_5394]) ).

fof(i_0_6465,plain,
    ! [X30906,X30907,X30908] :
      ( ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X30907,X30908)),X30906))
        | c_Enum_Oex__n__lists(X30908,hAPP(hAPP(c_COMBB(tc_fun(X30907,X30908),tc_HOL_Obool,tc_List_Olist(X30908)),X30906),hAPP(hAPP(c_COMBB(tc_fun(X30907,tc_Option_Ooption(X30908)),tc_fun(X30907,X30908),tc_List_Olist(X30908)),c_Fun_Ocomp(tc_Option_Ooption(X30908),X30908,X30907,c_Option_Othe(X30908))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X30907,X30908)),tc_fun(X30907,tc_Option_Ooption(X30908)),tc_List_Olist(X30908)),c_Map_Omap__of(X30907,X30908)),hAPP(c_List_Ozip(X30907,X30908),c_Enum_Oenum__class_Oenum(X30907))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30907)),c_Enum_Oenum__class_Oenum(X30907)))
        | ~ class_Enum_Oenum(X30908)
        | ~ class_Enum_Oenum(X30907)
        | ~ class_HOL_Oequal(X30907) )
      & ( ~ c_Enum_Oex__n__lists(X30908,hAPP(hAPP(c_COMBB(tc_fun(X30907,X30908),tc_HOL_Obool,tc_List_Olist(X30908)),X30906),hAPP(hAPP(c_COMBB(tc_fun(X30907,tc_Option_Ooption(X30908)),tc_fun(X30907,X30908),tc_List_Olist(X30908)),c_Fun_Ocomp(tc_Option_Ooption(X30908),X30908,X30907,c_Option_Othe(X30908))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X30907,X30908)),tc_fun(X30907,tc_Option_Ooption(X30908)),tc_List_Olist(X30908)),c_Map_Omap__of(X30907,X30908)),hAPP(c_List_Ozip(X30907,X30908),c_Enum_Oenum__class_Oenum(X30907))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30907)),c_Enum_Oenum__class_Oenum(X30907)))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X30907,X30908)),X30906))
        | ~ class_Enum_Oenum(X30908)
        | ~ class_Enum_Oenum(X30907)
        | ~ class_HOL_Oequal(X30907) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__ex__fun__code])])]) ).

fof(i_0_6466,plain,
    ! [X30917,X30918,X30919] :
      ( ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X30918,X30919)),X30917))
        | c_Enum_Oall__n__lists(X30919,hAPP(hAPP(c_COMBB(tc_fun(X30918,X30919),tc_HOL_Obool,tc_List_Olist(X30919)),X30917),hAPP(hAPP(c_COMBB(tc_fun(X30918,tc_Option_Ooption(X30919)),tc_fun(X30918,X30919),tc_List_Olist(X30919)),c_Fun_Ocomp(tc_Option_Ooption(X30919),X30919,X30918,c_Option_Othe(X30919))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X30918,X30919)),tc_fun(X30918,tc_Option_Ooption(X30919)),tc_List_Olist(X30919)),c_Map_Omap__of(X30918,X30919)),hAPP(c_List_Ozip(X30918,X30919),c_Enum_Oenum__class_Oenum(X30918))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30918)),c_Enum_Oenum__class_Oenum(X30918)))
        | ~ class_Enum_Oenum(X30919)
        | ~ class_Enum_Oenum(X30918)
        | ~ class_HOL_Oequal(X30918) )
      & ( ~ c_Enum_Oall__n__lists(X30919,hAPP(hAPP(c_COMBB(tc_fun(X30918,X30919),tc_HOL_Obool,tc_List_Olist(X30919)),X30917),hAPP(hAPP(c_COMBB(tc_fun(X30918,tc_Option_Ooption(X30919)),tc_fun(X30918,X30919),tc_List_Olist(X30919)),c_Fun_Ocomp(tc_Option_Ooption(X30919),X30919,X30918,c_Option_Othe(X30919))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X30918,X30919)),tc_fun(X30918,tc_Option_Ooption(X30919)),tc_List_Olist(X30919)),c_Map_Omap__of(X30918,X30919)),hAPP(c_List_Ozip(X30918,X30919),c_Enum_Oenum__class_Oenum(X30918))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30918)),c_Enum_Oenum__class_Oenum(X30918)))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X30918,X30919)),X30917))
        | ~ class_Enum_Oenum(X30919)
        | ~ class_Enum_Oenum(X30918)
        | ~ class_HOL_Oequal(X30918) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__all__fun__code])])]) ).

fof(i_0_6467,plain,
    ! [X30903,X30904,X30905] :
      ( ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X30904,X30905)),X30903))
        | c_Enum_Oex__n__lists(X30905,hAPP(hAPP(c_COMBB(tc_fun(X30904,X30905),tc_HOL_Obool,tc_List_Olist(X30905)),X30903),hAPP(hAPP(c_COMBB(tc_fun(X30904,tc_Option_Ooption(X30905)),tc_fun(X30904,X30905),tc_List_Olist(X30905)),c_Fun_Ocomp(tc_Option_Ooption(X30905),X30905,X30904,c_Option_Othe(X30905))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X30904,X30905)),tc_fun(X30904,tc_Option_Ooption(X30905)),tc_List_Olist(X30905)),c_Map_Omap__of(X30904,X30905)),hAPP(c_List_Ozip(X30904,X30905),c_Enum_Oenum__class_Oenum(X30904))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30904)),c_Enum_Oenum__class_Oenum(X30904)))
        | ~ class_Enum_Oenum(X30905)
        | ~ class_Enum_Oenum(X30904) )
      & ( ~ c_Enum_Oex__n__lists(X30905,hAPP(hAPP(c_COMBB(tc_fun(X30904,X30905),tc_HOL_Obool,tc_List_Olist(X30905)),X30903),hAPP(hAPP(c_COMBB(tc_fun(X30904,tc_Option_Ooption(X30905)),tc_fun(X30904,X30905),tc_List_Olist(X30905)),c_Fun_Ocomp(tc_Option_Ooption(X30905),X30905,X30904,c_Option_Othe(X30905))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X30904,X30905)),tc_fun(X30904,tc_Option_Ooption(X30905)),tc_List_Olist(X30905)),c_Map_Omap__of(X30904,X30905)),hAPP(c_List_Ozip(X30904,X30905),c_Enum_Oenum__class_Oenum(X30904))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30904)),c_Enum_Oenum__class_Oenum(X30904)))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X30904,X30905)),X30903))
        | ~ class_Enum_Oenum(X30905)
        | ~ class_Enum_Oenum(X30904) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__ex__fun__def])])]) ).

fof(i_0_6468,plain,
    ! [X30914,X30915,X30916] :
      ( ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X30915,X30916)),X30914))
        | c_Enum_Oall__n__lists(X30916,hAPP(hAPP(c_COMBB(tc_fun(X30915,X30916),tc_HOL_Obool,tc_List_Olist(X30916)),X30914),hAPP(hAPP(c_COMBB(tc_fun(X30915,tc_Option_Ooption(X30916)),tc_fun(X30915,X30916),tc_List_Olist(X30916)),c_Fun_Ocomp(tc_Option_Ooption(X30916),X30916,X30915,c_Option_Othe(X30916))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X30915,X30916)),tc_fun(X30915,tc_Option_Ooption(X30916)),tc_List_Olist(X30916)),c_Map_Omap__of(X30915,X30916)),hAPP(c_List_Ozip(X30915,X30916),c_Enum_Oenum__class_Oenum(X30915))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30915)),c_Enum_Oenum__class_Oenum(X30915)))
        | ~ class_Enum_Oenum(X30916)
        | ~ class_Enum_Oenum(X30915) )
      & ( ~ c_Enum_Oall__n__lists(X30916,hAPP(hAPP(c_COMBB(tc_fun(X30915,X30916),tc_HOL_Obool,tc_List_Olist(X30916)),X30914),hAPP(hAPP(c_COMBB(tc_fun(X30915,tc_Option_Ooption(X30916)),tc_fun(X30915,X30916),tc_List_Olist(X30916)),c_Fun_Ocomp(tc_Option_Ooption(X30916),X30916,X30915,c_Option_Othe(X30916))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X30915,X30916)),tc_fun(X30915,tc_Option_Ooption(X30916)),tc_List_Olist(X30916)),c_Map_Omap__of(X30915,X30916)),hAPP(c_List_Ozip(X30915,X30916),c_Enum_Oenum__class_Oenum(X30915))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30915)),c_Enum_Oenum__class_Oenum(X30915)))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X30915,X30916)),X30914))
        | ~ class_Enum_Oenum(X30916)
        | ~ class_Enum_Oenum(X30915) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__all__fun__def])])]) ).

fof(i_0_6469,plain,
    ! [X18840,X18841,X18842,X18843,X18844] : c_Map_Odom(X18844,X18843,c_Fun_Ooverride__on(X18844,tc_Option_Ooption(X18843),X18842,X18841,X18840)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18844,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18844,tc_HOL_Obool)),c_Map_Odom(X18844,X18843,X18842)),hAPP(c_Set_OCollect(X18844),hAPP(hAPP(c_COMBC(X18844,tc_fun(X18844,tc_HOL_Obool),tc_HOL_Obool),c_member(X18844)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18844,tc_HOL_Obool)),X18840),c_Map_Odom(X18844,X18843,X18841)))))),hAPP(c_Set_OCollect(X18844),hAPP(hAPP(c_COMBC(X18844,tc_fun(X18844,tc_HOL_Obool),tc_HOL_Obool),c_member(X18844)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18844,tc_HOL_Obool)),X18840),c_Map_Odom(X18844,X18843,X18841))))),
    inference(variable_rename,[status(thm)],[fact_dom__override__on]) ).

fof(i_0_6470,plain,
    ! [X32860,X32861,X32862,X32863] :
      ( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X32863),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X32863))),X32862)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32861),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32863))),c_List_Otranspose(X32863,X32862))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32860),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32863))),hAPP(c_List_Ofilter(tc_List_Olist(X32863),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X32863)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32861)),c_Nat_Osize__class_Osize(tc_List_Olist(X32863)))),X32862))))
      | hAPP(hAPP(c_List_Onth(X32863),hAPP(hAPP(c_List_Onth(tc_List_Olist(X32863)),c_List_Otranspose(X32863,X32862)),X32861)),X32860) = hAPP(hAPP(c_List_Onth(X32863),hAPP(hAPP(c_List_Onth(tc_List_Olist(X32863)),X32862),X32860)),X32861) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__nth__transpose__sorted])]) ).

cnf(i_0_6471,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_5395]) ).

cnf(i_0_6472,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_5373]) ).

cnf(i_0_6473,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_5396]) ).

cnf(i_0_6474,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_5397]) ).

cnf(i_0_6475,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_5398]) ).

cnf(i_0_6476,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_5375]) ).

cnf(i_0_6477,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_5399]) ).

cnf(i_0_6478,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_5400]) ).

cnf(i_0_6479,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_5401]) ).

fof(i_0_6480,plain,
    ! [X29424,X29425,X29426,X29427,X29428,X29430] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29427),esk356_5(X29424,X29425,X29426,X29427,X29428)),X29426))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29428),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29427,X29428),X29426),X29425)),X29424))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X29428)
        | ~ class_Orderings_Olinorder(X29428) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29428),hAPP(X29425,esk356_5(X29424,X29425,X29426,X29427,X29428))),X29424))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29428),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29427,X29428),X29426),X29425)),X29424))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X29428)
        | ~ class_Orderings_Olinorder(X29428) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X29427),X29430),X29426))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29428),hAPP(X29425,X29430)),X29424))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29428),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29427,X29428),X29426),X29425)),X29424))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X29428)
        | ~ class_Orderings_Olinorder(X29428) ) ),
    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_6481,plain,
    ! [X19579,X19580,X19581,X19582,X19583,X19585,X19586,X19587,X19588,X19589,X19590,X19591,X19594] :
      ( ( hBOOL(hAPP(hAPP(c_member(X19583),esk45_5(X19579,X19580,X19581,X19582,X19583)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19582,tc_fun(X19583,tc_HOL_Obool)),X19581),X19580)))
        | ~ hBOOL(hAPP(hAPP(c_member(X19582),X19585),X19581))
        | ~ hBOOL(hAPP(hAPP(c_member(X19583),X19586),hAPP(X19580,X19585)))
        | hBOOL(hAPP(X19579,X19586)) )
      & ( ~ hBOOL(hAPP(X19579,esk45_5(X19579,X19580,X19581,X19582,X19583)))
        | ~ hBOOL(hAPP(hAPP(c_member(X19582),X19585),X19581))
        | ~ hBOOL(hAPP(hAPP(c_member(X19583),X19586),hAPP(X19580,X19585)))
        | hBOOL(hAPP(X19579,X19586)) )
      & ( hBOOL(hAPP(hAPP(c_member(X19590),esk46_5(X19587,X19588,X19589,X19590,X19591)),X19589))
        | ~ hBOOL(hAPP(hAPP(c_member(X19591),X19594),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19590,tc_fun(X19591,tc_HOL_Obool)),X19589),X19588)))
        | hBOOL(hAPP(X19587,X19594)) )
      & ( hBOOL(hAPP(hAPP(c_member(X19591),esk47_5(X19587,X19588,X19589,X19590,X19591)),hAPP(X19588,esk46_5(X19587,X19588,X19589,X19590,X19591))))
        | ~ hBOOL(hAPP(hAPP(c_member(X19591),X19594),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19590,tc_fun(X19591,tc_HOL_Obool)),X19589),X19588)))
        | hBOOL(hAPP(X19587,X19594)) )
      & ( ~ hBOOL(hAPP(X19587,esk47_5(X19587,X19588,X19589,X19590,X19591)))
        | ~ hBOOL(hAPP(hAPP(c_member(X19591),X19594),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19590,tc_fun(X19591,tc_HOL_Obool)),X19589),X19588)))
        | hBOOL(hAPP(X19587,X19594)) ) ),
    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_6482,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_6483,plain,
    ! [X22981,X22982,X22983,X22984,X22985,X22986] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X22986,tc_HOL_Obool),tc_fun(X22986,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X22986,tc_HOL_Obool),tc_fun(X22986,tc_HOL_Obool)),X22985),X22984)),c_Wellfounded_Omax__ext(X22986,X22983)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X22986,tc_HOL_Obool),tc_fun(X22986,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X22986,tc_HOL_Obool),tc_fun(X22986,tc_HOL_Obool)),X22982),X22981)),c_Wellfounded_Omax__ext(X22986,X22983)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X22986,tc_HOL_Obool),tc_fun(X22986,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X22986,tc_HOL_Obool),tc_fun(X22986,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22986,tc_HOL_Obool)),X22985),X22982)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22986,tc_HOL_Obool)),X22984),X22981))),c_Wellfounded_Omax__ext(X22986,X22983))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__additive])]) ).

fof(i_0_6484,plain,
    ! [X27976,X27977,X27978,X27979,X27980] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27980),esk277_5(X27976,X27977,X27978,X27979,X27980)),X27977))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27980,X27979)),X27978),hAPP(hAPP(c_Product__Type_OSigma(X27980,X27979),X27977),X27976))) )
      & ( hBOOL(hAPP(hAPP(c_member(X27979),esk278_5(X27976,X27977,X27978,X27979,X27980)),hAPP(X27976,esk277_5(X27976,X27977,X27978,X27979,X27980))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27980,X27979)),X27978),hAPP(hAPP(c_Product__Type_OSigma(X27980,X27979),X27977),X27976))) )
      & ( X27978 = hAPP(hAPP(c_Product__Type_OPair(X27980,X27979),esk277_5(X27976,X27977,X27978,X27979,X27980)),esk278_5(X27976,X27977,X27978,X27979,X27980))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27980,X27979)),X27978),hAPP(hAPP(c_Product__Type_OSigma(X27980,X27979),X27977),X27976))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaE])])])]) ).

fof(i_0_6485,plain,
    ! [X32022,X32023,X32024,X32025,X32026,X32027,X32028] : hAPP(c_List_Ofoldl(X32028,X32027,X32026,X32025),hAPP(hAPP(c_List_Omap(X32024,X32027),X32023),X32022)) = hAPP(c_List_Ofoldl(X32028,X32024,hAPP(hAPP(c_COMBC(X32028,tc_fun(X32024,X32027),tc_fun(X32024,X32028)),hAPP(hAPP(c_COMBB(tc_fun(X32027,X32028),tc_fun(tc_fun(X32024,X32027),tc_fun(X32024,X32028)),X32028),c_COMBB(X32027,X32028,X32024)),X32026)),X32023),X32025),X32022),
    inference(variable_rename,[status(thm)],[fact_foldl__map]) ).

fof(i_0_6486,plain,
    ! [X27318,X27319,X27320,X27321,X27322,X27323,X27324] : hAPP(hAPP(c_Relation_Orel__comp(X27324,X27323,X27322),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27321,tc_fun(tc_prod(X27324,X27323),tc_HOL_Obool)),X27320),X27319)),X27318) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27321,tc_fun(tc_prod(X27324,X27322),tc_HOL_Obool)),X27320),hAPP(hAPP(c_COMBC(X27321,tc_fun(tc_prod(X27323,X27322),tc_HOL_Obool),tc_fun(tc_prod(X27324,X27322),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X27324,X27323),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X27323,X27322),tc_HOL_Obool),tc_fun(tc_prod(X27324,X27322),tc_HOL_Obool)),X27321),c_Relation_Orel__comp(X27324,X27323,X27322)),X27319)),X27318)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__UNION__distrib2]) ).

fof(i_0_6487,plain,
    ! [X24607,X24608] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24608),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24607)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24608)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24607) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24608),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24607)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24608)) = 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),X24607),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24608)))),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_5402])]) ).

cnf(i_0_6488,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_5403]) ).

fof(i_0_6489,plain,
    ! [X20494,X20495,X20496] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20496),hAPP(c_Set_OCollect(X20496),X20495)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20496),hAPP(c_Set_OCollect(X20496),hAPP(hAPP(c_COMBS(X20496,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X20496),c_fdisj),X20495)),X20494)))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20496),hAPP(c_Set_OCollect(X20496),X20494)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20496),hAPP(c_Set_OCollect(X20496),hAPP(hAPP(c_COMBS(X20496,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X20496),c_fdisj),X20495)),X20494)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20496),hAPP(c_Set_OCollect(X20496),X20495)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20496),hAPP(c_Set_OCollect(X20496),X20494)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20496),hAPP(c_Set_OCollect(X20496),hAPP(hAPP(c_COMBS(X20496,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X20496),c_fdisj),X20495)),X20494)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__disjI])])]) ).

fof(i_0_6490,plain,
    ! [X19370,X19371,X19372,X19373,X19374] :
      ( ( hBOOL(hAPP(hAPP(c_member(X19373),esk43_5(X19370,X19371,X19372,X19373,X19374)),hAPP(c_Set_Oimage(X19374,X19373,X19372),c_Orderings_Otop__class_Otop(tc_fun(X19374,tc_HOL_Obool)))))
        | hBOOL(hAPP(X19371,X19370))
        | ~ c_Fun_Oinj__on(X19374,X19373,X19372,c_Orderings_Otop__class_Otop(tc_fun(X19374,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(X19371,hAPP(c_Hilbert__Choice_Oinv__into(X19374,X19373,c_Orderings_Otop__class_Otop(tc_fun(X19374,tc_HOL_Obool)),X19372),esk43_5(X19370,X19371,X19372,X19373,X19374))))
        | hBOOL(hAPP(X19371,X19370))
        | ~ c_Fun_Oinj__on(X19374,X19373,X19372,c_Orderings_Otop__class_Otop(tc_fun(X19374,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_6491,plain,
    ! [X19976,X19977,X19978] :
      ( ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X19977,X19978)),X19976))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X19977),hAPP(hAPP(c_COMBB(tc_fun(X19978,tc_HOL_Obool),tc_HOL_Obool,X19977),c_Enum_Oenum__class_Oenum__ex(X19978)),hAPP(hAPP(c_COMBB(tc_fun(X19978,tc_prod(X19977,X19978)),tc_fun(X19978,tc_HOL_Obool),X19977),hAPP(c_COMBB(tc_prod(X19977,X19978),tc_HOL_Obool,X19978),X19976)),c_Product__Type_OPair(X19977,X19978)))))
        | ~ class_Enum_Oenum(X19978)
        | ~ class_Enum_Oenum(X19977) )
      & ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X19977),hAPP(hAPP(c_COMBB(tc_fun(X19978,tc_HOL_Obool),tc_HOL_Obool,X19977),c_Enum_Oenum__class_Oenum__ex(X19978)),hAPP(hAPP(c_COMBB(tc_fun(X19978,tc_prod(X19977,X19978)),tc_fun(X19978,tc_HOL_Obool),X19977),hAPP(c_COMBB(tc_prod(X19977,X19978),tc_HOL_Obool,X19978),X19976)),c_Product__Type_OPair(X19977,X19978)))))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X19977,X19978)),X19976))
        | ~ class_Enum_Oenum(X19978)
        | ~ class_Enum_Oenum(X19977) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__ex__prod__def])])]) ).

fof(i_0_6492,plain,
    ! [X19973,X19974,X19975] :
      ( ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X19974,X19975)),X19973))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X19974),hAPP(hAPP(c_COMBB(tc_fun(X19975,tc_HOL_Obool),tc_HOL_Obool,X19974),c_Enum_Oenum__class_Oenum__all(X19975)),hAPP(hAPP(c_COMBB(tc_fun(X19975,tc_prod(X19974,X19975)),tc_fun(X19975,tc_HOL_Obool),X19974),hAPP(c_COMBB(tc_prod(X19974,X19975),tc_HOL_Obool,X19975),X19973)),c_Product__Type_OPair(X19974,X19975)))))
        | ~ class_Enum_Oenum(X19975)
        | ~ class_Enum_Oenum(X19974) )
      & ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X19974),hAPP(hAPP(c_COMBB(tc_fun(X19975,tc_HOL_Obool),tc_HOL_Obool,X19974),c_Enum_Oenum__class_Oenum__all(X19975)),hAPP(hAPP(c_COMBB(tc_fun(X19975,tc_prod(X19974,X19975)),tc_fun(X19975,tc_HOL_Obool),X19974),hAPP(c_COMBB(tc_prod(X19974,X19975),tc_HOL_Obool,X19975),X19973)),c_Product__Type_OPair(X19974,X19975)))))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X19974,X19975)),X19973))
        | ~ class_Enum_Oenum(X19975)
        | ~ class_Enum_Oenum(X19974) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__all__prod__def])])]) ).

fof(i_0_6493,plain,
    ! [X33136,X33137,X33138,X33139] :
      ( ( hBOOL(hAPP(c_List_Olistsp(X33139,X33138),X33136))
        | ~ hBOOL(hAPP(c_List_Olistsp(X33139,hAPP(hAPP(c_COMBS(X33139,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33139),c_fconj),X33138)),X33137)),X33136)) )
      & ( hBOOL(hAPP(c_List_Olistsp(X33139,X33137),X33136))
        | ~ hBOOL(hAPP(c_List_Olistsp(X33139,hAPP(hAPP(c_COMBS(X33139,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33139),c_fconj),X33138)),X33137)),X33136)) )
      & ( ~ hBOOL(hAPP(c_List_Olistsp(X33139,X33138),X33136))
        | ~ hBOOL(hAPP(c_List_Olistsp(X33139,X33137),X33136))
        | hBOOL(hAPP(c_List_Olistsp(X33139,hAPP(hAPP(c_COMBS(X33139,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33139),c_fconj),X33138)),X33137)),X33136)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__conj__eq])])]) ).

fof(i_0_6494,plain,
    ! [X24584,X24585] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X24585))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X24584)),hAPP(c_Int_Onat,X24585)) = hAPP(c_Int_Onat,X24584) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X24585))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X24584)),hAPP(c_Int_Onat,X24585)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24584),X24585)),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_5404])]) ).

cnf(i_0_6495,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_5405]) ).

fof(i_0_6496,plain,
    ! [X20305,X20306,X20307,X20308,X20309] :
      ( ~ class_Groups_Oab__semigroup__mult(X20309)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X20309,X20309,c_Groups_Otimes__class_Otimes(X20309),X20308,X20307),X20306))
      | ~ hBOOL(hAPP(hAPP(c_member(X20309),X20305),X20307))
      | hBOOL(hAPP(hAPP(c_member(X20309),X20308),X20307))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X20309,X20309,c_Groups_Otimes__class_Otimes(X20309),X20305,hAPP(hAPP(c_Set_Oinsert(X20309),X20308),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20309,tc_HOL_Obool)),X20307),hAPP(hAPP(c_Set_Oinsert(X20309),X20305),c_Orderings_Obot__class_Obot(tc_fun(X20309,tc_HOL_Obool)))))),X20306)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5406])]) ).

fof(i_0_6497,plain,
    ! [X33113,X33114,X33115,X33116] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33116)),X33115),c_List_Olists(X33116,X33114)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33116)),X33115),c_List_Olists(X33116,X33113)))
      | hBOOL(hAPP(c_List_Olistsp(X33116,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33116,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X33116,tc_fun(X33116,tc_HOL_Obool),tc_HOL_Obool),c_member(X33116)),X33114)),hAPP(hAPP(c_COMBC(X33116,tc_fun(X33116,tc_HOL_Obool),tc_HOL_Obool),c_member(X33116)),X33113))),X33115)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__IntI])]) ).

fof(i_0_6498,plain,
    ! [X19546,X19547,X19548,X19549,X19550,X19551,X19552,X19553,X19554,X19555] :
      ( ~ c_Equiv__Relations_Oequiv(X19555,X19554,X19553)
      | ~ c_Equiv__Relations_Oequiv(X19552,X19551,X19550)
      | ~ c_Equiv__Relations_Ocongruent2(X19555,X19552,tc_fun(X19549,tc_HOL_Obool),X19553,X19550,X19548)
      | ~ hBOOL(hAPP(hAPP(c_member(X19555),X19547),X19554))
      | ~ hBOOL(hAPP(hAPP(c_member(X19552),X19546),X19551))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19555,tc_fun(X19549,tc_HOL_Obool)),hAPP(c_Relation_OImage(X19555,X19555,X19553),hAPP(hAPP(c_Set_Oinsert(X19555),X19547),c_Orderings_Obot__class_Obot(tc_fun(X19555,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X19552,tc_fun(X19549,tc_HOL_Obool)),tc_fun(X19549,tc_HOL_Obool),X19555),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19552,tc_fun(X19549,tc_HOL_Obool)),hAPP(c_Relation_OImage(X19552,X19552,X19550),hAPP(hAPP(c_Set_Oinsert(X19552),X19546),c_Orderings_Obot__class_Obot(tc_fun(X19552,tc_HOL_Obool)))))),X19548)) = hAPP(hAPP(X19548,X19547),X19546) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class2])]) ).

fof(i_0_6499,plain,
    ! [X30551,X30552,X30553] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30553)),c_List_Osublist(X30553,X30552,X30551)) = 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(X30553)),X30552)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X30551)))),
    inference(variable_rename,[status(thm)],[fact_length__sublist]) ).

cnf(i_0_6500,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_5407]) ).

fof(i_0_6501,plain,
    ! [X32311,X32312,X32313] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32313)),hAPP(c_List_Ofilter(X32313,X32312),X32311)) = 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(X32313)),X32311)))),hAPP(hAPP(c_COMBB(X32313,tc_HOL_Obool,tc_Nat_Onat),X32312),hAPP(c_List_Onth(X32313),X32311))))),
    inference(variable_rename,[status(thm)],[fact_length__filter__conv__card]) ).

fof(i_0_6502,plain,
    ! [X21372,X21373,X21374,X21375,X21376] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21376)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21375),X21374))
      | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21376,X21375,c_Groups_Otimes__class_Otimes(X21376)),hAPP(hAPP(c_COMBS(X21375,X21376,X21376),hAPP(hAPP(c_COMBB(X21376,tc_fun(X21376,X21376),X21375),c_Groups_Otimes__class_Otimes(X21376)),X21373)),X21372)),c_Groups_Oone__class_Oone(X21376)),X21374) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21376),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21376,X21375,c_Groups_Otimes__class_Otimes(X21376)),X21373),c_Groups_Oone__class_Oone(X21376)),X21374)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21376,X21375,c_Groups_Otimes__class_Otimes(X21376)),X21372),c_Groups_Oone__class_Oone(X21376)),X21374)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__distrib])]) ).

fof(i_0_6503,plain,
    ! [X31725,X31726,X31727,X31728,X31729,X31730] :
      ( ( X31729 = X31727
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31730),tc_List_Olist(X31730))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31730),tc_List_Olist(X31730)),X31729),X31727)),c_List_Olistrel1(X31730,X31725)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31730),tc_List_Olist(X31730))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31730),tc_List_Olist(X31730)),hAPP(hAPP(c_List_Oappend(X31730),X31729),hAPP(hAPP(c_List_Olist_OCons(X31730),X31728),c_List_Olist_ONil(X31730)))),hAPP(hAPP(c_List_Oappend(X31730),X31727),hAPP(hAPP(c_List_Olist_OCons(X31730),X31726),c_List_Olist_ONil(X31730))))),c_List_Olistrel1(X31730,X31725))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X31730,X31730)),hAPP(hAPP(c_Product__Type_OPair(X31730,X31730),X31728),X31726)),X31725))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31730),tc_List_Olist(X31730))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31730),tc_List_Olist(X31730)),X31729),X31727)),c_List_Olistrel1(X31730,X31725)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31730),tc_List_Olist(X31730))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31730),tc_List_Olist(X31730)),hAPP(hAPP(c_List_Oappend(X31730),X31729),hAPP(hAPP(c_List_Olist_OCons(X31730),X31728),c_List_Olist_ONil(X31730)))),hAPP(hAPP(c_List_Oappend(X31730),X31727),hAPP(hAPP(c_List_Olist_OCons(X31730),X31726),c_List_Olist_ONil(X31730))))),c_List_Olistrel1(X31730,X31725))) )
      & ( X31729 = X31727
        | X31728 = X31726
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31730),tc_List_Olist(X31730))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31730),tc_List_Olist(X31730)),hAPP(hAPP(c_List_Oappend(X31730),X31729),hAPP(hAPP(c_List_Olist_OCons(X31730),X31728),c_List_Olist_ONil(X31730)))),hAPP(hAPP(c_List_Oappend(X31730),X31727),hAPP(hAPP(c_List_Olist_OCons(X31730),X31726),c_List_Olist_ONil(X31730))))),c_List_Olistrel1(X31730,X31725))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X31730,X31730)),hAPP(hAPP(c_Product__Type_OPair(X31730,X31730),X31728),X31726)),X31725))
        | X31728 = X31726
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31730),tc_List_Olist(X31730))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31730),tc_List_Olist(X31730)),hAPP(hAPP(c_List_Oappend(X31730),X31729),hAPP(hAPP(c_List_Olist_OCons(X31730),X31728),c_List_Olist_ONil(X31730)))),hAPP(hAPP(c_List_Oappend(X31730),X31727),hAPP(hAPP(c_List_Olist_OCons(X31730),X31726),c_List_Olist_ONil(X31730))))),c_List_Olistrel1(X31730,X31725))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31730),tc_List_Olist(X31730))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31730),tc_List_Olist(X31730)),X31729),X31727)),c_List_Olistrel1(X31730,X31725)))
        | X31728 != X31726
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31730),tc_List_Olist(X31730))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31730),tc_List_Olist(X31730)),hAPP(hAPP(c_List_Oappend(X31730),X31729),hAPP(hAPP(c_List_Olist_OCons(X31730),X31728),c_List_Olist_ONil(X31730)))),hAPP(hAPP(c_List_Oappend(X31730),X31727),hAPP(hAPP(c_List_Olist_OCons(X31730),X31726),c_List_Olist_ONil(X31730))))),c_List_Olistrel1(X31730,X31725))) )
      & ( X31729 != X31727
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31730,X31730)),hAPP(hAPP(c_Product__Type_OPair(X31730,X31730),X31728),X31726)),X31725))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31730),tc_List_Olist(X31730))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31730),tc_List_Olist(X31730)),hAPP(hAPP(c_List_Oappend(X31730),X31729),hAPP(hAPP(c_List_Olist_OCons(X31730),X31728),c_List_Olist_ONil(X31730)))),hAPP(hAPP(c_List_Oappend(X31730),X31727),hAPP(hAPP(c_List_Olist_OCons(X31730),X31726),c_List_Olist_ONil(X31730))))),c_List_Olistrel1(X31730,X31725))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__listrel1__snoc__iff])])]) ).

fof(i_0_6504,plain,
    ! [X33217,X33218,X33219,X33220,X33221,X33222,X33223] :
      ( ( ~ c_List_Olist__all2(X33223,X33222,X33221,X33220,hAPP(hAPP(c_List_Omap(X33219,X33222),X33218),X33217))
        | c_List_Olist__all2(X33223,X33219,hAPP(hAPP(c_COMBC(X33223,tc_fun(X33219,X33222),tc_fun(X33219,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33222,tc_HOL_Obool),tc_fun(tc_fun(X33219,X33222),tc_fun(X33219,tc_HOL_Obool)),X33223),c_COMBB(X33222,tc_HOL_Obool,X33219)),X33221)),X33218),X33220,X33217) )
      & ( ~ c_List_Olist__all2(X33223,X33219,hAPP(hAPP(c_COMBC(X33223,tc_fun(X33219,X33222),tc_fun(X33219,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33222,tc_HOL_Obool),tc_fun(tc_fun(X33219,X33222),tc_fun(X33219,tc_HOL_Obool)),X33223),c_COMBB(X33222,tc_HOL_Obool,X33219)),X33221)),X33218),X33220,X33217)
        | c_List_Olist__all2(X33223,X33222,X33221,X33220,hAPP(hAPP(c_List_Omap(X33219,X33222),X33218),X33217)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__map2])]) ).

fof(i_0_6505,plain,
    ! [X26424,X26425,X26426,X26427] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26427,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk227_4(X26424,X26425,X26426,X26427))),X26426) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26427,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),esk227_4(X26424,X26425,X26426,X26427)),X26425))),X26424)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26427,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X26426) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26427,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X26424) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__finite2__eq])])]) ).

fof(i_0_6506,plain,
    ! [X27488,X27489,X27490,X27491,X27493] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27491),esk263_4(X27488,X27489,X27490,X27491)),X27490))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X27491,tc_HOL_Obool),tc_fun(X27491,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X27491,tc_HOL_Obool),tc_fun(X27491,tc_HOL_Obool)),X27490),X27489)),c_Wellfounded_Omax__ext(X27491,X27488)))
        | X27489 = c_Orderings_Obot__class_Obot(tc_fun(X27491,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27491),X27489))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27491),X27490)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27491),X27493),X27489))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27491,X27491)),hAPP(hAPP(c_Product__Type_OPair(X27491,X27491),esk263_4(X27488,X27489,X27490,X27491)),X27493)),X27488))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X27491,tc_HOL_Obool),tc_fun(X27491,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X27491,tc_HOL_Obool),tc_fun(X27491,tc_HOL_Obool)),X27490),X27489)),c_Wellfounded_Omax__ext(X27491,X27488)))
        | X27489 = c_Orderings_Obot__class_Obot(tc_fun(X27491,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27491),X27489))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27491),X27490)) ) ),
    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_6507,plain,
    ! [X21091,X21092,X21093] : c_Map_Oran(X21093,X21092,X21091) = hAPP(c_Set_OCollect(X21092),hAPP(hAPP(c_COMBB(tc_fun(X21093,tc_HOL_Obool),tc_HOL_Obool,X21092),c_HOL_OEx(X21093)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X21092),tc_fun(X21093,tc_HOL_Obool),X21092),hAPP(c_COMBC(X21093,tc_Option_Ooption(X21092),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X21092),tc_fun(tc_Option_Ooption(X21092),tc_HOL_Obool),X21093),c_fequal),X21091))),c_Option_Ooption_OSome(X21092)))),
    inference(variable_rename,[status(thm)],[fact_ran__def]) ).

fof(i_0_6508,plain,
    ! [X27412,X27413,X27414,X27415,X27416,X27417,X27418,X27420,X27421,X27422,X27423,X27424,X27425,X27426,X27427] :
      ( ( hBOOL(hAPP(hAPP(X27415,X27413),esk258_4(X27412,X27413,X27414,X27415)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X27418,X27417,X27416,X27415,X27414),X27413),X27412)) )
      & ( hBOOL(hAPP(hAPP(X27414,esk258_4(X27412,X27413,X27414,X27415)),X27412))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X27418,X27417,X27416,X27415,X27414),X27413),X27412)) )
      & ( ~ hBOOL(hAPP(hAPP(X27423,X27421),X27424))
        | ~ hBOOL(hAPP(hAPP(X27422,X27424),X27420))
        | hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X27427,X27426,X27425,X27423,X27422),X27421),X27420)) ) ),
    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_6509,plain,
    ! [X28394,X28395,X28396] :
      ( ~ c_Wellfounded_Owf(X28396,X28395)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28396,X28396)),hAPP(hAPP(c_Product__Type_OPair(X28396,X28396),hAPP(X28394,hAPP(c_Nat_OSuc,esk323_3(X28394,X28395,X28396)))),hAPP(X28394,esk323_3(X28394,X28395,X28396)))),X28395)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__no__infinite__down__chainE])])]) ).

fof(i_0_6510,plain,
    ! [X27460,X27461,X27462,X27464,X27465,X27467] :
      ( ( ~ c_Wellfounded_Owf(X27461,X27460)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27461,X27461)),hAPP(hAPP(c_Product__Type_OPair(X27461,X27461),hAPP(X27462,hAPP(c_Nat_OSuc,esk260_3(X27460,X27461,X27462)))),hAPP(X27462,esk260_3(X27460,X27461,X27462)))),X27460)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X27465,X27465)),hAPP(hAPP(c_Product__Type_OPair(X27465,X27465),hAPP(esk261_2(X27464,X27465),hAPP(c_Nat_OSuc,X27467))),hAPP(esk261_2(X27464,X27465),X27467))),X27464))
        | c_Wellfounded_Owf(X27465,X27464) ) ),
    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_6511,plain,
    ! [X19619,X19620,X19621,X19622,X19623,X19624,X19625,X19626,X19627] :
      ( ~ c_Equiv__Relations_Oequiv(X19627,X19626,X19625)
      | ~ c_Equiv__Relations_Oequiv(X19624,X19623,X19622)
      | ~ c_Equiv__Relations_Ocongruent2(X19627,X19624,tc_fun(X19621,tc_HOL_Obool),X19625,X19622,X19620)
      | ~ hBOOL(hAPP(hAPP(c_member(X19624),X19619),X19623))
      | c_Equiv__Relations_Ocongruent(X19627,tc_fun(X19621,tc_HOL_Obool),X19625,hAPP(hAPP(c_COMBB(tc_fun(X19624,tc_fun(X19621,tc_HOL_Obool)),tc_fun(X19621,tc_HOL_Obool),X19627),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19624,tc_fun(X19621,tc_HOL_Obool)),hAPP(c_Relation_OImage(X19624,X19624,X19622),hAPP(hAPP(c_Set_Oinsert(X19624),X19619),c_Orderings_Obot__class_Obot(tc_fun(X19624,tc_HOL_Obool)))))),X19620)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent__UN])]) ).

cnf(i_0_6512,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_5408]) ).

cnf(i_0_6513,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_5409]) ).

fof(i_0_6514,plain,
    ! [X19034,X19035,X19036,X19037,X19038,X19039,X19040] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19040,X19039,X19038,X19037,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19040,tc_HOL_Obool)),X19036),hAPP(hAPP(c_Set_Oinsert(X19040),X19035),c_Orderings_Obot__class_Obot(tc_fun(X19040,tc_HOL_Obool))))),X19034))
      | ~ hBOOL(hAPP(hAPP(c_member(X19040),X19035),X19036))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19040,X19039,X19038,X19037,X19036),hAPP(hAPP(X19038,X19035),X19034))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff1__fold__graph])]) ).

fof(i_0_6515,plain,
    ! [X26779,X26780,X26781,X26782,X26783] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26782),esk240_5(X26779,X26780,X26781,X26782,X26783)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26782,tc_HOL_Obool)),X26781),X26780)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26783),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26782,X26783),X26779),X26780)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26782,X26783),X26779),X26781)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26782,tc_HOL_Obool)),X26780),X26781))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26782),X26781))
        | ~ class_Groups_Ocomm__monoid__add(X26783)
        | ~ class_Groups_Oordered__ab__semigroup__add(X26783) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26783),c_Groups_Ozero__class_Ozero(X26783)),hAPP(X26779,esk240_5(X26779,X26780,X26781,X26782,X26783))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26783),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26782,X26783),X26779),X26780)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26782,X26783),X26779),X26781)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26782,tc_HOL_Obool)),X26780),X26781))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26782),X26781))
        | ~ class_Groups_Ocomm__monoid__add(X26783)
        | ~ class_Groups_Oordered__ab__semigroup__add(X26783) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mono3])])])]) ).

fof(i_0_6516,plain,
    ! [X26694,X26695,X26696,X26697,X26698] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26697),esk229_5(X26694,X26695,X26696,X26697,X26698)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26697,tc_HOL_Obool)),X26696),X26695)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26698),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26697,X26698),X26694),X26695)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26697,X26698),X26694),X26696)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26697,tc_HOL_Obool)),X26695),X26696))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26697),X26696))
        | ~ class_Groups_Oordered__comm__monoid__add(X26698) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26698),c_Groups_Ozero__class_Ozero(X26698)),hAPP(X26694,esk229_5(X26694,X26695,X26696,X26697,X26698))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26698),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26697,X26698),X26694),X26695)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26697,X26698),X26694),X26696)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26697,tc_HOL_Obool)),X26695),X26696))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26697),X26696))
        | ~ class_Groups_Oordered__comm__monoid__add(X26698) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mono2])])])]) ).

fof(i_0_6517,plain,
    ! [X29300,X29301,X29302,X29303] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29303,tc_fun(X29302,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X29303,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29302,tc_HOL_Obool),tc_fun(X29302,tc_HOL_Obool),X29303),hAPP(c_COMBC(X29302,tc_fun(X29302,tc_HOL_Obool),tc_HOL_Obool),c_member(X29302))),X29301)),X29300))
        | hBOOL(hAPP(hAPP(c_member(X29302),X29300),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29303,tc_fun(X29302,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X29303,tc_HOL_Obool))),X29301))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X29302),X29300),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29303,tc_fun(X29302,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X29303,tc_HOL_Obool))),X29301)))
        | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29303,tc_fun(X29302,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X29303,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29302,tc_HOL_Obool),tc_fun(X29302,tc_HOL_Obool),X29303),hAPP(c_COMBC(X29302,tc_fun(X29302,tc_HOL_Obool),tc_HOL_Obool),c_member(X29302))),X29301)),X29300)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__INT__eq])]) ).

fof(i_0_6518,plain,
    ! [X19478,X19479,X19480,X19481] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19481,tc_fun(X19480,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X19481,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X19480,tc_HOL_Obool),tc_fun(X19480,tc_HOL_Obool),X19481),hAPP(c_COMBC(X19480,tc_fun(X19480,tc_HOL_Obool),tc_HOL_Obool),c_member(X19480))),X19479)),X19478))
        | hBOOL(hAPP(hAPP(c_member(X19480),X19478),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19481,tc_fun(X19480,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X19481,tc_HOL_Obool))),X19479))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X19480),X19478),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19481,tc_fun(X19480,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X19481,tc_HOL_Obool))),X19479)))
        | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19481,tc_fun(X19480,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X19481,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X19480,tc_HOL_Obool),tc_fun(X19480,tc_HOL_Obool),X19481),hAPP(c_COMBC(X19480,tc_fun(X19480,tc_HOL_Obool),tc_HOL_Obool),c_member(X19480))),X19479)),X19478)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq])]) ).

fof(i_0_6519,plain,
    ! [X21887,X21888,X21889,X21890,X21891,X21892] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21892),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21892),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21892),X21891),X21890)),X21889)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21892),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21892),X21888),X21890)),X21887)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21892),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21892),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21892),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21892),X21891),X21888)),X21890)),X21889)),X21887))
        | ~ class_Rings_Oordered__ring(X21892) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21892),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21892),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21892),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21892),X21891),X21888)),X21890)),X21889)),X21887))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21892),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21892),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21892),X21891),X21890)),X21889)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21892),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21892),X21888),X21890)),X21887)))
        | ~ class_Rings_Oordered__ring(X21892) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff1])])]) ).

fof(i_0_6520,plain,
    ! [X21875,X21876,X21877,X21878,X21879,X21880] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21880),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21880),X21879),X21878)),X21877)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21880),X21876),X21878)),X21875)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21880),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21880),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21880),X21879),X21876)),X21878)),X21877)),X21875))
        | ~ class_Rings_Oordered__ring(X21880) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21880),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21880),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21880),X21879),X21876)),X21878)),X21877)),X21875))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21880),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21880),X21879),X21878)),X21877)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21880),X21876),X21878)),X21875)))
        | ~ class_Rings_Oordered__ring(X21880) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff1])])]) ).

cnf(i_0_6521,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_5410]) ).

fof(i_0_6522,plain,
    ! [X18343,X18344,X18345,X18346,X18347,X18348,X18349] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X18349),X18348),X18347))
      | ~ c_Nitpick_Ofold__graph_H(X18349,X18346,X18345,X18344,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18349,tc_HOL_Obool)),X18347),hAPP(hAPP(c_Set_Oinsert(X18349),X18348),c_Orderings_Obot__class_Obot(tc_fun(X18349,tc_HOL_Obool)))),X18343)
      | c_Nitpick_Ofold__graph_H(X18349,X18346,X18345,X18344,X18347,hAPP(hAPP(X18345,X18348),X18343)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Ointros_I2_J])]) ).

fof(i_0_6523,plain,
    ! [X29438,X29439,X29440,X29441,X29442,X29443,X29444,X29445,X29446,X29447,X29448] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29442,tc_HOL_Obool)),X29441),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29440,tc_fun(X29442,tc_HOL_Obool)),X29439),X29438)))
        | ~ hBOOL(hAPP(hAPP(c_member(X29440),X29443),X29439))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29442,tc_HOL_Obool)),X29441),hAPP(X29438,X29443))) )
      & ( hBOOL(hAPP(hAPP(c_member(X29446),esk358_5(X29444,X29445,X29446,X29447,X29448)),X29445))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29448,tc_HOL_Obool)),X29447),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29446,tc_fun(X29448,tc_HOL_Obool)),X29445),X29444))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29448,tc_HOL_Obool)),X29447),hAPP(X29444,esk358_5(X29444,X29445,X29446,X29447,X29448))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29448,tc_HOL_Obool)),X29447),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29446,tc_fun(X29448,tc_HOL_Obool)),X29445),X29444))) ) ),
    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_6524,plain,
    ! [X34069,X34070,X34071,X34072,X34073] :
      ( ( hBOOL(hAPP(hAPP(c_member(X34073),esk520_5(X34069,X34070,X34071,X34072,X34073)),X34072))
        | c_Relation_Orefl__on(X34071,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X34073,tc_fun(X34071,tc_HOL_Obool)),X34072),X34070),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X34073,tc_fun(tc_prod(X34071,X34071),tc_HOL_Obool)),X34072),X34069)) )
      & ( ~ c_Relation_Orefl__on(X34071,hAPP(X34070,esk520_5(X34069,X34070,X34071,X34072,X34073)),hAPP(X34069,esk520_5(X34069,X34070,X34071,X34072,X34073)))
        | c_Relation_Orefl__on(X34071,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X34073,tc_fun(X34071,tc_HOL_Obool)),X34072),X34070),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X34073,tc_fun(tc_prod(X34071,X34071),tc_HOL_Obool)),X34072),X34069)) ) ),
    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_6525,plain,
    ! [X23239,X23240,X23241,X23242] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X23242,X23241),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X23240),X23239)))
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23242),X23241),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X23239),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23240)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23240)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X23239),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),X23241),X23239))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zminus1__lemma])]) ).

cnf(i_0_6526,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_5411]) ).

fof(i_0_6527,plain,
    ! [X29314,X29315,X29316,X29317,X29318,X29319,X29320,X29321,X29322,X29323,X29324] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X29318),X29317),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29316,tc_fun(X29318,tc_HOL_Obool)),X29315),X29314)))
        | ~ hBOOL(hAPP(hAPP(c_member(X29316),X29319),X29315))
        | hBOOL(hAPP(hAPP(c_member(X29318),X29317),hAPP(X29314,X29319))) )
      & ( hBOOL(hAPP(hAPP(c_member(X29322),esk353_5(X29320,X29321,X29322,X29323,X29324)),X29321))
        | hBOOL(hAPP(hAPP(c_member(X29324),X29323),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29322,tc_fun(X29324,tc_HOL_Obool)),X29321),X29320))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X29324),X29323),hAPP(X29320,esk353_5(X29320,X29321,X29322,X29323,X29324))))
        | hBOOL(hAPP(hAPP(c_member(X29324),X29323),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29322,tc_fun(X29324,tc_HOL_Obool)),X29321),X29320))) ) ),
    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_6528,plain,
    ! [X27860,X27861,X27862,X27863,X27864,X27865] : hAPP(c_Set_Ovimage(X27865,tc_prod(X27864,X27863),X27862),hAPP(hAPP(c_Product__Type_OSigma(X27864,X27863),X27861),hAPP(c_COMBK(tc_fun(X27863,tc_HOL_Obool),X27864),X27860))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27865,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X27865,X27864,hAPP(c_Fun_Ocomp(tc_prod(X27864,X27863),X27864,X27865,c_Product__Type_Ofst(X27864,X27863)),X27862)),X27861)),hAPP(c_Set_Ovimage(X27865,X27863,hAPP(c_Fun_Ocomp(tc_prod(X27864,X27863),X27863,X27865,c_Product__Type_Osnd(X27864,X27863)),X27862)),X27860)),
    inference(variable_rename,[status(thm)],[fact_vimage__Times]) ).

fof(i_0_6529,plain,
    ! [X22828,X22829,X22830,X22831,X22832,X22833,X22834,X22835] :
      ( ( X22833 = X22831
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X22835,X22835)),hAPP(hAPP(c_Product__Type_OPair(X22835,X22835),X22833),X22831)),X22829))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X22835,X22834),tc_prod(X22835,X22834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X22835,X22834),tc_prod(X22835,X22834)),hAPP(hAPP(c_Product__Type_OPair(X22835,X22834),X22833),X22832)),hAPP(hAPP(c_Product__Type_OPair(X22835,X22834),X22831),X22830))),c_Wellfounded_Olex__prod(X22835,X22834,X22829,X22828))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X22834,X22834)),hAPP(hAPP(c_Product__Type_OPair(X22834,X22834),X22832),X22830)),X22828))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X22835,X22835)),hAPP(hAPP(c_Product__Type_OPair(X22835,X22835),X22833),X22831)),X22829))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X22835,X22834),tc_prod(X22835,X22834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X22835,X22834),tc_prod(X22835,X22834)),hAPP(hAPP(c_Product__Type_OPair(X22835,X22834),X22833),X22832)),hAPP(hAPP(c_Product__Type_OPair(X22835,X22834),X22831),X22830))),c_Wellfounded_Olex__prod(X22835,X22834,X22829,X22828))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22835,X22835)),hAPP(hAPP(c_Product__Type_OPair(X22835,X22835),X22833),X22831)),X22829))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X22835,X22834),tc_prod(X22835,X22834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X22835,X22834),tc_prod(X22835,X22834)),hAPP(hAPP(c_Product__Type_OPair(X22835,X22834),X22833),X22832)),hAPP(hAPP(c_Product__Type_OPair(X22835,X22834),X22831),X22830))),c_Wellfounded_Olex__prod(X22835,X22834,X22829,X22828))) )
      & ( X22833 != X22831
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22834,X22834)),hAPP(hAPP(c_Product__Type_OPair(X22834,X22834),X22832),X22830)),X22828))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X22835,X22834),tc_prod(X22835,X22834))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X22835,X22834),tc_prod(X22835,X22834)),hAPP(hAPP(c_Product__Type_OPair(X22835,X22834),X22833),X22832)),hAPP(hAPP(c_Product__Type_OPair(X22835,X22834),X22831),X22830))),c_Wellfounded_Olex__prod(X22835,X22834,X22829,X22828))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])]) ).

fof(i_0_6530,plain,
    ! [X29610,X29611,X29612,X29613,X29614,X29615,X29616,X29617,X29618,X29619,X29620] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29614,tc_fun(X29613,tc_HOL_Obool)),X29612),X29611),X29610))
        | ~ hBOOL(hAPP(hAPP(c_member(X29614),X29615),X29612))
        | hBOOL(hAPP(hAPP(X29611,X29615),X29610)) )
      & ( hBOOL(hAPP(hAPP(c_member(X29620),esk360_5(X29616,X29617,X29618,X29619,X29620)),X29618))
        | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29620,tc_fun(X29619,tc_HOL_Obool)),X29618),X29617),X29616)) )
      & ( ~ hBOOL(hAPP(hAPP(X29617,esk360_5(X29616,X29617,X29618,X29619,X29620)),X29616))
        | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29620,tc_fun(X29619,tc_HOL_Obool)),X29618),X29617),X29616)) ) ),
    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_6531,plain,
    ! [X20799,X20800] : 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),X20800)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X20799))))),
    inference(variable_rename,[status(thm)],[fact_finite__M__bounded__by__nat]) ).

fof(i_0_6532,plain,
    ! [X26998,X26999,X27000] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X27000))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26999),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26998),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),X26998),X26999))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X27000)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_incr__lemma])]) ).

fof(i_0_6533,plain,
    ! [X29431,X29432,X29433,X29434,X29435,X29436] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29435),X29434),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29433,X29435),X29432),X29431)))
        | ~ hBOOL(hAPP(hAPP(c_member(X29433),X29436),X29432))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29435),X29434),hAPP(X29431,X29436)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X29435) )
      & ( hBOOL(hAPP(hAPP(c_member(X29433),esk357_5(X29431,X29432,X29433,X29434,X29435)),X29432))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29435),X29434),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29433,X29435),X29432),X29431)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X29435) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29435),X29434),hAPP(X29431,esk357_5(X29431,X29432,X29433,X29434,X29435))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29435),X29434),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29433,X29435),X29432),X29431)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X29435) ) ),
    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_6534,plain,
    ! [X33445,X33446,X33447,X33448,X33449] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33448),esk484_5(X33445,X33446,X33447,X33448,X33449)),hAPP(c_List_Oset(X33448),X33447)))
        | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X33448,X33449,X33446),X33445),X33447) = hAPP(hAPP(c_List_Olist_OCons(X33448),X33445),X33447)
        | ~ class_Orderings_Olinorder(X33449) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33449),hAPP(X33446,X33445)),hAPP(X33446,esk484_5(X33445,X33446,X33447,X33448,X33449))))
        | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X33448,X33449,X33446),X33445),X33447) = hAPP(hAPP(c_List_Olist_OCons(X33448),X33445),X33447)
        | ~ class_Orderings_Olinorder(X33449) ) ),
    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_6535,plain,
    ! [X26850,X26851,X26852,X26853,X26854] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26853),esk244_5(X26850,X26851,X26852,X26853,X26854)),X26852))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26853,X26854),X26851),X26852) != c_Groups_Ozero__class_Ozero(X26854)
        | ~ hBOOL(hAPP(hAPP(c_member(X26853),X26850),X26852))
        | hAPP(X26851,X26850) = c_Groups_Ozero__class_Ozero(X26854)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26853),X26852))
        | ~ class_Groups_Oordered__ab__group__add(X26854) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26854),c_Groups_Ozero__class_Ozero(X26854)),hAPP(X26851,esk244_5(X26850,X26851,X26852,X26853,X26854))))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26853,X26854),X26851),X26852) != c_Groups_Ozero__class_Ozero(X26854)
        | ~ hBOOL(hAPP(hAPP(c_member(X26853),X26850),X26852))
        | hAPP(X26851,X26850) = c_Groups_Ozero__class_Ozero(X26854)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26853),X26852))
        | ~ class_Groups_Oordered__ab__group__add(X26854) ) ),
    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_6536,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_5412]) ).

fof(i_0_6537,plain,
    ! [X28324,X28325,X28326,X28327,X28328] : hAPP(c_Hilbert__Choice_Oinv__into(X28328,X28327,X28326,X28325),X28324) = c_Hilbert__Choice_OEps(X28328,hAPP(hAPP(c_COMBS(X28328,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28328),c_fconj),hAPP(hAPP(c_COMBC(X28328,tc_fun(X28328,tc_HOL_Obool),tc_HOL_Obool),c_member(X28328)),X28326))),hAPP(hAPP(c_COMBC(X28328,X28327,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X28327,tc_fun(X28327,tc_HOL_Obool),X28328),c_fequal),X28325)),X28324))),
    inference(variable_rename,[status(thm)],[fact_inv__into__def]) ).

fof(i_0_6538,plain,
    ! [X18677,X18678,X18679,X18680,X18681] : hAPP(c_Fun_Othe__inv__into(X18681,X18680,X18679,X18678),X18677) = c_HOL_OThe(X18681,hAPP(hAPP(c_COMBS(X18681,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X18681),c_fconj),hAPP(hAPP(c_COMBC(X18681,tc_fun(X18681,tc_HOL_Obool),tc_HOL_Obool),c_member(X18681)),X18679))),hAPP(hAPP(c_COMBC(X18681,X18680,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X18680,tc_fun(X18680,tc_HOL_Obool),X18681),c_fequal),X18678)),X18677))),
    inference(variable_rename,[status(thm)],[fact_the__inv__into__def]) ).

cnf(i_0_6539,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_5413]) ).

fof(i_0_6540,plain,
    ! [X31735,X31736,X31737,X31738] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X31738,X31738)),hAPP(hAPP(c_Product__Type_OPair(X31738,X31738),esk428_4(X31735,X31736,X31737,X31738)),esk429_4(X31735,X31736,X31737,X31738))),X31735))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31738),tc_List_Olist(X31738))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31738),tc_List_Olist(X31738)),X31737),X31736)),c_List_Olistrel1(X31738,X31735))) )
      & ( X31737 = hAPP(hAPP(c_List_Oappend(X31738),esk430_4(X31735,X31736,X31737,X31738)),hAPP(hAPP(c_List_Olist_OCons(X31738),esk428_4(X31735,X31736,X31737,X31738)),esk431_4(X31735,X31736,X31737,X31738)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31738),tc_List_Olist(X31738))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31738),tc_List_Olist(X31738)),X31737),X31736)),c_List_Olistrel1(X31738,X31735))) )
      & ( X31736 = hAPP(hAPP(c_List_Oappend(X31738),esk430_4(X31735,X31736,X31737,X31738)),hAPP(hAPP(c_List_Olist_OCons(X31738),esk429_4(X31735,X31736,X31737,X31738)),esk431_4(X31735,X31736,X31737,X31738)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31738),tc_List_Olist(X31738))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31738),tc_List_Olist(X31738)),X31737),X31736)),c_List_Olistrel1(X31738,X31735))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1E])])])]) ).

fof(i_0_6541,plain,
    ! [X29172,X29173,X29174,X29175,X29176,X29177,X29178] :
      ( ~ c_Finite__Set_Ofun__left__comm(X29178,X29177,X29176)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X29178,X29177,X29176,X29175,X29174),X29173))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X29178,X29177,X29176,X29175,X29174),X29172))
      | X29172 = X29173 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__determ])]) ).

fof(i_0_6542,plain,
    ! [X30389,X30390,X30391,X30392,X30393] :
      ( ~ class_Groups_Ocomm__monoid__add(X30393)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30393),hAPP(hAPP(c_List_Omap(X30392,X30393),hAPP(hAPP(c_COMBS(X30392,X30393,X30393),hAPP(hAPP(c_COMBB(X30393,tc_fun(X30393,X30393),X30392),c_Groups_Oplus__class_Oplus(X30393)),X30391)),X30390)),X30389)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X30393),hAPP(c_List_Omonoid__add__class_Olistsum(X30393),hAPP(hAPP(c_List_Omap(X30392,X30393),X30391),X30389))),hAPP(c_List_Omonoid__add__class_Olistsum(X30393),hAPP(hAPP(c_List_Omap(X30392,X30393),X30390),X30389))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__addf])]) ).

fof(i_0_6543,plain,
    ! [X30404,X30405,X30406,X30407,X30408] :
      ( ~ class_Groups_Oab__group__add(X30408)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30408),hAPP(hAPP(c_List_Omap(X30407,X30408),hAPP(hAPP(c_COMBS(X30407,X30408,X30408),hAPP(hAPP(c_COMBB(X30408,tc_fun(X30408,X30408),X30407),c_Groups_Ominus__class_Ominus(X30408)),X30406)),X30405)),X30404)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X30408),hAPP(c_List_Omonoid__add__class_Olistsum(X30408),hAPP(hAPP(c_List_Omap(X30407,X30408),X30406),X30404))),hAPP(c_List_Omonoid__add__class_Olistsum(X30408),hAPP(hAPP(c_List_Omap(X30407,X30408),X30405),X30404))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__subtractf])]) ).

fof(i_0_6544,plain,
    ! [X19528,X19529,X19530,X19531] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X19531,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19530,tc_fun(tc_fun(X19531,tc_HOL_Obool),tc_HOL_Obool)),X19529),hAPP(hAPP(c_COMBB(tc_fun(X19531,tc_HOL_Obool),tc_fun(tc_fun(X19531,tc_HOL_Obool),tc_HOL_Obool),X19530),c_Set_OPow(X19531)),X19528))),hAPP(c_Set_OPow(X19531),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19530,tc_fun(X19531,tc_HOL_Obool)),X19529),X19528)))),
    inference(variable_rename,[status(thm)],[fact_UN__Pow__subset]) ).

fof(i_0_6545,plain,
    ! [X21953,X21954,X21955,X21956,X21957] :
      ( ( ~ 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),X21956),X21955)),X21954)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21957),X21955)),X21953)))
        | 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),X21956),X21957)),X21955)),X21954)),X21953))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21957),X21956)) )
      & ( ~ 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),X21956),X21957)),X21955)),X21954)),X21953))
        | 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),X21956),X21955)),X21954)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21957),X21955)),X21953)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21957),X21956)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff1])])]) ).

fof(i_0_6546,plain,
    ! [X21958,X21959,X21960,X21961,X21962] :
      ( ( ~ 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),X21961),X21960)),X21959)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21962),X21960)),X21958)))
        | 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),X21961),X21962)),X21960)),X21959)),X21958))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21962),X21961)) )
      & ( ~ 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),X21961),X21962)),X21960)),X21959)),X21958))
        | 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),X21961),X21960)),X21959)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21962),X21960)),X21958)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21962),X21961)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff1])])]) ).

fof(i_0_6547,plain,
    ! [X30399,X30400,X30401,X30402,X30403] :
      ( ~ class_Rings_Osemiring__0(X30403)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30403),hAPP(hAPP(c_List_Omap(X30402,X30403),hAPP(hAPP(c_COMBC(X30402,X30403,X30403),hAPP(hAPP(c_COMBB(X30403,tc_fun(X30403,X30403),X30402),c_Groups_Otimes__class_Otimes(X30403)),X30401)),X30400)),X30399)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X30403),hAPP(c_List_Omonoid__add__class_Olistsum(X30403),hAPP(hAPP(c_List_Omap(X30402,X30403),X30401),X30399))),X30400) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__mult__const])]) ).

fof(i_0_6548,plain,
    ! [X23981] : c_Int_Oint__ge__less__than2(X23981) = 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),X23981)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[fact_int__ge__less__than2__def]) ).

fof(i_0_6549,plain,
    ! [X21396,X21397,X21398,X21399,X21400] :
      ( ( hBOOL(hAPP(hAPP(c_member(X21399),esk106_5(X21396,X21397,X21398,X21399,X21400)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21399,tc_HOL_Obool)),X21398),X21397)))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21400,X21399,c_Groups_Otimes__class_Otimes(X21400)),X21396),c_Groups_Oone__class_Oone(X21400)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21399,tc_HOL_Obool)),X21398),X21397)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21400),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21400,X21399,c_Groups_Otimes__class_Otimes(X21400)),X21396),c_Groups_Oone__class_Oone(X21400)),X21398)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21400,X21399,c_Groups_Otimes__class_Otimes(X21400)),X21396),c_Groups_Oone__class_Oone(X21400)),X21397))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21399),X21397))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21399),X21398))
        | ~ class_Groups_Ocomm__monoid__mult(X21400) )
      & ( hAPP(X21396,esk106_5(X21396,X21397,X21398,X21399,X21400)) != c_Groups_Oone__class_Oone(X21400)
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21400,X21399,c_Groups_Otimes__class_Otimes(X21400)),X21396),c_Groups_Oone__class_Oone(X21400)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21399,tc_HOL_Obool)),X21398),X21397)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21400),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21400,X21399,c_Groups_Otimes__class_Otimes(X21400)),X21396),c_Groups_Oone__class_Oone(X21400)),X21398)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21400,X21399,c_Groups_Otimes__class_Otimes(X21400)),X21396),c_Groups_Oone__class_Oone(X21400)),X21397))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21399),X21397))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21399),X21398))
        | ~ class_Groups_Ocomm__monoid__mult(X21400) ) ),
    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_6550,plain,
    ! [X18160,X18161,X18162,X18163] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18163,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X18163,tc_fun(X18163,tc_HOL_Obool),tc_HOL_Obool),c_member(X18163)),X18162)),hAPP(hAPP(c_COMBC(X18163,tc_fun(X18163,tc_HOL_Obool),tc_HOL_Obool),c_member(X18163)),X18161)),X18160))
        | hBOOL(hAPP(hAPP(c_member(X18163),X18160),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18163,tc_HOL_Obool)),X18162),X18161))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18163),X18160),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18163,tc_HOL_Obool)),X18162),X18161)))
        | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18163,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X18163,tc_fun(X18163,tc_HOL_Obool),tc_HOL_Obool),c_member(X18163)),X18162)),hAPP(hAPP(c_COMBC(X18163,tc_fun(X18163,tc_HOL_Obool),tc_HOL_Obool),c_member(X18163)),X18161)),X18160)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq])]) ).

fof(i_0_6551,plain,
    ! [X17312,X17313,X17314,X17315] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17315,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X17315,tc_fun(X17315,tc_HOL_Obool),tc_HOL_Obool),c_member(X17315)),X17314)),hAPP(hAPP(c_COMBC(X17315,tc_fun(X17315,tc_HOL_Obool),tc_HOL_Obool),c_member(X17315)),X17313)),X17312))
        | hBOOL(hAPP(hAPP(c_member(X17315),X17312),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17315,tc_HOL_Obool)),X17314),X17313))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17315),X17312),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17315,tc_HOL_Obool)),X17314),X17313)))
        | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17315,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X17315,tc_fun(X17315,tc_HOL_Obool),tc_HOL_Obool),c_member(X17315)),X17314)),hAPP(hAPP(c_COMBC(X17315,tc_fun(X17315,tc_HOL_Obool),tc_HOL_Obool),c_member(X17315)),X17313)),X17312)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Un__eq])]) ).

fof(i_0_6552,plain,
    ! [X17219,X17220,X17221] : hAPP(hAPP(c_Set_Oinsert(X17221),X17220),hAPP(c_Set_OCollect(X17221),X17219)) = hAPP(c_Set_OCollect(X17221),hAPP(hAPP(c_COMBS(X17221,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17221),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X17221),c_fNot),hAPP(hAPP(c_COMBC(X17221,X17221,tc_HOL_Obool),c_fequal),X17220)))),X17219)),
    inference(variable_rename,[status(thm)],[fact_insert__Collect]) ).

cnf(i_0_6553,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_5414]) ).

fof(i_0_6554,plain,
    ! [X19848,X19849,X19850,X19851,X19852,X19853] :
      ( ~ c_Equiv__Relations_Oequiv(X19853,X19852,X19851)
      | ~ hBOOL(hAPP(hAPP(c_member(X19853),X19850),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19853,tc_HOL_Obool)),hAPP(c_Relation_OImage(X19853,X19853,X19851),hAPP(hAPP(c_Set_Oinsert(X19853),X19849),c_Orderings_Obot__class_Obot(tc_fun(X19853,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X19853,X19853,X19851),hAPP(hAPP(c_Set_Oinsert(X19853),X19848),c_Orderings_Obot__class_Obot(tc_fun(X19853,tc_HOL_Obool)))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X19853,X19853)),hAPP(hAPP(c_Product__Type_OPair(X19853,X19853),X19849),X19848)),X19851)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__nondisjoint])]) ).

fof(i_0_6555,plain,
    ! [X33390,X33391] : c_List_Omeasures(X33391,X33390) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),X33391),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(X33391,tc_List_Olist(tc_fun(X33391,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33391,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(X33391,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),X33391),c_List_Omap(tc_fun(X33391,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(X33391,tc_Nat_Onat),X33391,tc_Nat_Onat),c_COMBI(tc_fun(X33391,tc_Nat_Onat))))),X33390)),
    inference(variable_rename,[status(thm)],[fact_measures__def]) ).

fof(i_0_6556,plain,
    ! [X23753,X23754,X23755,X23756,X23757,X23758,X23759] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23759,X23758),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X23757),X23756)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23755,X23758),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X23754),X23753)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23758))
      | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23759),X23755),X23758),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),X23757),X23754)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23756),X23753)),X23758))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23756),X23753),X23758)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__add1__eq])]) ).

fof(i_0_6557,plain,
    ! [X34216,X34217,X34218,X34219] : c_Random__Sequence_Omap(X34219,X34218,X34217,X34216) = c_Random__Sequence_Obind(X34219,X34218,X34216,hAPP(c_Fun_Ocomp(X34218,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(X34218)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),X34219,c_Random__Sequence_Osingle(X34218)),X34217)),
    inference(variable_rename,[status(thm)],[fact_Random__Sequence_Omap__def]) ).

fof(i_0_6558,plain,
    ! [X24492,X24493,X24494,X24495,X24496] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24495),esk143_5(X24492,X24493,X24494,X24495,X24496)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24495,tc_HOL_Obool)),X24494),X24493)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24495,X24496),X24492),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24495,tc_HOL_Obool)),X24494),X24493)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24496),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24496),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24495,X24496),X24492),X24494)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24495,X24496),X24492),X24493))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24495,X24496),X24492),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24495,tc_HOL_Obool)),X24494),X24493)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24495),X24493))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24495),X24494))
        | ~ class_Fields_Ofield(X24496) )
      & ( hAPP(X24492,esk143_5(X24492,X24493,X24494,X24495,X24496)) = c_Groups_Ozero__class_Ozero(X24496)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24495,X24496),X24492),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24495,tc_HOL_Obool)),X24494),X24493)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24496),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24496),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24495,X24496),X24492),X24494)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24495,X24496),X24492),X24493))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24495,X24496),X24492),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24495,tc_HOL_Obool)),X24494),X24493)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24495),X24493))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24495),X24494))
        | ~ class_Fields_Ofield(X24496) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Un])])])]) ).

fof(i_0_6559,plain,
    ! [X23569,X23570,X23571,X23572,X23573,X23574,X23575] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X23575,X23574),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X23573),X23572)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X23571,X23574),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X23570),X23569)))
      | X23574 = 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),X23575),X23571),X23574),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),X23573),X23570)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23572),X23569)),X23574))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23572),X23569),X23574)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd1__lemma])]) ).

fof(i_0_6560,plain,
    ! [X27683,X27684,X27685,X27686,X27687,X27688] :
      ( ~ class_Groups_Ocomm__monoid__add(X27688)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27687,X27688),hAPP(hAPP(c_COMBC(X27687,tc_fun(X27686,tc_HOL_Obool),X27688),hAPP(hAPP(c_COMBB(tc_fun(X27686,X27688),tc_fun(tc_fun(X27686,tc_HOL_Obool),X27688),X27687),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27686,X27688)),X27685)),X27684)),X27683) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X27687,X27686),X27688),hAPP(c_Product__Type_Oprod_Oprod__case(X27687,X27686,X27688),X27685)),hAPP(hAPP(c_Product__Type_OSigma(X27687,X27686),X27683),hAPP(c_COMBK(tc_fun(X27686,tc_HOL_Obool),X27687),X27684))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__cartesian__product])]) ).

fof(i_0_6561,plain,
    ! [X27702,X27703,X27704,X27705,X27706,X27707] :
      ( ~ class_Groups_Ocomm__monoid__mult(X27707)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27706,X27707),hAPP(hAPP(c_COMBC(X27706,tc_fun(X27705,tc_HOL_Obool),X27707),hAPP(hAPP(c_COMBB(tc_fun(X27705,X27707),tc_fun(tc_fun(X27705,tc_HOL_Obool),X27707),X27706),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27705,X27707)),X27704)),X27703)),X27702) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X27706,X27705),X27707),hAPP(c_Product__Type_Oprod_Oprod__case(X27706,X27705,X27707),X27704)),hAPP(hAPP(c_Product__Type_OSigma(X27706,X27705),X27702),hAPP(c_COMBK(tc_fun(X27705,tc_HOL_Obool),X27706),X27703))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__cartesian__product])]) ).

fof(i_0_6562,plain,
    ! [X18313,X18314,X18315,X18316,X18317] :
      ( ( hBOOL(hAPP(hAPP(c_member(X18316),esk25_5(X18313,X18314,X18315,X18316,X18317)),X18313))
        | hBOOL(hAPP(hAPP(c_member(X18316),X18314),X18317))
        | ~ hBOOL(hAPP(hAPP(c_member(X18316),X18314),X18313))
        | ~ c_Orderings_Oorder__class_Omono(tc_fun(X18316,tc_HOL_Obool),tc_fun(X18316,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X18316,tc_HOL_Obool),tc_fun(X18316,tc_HOL_Obool),tc_fun(X18316,tc_HOL_Obool)),c_Set_OCollect(X18316)),X18315))
        | X18317 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X18316,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X18316,tc_HOL_Obool),tc_fun(X18316,tc_HOL_Obool),tc_fun(X18316,tc_HOL_Obool)),c_Set_OCollect(X18316)),X18315)) )
      & ( ~ hBOOL(hAPP(hAPP(X18315,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18316,tc_HOL_Obool)),X18313),X18317)),esk25_5(X18313,X18314,X18315,X18316,X18317)))
        | hBOOL(hAPP(hAPP(c_member(X18316),X18314),X18317))
        | ~ hBOOL(hAPP(hAPP(c_member(X18316),X18314),X18313))
        | ~ c_Orderings_Oorder__class_Omono(tc_fun(X18316,tc_HOL_Obool),tc_fun(X18316,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X18316,tc_HOL_Obool),tc_fun(X18316,tc_HOL_Obool),tc_fun(X18316,tc_HOL_Obool)),c_Set_OCollect(X18316)),X18315))
        | X18317 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X18316,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X18316,tc_HOL_Obool),tc_fun(X18316,tc_HOL_Obool),tc_fun(X18316,tc_HOL_Obool)),c_Set_OCollect(X18316)),X18315)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_def__Collect__coinduct])])])]) ).

fof(i_0_6563,plain,
    ! [X29946,X29947,X29948,X29949] :
      ( ( X29947 = hAPP(hAPP(c_Product__Type_OPair(X29949,X29948),esk389_4(X29946,X29947,X29948,X29949)),esk388_4(X29946,X29947,X29948,X29949))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29949,X29948)),X29947),hAPP(c_Relation_Oconverse(X29948,X29949),X29946))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29948,X29949)),hAPP(hAPP(c_Product__Type_OPair(X29948,X29949),esk388_4(X29946,X29947,X29948,X29949)),esk389_4(X29946,X29947,X29948,X29949))),X29946))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29949,X29948)),X29947),hAPP(c_Relation_Oconverse(X29948,X29949),X29946))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5415])])])]) ).

fof(i_0_6564,plain,
    ! [X28098,X28099,X28100,X28101,X28102,X28103,X28104,X28105] :
      ( ~ c_Fun_Oinj__on(X28105,X28104,X28103,X28102)
      | ~ c_Fun_Oinj__on(X28101,X28100,X28099,X28098)
      | c_Fun_Oinj__on(tc_prod(X28105,X28101),tc_prod(X28104,X28100),c_Product__Type_Omap__pair(X28105,X28104,X28101,X28100,X28103,X28099),hAPP(hAPP(c_Product__Type_OSigma(X28105,X28101),X28102),hAPP(c_COMBK(tc_fun(X28101,tc_HOL_Obool),X28105),X28098))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__inj__on])]) ).

fof(i_0_6565,plain,
    ! [X23712,X23713,X23714,X23715,X23716] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23716,X23715),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X23714),X23713)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23715))
      | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23712),X23716),X23715),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),X23712),X23714)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23712),X23713)),X23715))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23712),X23713),X23715)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__mult1__eq])]) ).

fof(i_0_6566,plain,
    ! [X20220,X20221,X20222,X20223,X20224] :
      ( ( hBOOL(hAPP(hAPP(c_member(X20222),esk71_5(X20220,X20221,X20222,X20223,X20224)),X20220))
        | ~ hBOOL(hAPP(hAPP(c_member(X20224),X20223),c_Map_Oran(X20222,X20224,c_Map_Orestrict__map(X20222,X20224,X20221,X20220)))) )
      & ( hAPP(X20221,esk71_5(X20220,X20221,X20222,X20223,X20224)) = hAPP(c_Option_Ooption_OSome(X20224),X20223)
        | ~ hBOOL(hAPP(hAPP(c_member(X20224),X20223),c_Map_Oran(X20222,X20224,c_Map_Orestrict__map(X20222,X20224,X20221,X20220)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ran__restrictD])])])]) ).

fof(i_0_6567,plain,
    ! [X23590,X23591,X23592,X23593,X23594] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X23594,X23593),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X23592),X23591)))
      | X23593 = 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),X23590),X23594),X23593),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),X23590),X23592)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23590),X23591)),X23593))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23590),X23591),X23593)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult1__lemma])]) ).

fof(i_0_6568,plain,
    ! [X33811,X33812,X33813,X33814] : c_Lazy__Sequence_Oproduct(X33814,X33813,X33812,X33811) = hAPP(c_Lazy__Sequence_Obind(X33814,tc_prod(X33814,X33813),X33812),hAPP(hAPP(c_COMBB(tc_fun(X33813,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X33814,X33813))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X33814,X33813)),X33814),c_Lazy__Sequence_Obind(X33813,tc_prod(X33814,X33813),X33811)),hAPP(hAPP(c_COMBB(tc_fun(X33813,tc_prod(X33814,X33813)),tc_fun(X33813,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X33814,X33813))),X33814),hAPP(c_COMBB(tc_prod(X33814,X33813),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X33814,X33813)),X33813),c_Lazy__Sequence_Osingle(tc_prod(X33814,X33813)))),c_Product__Type_OPair(X33814,X33813)))),
    inference(variable_rename,[status(thm)],[fact__02]) ).

fof(i_0_6569,plain,
    ! [X26686,X26687,X26688,X26689] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26688),X26687))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26689),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X26689,X26689),hAPP(hAPP(c_COMBB(X26689,tc_fun(X26689,X26689),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X26689)),X26686)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X26689,tc_Nat_Onat),X26686),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,X26688,X26687)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26689),hAPP(X26686,X26688)),hAPP(X26686,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26687),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ class_Groups_Oab__group__add(X26689) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26688),X26687))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26689),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X26689,X26689),hAPP(hAPP(c_COMBB(X26689,tc_fun(X26689,X26689),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X26689)),X26686)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X26689,tc_Nat_Onat),X26686),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,X26688,X26687)) = c_Groups_Ozero__class_Ozero(X26689)
        | ~ class_Groups_Oab__group__add(X26689) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5416])])]) ).

fof(i_0_6570,plain,
    ! [X31227,X31228,X31229,X31230,X31231,X31232,X31233] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X31233),X31232),hAPP(c_List_Oset(X31233),hAPP(hAPP(c_List_Otake(X31233),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31231)),X31230)),X31229))))
        | c_Map_Omap__upds(X31233,X31231,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X31233,tc_Option_Ooption(X31231)),X31228),X31232),hAPP(c_Option_Ooption_OSome(X31231),X31227)),X31229,X31230) = c_Map_Omap__upds(X31233,X31231,X31228,X31229,X31230) )
      & ( hBOOL(hAPP(hAPP(c_member(X31233),X31232),hAPP(c_List_Oset(X31233),hAPP(hAPP(c_List_Otake(X31233),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31231)),X31230)),X31229))))
        | c_Map_Omap__upds(X31233,X31231,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X31233,tc_Option_Ooption(X31231)),X31228),X31232),hAPP(c_Option_Ooption_OSome(X31231),X31227)),X31229,X31230) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X31233,tc_Option_Ooption(X31231)),c_Map_Omap__upds(X31233,X31231,X31228,X31229,X31230)),X31232),hAPP(c_Option_Ooption_OSome(X31231),X31227)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5417])]) ).

fof(i_0_6571,plain,
    ! [X27888,X27889,X27890,X27891] :
      ( c_Fun_Oinj__on(X27891,tc_prod(X27890,X27891),esk271_4(X27888,X27889,X27890,X27891),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27890,tc_fun(X27891,tc_HOL_Obool)),X27889),X27888))
      & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27890,X27891),tc_HOL_Obool)),hAPP(c_Set_Oimage(X27891,tc_prod(X27890,X27891),esk271_4(X27888,X27889,X27890,X27891)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27890,tc_fun(X27891,tc_HOL_Obool)),X27889),X27888))),hAPP(hAPP(c_Product__Type_OSigma(X27890,X27891),X27889),X27888))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_Ex__inj__on__UNION__Sigma])]) ).

fof(i_0_6572,plain,
    ! [X30899,X30900] :
      ( ~ class_Enum_Oenum(X30900)
      | ~ class_HOL_Oequal(X30900)
      | ~ class_Enum_Oenum(X30899)
      | c_Enum_Oenum__class_Oenum(tc_fun(X30900,X30899)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X30899),tc_fun(X30900,X30899)),hAPP(hAPP(c_COMBB(tc_fun(X30900,tc_Option_Ooption(X30899)),tc_fun(X30900,X30899),tc_List_Olist(X30899)),c_Fun_Ocomp(tc_Option_Ooption(X30899),X30899,X30900,c_Option_Othe(X30899))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X30900,X30899)),tc_fun(X30900,tc_Option_Ooption(X30899)),tc_List_Olist(X30899)),c_Map_Omap__of(X30900,X30899)),hAPP(c_List_Ozip(X30900,X30899),c_Enum_Oenum__class_Oenum(X30900))))),c_Enum_On__lists(X30899,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30900)),c_Enum_Oenum__class_Oenum(X30900)),c_Enum_Oenum__class_Oenum(X30899))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__fun__code])]) ).

fof(i_0_6573,plain,
    ! [X20577,X20578,X20579,X20580,X20581] :
      ( ~ class_Groups_Oab__semigroup__mult(X20581)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X20581,X20581,c_Groups_Otimes__class_Otimes(X20581),X20580,X20579),X20578))
      | hBOOL(hAPP(hAPP(c_member(X20581),X20580),X20579))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X20581,X20581,c_Groups_Otimes__class_Otimes(X20581),X20577,hAPP(hAPP(c_Set_Oinsert(X20581),X20580),X20579)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20581),X20577),X20578))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5418])]) ).

fof(i_0_6574,plain,
    ! [X30901,X30902] :
      ( ~ class_Enum_Oenum(X30902)
      | ~ class_Enum_Oenum(X30901)
      | c_Enum_Oenum__class_Oenum(tc_fun(X30902,X30901)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X30901),tc_fun(X30902,X30901)),hAPP(hAPP(c_COMBB(tc_fun(X30902,tc_Option_Ooption(X30901)),tc_fun(X30902,X30901),tc_List_Olist(X30901)),c_Fun_Ocomp(tc_Option_Ooption(X30901),X30901,X30902,c_Option_Othe(X30901))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X30902,X30901)),tc_fun(X30902,tc_Option_Ooption(X30901)),tc_List_Olist(X30901)),c_Map_Omap__of(X30902,X30901)),hAPP(c_List_Ozip(X30902,X30901),c_Enum_Oenum__class_Oenum(X30902))))),c_Enum_On__lists(X30901,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30902)),c_Enum_Oenum__class_Oenum(X30902)),c_Enum_Oenum__class_Oenum(X30901))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__fun__def])]) ).

fof(i_0_6575,plain,
    ! [X32377,X32378,X32379,X32380] : hAPP(hAPP(c_List_Omap(tc_prod(X32380,tc_Nat_Onat),X32380),c_Product__Type_Ofst(X32380,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X32380,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X32380,tc_Nat_Onat)),X32379),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(X32380,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(X32380,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(X32380,tc_Nat_Onat),X32378),X32377))) = hAPP(hAPP(c_List_Omap(tc_prod(X32380,tc_Nat_Onat),X32380),c_Product__Type_Ofst(X32380,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X32380,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X32380,tc_Nat_Onat)),X32379),c_Product__Type_Osnd(X32380,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X32380,tc_Nat_Onat),X32378),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X32377)))),
    inference(variable_rename,[status(thm)],[fact_sublist__shift__lemma__Suc]) ).

fof(i_0_6576,plain,
    ! [X28029,X28030,X28031,X28032,X28033,X28034] : hAPP(c_Fun_Ocomp(tc_prod(X28034,X28033),X28034,tc_prod(X28032,X28031),c_Product__Type_Ofst(X28034,X28033)),c_Product__Type_Omap__pair(X28032,X28034,X28031,X28033,X28030,X28029)) = hAPP(c_Fun_Ocomp(X28032,X28034,tc_prod(X28032,X28031),X28030),c_Product__Type_Ofst(X28032,X28031)),
    inference(variable_rename,[status(thm)],[fact_fst__comp__map__pair]) ).

fof(i_0_6577,plain,
    ! [X28023,X28024,X28025,X28026,X28027,X28028] : hAPP(c_Fun_Ocomp(tc_prod(X28028,X28027),X28027,tc_prod(X28026,X28025),c_Product__Type_Osnd(X28028,X28027)),c_Product__Type_Omap__pair(X28026,X28028,X28025,X28027,X28024,X28023)) = hAPP(c_Fun_Ocomp(X28025,X28027,tc_prod(X28026,X28025),X28023),c_Product__Type_Osnd(X28026,X28025)),
    inference(variable_rename,[status(thm)],[fact_snd__comp__map__pair]) ).

fof(i_0_6578,plain,
    ! [X29278,X29279,X29280,X29281,X29282,X29283] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29283,tc_fun(X29282,tc_HOL_Obool)),X29281),hAPP(hAPP(c_COMBC(X29283,tc_fun(X29280,tc_fun(X29282,tc_HOL_Obool)),tc_fun(X29282,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29280,tc_HOL_Obool),tc_fun(tc_fun(X29280,tc_fun(X29282,tc_HOL_Obool)),tc_fun(X29282,tc_HOL_Obool)),X29283),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29280,tc_fun(X29282,tc_HOL_Obool))),X29279)),X29278)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29280,tc_fun(X29282,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29283,tc_fun(X29280,tc_HOL_Obool)),X29281),X29279)),X29278),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I9_J]) ).

fof(i_0_6579,plain,
    ! [X19601,X19602,X19603,X19604,X19605,X19606] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19606,tc_fun(X19605,tc_HOL_Obool)),X19604),hAPP(hAPP(c_COMBC(X19606,tc_fun(X19603,tc_fun(X19605,tc_HOL_Obool)),tc_fun(X19605,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19603,tc_HOL_Obool),tc_fun(tc_fun(X19603,tc_fun(X19605,tc_HOL_Obool)),tc_fun(X19605,tc_HOL_Obool)),X19606),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19603,tc_fun(X19605,tc_HOL_Obool))),X19602)),X19601)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19603,tc_fun(X19605,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19606,tc_fun(X19603,tc_HOL_Obool)),X19604),X19602)),X19601),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I9_J]) ).

fof(i_0_6580,plain,
    ! [X29284,X29285,X29286,X29287,X29288,X29289] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29289,tc_fun(X29288,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29287,tc_fun(X29289,tc_HOL_Obool)),X29286),X29285)),X29284) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29287,tc_fun(X29288,tc_HOL_Obool)),X29286),hAPP(hAPP(c_COMBC(X29287,tc_fun(X29289,tc_fun(X29288,tc_HOL_Obool)),tc_fun(X29288,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29289,tc_HOL_Obool),tc_fun(tc_fun(X29289,tc_fun(X29288,tc_HOL_Obool)),tc_fun(X29288,tc_HOL_Obool)),X29287),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29289,tc_fun(X29288,tc_HOL_Obool))),X29285)),X29284)),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I9_J]) ).

fof(i_0_6581,plain,
    ! [X19613,X19614,X19615,X19616,X19617,X19618] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19618,tc_fun(X19617,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19616,tc_fun(X19618,tc_HOL_Obool)),X19615),X19614)),X19613) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19616,tc_fun(X19617,tc_HOL_Obool)),X19615),hAPP(hAPP(c_COMBC(X19616,tc_fun(X19618,tc_fun(X19617,tc_HOL_Obool)),tc_fun(X19617,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19618,tc_HOL_Obool),tc_fun(tc_fun(X19618,tc_fun(X19617,tc_HOL_Obool)),tc_fun(X19617,tc_HOL_Obool)),X19616),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19618,tc_fun(X19617,tc_HOL_Obool))),X19614)),X19613)),
    inference(variable_rename,[status(thm)],[fact_UN__UN__flatten]) ).

fof(i_0_6582,plain,
    ! [X19607,X19608,X19609,X19610,X19611,X19612] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19612,tc_fun(X19611,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19610,tc_fun(X19612,tc_HOL_Obool)),X19609),X19608)),X19607) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19610,tc_fun(X19611,tc_HOL_Obool)),X19609),hAPP(hAPP(c_COMBC(X19610,tc_fun(X19612,tc_fun(X19611,tc_HOL_Obool)),tc_fun(X19611,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19612,tc_HOL_Obool),tc_fun(tc_fun(X19612,tc_fun(X19611,tc_HOL_Obool)),tc_fun(X19611,tc_HOL_Obool)),X19610),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19612,tc_fun(X19611,tc_HOL_Obool))),X19608)),X19607)),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I9_J]) ).

fof(i_0_6583,plain,
    ! [X19252,X19253,X19254,X19255,X19256,X19257,X19258] :
      ( hBOOL(hAPP(hAPP(c_member(X19258),X19257),X19256))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19258,X19255,X19254,X19253,X19256),X19252))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19258,X19255,X19254,X19253,hAPP(hAPP(c_Set_Oinsert(X19258),X19257),X19256)),hAPP(hAPP(X19254,X19257),X19252))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5419])]) ).

fof(i_0_6584,plain,
    ! [X33658,X33659] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk511_2(X33658,X33659)),hAPP(X33659,esk511_2(X33658,X33659))))
      | 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)),X33659)),X33658)))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__less__ub])])]) ).

cnf(i_0_6585,plain,
    ( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),esk398_6(X2,X1,X4,X5,X6,X3))
    | hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
    | c_Map_Omap__comp(X3,X6,X5,X4,X1,X2) != c_Option_Ooption_ONone(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_5420]) ).

cnf(i_0_6586,plain,
    ( hAPP(X1,esk398_6(X2,X3,X1,X4,X5,X6)) = c_Option_Ooption_ONone(X5)
    | hAPP(X3,X2) = c_Option_Ooption_ONone(X6)
    | c_Map_Omap__comp(X6,X5,X4,X1,X3,X2) != c_Option_Ooption_ONone(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_5420]) ).

fof(i_0_6587,plain,
    ! [X19953,X19954,X19955,X19956,X19957,X19958,X19959,X19960,X19961,X19962] :
      ( ~ c_Equiv__Relations_Ocongruent2(X19962,X19961,X19960,X19959,X19958,X19957)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X19962,X19962)),hAPP(hAPP(c_Product__Type_OPair(X19962,X19962),X19956),X19955)),X19959))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X19961,X19961)),hAPP(hAPP(c_Product__Type_OPair(X19961,X19961),X19954),X19953)),X19958))
      | hAPP(hAPP(X19957,X19956),X19954) = hAPP(hAPP(X19957,X19955),X19953) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent2D])]) ).

fof(i_0_6588,plain,
    ! [X18337,X18338,X18339,X18340,X18341] :
      ( ( hBOOL(hAPP(hAPP(c_member(X18341),esk26_5(X18337,X18338,X18339,X18340,X18341)),X18340))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18341,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18341,tc_HOL_Obool)),X18340),hAPP(c_Set_OCollect(X18341),X18338))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18341,tc_HOL_Obool)),X18339),hAPP(c_Set_OCollect(X18341),X18337))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18341,tc_HOL_Obool)),X18340),X18339)) )
      & ( hBOOL(hAPP(X18338,esk26_5(X18337,X18338,X18339,X18340,X18341)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18341,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18341,tc_HOL_Obool)),X18340),hAPP(c_Set_OCollect(X18341),X18338))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18341,tc_HOL_Obool)),X18339),hAPP(c_Set_OCollect(X18341),X18337))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18341,tc_HOL_Obool)),X18340),X18339)) )
      & ( ~ hBOOL(hAPP(X18337,esk26_5(X18337,X18338,X18339,X18340,X18341)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18341,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18341,tc_HOL_Obool)),X18340),hAPP(c_Set_OCollect(X18341),X18338))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18341,tc_HOL_Obool)),X18339),hAPP(c_Set_OCollect(X18341),X18337))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18341,tc_HOL_Obool)),X18340),X18339)) ) ),
    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_6589,plain,
    ! [X31502,X31503,X31504,X31505,X31506,X31507] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31507)),X31506)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31505)),X31504)))
      | c_Map_Omap__upds(X31507,X31505,X31503,hAPP(hAPP(c_List_Oappend(X31507),X31506),hAPP(hAPP(c_List_Olist_OCons(X31507),X31502),c_List_Olist_ONil(X31507))),X31504) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X31507,tc_Option_Ooption(X31505)),c_Map_Omap__upds(X31507,X31505,X31503,X31506,X31504)),X31502),hAPP(c_Option_Ooption_OSome(X31505),hAPP(hAPP(c_List_Onth(X31505),X31504),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31507)),X31506)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__upds__append1])]) ).

fof(i_0_6590,plain,
    ! [X17440,X17441,X17442,X17443,X17444] :
      ( ( hBOOL(hAPP(hAPP(c_member(X17442),esk17_5(X17440,X17441,X17442,X17443,X17444)),X17440))
        | ~ hBOOL(hAPP(hAPP(c_member(X17442),X17444),X17440))
        | c_Orderings_Oord__class_OLeast(X17443,hAPP(hAPP(c_COMBC(X17443,tc_fun(X17443,tc_HOL_Obool),tc_HOL_Obool),c_member(X17443)),hAPP(c_Set_Oimage(X17442,X17443,X17441),X17440))) = hAPP(X17441,c_Orderings_Oord__class_OLeast(X17442,hAPP(hAPP(c_COMBC(X17442,tc_fun(X17442,tc_HOL_Obool),tc_HOL_Obool),c_member(X17442)),X17440)))
        | ~ c_Orderings_Oorder__class_Omono(X17442,X17443,X17441)
        | ~ class_Orderings_Oorder(X17443)
        | ~ class_Orderings_Oorder(X17442) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17442),X17444),esk17_5(X17440,X17441,X17442,X17443,X17444)))
        | ~ hBOOL(hAPP(hAPP(c_member(X17442),X17444),X17440))
        | c_Orderings_Oord__class_OLeast(X17443,hAPP(hAPP(c_COMBC(X17443,tc_fun(X17443,tc_HOL_Obool),tc_HOL_Obool),c_member(X17443)),hAPP(c_Set_Oimage(X17442,X17443,X17441),X17440))) = hAPP(X17441,c_Orderings_Oord__class_OLeast(X17442,hAPP(hAPP(c_COMBC(X17442,tc_fun(X17442,tc_HOL_Obool),tc_HOL_Obool),c_member(X17442)),X17440)))
        | ~ c_Orderings_Oorder__class_Omono(X17442,X17443,X17441)
        | ~ class_Orderings_Oorder(X17443)
        | ~ class_Orderings_Oorder(X17442) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Least__mono])])])])]) ).

fof(i_0_6591,plain,
    ! [X26429,X26430,X26431] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26431,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26431,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk228_3(X26429,X26430,X26431))),X26430)),X26429))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26431,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26431,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X26430)),X26429)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__finite__subset])])]) ).

fof(i_0_6592,plain,
    ! [X18260,X18261,X18262] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18262,tc_HOL_Obool)),X18261),X18260) = hAPP(c_Set_OCollect(X18262),hAPP(hAPP(c_COMBS(X18262,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X18262),c_fconj),hAPP(hAPP(c_COMBC(X18262,tc_fun(X18262,tc_HOL_Obool),tc_HOL_Obool),c_member(X18262)),X18261))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X18262),c_fNot),hAPP(hAPP(c_COMBC(X18262,tc_fun(X18262,tc_HOL_Obool),tc_HOL_Obool),c_member(X18262)),X18260)))),
    inference(variable_rename,[status(thm)],[fact_set__diff__eq]) ).

fof(i_0_6593,plain,
    ! [X20344,X20345,X20346] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20346),hAPP(c_Set_OCollect(X20346),X20345)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20346),hAPP(c_Set_OCollect(X20346),hAPP(hAPP(c_COMBS(X20346,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X20346),c_fconj),X20345)),X20344)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20346),hAPP(c_Set_OCollect(X20346),X20344)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20346),hAPP(c_Set_OCollect(X20346),hAPP(hAPP(c_COMBS(X20346,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X20346),c_fconj),X20345)),X20344)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__conjI])])]) ).

fof(i_0_6594,plain,
    ! [X26188,X26189] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26189,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(X26189,tc_HOL_Obool)),tc_fun(X26189,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(X26189,tc_HOL_Obool)),tc_fun(X26189,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26189,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X26188)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26189,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X26188),
    inference(variable_rename,[status(thm)],[fact_UN__UN__finite__eq]) ).

cnf(i_0_6595,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk347_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_5421]) ).

cnf(i_0_6596,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk348_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_5422]) ).

fof(i_0_6597,plain,
    ! [X28001,X28002,X28003,X28004,X28005,X28006,X28007,X28008] : hAPP(c_Product__Type_Omap__pair(X28008,X28007,X28006,X28005,X28004,X28003),hAPP(hAPP(c_Product__Type_OPair(X28008,X28006),X28002),X28001)) = hAPP(hAPP(c_Product__Type_OPair(X28007,X28005),hAPP(X28004,X28002)),hAPP(X28003,X28001)),
    inference(variable_rename,[status(thm)],[fact_map__pair__simp]) ).

cnf(i_0_6598,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_5423]) ).

cnf(i_0_6599,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_5424]) ).

fof(i_0_6600,plain,
    ! [X33290,X33291,X33292,X33293,X33294] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33294,X33293)),esk473_5(X33290,X33291,X33292,X33293,X33294)),hAPP(c_List_Oset(tc_prod(X33294,X33293)),hAPP(hAPP(c_List_Ozip(X33294,X33293),X33292),X33291))))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33294)),X33292) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33293)),X33291)
        | c_List_Olist__all2(X33294,X33293,X33290,X33292,X33291) )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X33294,X33293,tc_HOL_Obool),X33290),esk473_5(X33290,X33291,X33292,X33293,X33294)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33294)),X33292) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33293)),X33291)
        | c_List_Olist__all2(X33294,X33293,X33290,X33292,X33291) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2I])])])]) ).

fof(i_0_6601,plain,
    ! [X33157,X33158,X33159,X33160,X33161,X33162,X33163,X33164,X33165,X33166,X33167] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33161)),X33158) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33160)),X33157)
        | ~ c_List_Olist__all2(X33161,X33160,X33159,X33158,X33157) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33161,X33160)),X33162),hAPP(c_List_Oset(tc_prod(X33161,X33160)),hAPP(hAPP(c_List_Ozip(X33161,X33160),X33158),X33157))))
        | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X33161,X33160,tc_HOL_Obool),X33159),X33162))
        | ~ c_List_Olist__all2(X33161,X33160,X33159,X33158,X33157) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33167,X33166)),esk468_5(X33163,X33164,X33165,X33166,X33167)),hAPP(c_List_Oset(tc_prod(X33167,X33166)),hAPP(hAPP(c_List_Ozip(X33167,X33166),X33164),X33163))))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33167)),X33164) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33166)),X33163)
        | c_List_Olist__all2(X33167,X33166,X33165,X33164,X33163) )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X33167,X33166,tc_HOL_Obool),X33165),esk468_5(X33163,X33164,X33165,X33166,X33167)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33167)),X33164) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33166)),X33163)
        | c_List_Olist__all2(X33167,X33166,X33165,X33164,X33163) ) ),
    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_6602,plain,
    ! [X27998,X27999,X28000] : hAPP(c_Product__Type_Omap__pair(X28000,X28000,X27999,X27999,c_COMBI(X28000),c_COMBI(X27999)),X27998) = X27998,
    inference(variable_rename,[status(thm)],[fact_map__pair__ident]) ).

fof(i_0_6603,plain,
    ! [X31260,X31261,X31262,X31263,X31264,X31265,X31266] :
      ( hBOOL(hAPP(hAPP(c_member(X31266),X31265),hAPP(c_List_Oset(X31266),X31264)))
      | c_Map_Omap__upds(X31266,X31263,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X31266,tc_Option_Ooption(X31263)),X31262),X31265),hAPP(c_Option_Ooption_OSome(X31263),X31261)),X31264,X31260) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X31266,tc_Option_Ooption(X31263)),c_Map_Omap__upds(X31266,X31263,X31262,X31264,X31260)),X31265),hAPP(c_Option_Ooption_OSome(X31263),X31261)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5425])]) ).

fof(i_0_6604,plain,
    ! [X18639,X18640,X18641,X18642,X18643] :
      ( ( hBOOL(hAPP(hAPP(c_member(X18642),esk28_5(X18639,X18640,X18641,X18642,X18643)),hAPP(X18641,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18642,tc_HOL_Obool)),X18643),hAPP(c_Set_OCollect(X18642),X18639)))))
        | hBOOL(hAPP(X18639,X18640))
        | ~ hBOOL(hAPP(hAPP(c_member(X18642),X18640),X18643))
        | ~ c_Orderings_Oorder__class_Omono(tc_fun(X18642,tc_HOL_Obool),tc_fun(X18642,tc_HOL_Obool),X18641)
        | X18643 != c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X18642,tc_HOL_Obool),X18641) )
      & ( ~ hBOOL(hAPP(X18639,esk28_5(X18639,X18640,X18641,X18642,X18643)))
        | hBOOL(hAPP(X18639,X18640))
        | ~ hBOOL(hAPP(hAPP(c_member(X18642),X18640),X18643))
        | ~ c_Orderings_Oorder__class_Omono(tc_fun(X18642,tc_HOL_Obool),tc_fun(X18642,tc_HOL_Obool),X18641)
        | X18643 != c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X18642,tc_HOL_Obool),X18641) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_def__lfp__induct__set])])])]) ).

fof(i_0_6605,plain,
    ! [X20756,X20757,X20758,X20759,X20760,X20761,X20762,X20763] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X20763,X20762,X20761,X20760,X20759,X20758)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20762),X20757))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20762),X20756))
      | hAPP(hAPP(X20761,hAPP(X20758,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20762,tc_HOL_Obool)),X20757),X20756))),hAPP(X20758,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20762,tc_HOL_Obool)),X20757),X20756))) = hAPP(hAPP(X20761,hAPP(X20758,X20757)),hAPP(X20758,X20756)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__inter])]) ).

fof(i_0_6606,plain,
    ! [X26773,X26774,X26775,X26776,X26777] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26776),esk239_5(X26773,X26774,X26775,X26776,X26777)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26776,tc_HOL_Obool)),X26775),X26774)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26776,X26777),X26773),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26776,tc_HOL_Obool)),X26775),X26774)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26777),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26776,X26777),X26773),X26775)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26776,X26777),X26773),X26774))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26776),X26774))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26776),X26775))
        | ~ class_Groups_Ocomm__monoid__add(X26777) )
      & ( hAPP(X26773,esk239_5(X26773,X26774,X26775,X26776,X26777)) != c_Groups_Ozero__class_Ozero(X26777)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26776,X26777),X26773),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26776,tc_HOL_Obool)),X26775),X26774)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26777),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26776,X26777),X26773),X26775)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26776,X26777),X26773),X26774))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26776),X26774))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26776),X26775))
        | ~ class_Groups_Ocomm__monoid__add(X26777) ) ),
    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_6607,plain,
    ! [X26706,X26707,X26708,X26709,X26710] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26709),esk231_5(X26706,X26707,X26708,X26709,X26710)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26709,tc_HOL_Obool)),X26708),X26707)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26709,X26710),X26706),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26709,tc_HOL_Obool)),X26708),X26707)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26710),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26709,X26710),X26706),X26708)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26709,X26710),X26706),X26707))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26709),X26707))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26709),X26708))
        | ~ class_Groups_Ocomm__monoid__add(X26710) )
      & ( hAPP(X26706,esk231_5(X26706,X26707,X26708,X26709,X26710)) != c_Groups_Ozero__class_Ozero(X26710)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26709,X26710),X26706),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26709,tc_HOL_Obool)),X26708),X26707)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26710),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26709,X26710),X26706),X26708)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26709,X26710),X26706),X26707))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26709),X26707))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26709),X26708))
        | ~ class_Groups_Ocomm__monoid__add(X26710) ) ),
    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_6608,plain,
    ! [X23257,X23258,X23259,X23260,X23261] :
      ( ( hBOOL(hAPP(hAPP(c_member(X23260),esk122_5(X23257,X23258,X23259,X23260,X23261)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23260,tc_HOL_Obool)),X23259),X23258)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23260,X23261),X23257),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23260,tc_HOL_Obool)),X23259),X23258)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23261),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23260,X23261),X23257),X23259)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23260,X23261),X23257),X23258))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23260),X23258))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23260),X23259))
        | ~ class_Groups_Ocomm__monoid__mult(X23261) )
      & ( hAPP(X23257,esk122_5(X23257,X23258,X23259,X23260,X23261)) != c_Groups_Oone__class_Oone(X23261)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23260,X23261),X23257),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23260,tc_HOL_Obool)),X23259),X23258)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23261),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23260,X23261),X23257),X23259)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23260,X23261),X23257),X23258))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23260),X23258))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23260),X23259))
        | ~ class_Groups_Ocomm__monoid__mult(X23261) ) ),
    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_6609,plain,
    ! [X23251,X23252,X23253,X23254,X23255] :
      ( ( hBOOL(hAPP(hAPP(c_member(X23254),esk121_5(X23251,X23252,X23253,X23254,X23255)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23254,tc_HOL_Obool)),X23253),X23252)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23254,X23255),X23251),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23254,tc_HOL_Obool)),X23253),X23252)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23255),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23254,X23255),X23251),X23253)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23254,X23255),X23251),X23252))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23254),X23252))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23254),X23253))
        | ~ class_Groups_Ocomm__monoid__mult(X23255) )
      & ( hAPP(X23251,esk121_5(X23251,X23252,X23253,X23254,X23255)) != c_Groups_Oone__class_Oone(X23255)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23254,X23255),X23251),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23254,tc_HOL_Obool)),X23253),X23252)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23255),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23254,X23255),X23251),X23253)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23254,X23255),X23251),X23252))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23254),X23252))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23254),X23253))
        | ~ class_Groups_Ocomm__monoid__mult(X23255) ) ),
    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_6610,plain,
    ! [X20049,X20050,X20051,X20052] : hAPP(c_Relation_OImage(X20052,X20051,X20050),hAPP(hAPP(c_Set_Oinsert(X20052),X20049),c_Orderings_Obot__class_Obot(tc_fun(X20052,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(X20051),hAPP(hAPP(c_COMBC(X20051,tc_fun(tc_prod(X20052,X20051),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X20052,X20051),tc_fun(tc_fun(tc_prod(X20052,X20051),tc_HOL_Obool),tc_HOL_Obool),X20051),c_member(tc_prod(X20052,X20051))),hAPP(c_Product__Type_OPair(X20052,X20051),X20049))),X20050)),
    inference(variable_rename,[status(thm)],[fact_Image__singleton]) ).

fof(i_0_6611,plain,
    ! [X33622,X33623,X33624,X33625] :
      ( ( ~ hBOOL(hAPP(X33624,X33623))
        | c_List_Olist__all(X33625,hAPP(hAPP(c_COMBS(X33625,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33625),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33625),c_fNot),X33624))),hAPP(c_fequal,X33623)),X33622)
        | ~ c_List_Olist__ex1(X33625,X33624,hAPP(hAPP(c_List_Olist_OCons(X33625),X33623),X33622)) )
      & ( hBOOL(hAPP(X33624,X33623))
        | c_List_Olist__ex1(X33625,X33624,X33622)
        | ~ c_List_Olist__ex1(X33625,X33624,hAPP(hAPP(c_List_Olist_OCons(X33625),X33623),X33622)) )
      & ( ~ hBOOL(hAPP(X33624,X33623))
        | hBOOL(hAPP(X33624,X33623))
        | c_List_Olist__ex1(X33625,X33624,hAPP(hAPP(c_List_Olist_OCons(X33625),X33623),X33622)) )
      & ( ~ c_List_Olist__ex1(X33625,X33624,X33622)
        | hBOOL(hAPP(X33624,X33623))
        | c_List_Olist__ex1(X33625,X33624,hAPP(hAPP(c_List_Olist_OCons(X33625),X33623),X33622)) )
      & ( ~ hBOOL(hAPP(X33624,X33623))
        | ~ c_List_Olist__all(X33625,hAPP(hAPP(c_COMBS(X33625,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33625),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33625),c_fNot),X33624))),hAPP(c_fequal,X33623)),X33622)
        | c_List_Olist__ex1(X33625,X33624,hAPP(hAPP(c_List_Olist_OCons(X33625),X33623),X33622)) )
      & ( ~ c_List_Olist__ex1(X33625,X33624,X33622)
        | ~ c_List_Olist__all(X33625,hAPP(hAPP(c_COMBS(X33625,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33625),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33625),c_fNot),X33624))),hAPP(c_fequal,X33623)),X33622)
        | c_List_Olist__ex1(X33625,X33624,hAPP(hAPP(c_List_Olist_OCons(X33625),X33623),X33622)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5426])])]) ).

cnf(i_0_6612,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_5427]) ).

fof(i_0_6613,plain,
    ! [X20627,X20628,X20629,X20630,X20631,X20632,X20633,X20634] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X20634,X20633,X20632,X20631,X20630,X20629)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20633),X20628))
      | ~ hBOOL(hAPP(hAPP(c_member(X20633),X20627),X20628))
      | hAPP(X20629,X20628) = hAPP(hAPP(X20632,hAPP(X20630,X20627)),hAPP(X20629,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20633,tc_HOL_Obool)),X20628),hAPP(hAPP(c_Set_Oinsert(X20633),X20627),c_Orderings_Obot__class_Obot(tc_fun(X20633,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oremove])]) ).

fof(i_0_6614,plain,
    ! [X17467,X17468,X17469,X17470,X17471,X17473,X17474,X17475,X17476,X17477,X17478] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17469,tc_HOL_Obool)),esk18_5(X17467,X17468,X17469,X17470,X17471)),X17467))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17471,tc_HOL_Obool)),X17470),hAPP(c_Set_Oimage(X17469,X17471,X17468),X17467))) )
      & ( X17470 = hAPP(c_Set_Oimage(X17469,X17471,X17468),esk18_5(X17467,X17468,X17469,X17470,X17471))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17471,tc_HOL_Obool)),X17470),hAPP(c_Set_Oimage(X17469,X17471,X17468),X17467))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17475,tc_HOL_Obool)),X17478),X17473))
        | X17476 != hAPP(c_Set_Oimage(X17475,X17477,X17474),X17478)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17477,tc_HOL_Obool)),X17476),hAPP(c_Set_Oimage(X17475,X17477,X17474),X17473))) ) ),
    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_6615,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_5428]) ).

fof(i_0_6616,plain,
    ! [X19642,X19643,X19644,X19645,X19646,X19648,X19649,X19650,X19651,X19652,X19653] :
      ( ( hBOOL(hAPP(hAPP(c_member(X19644),esk50_5(X19642,X19643,X19644,X19645,X19646)),X19643))
        | ~ hBOOL(hAPP(hAPP(c_member(X19646),X19645),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19644,tc_fun(X19646,tc_HOL_Obool)),X19643),X19642))) )
      & ( hBOOL(hAPP(hAPP(c_member(X19646),X19645),hAPP(X19642,esk50_5(X19642,X19643,X19644,X19645,X19646))))
        | ~ hBOOL(hAPP(hAPP(c_member(X19646),X19645),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19644,tc_fun(X19646,tc_HOL_Obool)),X19643),X19642))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X19650),X19653),X19649))
        | ~ hBOOL(hAPP(hAPP(c_member(X19652),X19651),hAPP(X19648,X19653)))
        | hBOOL(hAPP(hAPP(c_member(X19652),X19651),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19650,tc_fun(X19652,tc_HOL_Obool)),X19649),X19648))) ) ),
    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_6617,plain,
    ! [X20786,X20787,X20788,X20789,X20790,X20791,X20792,X20793] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X20793,X20792,X20791,X20790,X20789,X20788)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20792),X20787))
      | hAPP(X20788,hAPP(hAPP(c_Set_Oinsert(X20792),X20786),X20787)) = hAPP(hAPP(X20791,hAPP(X20789,X20786)),hAPP(X20788,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20792,tc_HOL_Obool)),X20787),hAPP(hAPP(c_Set_Oinsert(X20792),X20786),c_Orderings_Obot__class_Obot(tc_fun(X20792,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oinsert__remove])]) ).

fof(i_0_6618,plain,
    ! [X19041,X19042,X19043,X19044,X19045,X19046,X19047] :
      ( ~ c_Fun_Oinj__on(X19047,X19046,X19045,hAPP(c_Set_Oimage(X19044,X19047,X19043),X19042))
      | ~ c_Fun_Oinj__on(X19044,X19047,X19043,X19042)
      | ~ hBOOL(hAPP(hAPP(c_member(X19046),X19041),hAPP(c_Set_Oimage(X19047,X19046,X19045),hAPP(c_Set_Oimage(X19044,X19047,X19043),X19042))))
      | hAPP(c_Hilbert__Choice_Oinv__into(X19044,X19046,X19042,hAPP(c_Fun_Ocomp(X19047,X19046,X19044,X19045),X19043)),X19041) = hAPP(hAPP(c_Fun_Ocomp(X19047,X19044,X19046,c_Hilbert__Choice_Oinv__into(X19044,X19047,X19042,X19043)),c_Hilbert__Choice_Oinv__into(X19047,X19046,hAPP(c_Set_Oimage(X19044,X19047,X19043),X19042),X19045)),X19041) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__comp])]) ).

fof(i_0_6619,plain,
    ! [X18845,X18846,X18847,X18848,X18849,X18850,X18851] :
      ( ~ c_Fun_Oinj__on(X18851,X18850,X18849,hAPP(c_Set_Oimage(X18848,X18851,X18847),X18846))
      | ~ c_Fun_Oinj__on(X18848,X18851,X18847,X18846)
      | ~ hBOOL(hAPP(hAPP(c_member(X18850),X18845),hAPP(c_Set_Oimage(X18851,X18850,X18849),hAPP(c_Set_Oimage(X18848,X18851,X18847),X18846))))
      | hAPP(c_Fun_Othe__inv__into(X18848,X18850,X18846,hAPP(c_Fun_Ocomp(X18851,X18850,X18848,X18849),X18847)),X18845) = hAPP(hAPP(c_Fun_Ocomp(X18851,X18848,X18850,c_Fun_Othe__inv__into(X18848,X18851,X18846,X18847)),c_Fun_Othe__inv__into(X18851,X18850,hAPP(c_Set_Oimage(X18848,X18851,X18847),X18846),X18849)),X18845) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__comp])]) ).

cnf(i_0_6620,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_5429]) ).

fof(i_0_6621,plain,
    ! [X26903,X26904,X26905,X26906,X26907] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26906),esk248_5(X26903,X26904,X26905,X26906,X26907)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26906,tc_HOL_Obool)),X26905),X26904)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26906,X26907),X26903),X26904) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26906,X26907),X26903),X26905)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26906,tc_HOL_Obool)),X26904),X26905))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26906),X26905))
        | ~ class_Groups_Ocomm__monoid__add(X26907) )
      & ( hAPP(X26903,esk248_5(X26903,X26904,X26905,X26906,X26907)) != c_Groups_Ozero__class_Ozero(X26907)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26906,X26907),X26903),X26904) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26906,X26907),X26903),X26905)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26906,tc_HOL_Obool)),X26904),X26905))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26906),X26905))
        | ~ class_Groups_Ocomm__monoid__add(X26907) ) ),
    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_6622,plain,
    ! [X26867,X26868,X26869,X26870,X26871] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26870),esk247_5(X26867,X26868,X26869,X26870,X26871)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26870,tc_HOL_Obool)),X26869),X26868)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26870,X26871),X26867),X26869) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26870,X26871),X26867),X26868)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26870,tc_HOL_Obool)),X26868),X26869))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26870),X26869))
        | ~ class_Groups_Ocomm__monoid__add(X26871) )
      & ( hAPP(X26867,esk247_5(X26867,X26868,X26869,X26870,X26871)) != c_Groups_Ozero__class_Ozero(X26871)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26870,X26871),X26867),X26869) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26870,X26871),X26867),X26868)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26870,tc_HOL_Obool)),X26868),X26869))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26870),X26869))
        | ~ class_Groups_Ocomm__monoid__add(X26871) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mono__zero__right])])])]) ).

fof(i_0_6623,plain,
    ! [X26064,X26065,X26066,X26067,X26068] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26067),esk188_5(X26064,X26065,X26066,X26067,X26068)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26067,tc_HOL_Obool)),X26066),X26065)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26067,X26068),X26064),X26066) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26067,X26068),X26064),X26065)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26067,tc_HOL_Obool)),X26065),X26066))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26067),X26066))
        | ~ class_Groups_Ocomm__monoid__mult(X26068) )
      & ( hAPP(X26064,esk188_5(X26064,X26065,X26066,X26067,X26068)) != c_Groups_Oone__class_Oone(X26068)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26067,X26068),X26064),X26066) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26067,X26068),X26064),X26065)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26067,tc_HOL_Obool)),X26065),X26066))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26067),X26066))
        | ~ class_Groups_Ocomm__monoid__mult(X26068) ) ),
    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_6624,plain,
    ! [X26058,X26059,X26060,X26061,X26062] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26061),esk187_5(X26058,X26059,X26060,X26061,X26062)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26061,tc_HOL_Obool)),X26060),X26059)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26061,X26062),X26058),X26059) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26061,X26062),X26058),X26060)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26061,tc_HOL_Obool)),X26059),X26060))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26061),X26060))
        | ~ class_Groups_Ocomm__monoid__mult(X26062) )
      & ( hAPP(X26058,esk187_5(X26058,X26059,X26060,X26061,X26062)) != c_Groups_Oone__class_Oone(X26062)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26061,X26062),X26058),X26059) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26061,X26062),X26058),X26060)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26061,tc_HOL_Obool)),X26059),X26060))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26061),X26060))
        | ~ class_Groups_Ocomm__monoid__mult(X26062) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__mono__one__left])])])]) ).

cnf(i_0_6625,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_5409]) ).

cnf(i_0_6626,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_5408]) ).

fof(i_0_6627,plain,
    ! [X19393,X19394,X19395,X19396,X19397,X19399,X19400,X19401,X19402,X19403,X19404] :
      ( ( hBOOL(hAPP(hAPP(c_member(X19397),esk44_5(X19393,X19394,X19395,X19396,X19397)),X19395))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19397,tc_fun(X19396,tc_HOL_Obool)),X19395),X19394),X19393)) )
      & ( hBOOL(hAPP(hAPP(X19394,esk44_5(X19393,X19394,X19395,X19396,X19397)),X19393))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19397,tc_fun(X19396,tc_HOL_Obool)),X19395),X19394),X19393)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X19403),X19404),X19401))
        | ~ hBOOL(hAPP(hAPP(X19400,X19404),X19399))
        | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19403,tc_fun(X19402,tc_HOL_Obool)),X19401),X19400),X19399)) ) ),
    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_6628,plain,
    ! [X17156,X17157,X17158,X17159] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17158,X17159)),X17157),X17156))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X17158),hAPP(hAPP(c_COMBS(X17158,X17159,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X17159,tc_fun(X17159,tc_HOL_Obool),X17158),c_Orderings_Oord__class_Oless__eq(X17159)),X17157)),X17156)))
        | ~ class_Orderings_Oorder(X17159)
        | ~ class_Enum_Oenum(X17158) )
      & ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X17158),hAPP(hAPP(c_COMBS(X17158,X17159,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X17159,tc_fun(X17159,tc_HOL_Obool),X17158),c_Orderings_Oord__class_Oless__eq(X17159)),X17157)),X17156)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17158,X17159)),X17157),X17156))
        | ~ class_Orderings_Oorder(X17159)
        | ~ class_Enum_Oenum(X17158) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__fun_I1_J])])]) ).

fof(i_0_6629,plain,
    ! [X28824,X28825,X28826] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28826,X28826)),X28825),c_Transitive__Closure_Ortrancl(X28826,X28824)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28826,X28826)),X28825),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X28826,X28826),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(X28826,X28826),tc_HOL_Obool),tc_fun(tc_prod(X28826,X28826),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X28826,X28826),tc_HOL_Obool)),X28824)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__imp__UN__rel__pow])]) ).

fof(i_0_6630,plain,
    ! [X29758,X29759,X29760,X29761,X29762] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29762,tc_fun(X29761,tc_HOL_Obool)),X29760),hAPP(hAPP(c_COMBS(X29762,tc_fun(X29761,tc_HOL_Obool),tc_fun(X29761,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29761,tc_HOL_Obool),tc_fun(tc_fun(X29761,tc_HOL_Obool),tc_fun(X29761,tc_HOL_Obool)),X29762),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29761,tc_HOL_Obool))),X29759)),X29758)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29761,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X29761,tc_HOL_Obool),hAPP(c_Set_Oimage(X29762,tc_fun(X29761,tc_HOL_Obool),X29759),X29760))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X29761,tc_HOL_Obool),hAPP(c_Set_Oimage(X29762,tc_fun(X29761,tc_HOL_Obool),X29758),X29760))),
    inference(variable_rename,[status(thm)],[fact_Int__Inter__image]) ).

fof(i_0_6631,plain,
    ! [X29774,X29775,X29776,X29777,X29778] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29778,tc_fun(X29777,tc_HOL_Obool)),X29776),hAPP(hAPP(c_COMBS(X29778,tc_fun(X29777,tc_HOL_Obool),tc_fun(X29777,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29777,tc_HOL_Obool),tc_fun(tc_fun(X29777,tc_HOL_Obool),tc_fun(X29777,tc_HOL_Obool)),X29778),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29777,tc_HOL_Obool))),X29775)),X29774)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29777,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29777,tc_HOL_Obool),hAPP(c_Set_Oimage(X29778,tc_fun(X29777,tc_HOL_Obool),X29775),X29776))),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29777,tc_HOL_Obool),hAPP(c_Set_Oimage(X29778,tc_fun(X29777,tc_HOL_Obool),X29774),X29776))),
    inference(variable_rename,[status(thm)],[fact_Un__Union__image]) ).

fof(i_0_6632,plain,
    ! [X31715,X31716,X31717,X31718,X31719,X31720,X31721] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31721,X31721)),hAPP(hAPP(c_Product__Type_OPair(X31721,X31721),X31720),X31719)),X31718))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31721),tc_List_Olist(X31721))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31721),tc_List_Olist(X31721)),hAPP(hAPP(c_List_Oappend(X31721),X31717),hAPP(hAPP(c_List_Olist_OCons(X31721),X31720),X31716))),hAPP(hAPP(c_List_Oappend(X31721),X31717),hAPP(hAPP(c_List_Olist_OCons(X31721),X31719),X31715)))),c_List_Olexord(X31721,X31718))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__left__rightI])]) ).

fof(i_0_6633,plain,
    ! [X25575,X25576,X25577,X25578] :
      ( ( ~ 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),X25578),X25577)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X25576),X25575))),c_Int_Ointrel))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25578),X25575) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25576),X25577) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25578),X25575) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25576),X25577)
        | 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),X25578),X25577)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X25576),X25575))),c_Int_Ointrel)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_intrel__iff])]) ).

fof(i_0_6634,plain,
    ! [X22952,X22953,X22954,X22955,X22956,X22957,X22958] :
      ( ~ hBOOL(hAPP(X22958,X22957))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22956,X22956)),hAPP(hAPP(c_Product__Type_OPair(X22956,X22956),X22955),X22954)),hAPP(X22953,X22957)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X22952,X22956),tc_prod(X22952,X22956))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X22952,X22956),tc_prod(X22952,X22956)),hAPP(hAPP(c_Product__Type_OPair(X22952,X22956),X22957),X22955)),hAPP(hAPP(c_Product__Type_OPair(X22952,X22956),X22957),X22954))),c_Recdef_Osame__fst(X22952,X22956,X22958,X22953))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__fstI])]) ).

fof(i_0_6635,plain,
    ! [X19635,X19636,X19637,X19638,X19639,X19641] :
      ( ( hBOOL(hAPP(hAPP(c_member(X19637),esk49_5(X19635,X19636,X19637,X19638,X19639)),X19636))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19639),X19638),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19637,X19639),X19636),X19635)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X19639)
        | ~ class_Orderings_Olinorder(X19639) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19639),X19638),hAPP(X19635,esk49_5(X19635,X19636,X19637,X19638,X19639))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19639),X19638),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19637,X19639),X19636),X19635)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X19639)
        | ~ class_Orderings_Olinorder(X19639) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X19637),X19641),X19636))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19639),X19638),hAPP(X19635,X19641)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19639),X19638),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19637,X19639),X19636),X19635)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X19639)
        | ~ class_Orderings_Olinorder(X19639) ) ),
    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_6636,plain,
    ! [X23946,X23947,X23948,X23949,X23950,X23951,X23952,X23953] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X23953,X23952,X23951),X23950),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X23949,X23948,tc_prod(X23953,X23952)),X23947),X23946)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X23949,X23948,X23951),hAPP(hAPP(c_COMBB(tc_fun(X23948,tc_prod(X23953,X23952)),tc_fun(X23948,X23951),X23949),hAPP(c_COMBB(tc_prod(X23953,X23952),X23951,X23948),hAPP(c_Product__Type_Oprod_Oprod__case(X23953,X23952,X23951),X23950))),X23947)),X23946),
    inference(variable_rename,[status(thm)],[fact_split__twice]) ).

cnf(i_0_6637,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_5430]) ).

cnf(i_0_6638,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_5431]) ).

cnf(i_0_6639,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_5432]) ).

fof(i_0_6640,plain,
    ! [X21122,X21123,X21124,X21125] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X21125),esk94_4(X21122,X21123,X21124,X21125)))
        | hBOOL(hAPP(X21122,X21124))
        | ~ hBOOL(hAPP(X21122,c_Orderings_Obot__class_Obot(tc_fun(X21125,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21125,tc_HOL_Obool)),X21124),X21123))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21125),X21124)) )
      & ( hBOOL(hAPP(hAPP(c_member(X21125),esk93_4(X21122,X21123,X21124,X21125)),X21123))
        | hBOOL(hAPP(X21122,X21124))
        | ~ hBOOL(hAPP(X21122,c_Orderings_Obot__class_Obot(tc_fun(X21125,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21125,tc_HOL_Obool)),X21124),X21123))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21125),X21124)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X21125),esk93_4(X21122,X21123,X21124,X21125)),esk94_4(X21122,X21123,X21124,X21125)))
        | hBOOL(hAPP(X21122,X21124))
        | ~ hBOOL(hAPP(X21122,c_Orderings_Obot__class_Obot(tc_fun(X21125,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21125,tc_HOL_Obool)),X21124),X21123))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21125),X21124)) )
      & ( hBOOL(hAPP(X21122,esk94_4(X21122,X21123,X21124,X21125)))
        | hBOOL(hAPP(X21122,X21124))
        | ~ hBOOL(hAPP(X21122,c_Orderings_Obot__class_Obot(tc_fun(X21125,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21125,tc_HOL_Obool)),X21124),X21123))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21125),X21124)) )
      & ( ~ hBOOL(hAPP(X21122,hAPP(hAPP(c_Set_Oinsert(X21125),esk93_4(X21122,X21123,X21124,X21125)),esk94_4(X21122,X21123,X21124,X21125))))
        | hBOOL(hAPP(X21122,X21124))
        | ~ hBOOL(hAPP(X21122,c_Orderings_Obot__class_Obot(tc_fun(X21125,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21125,tc_HOL_Obool)),X21124),X21123))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21125),X21124)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5433])])])]) ).

fof(i_0_6641,plain,
    ! [X32168,X32169,X32170,X32171] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32171),esk443_4(X32168,X32169,X32170,X32171)),hAPP(c_List_Oset(X32171),X32170)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X32171,X32169,X32170)),c_List_Olist_Olist__size(X32171,X32168,X32170))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X32169,esk443_4(X32168,X32169,X32170,X32171))),hAPP(X32168,esk443_4(X32168,X32169,X32170,X32171))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X32171,X32169,X32170)),c_List_Olist_Olist__size(X32171,X32168,X32170))) ) ),
    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_6642,plain,
    ! [X23850,X23851] : c_Fun_Oinj__on(tc_fun(X23851,X23850),tc_fun(tc_prod(X23851,X23850),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X23851,X23850),tc_HOL_Obool),tc_fun(tc_prod(X23851,X23850),tc_HOL_Obool),tc_fun(X23851,X23850)),c_Set_OCollect(tc_prod(X23851,X23850))),hAPP(hAPP(c_COMBB(tc_fun(X23851,tc_fun(X23850,tc_HOL_Obool)),tc_fun(tc_prod(X23851,X23850),tc_HOL_Obool),tc_fun(X23851,X23850)),c_Product__Type_Oprod_Oprod__case(X23851,X23850,tc_HOL_Obool)),hAPP(c_COMBB(X23850,tc_fun(X23850,tc_HOL_Obool),X23851),hAPP(c_COMBC(X23850,X23850,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X23851,X23850),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_inj__graph]) ).

cnf(i_0_6643,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_6644,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_5434]) ).

cnf(i_0_6645,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_6646,plain,
    ! [X32532,X32533,X32534,X32535,X32536] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32535),esk453_5(X32532,X32533,X32534,X32535,X32536)),hAPP(c_List_Oset(X32535),X32534)))
        | hAPP(c_List_Omonoid__add__class_Olistsum(X32536),hAPP(hAPP(c_List_Omap(X32535,X32536),X32532),hAPP(c_List_Ofilter(X32535,X32533),X32534))) = hAPP(c_List_Omonoid__add__class_Olistsum(X32536),hAPP(hAPP(c_List_Omap(X32535,X32536),X32532),X32534))
        | ~ class_Groups_Omonoid__add(X32536) )
      & ( ~ hBOOL(hAPP(X32533,esk453_5(X32532,X32533,X32534,X32535,X32536)))
        | hAPP(c_List_Omonoid__add__class_Olistsum(X32536),hAPP(hAPP(c_List_Omap(X32535,X32536),X32532),hAPP(c_List_Ofilter(X32535,X32533),X32534))) = hAPP(c_List_Omonoid__add__class_Olistsum(X32536),hAPP(hAPP(c_List_Omap(X32535,X32536),X32532),X32534))
        | ~ class_Groups_Omonoid__add(X32536) )
      & ( hAPP(X32532,esk453_5(X32532,X32533,X32534,X32535,X32536)) != c_Groups_Ozero__class_Ozero(X32536)
        | hAPP(c_List_Omonoid__add__class_Olistsum(X32536),hAPP(hAPP(c_List_Omap(X32535,X32536),X32532),hAPP(c_List_Ofilter(X32535,X32533),X32534))) = hAPP(c_List_Omonoid__add__class_Olistsum(X32536),hAPP(hAPP(c_List_Omap(X32535,X32536),X32532),X32534))
        | ~ class_Groups_Omonoid__add(X32536) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5435])])])]) ).

cnf(i_0_6647,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_5436]) ).

cnf(i_0_6648,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_5437]) ).

fof(i_0_6649,plain,
    ! [X27364,X27365,X27366,X27367,X27368,X27370,X27371,X27372,X27373,X27375] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X27367),X27365))
        | ~ c_Wellfounded_Omax__extp(X27367,X27366,X27365,X27364) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X27367),X27364))
        | ~ c_Wellfounded_Omax__extp(X27367,X27366,X27365,X27364) )
      & ( X27364 != c_Orderings_Obot__class_Obot(tc_fun(X27367,tc_HOL_Obool))
        | ~ c_Wellfounded_Omax__extp(X27367,X27366,X27365,X27364) )
      & ( hBOOL(hAPP(hAPP(c_member(X27367),esk256_5(X27364,X27365,X27366,X27367,X27368)),X27364))
        | ~ hBOOL(hAPP(hAPP(c_member(X27367),X27368),X27365))
        | ~ c_Wellfounded_Omax__extp(X27367,X27366,X27365,X27364) )
      & ( hBOOL(hAPP(hAPP(X27366,X27368),esk256_5(X27364,X27365,X27366,X27367,X27368)))
        | ~ hBOOL(hAPP(hAPP(c_member(X27367),X27368),X27365))
        | ~ c_Wellfounded_Omax__extp(X27367,X27366,X27365,X27364) )
      & ( hBOOL(hAPP(hAPP(c_member(X27373),esk257_4(X27370,X27371,X27372,X27373)),X27371))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27373),X27371))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27373),X27370))
        | X27370 = c_Orderings_Obot__class_Obot(tc_fun(X27373,tc_HOL_Obool))
        | c_Wellfounded_Omax__extp(X27373,X27372,X27371,X27370) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27373),X27375),X27370))
        | ~ hBOOL(hAPP(hAPP(X27372,esk257_4(X27370,X27371,X27372,X27373)),X27375))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27373),X27371))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27373),X27370))
        | X27370 = c_Orderings_Obot__class_Obot(tc_fun(X27373,tc_HOL_Obool))
        | c_Wellfounded_Omax__extp(X27373,X27372,X27371,X27370) ) ),
    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_6650,plain,
    ! [X18272,X18273,X18274] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18274,tc_HOL_Obool)),X18273),X18272) = hAPP(c_Set_OCollect(X18274),hAPP(hAPP(c_COMBS(X18274,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X18274),c_fconj),hAPP(hAPP(c_COMBC(X18274,tc_fun(X18274,tc_HOL_Obool),tc_HOL_Obool),c_member(X18274)),X18273))),hAPP(hAPP(c_COMBC(X18274,tc_fun(X18274,tc_HOL_Obool),tc_HOL_Obool),c_member(X18274)),X18272))),
    inference(variable_rename,[status(thm)],[fact_Int__def]) ).

fof(i_0_6651,plain,
    ! [X17437,X17438,X17439] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17439,tc_HOL_Obool)),X17438),X17437) = hAPP(c_Set_OCollect(X17439),hAPP(hAPP(c_COMBS(X17439,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17439),c_fdisj),hAPP(hAPP(c_COMBC(X17439,tc_fun(X17439,tc_HOL_Obool),tc_HOL_Obool),c_member(X17439)),X17438))),hAPP(hAPP(c_COMBC(X17439,tc_fun(X17439,tc_HOL_Obool),tc_HOL_Obool),c_member(X17439)),X17437))),
    inference(variable_rename,[status(thm)],[fact_Un__def]) ).

fof(i_0_6652,plain,
    ! [X20660,X20661,X20662,X20663,X20664,X20665,X20666,X20667] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X20667,X20666,X20665,X20664,X20663,X20662)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20666),X20661))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20666),X20660))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20666,tc_HOL_Obool)),X20661),X20660) != c_Orderings_Obot__class_Obot(tc_fun(X20666,tc_HOL_Obool))
      | hAPP(X20662,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20666,tc_HOL_Obool)),X20661),X20660)) = hAPP(hAPP(X20665,hAPP(X20662,X20661)),hAPP(X20662,X20660)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__disjoint])]) ).

fof(i_0_6653,plain,
    ! [X18861,X18862,X18863,X18864,X18865,X18866] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X18866),X18865),X18864))
      | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18866,tc_Option_Ooption(X18863)),c_Map_Orestrict__map(X18866,X18863,X18862,X18864)),X18865),X18861) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18866,tc_Option_Ooption(X18863)),c_Map_Orestrict__map(X18866,X18863,X18862,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18866,tc_HOL_Obool)),X18864),hAPP(hAPP(c_Set_Oinsert(X18866),X18865),c_Orderings_Obot__class_Obot(tc_fun(X18866,tc_HOL_Obool)))))),X18865),X18861) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__restrict__conv])]) ).

cnf(i_0_6654,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_5438]) ).

fof(i_0_6655,plain,
    ! [X21881,X21882,X21883,X21884,X21885,X21886] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21886),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21886),X21885),X21884)),X21883)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21886),X21882),X21884)),X21881)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21886),X21883),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21886),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21886),X21882),X21885)),X21884)),X21881)))
        | ~ class_Rings_Oordered__ring(X21886) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21886),X21883),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21886),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21886),X21882),X21885)),X21884)),X21881)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21886),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21886),X21885),X21884)),X21883)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21886),X21882),X21884)),X21881)))
        | ~ class_Rings_Oordered__ring(X21886) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff2])])]) ).

fof(i_0_6656,plain,
    ! [X21869,X21870,X21871,X21872,X21873,X21874] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21874),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21874),X21873),X21872)),X21871)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21874),X21870),X21872)),X21869)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21874),X21871),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21874),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21874),X21870),X21873)),X21872)),X21869)))
        | ~ class_Rings_Oordered__ring(X21874) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21874),X21871),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21874),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21874),X21870),X21873)),X21872)),X21869)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21874),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21874),X21873),X21872)),X21871)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21874),X21870),X21872)),X21869)))
        | ~ class_Rings_Oordered__ring(X21874) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff2])])]) ).

fof(i_0_6657,plain,
    ! [X29506,X29507,X29508,X29509,X29510,X29511] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29511,tc_HOL_Obool)),hAPP(c_Relation_OImage(X29510,X29511,X29509),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29508,tc_fun(X29510,tc_HOL_Obool)),X29507),X29506))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29508,tc_fun(X29511,tc_HOL_Obool)),X29507),hAPP(hAPP(c_COMBB(tc_fun(X29510,tc_HOL_Obool),tc_fun(X29511,tc_HOL_Obool),X29508),c_Relation_OImage(X29510,X29511,X29509)),X29506)))),
    inference(variable_rename,[status(thm)],[fact_Image__INT__subset]) ).

fof(i_0_6658,plain,
    ! [X29925,X29926,X29927,X29928,X29929,X29930,X29931,X29932] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X29932,X29931,X29930,X29929,X29928,X29927)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29931),X29926))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29931,tc_HOL_Obool)),X29925),X29926))
      | hAPP(hAPP(X29930,hAPP(X29927,X29925)),hAPP(X29927,X29926)) = hAPP(X29927,X29926) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Osubset__idem])]) ).

fof(i_0_6659,plain,
    ! [X17163,X17164,X17165,X17166] :
      ( ~ class_Orderings_Oord(X17166)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17166),hAPP(X17165,esk3_4(X17163,X17164,X17165,X17166))),hAPP(X17164,esk3_4(X17163,X17164,X17165,X17166))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17163,X17166)),X17165),X17164)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funI])])]) ).

fof(i_0_6660,plain,
    ! [X17134,X17135,X17136,X17137,X17138] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17136,X17137)),X17135),X17134))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17137),hAPP(X17135,X17138)),hAPP(X17134,X17138)))
        | ~ class_Orderings_Oord(X17137) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17137),hAPP(X17135,esk2_4(X17134,X17135,X17136,X17137))),hAPP(X17134,esk2_4(X17134,X17135,X17136,X17137))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17136,X17137)),X17135),X17134))
        | ~ class_Orderings_Oord(X17137) ) ),
    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_6661,plain,
    ! [X18995,X18996,X18997,X18998,X18999,X19000] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X19000,tc_Option_Ooption(X18999)),c_Map_Orestrict__map(X19000,X18999,X18998,X18997)),X18996),X18995) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X19000,tc_Option_Ooption(X18999)),c_Map_Orestrict__map(X19000,X18999,X18998,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19000,tc_HOL_Obool)),X18997),hAPP(hAPP(c_Set_Oinsert(X19000),X18996),c_Orderings_Obot__class_Obot(tc_fun(X19000,tc_HOL_Obool)))))),X18996),X18995),
    inference(variable_rename,[status(thm)],[fact_fun__upd__restrict]) ).

fof(i_0_6662,plain,
    ! [X21206,X21207,X21208,X21209,X21210,X21211,X21212] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X21212,X21211,X21210,X21209,X21208,X21207)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21211),X21206))
      | hAPP(X21207,X21206) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21212,X21211,X21210),X21208),X21209),X21206) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oeq__fold__g])]) ).

fof(i_0_6663,plain,
    ! [X30267,X30268,X30269,X30270,X30271,X30272,X30273,X30274,X30275,X30276,X30277] :
      ( ( hAPP(hAPP(c_List_Omap(X30271,X30270),X30269),X30268) != hAPP(hAPP(c_List_Omap(X30271,X30270),X30267),X30268)
        | ~ hBOOL(hAPP(hAPP(c_member(X30271),X30272),hAPP(c_List_Oset(X30271),X30268)))
        | hAPP(X30269,X30272) = hAPP(X30267,X30272) )
      & ( hBOOL(hAPP(hAPP(c_member(X30277),esk399_5(X30273,X30274,X30275,X30276,X30277)),hAPP(c_List_Oset(X30277),X30274)))
        | hAPP(hAPP(c_List_Omap(X30277,X30276),X30275),X30274) = hAPP(hAPP(c_List_Omap(X30277,X30276),X30273),X30274) )
      & ( hAPP(X30275,esk399_5(X30273,X30274,X30275,X30276,X30277)) != hAPP(X30273,esk399_5(X30273,X30274,X30275,X30276,X30277))
        | hAPP(hAPP(c_List_Omap(X30277,X30276),X30275),X30274) = hAPP(hAPP(c_List_Omap(X30277,X30276),X30273),X30274) ) ),
    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_6664,plain,
    ! [X27376,X27377,X27378,X27379,X27380,X27381,X27382,X27383] :
      ( ~ hBOOL(hAPP(hAPP(X27383,X27382),X27381))
      | ~ hBOOL(hAPP(hAPP(X27380,X27381),X27379))
      | hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X27378,X27377,X27376,X27383,X27380),X27382),X27379)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__comp_Ointros])]) ).

fof(i_0_6665,plain,
    ! [X29894,X29895,X29896,X29897,X29898,X29899,X29900,X29901] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X29901,X29900,X29899,X29898,X29897,X29896)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29900),X29895))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29900),X29894))
      | hAPP(X29896,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29900,tc_HOL_Obool)),X29895),X29894)) = hAPP(hAPP(X29899,hAPP(X29896,X29895)),hAPP(X29896,X29894)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Ounion__idem])]) ).

fof(i_0_6666,plain,
    ! [X19571,X19572,X19573,X19574,X19575,X19576,X19577,X19578] :
      ( ~ c_Equiv__Relations_Oequiv(X19578,X19577,X19576)
      | ~ c_Equiv__Relations_Ocongruent2(X19578,X19575,X19574,X19576,X19573,X19572)
      | ~ hBOOL(hAPP(hAPP(c_member(X19578),X19571),X19577))
      | c_Equiv__Relations_Ocongruent(X19575,X19574,X19573,hAPP(X19572,X19571)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent])]) ).

fof(i_0_6667,plain,
    ! [X31596,X31597,X31598,X31599,X31600,X31603,X31604,X31605,X31606,X31607,X31608,X31609] :
      ( ( hAPP(hAPP(c_List_Oappend(X31600),X31599),esk427_5(X31596,X31597,X31598,X31599,X31600)) = X31597
        | X31599 = hAPP(hAPP(c_List_Oappend(X31600),X31597),esk426_5(X31596,X31597,X31598,X31599,X31600))
        | hAPP(hAPP(c_List_Oappend(X31600),X31599),X31598) != hAPP(hAPP(c_List_Oappend(X31600),X31597),X31596) )
      & ( X31598 = hAPP(hAPP(c_List_Oappend(X31600),esk427_5(X31596,X31597,X31598,X31599,X31600)),X31596)
        | X31599 = hAPP(hAPP(c_List_Oappend(X31600),X31597),esk426_5(X31596,X31597,X31598,X31599,X31600))
        | hAPP(hAPP(c_List_Oappend(X31600),X31599),X31598) != hAPP(hAPP(c_List_Oappend(X31600),X31597),X31596) )
      & ( hAPP(hAPP(c_List_Oappend(X31600),X31599),esk427_5(X31596,X31597,X31598,X31599,X31600)) = X31597
        | hAPP(hAPP(c_List_Oappend(X31600),esk426_5(X31596,X31597,X31598,X31599,X31600)),X31598) = X31596
        | hAPP(hAPP(c_List_Oappend(X31600),X31599),X31598) != hAPP(hAPP(c_List_Oappend(X31600),X31597),X31596) )
      & ( X31598 = hAPP(hAPP(c_List_Oappend(X31600),esk427_5(X31596,X31597,X31598,X31599,X31600)),X31596)
        | hAPP(hAPP(c_List_Oappend(X31600),esk426_5(X31596,X31597,X31598,X31599,X31600)),X31598) = X31596
        | hAPP(hAPP(c_List_Oappend(X31600),X31599),X31598) != hAPP(hAPP(c_List_Oappend(X31600),X31597),X31596) )
      & ( X31606 != hAPP(hAPP(c_List_Oappend(X31607),X31604),X31608)
        | hAPP(hAPP(c_List_Oappend(X31607),X31608),X31605) != X31603
        | hAPP(hAPP(c_List_Oappend(X31607),X31606),X31605) = hAPP(hAPP(c_List_Oappend(X31607),X31604),X31603) )
      & ( hAPP(hAPP(c_List_Oappend(X31607),X31606),X31609) != X31604
        | X31605 != hAPP(hAPP(c_List_Oappend(X31607),X31609),X31603)
        | hAPP(hAPP(c_List_Oappend(X31607),X31606),X31605) = hAPP(hAPP(c_List_Oappend(X31607),X31604),X31603) ) ),
    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_6668,plain,
    ! [X20748,X20749,X20750,X20751,X20752,X20753,X20754,X20755] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X20755,X20754,X20753,X20752,X20751,X20750)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20754),X20749))
      | hBOOL(hAPP(hAPP(c_member(X20754),X20748),X20749))
      | hAPP(X20750,hAPP(hAPP(c_Set_Oinsert(X20754),X20748),X20749)) = hAPP(hAPP(X20753,hAPP(X20751,X20748)),hAPP(X20750,X20749)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5439])]) ).

fof(i_0_6669,plain,
    ! [X21308,X21309,X21310,X21311,X21312] :
      ( ( ~ c_Fun_Oinj__on(X21311,X21309,X21312,X21310)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21309,tc_HOL_Obool)),hAPP(c_Set_Oimage(X21311,X21309,X21312),X21310)),X21308))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21311),X21310)),hAPP(c_Finite__Set_Ocard(X21309),X21308)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21309),X21308))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21311),X21310)) )
      & ( c_Fun_Oinj__on(X21311,X21309,esk101_4(X21308,X21309,X21310,X21311),X21310)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21311),X21310)),hAPP(c_Finite__Set_Ocard(X21309),X21308)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21309),X21308))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21311),X21310)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21309,tc_HOL_Obool)),hAPP(c_Set_Oimage(X21311,X21309,esk101_4(X21308,X21309,X21310,X21311)),X21310)),X21308))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21311),X21310)),hAPP(c_Finite__Set_Ocard(X21309),X21308)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21309),X21308))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21311),X21310)) ) ),
    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_6670,plain,
    ! [X29909,X29910,X29911,X29912,X29913,X29914,X29915,X29916] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X29916,X29915,X29914,X29913,X29912,X29911)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29915),X29910))
      | ~ hBOOL(hAPP(hAPP(c_member(X29915),X29909),X29910))
      | hAPP(hAPP(X29914,hAPP(X29912,X29909)),hAPP(X29911,X29910)) = hAPP(X29911,X29910) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oin__idem])]) ).

fof(i_0_6671,plain,
    ! [X31650,X31651,X31652] : c_Enum_Osublists(X31652,hAPP(hAPP(c_List_Olist_OCons(X31652),X31651),X31650)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(X31652)),tc_List_Olist(tc_List_Olist(X31652))),c_Enum_Osublists(X31652,X31650)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(X31652)),tc_List_Olist(tc_List_Olist(X31652)),tc_List_Olist(tc_List_Olist(X31652))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(X31652)),tc_fun(tc_List_Olist(tc_List_Olist(X31652)),tc_List_Olist(tc_List_Olist(X31652))),tc_List_Olist(tc_List_Olist(X31652))),c_List_Oappend(tc_List_Olist(X31652))),hAPP(c_List_Omap(tc_List_Olist(X31652),tc_List_Olist(X31652)),hAPP(c_List_Olist_OCons(X31652),X31651)))),c_COMBI(tc_List_Olist(tc_List_Olist(X31652))))),
    inference(variable_rename,[status(thm)],[fact_sublists_Osimps_I2_J]) ).

fof(i_0_6672,plain,
    ! [X29917,X29918,X29919,X29920,X29921,X29922,X29923,X29924] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X29924,X29923,X29922,X29921,X29920,X29919)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29923),X29918))
      | hAPP(X29919,hAPP(hAPP(c_Set_Oinsert(X29923),X29917),X29918)) = hAPP(hAPP(X29922,hAPP(X29920,X29917)),hAPP(X29919,X29918)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oinsert__idem])]) ).

fof(i_0_6673,plain,
    ! [X29362,X29363,X29364,X29365,X29366] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29366,tc_fun(X29365,tc_HOL_Obool)),X29364),hAPP(hAPP(c_COMBS(X29366,tc_fun(X29365,tc_HOL_Obool),tc_fun(X29365,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29365,tc_HOL_Obool),tc_fun(tc_fun(X29365,tc_HOL_Obool),tc_fun(X29365,tc_HOL_Obool)),X29366),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29365,tc_HOL_Obool))),X29363)),X29362)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29365,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29366,tc_fun(X29365,tc_HOL_Obool)),X29364),X29363)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29366,tc_fun(X29365,tc_HOL_Obool)),X29364),X29362)),
    inference(variable_rename,[status(thm)],[fact_INT__Int__distrib]) ).

fof(i_0_6674,plain,
    ! [X19715,X19716,X19717,X19718,X19719] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19719,tc_fun(X19718,tc_HOL_Obool)),X19717),hAPP(hAPP(c_COMBS(X19719,tc_fun(X19718,tc_HOL_Obool),tc_fun(X19718,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19718,tc_HOL_Obool),tc_fun(tc_fun(X19718,tc_HOL_Obool),tc_fun(X19718,tc_HOL_Obool)),X19719),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19718,tc_HOL_Obool))),X19716)),X19715)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19718,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19719,tc_fun(X19718,tc_HOL_Obool)),X19717),X19716)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19719,tc_fun(X19718,tc_HOL_Obool)),X19717),X19715)),
    inference(variable_rename,[status(thm)],[fact_UN__Un__distrib]) ).

fof(i_0_6675,plain,
    ! [X17523,X17524,X17525,X17526,X17527,X17528] :
      ( ( ~ c_Predicate_Oinv__imagep(X17528,X17527,X17526,X17525,X17524,X17523)
        | hBOOL(hAPP(hAPP(X17526,hAPP(X17525,X17524)),hAPP(X17525,X17523))) )
      & ( ~ hBOOL(hAPP(hAPP(X17526,hAPP(X17525,X17524)),hAPP(X17525,X17523)))
        | c_Predicate_Oinv__imagep(X17528,X17527,X17526,X17525,X17524,X17523) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__inv__imagep])]) ).

fof(i_0_6676,plain,
    ! [X17245,X17246,X17247,X17248,X17249,X17250] :
      ( ( ~ c_Predicate_Oinv__imagep(X17250,X17249,X17248,X17247,X17246,X17245)
        | hBOOL(hAPP(hAPP(X17248,hAPP(X17247,X17246)),hAPP(X17247,X17245))) )
      & ( ~ hBOOL(hAPP(hAPP(X17248,hAPP(X17247,X17246)),hAPP(X17247,X17245)))
        | c_Predicate_Oinv__imagep(X17250,X17249,X17248,X17247,X17246,X17245) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__imagep__def])]) ).

fof(i_0_6677,plain,
    ! [X20702,X20703,X20704,X20705,X20706,X20707] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X20707,X20706,X20705,X20704,X20703,X20702)
      | hAPP(X20702,c_Orderings_Obot__class_Obot(tc_fun(X20706,tc_HOL_Obool))) = X20704 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oempty])]) ).

fof(i_0_6678,plain,
    ! [X29902,X29903,X29904,X29905,X29906,X29907,X29908] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X29908,X29907,X29906,X29905,X29904,X29903)
      | hAPP(hAPP(X29906,X29902),X29902) = X29902 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oidem])]) ).

fof(i_0_6679,plain,
    ! [X24498] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X24498))
      | X24498 = 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))),X24498)),c_FunDef_Omax__strict)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smax__emptyI])]) ).

fof(i_0_6680,plain,
    ! [X32298,X32299,X32300] : hAPP(c_List_Oset(X32300),hAPP(c_List_Ofilter(X32300,X32299),X32298)) = hAPP(c_Set_OCollect(X32300),hAPP(hAPP(c_COMBS(X32300,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X32300),c_fconj),hAPP(hAPP(c_COMBC(X32300,tc_fun(X32300,tc_HOL_Obool),tc_HOL_Obool),c_member(X32300)),hAPP(c_List_Oset(X32300),X32298)))),X32299)),
    inference(variable_rename,[status(thm)],[fact_set__filter]) ).

fof(i_0_6681,plain,
    ! [X26863,X26864,X26865] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X26865,esk246_3(X26863,X26864,X26865))),hAPP(X26864,esk246_3(X26863,X26864,X26865))))
      | 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),X26864),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26863))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X26865),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26863))) = 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)),X26864)),X26865)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26863)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__diff__distrib])])]) ).

fof(i_0_6682,plain,
    ! [X18832,X18833,X18834,X18835,X18836,X18838] :
      ( ( ~ c_Fun_Oinj__on(X18834,X18833,X18836,X18835)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18833,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18834,X18833,X18836),X18835)),X18832))
        | hAPP(c_Set_Oimage(X18833,X18834,esk36_4(X18832,X18833,X18834,X18835)),X18832) = X18835
        | X18835 = c_Orderings_Obot__class_Obot(tc_fun(X18834,tc_HOL_Obool)) )
      & ( c_Fun_Oinj__on(X18834,X18833,esk37_4(X18832,X18833,X18834,X18835),X18835)
        | hAPP(c_Set_Oimage(X18833,X18834,X18838),X18832) != X18835
        | X18835 = c_Orderings_Obot__class_Obot(tc_fun(X18834,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18833,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18834,X18833,esk37_4(X18832,X18833,X18834,X18835)),X18835)),X18832))
        | hAPP(c_Set_Oimage(X18833,X18834,X18838),X18832) != X18835
        | X18835 = c_Orderings_Obot__class_Obot(tc_fun(X18834,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_6683,plain,
    ! [X27582,X27583,X27584,X27585] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X27585),X27584),hAPP(c_Relation_ORange(X27583,X27585),X27582)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X27583,X27585)),hAPP(hAPP(c_Product__Type_OPair(X27583,X27585),esk267_4(X27582,X27583,X27584,X27585)),X27584)),X27582)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5440])])]) ).

fof(i_0_6684,plain,
    ! [X27538,X27539,X27540,X27541,X27543,X27544,X27545,X27546,X27547] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X27541),X27540),hAPP(c_Relation_ORange(X27539,X27541),X27538)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X27539,X27541)),hAPP(hAPP(c_Product__Type_OPair(X27539,X27541),esk265_4(X27538,X27539,X27540,X27541)),X27540)),X27538)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27544,X27546)),hAPP(hAPP(c_Product__Type_OPair(X27544,X27546),X27547),X27545)),X27543))
        | hBOOL(hAPP(hAPP(c_member(X27546),X27545),hAPP(c_Relation_ORange(X27544,X27546),X27543))) ) ),
    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_6685,plain,
    ! [X24509] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X24509))
      | 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))),X24509)),c_FunDef_Omax__weak)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wmax__emptyI])]) ).

fof(i_0_6686,plain,
    ! [X29521,X29522,X29523,X29524,X29525] :
      ( ( X29525 != c_Orderings_Obot__class_Obot(tc_fun(X29524,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29524,tc_fun(X29523,tc_HOL_Obool)),X29525),hAPP(hAPP(c_COMBC(X29524,tc_fun(X29523,tc_HOL_Obool),tc_fun(X29523,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29523,tc_HOL_Obool),tc_fun(tc_fun(X29523,tc_HOL_Obool),tc_fun(X29523,tc_HOL_Obool)),X29524),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29523,tc_HOL_Obool))),X29522)),X29521)) = c_Orderings_Otop__class_Otop(tc_fun(X29523,tc_HOL_Obool)) )
      & ( X29525 = c_Orderings_Obot__class_Obot(tc_fun(X29524,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29524,tc_fun(X29523,tc_HOL_Obool)),X29525),hAPP(hAPP(c_COMBC(X29524,tc_fun(X29523,tc_HOL_Obool),tc_fun(X29523,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29523,tc_HOL_Obool),tc_fun(tc_fun(X29523,tc_HOL_Obool),tc_fun(X29523,tc_HOL_Obool)),X29524),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29523,tc_HOL_Obool))),X29522)),X29521)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29523,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29524,tc_fun(X29523,tc_HOL_Obool)),X29525),X29522)),X29521) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I1_J])]) ).

fof(i_0_6687,plain,
    ! [X29536,X29537,X29538,X29539,X29540] :
      ( ( X29540 != c_Orderings_Obot__class_Obot(tc_fun(X29539,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29539,tc_fun(X29538,tc_HOL_Obool)),X29540),hAPP(hAPP(c_COMBC(X29539,tc_fun(X29538,tc_HOL_Obool),tc_fun(X29538,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29538,tc_HOL_Obool),tc_fun(tc_fun(X29538,tc_HOL_Obool),tc_fun(X29538,tc_HOL_Obool)),X29539),c_Groups_Ominus__class_Ominus(tc_fun(X29538,tc_HOL_Obool))),X29537)),X29536)) = c_Orderings_Otop__class_Otop(tc_fun(X29538,tc_HOL_Obool)) )
      & ( X29540 = c_Orderings_Obot__class_Obot(tc_fun(X29539,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29539,tc_fun(X29538,tc_HOL_Obool)),X29540),hAPP(hAPP(c_COMBC(X29539,tc_fun(X29538,tc_HOL_Obool),tc_fun(X29538,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29538,tc_HOL_Obool),tc_fun(tc_fun(X29538,tc_HOL_Obool),tc_fun(X29538,tc_HOL_Obool)),X29539),c_Groups_Ominus__class_Ominus(tc_fun(X29538,tc_HOL_Obool))),X29537)),X29536)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29538,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29539,tc_fun(X29538,tc_HOL_Obool)),X29540),X29537)),X29536) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I3_J])]) ).

fof(i_0_6688,plain,
    ! [X19822,X19823,X19824,X19825,X19826] :
      ( ( X19826 != c_Orderings_Obot__class_Obot(tc_fun(X19825,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19825,tc_fun(X19824,tc_HOL_Obool)),X19826),hAPP(hAPP(c_COMBC(X19825,tc_fun(X19824,tc_HOL_Obool),tc_fun(X19824,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19824,tc_HOL_Obool),tc_fun(tc_fun(X19824,tc_HOL_Obool),tc_fun(X19824,tc_HOL_Obool)),X19825),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19824,tc_HOL_Obool))),X19823)),X19822)) = c_Orderings_Obot__class_Obot(tc_fun(X19824,tc_HOL_Obool)) )
      & ( X19826 = c_Orderings_Obot__class_Obot(tc_fun(X19825,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19825,tc_fun(X19824,tc_HOL_Obool)),X19826),hAPP(hAPP(c_COMBC(X19825,tc_fun(X19824,tc_HOL_Obool),tc_fun(X19824,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19824,tc_HOL_Obool),tc_fun(tc_fun(X19824,tc_HOL_Obool),tc_fun(X19824,tc_HOL_Obool)),X19825),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19824,tc_HOL_Obool))),X19823)),X19822)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19824,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19825,tc_fun(X19824,tc_HOL_Obool)),X19826),X19823)),X19822) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__simps_I2_J])]) ).

fof(i_0_6689,plain,
    ! [X29412,X29413,X29414,X29415,X29416] :
      ( ( X29416 != c_Orderings_Obot__class_Obot(tc_fun(X29415,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29414,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29415,tc_fun(X29414,tc_HOL_Obool)),X29416),X29413)),X29412) = X29412 )
      & ( X29416 = c_Orderings_Obot__class_Obot(tc_fun(X29415,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29414,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29415,tc_fun(X29414,tc_HOL_Obool)),X29416),X29413)),X29412) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29415,tc_fun(X29414,tc_HOL_Obool)),X29416),hAPP(hAPP(c_COMBC(X29415,tc_fun(X29414,tc_HOL_Obool),tc_fun(X29414,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29414,tc_HOL_Obool),tc_fun(tc_fun(X29414,tc_HOL_Obool),tc_fun(X29414,tc_HOL_Obool)),X29415),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29414,tc_HOL_Obool))),X29413)),X29412)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I1_J])]) ).

fof(i_0_6690,plain,
    ! [X29531,X29532,X29533,X29534,X29535] :
      ( ( X29535 != c_Orderings_Obot__class_Obot(tc_fun(X29534,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29533,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29534,tc_fun(X29533,tc_HOL_Obool)),X29535),X29532)),X29531) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29533,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X29533,tc_HOL_Obool))),X29531) )
      & ( X29535 = c_Orderings_Obot__class_Obot(tc_fun(X29534,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29533,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29534,tc_fun(X29533,tc_HOL_Obool)),X29535),X29532)),X29531) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29534,tc_fun(X29533,tc_HOL_Obool)),X29535),hAPP(hAPP(c_COMBC(X29534,tc_fun(X29533,tc_HOL_Obool),tc_fun(X29533,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29533,tc_HOL_Obool),tc_fun(tc_fun(X29533,tc_HOL_Obool),tc_fun(X29533,tc_HOL_Obool)),X29534),c_Groups_Ominus__class_Ominus(tc_fun(X29533,tc_HOL_Obool))),X29532)),X29531)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I3_J])]) ).

fof(i_0_6691,plain,
    ! [X19561,X19562,X19563,X19564,X19565] :
      ( ( X19565 != c_Orderings_Obot__class_Obot(tc_fun(X19564,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19563,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19564,tc_fun(X19563,tc_HOL_Obool)),X19565),X19562)),X19561) = X19561 )
      & ( X19565 = c_Orderings_Obot__class_Obot(tc_fun(X19564,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19563,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19564,tc_fun(X19563,tc_HOL_Obool)),X19565),X19562)),X19561) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19564,tc_fun(X19563,tc_HOL_Obool)),X19565),hAPP(hAPP(c_COMBC(X19564,tc_fun(X19563,tc_HOL_Obool),tc_fun(X19563,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19563,tc_HOL_Obool),tc_fun(tc_fun(X19563,tc_HOL_Obool),tc_fun(X19563,tc_HOL_Obool)),X19564),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19563,tc_HOL_Obool))),X19562)),X19561)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I2_J])]) ).

fof(i_0_6692,plain,
    ! [X29496,X29497,X29498,X29499,X29500] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29500,tc_fun(X29499,tc_HOL_Obool)),X29498),hAPP(hAPP(c_COMBC(X29500,tc_fun(X29499,tc_HOL_Obool),tc_fun(X29499,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29499,tc_HOL_Obool),tc_fun(tc_fun(X29499,tc_HOL_Obool),tc_fun(X29499,tc_HOL_Obool)),X29500),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29499,tc_HOL_Obool))),X29497)),X29496)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29499,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29500,tc_fun(X29499,tc_HOL_Obool)),X29498),X29497)),X29496),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I6_J]) ).

fof(i_0_6693,plain,
    ! [X19730,X19731,X19732,X19733,X19734] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19734,tc_fun(X19733,tc_HOL_Obool)),X19732),hAPP(hAPP(c_COMBC(X19734,tc_fun(X19733,tc_HOL_Obool),tc_fun(X19733,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19733,tc_HOL_Obool),tc_fun(tc_fun(X19733,tc_HOL_Obool),tc_fun(X19733,tc_HOL_Obool)),X19734),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19733,tc_HOL_Obool))),X19731)),X19730)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19733,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19734,tc_fun(X19733,tc_HOL_Obool)),X19732),X19731)),X19730),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I4_J]) ).

fof(i_0_6694,plain,
    ! [X19763,X19764,X19765,X19766,X19767] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19767,tc_fun(X19766,tc_HOL_Obool)),X19765),hAPP(hAPP(c_COMBC(X19767,tc_fun(X19766,tc_HOL_Obool),tc_fun(X19766,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19766,tc_HOL_Obool),tc_fun(tc_fun(X19766,tc_HOL_Obool),tc_fun(X19766,tc_HOL_Obool)),X19767),c_Groups_Ominus__class_Ominus(tc_fun(X19766,tc_HOL_Obool))),X19764)),X19763)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19766,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19767,tc_fun(X19766,tc_HOL_Obool)),X19765),X19764)),X19763),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I6_J]) ).

fof(i_0_6695,plain,
    ! [X19745,X19746,X19747,X19748,X19749] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19749,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19748,tc_fun(X19749,tc_HOL_Obool)),X19747),X19746)),X19745) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19748,tc_fun(X19749,tc_HOL_Obool)),X19747),hAPP(hAPP(c_COMBC(X19748,tc_fun(X19749,tc_HOL_Obool),tc_fun(X19749,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19749,tc_HOL_Obool),tc_fun(tc_fun(X19749,tc_HOL_Obool),tc_fun(X19749,tc_HOL_Obool)),X19748),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19749,tc_HOL_Obool))),X19746)),X19745)),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I4_J]) ).

fof(i_0_6696,plain,
    ! [X19768,X19769,X19770,X19771,X19772] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19772,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19771,tc_fun(X19772,tc_HOL_Obool)),X19770),X19769)),X19768) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19771,tc_fun(X19772,tc_HOL_Obool)),X19770),hAPP(hAPP(c_COMBC(X19771,tc_fun(X19772,tc_HOL_Obool),tc_fun(X19772,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X19772,tc_HOL_Obool),tc_fun(tc_fun(X19772,tc_HOL_Obool),tc_fun(X19772,tc_HOL_Obool)),X19771),c_Groups_Ominus__class_Ominus(tc_fun(X19772,tc_HOL_Obool))),X19769)),X19768)),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I6_J]) ).

fof(i_0_6697,plain,
    ! [X29481,X29482,X29483,X29484,X29485] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29485,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29484,tc_fun(X29485,tc_HOL_Obool)),X29483),X29482)),X29481) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29484,tc_fun(X29485,tc_HOL_Obool)),X29483),hAPP(hAPP(c_COMBC(X29484,tc_fun(X29485,tc_HOL_Obool),tc_fun(X29485,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29485,tc_HOL_Obool),tc_fun(tc_fun(X29485,tc_HOL_Obool),tc_fun(X29485,tc_HOL_Obool)),X29484),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29485,tc_HOL_Obool))),X29482)),X29481)),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I6_J]) ).

fof(i_0_6698,plain,
    ! [X27723,X27724,X27725,X27726,X27727,X27728,X27729,X27730] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27730,X27729),tc_HOL_Obool)),X27728),hAPP(hAPP(c_Product__Type_OSigma(X27730,X27729),X27727),hAPP(c_COMBK(tc_fun(X27729,tc_HOL_Obool),X27730),X27726))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27729,X27725),tc_HOL_Obool)),X27724),hAPP(hAPP(c_Product__Type_OSigma(X27729,X27725),X27726),hAPP(c_COMBK(tc_fun(X27725,tc_HOL_Obool),X27729),X27723))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27730,X27725),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27730,X27729,X27725),X27728),X27724)),hAPP(hAPP(c_Product__Type_OSigma(X27730,X27725),X27727),hAPP(c_COMBK(tc_fun(X27725,tc_HOL_Obool),X27730),X27723)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__comp__subset__Sigma])]) ).

fof(i_0_6699,plain,
    ! [X30641,X30642,X30643,X30644,X30645,X30646] :
      ( ( X30645 = X30643
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X30646,X30646)),hAPP(hAPP(c_Product__Type_OPair(X30646,X30646),X30645),X30643)),X30641))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30646),tc_List_Olist(X30646))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30646),tc_List_Olist(X30646)),hAPP(hAPP(c_List_Olist_OCons(X30646),X30645),X30644)),hAPP(hAPP(c_List_Olist_OCons(X30646),X30643),X30642))),c_List_Olistrel1(X30646,X30641))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30646),tc_List_Olist(X30646))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30646),tc_List_Olist(X30646)),X30644),X30642)),c_List_Olistrel1(X30646,X30641)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X30646,X30646)),hAPP(hAPP(c_Product__Type_OPair(X30646,X30646),X30645),X30643)),X30641))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30646),tc_List_Olist(X30646))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30646),tc_List_Olist(X30646)),hAPP(hAPP(c_List_Olist_OCons(X30646),X30645),X30644)),hAPP(hAPP(c_List_Olist_OCons(X30646),X30643),X30642))),c_List_Olistrel1(X30646,X30641))) )
      & ( X30645 = X30643
        | X30644 = X30642
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30646),tc_List_Olist(X30646))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30646),tc_List_Olist(X30646)),hAPP(hAPP(c_List_Olist_OCons(X30646),X30645),X30644)),hAPP(hAPP(c_List_Olist_OCons(X30646),X30643),X30642))),c_List_Olistrel1(X30646,X30641))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30646),tc_List_Olist(X30646))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30646),tc_List_Olist(X30646)),X30644),X30642)),c_List_Olistrel1(X30646,X30641)))
        | X30644 = X30642
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30646),tc_List_Olist(X30646))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30646),tc_List_Olist(X30646)),hAPP(hAPP(c_List_Olist_OCons(X30646),X30645),X30644)),hAPP(hAPP(c_List_Olist_OCons(X30646),X30643),X30642))),c_List_Olistrel1(X30646,X30641))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30646,X30646)),hAPP(hAPP(c_Product__Type_OPair(X30646,X30646),X30645),X30643)),X30641))
        | X30644 != X30642
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30646),tc_List_Olist(X30646))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30646),tc_List_Olist(X30646)),hAPP(hAPP(c_List_Olist_OCons(X30646),X30645),X30644)),hAPP(hAPP(c_List_Olist_OCons(X30646),X30643),X30642))),c_List_Olistrel1(X30646,X30641))) )
      & ( X30645 != X30643
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30646),tc_List_Olist(X30646))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30646),tc_List_Olist(X30646)),X30644),X30642)),c_List_Olistrel1(X30646,X30641)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30646),tc_List_Olist(X30646))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30646),tc_List_Olist(X30646)),hAPP(hAPP(c_List_Olist_OCons(X30646),X30645),X30644)),hAPP(hAPP(c_List_Olist_OCons(X30646),X30643),X30642))),c_List_Olistrel1(X30646,X30641))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__listrel1__Cons])])]) ).

fof(i_0_6700,plain,
    ! [X30554,X30555,X30556,X30557,X30558,X30559] :
      ( ( X30558 = X30556
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X30559,X30559)),hAPP(hAPP(c_Product__Type_OPair(X30559,X30559),X30558),X30556)),X30554))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30559),tc_List_Olist(X30559))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30559),tc_List_Olist(X30559)),hAPP(hAPP(c_List_Olist_OCons(X30559),X30558),X30557)),hAPP(hAPP(c_List_Olist_OCons(X30559),X30556),X30555))),c_List_Olexord(X30559,X30554))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30559),tc_List_Olist(X30559))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30559),tc_List_Olist(X30559)),X30557),X30555)),c_List_Olexord(X30559,X30554)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X30559,X30559)),hAPP(hAPP(c_Product__Type_OPair(X30559,X30559),X30558),X30556)),X30554))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30559),tc_List_Olist(X30559))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30559),tc_List_Olist(X30559)),hAPP(hAPP(c_List_Olist_OCons(X30559),X30558),X30557)),hAPP(hAPP(c_List_Olist_OCons(X30559),X30556),X30555))),c_List_Olexord(X30559,X30554))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30559,X30559)),hAPP(hAPP(c_Product__Type_OPair(X30559,X30559),X30558),X30556)),X30554))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30559),tc_List_Olist(X30559))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30559),tc_List_Olist(X30559)),hAPP(hAPP(c_List_Olist_OCons(X30559),X30558),X30557)),hAPP(hAPP(c_List_Olist_OCons(X30559),X30556),X30555))),c_List_Olexord(X30559,X30554))) )
      & ( X30558 != X30556
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30559),tc_List_Olist(X30559))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30559),tc_List_Olist(X30559)),X30557),X30555)),c_List_Olexord(X30559,X30554)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30559),tc_List_Olist(X30559))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30559),tc_List_Olist(X30559)),hAPP(hAPP(c_List_Olist_OCons(X30559),X30558),X30557)),hAPP(hAPP(c_List_Olist_OCons(X30559),X30556),X30555))),c_List_Olexord(X30559,X30554))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__cons__cons])])]) ).

fof(i_0_6701,plain,
    ! [X30519,X30520,X30521,X30522,X30523,X30524] :
      ( ( X30523 = X30521
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X30524,X30524)),hAPP(hAPP(c_Product__Type_OPair(X30524,X30524),X30523),X30521)),X30519))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30524),tc_List_Olist(X30524))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30524),tc_List_Olist(X30524)),hAPP(hAPP(c_List_Olist_OCons(X30524),X30523),X30522)),hAPP(hAPP(c_List_Olist_OCons(X30524),X30521),X30520))),c_List_Olex(X30524,X30519))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30524),tc_List_Olist(X30524))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30524),tc_List_Olist(X30524)),X30522),X30520)),c_List_Olex(X30524,X30519)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X30524,X30524)),hAPP(hAPP(c_Product__Type_OPair(X30524,X30524),X30523),X30521)),X30519))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30524),tc_List_Olist(X30524))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30524),tc_List_Olist(X30524)),hAPP(hAPP(c_List_Olist_OCons(X30524),X30523),X30522)),hAPP(hAPP(c_List_Olist_OCons(X30524),X30521),X30520))),c_List_Olex(X30524,X30519))) )
      & ( X30523 = X30521
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30524)),X30522) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30524)),X30520)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30524),tc_List_Olist(X30524))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30524),tc_List_Olist(X30524)),hAPP(hAPP(c_List_Olist_OCons(X30524),X30523),X30522)),hAPP(hAPP(c_List_Olist_OCons(X30524),X30521),X30520))),c_List_Olex(X30524,X30519))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30524),tc_List_Olist(X30524))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30524),tc_List_Olist(X30524)),X30522),X30520)),c_List_Olex(X30524,X30519)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30524)),X30522) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30524)),X30520)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30524),tc_List_Olist(X30524))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30524),tc_List_Olist(X30524)),hAPP(hAPP(c_List_Olist_OCons(X30524),X30523),X30522)),hAPP(hAPP(c_List_Olist_OCons(X30524),X30521),X30520))),c_List_Olex(X30524,X30519))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30524,X30524)),hAPP(hAPP(c_Product__Type_OPair(X30524,X30524),X30523),X30521)),X30519))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30524)),X30522) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30524)),X30520)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30524),tc_List_Olist(X30524))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30524),tc_List_Olist(X30524)),hAPP(hAPP(c_List_Olist_OCons(X30524),X30523),X30522)),hAPP(hAPP(c_List_Olist_OCons(X30524),X30521),X30520))),c_List_Olex(X30524,X30519))) )
      & ( X30523 != X30521
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30524),tc_List_Olist(X30524))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30524),tc_List_Olist(X30524)),X30522),X30520)),c_List_Olex(X30524,X30519)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30524),tc_List_Olist(X30524))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30524),tc_List_Olist(X30524)),hAPP(hAPP(c_List_Olist_OCons(X30524),X30523),X30522)),hAPP(hAPP(c_List_Olist_OCons(X30524),X30521),X30520))),c_List_Olex(X30524,X30519))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lex])])]) ).

fof(i_0_6702,plain,
    ! [X27752,X27753,X27754,X27755,X27756] : hAPP(hAPP(c_Product__Type_OSigma(X27756,X27755),X27754),hAPP(hAPP(c_COMBS(X27756,tc_fun(X27755,tc_HOL_Obool),tc_fun(X27755,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27755,tc_HOL_Obool),tc_fun(tc_fun(X27755,tc_HOL_Obool),tc_fun(X27755,tc_HOL_Obool)),X27756),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27755,tc_HOL_Obool))),X27753)),X27752)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27756,X27755),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27756,X27755),X27754),X27753)),hAPP(hAPP(c_Product__Type_OSigma(X27756,X27755),X27754),X27752)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib2]) ).

fof(i_0_6703,plain,
    ! [X27759,X27760,X27761,X27762,X27763] : hAPP(hAPP(c_Product__Type_OSigma(X27763,X27762),X27761),hAPP(hAPP(c_COMBS(X27763,tc_fun(X27762,tc_HOL_Obool),tc_fun(X27762,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27762,tc_HOL_Obool),tc_fun(tc_fun(X27762,tc_HOL_Obool),tc_fun(X27762,tc_HOL_Obool)),X27763),c_Groups_Ominus__class_Ominus(tc_fun(X27762,tc_HOL_Obool))),X27760)),X27759)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X27763,X27762),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27763,X27762),X27761),X27760)),hAPP(hAPP(c_Product__Type_OSigma(X27763,X27762),X27761),X27759)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Diff__distrib2]) ).

fof(i_0_6704,plain,
    ! [X27718,X27719,X27720,X27721,X27722] : hAPP(hAPP(c_Product__Type_OSigma(X27722,X27721),X27720),hAPP(hAPP(c_COMBS(X27722,tc_fun(X27721,tc_HOL_Obool),tc_fun(X27721,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27721,tc_HOL_Obool),tc_fun(tc_fun(X27721,tc_HOL_Obool),tc_fun(X27721,tc_HOL_Obool)),X27722),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27721,tc_HOL_Obool))),X27719)),X27718)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27722,X27721),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27722,X27721),X27720),X27719)),hAPP(hAPP(c_Product__Type_OSigma(X27722,X27721),X27720),X27718)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Un__distrib2]) ).

fof(i_0_6705,plain,
    ! [X27111,X27112,X27113,X27114,X27115] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27115)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27115),hAPP(c_Groups_Oabs__class_Oabs(X27115),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27115),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27115),X27114),X27113)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27115),X27112),X27111)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27115),hAPP(c_Groups_Oabs__class_Oabs(X27115),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27115),X27114),X27112))),hAPP(c_Groups_Oabs__class_Oabs(X27115),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27115),X27113),X27111))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__triangle__ineq])]) ).

fof(i_0_6706,plain,
    ! [X21948,X21949,X21950,X21951,X21952] :
      ( ( ~ 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),X21952),X21950)),X21949)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21951),X21950)),X21948)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21949),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),X21951),X21952)),X21950)),X21948)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21952),X21951)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21949),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),X21951),X21952)),X21950)),X21948)))
        | 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),X21952),X21950)),X21949)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21951),X21950)),X21948)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21952),X21951)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff2])])]) ).

fof(i_0_6707,plain,
    ! [X21973,X21974,X21975,X21976,X21977] :
      ( ( ~ 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),X21977),X21975)),X21974)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21976),X21975)),X21973)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21974),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),X21976),X21977)),X21975)),X21973)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21977),X21976)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21974),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),X21976),X21977)),X21975)),X21973)))
        | 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),X21977),X21975)),X21974)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21976),X21975)),X21973)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21977),X21976)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff2])])]) ).

fof(i_0_6708,plain,
    ! [X20708,X20709,X20710,X20711,X20712,X20713,X20714,X20715] :
      ( ~ c_Finite__Set_Ofolding__image(X20715,X20714,X20713,X20712,X20711)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20714),X20710))
      | hAPP(hAPP(X20711,hAPP(hAPP(c_COMBS(X20714,X20715,X20715),hAPP(hAPP(c_COMBB(X20715,tc_fun(X20715,X20715),X20714),X20713),X20709)),X20708)),X20710) = hAPP(hAPP(X20713,hAPP(hAPP(X20711,X20709),X20710)),hAPP(hAPP(X20711,X20708),X20710)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image_Odistrib])]) ).

cnf(i_0_6709,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_5441]) ).

fof(i_0_6710,plain,
    ! [X21384,X21385,X21386,X21387,X21388] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21388)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21387),X21386))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21387),X21385))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21388),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21388,X21387,c_Groups_Otimes__class_Otimes(X21388)),X21384),c_Groups_Oone__class_Oone(X21388)),X21386)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21388,X21387,c_Groups_Otimes__class_Otimes(X21388)),X21384),c_Groups_Oone__class_Oone(X21388)),X21385)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21388),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21388,X21387,c_Groups_Otimes__class_Otimes(X21388)),X21384),c_Groups_Oone__class_Oone(X21388)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21387,tc_HOL_Obool)),X21386),X21385))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21388,X21387,c_Groups_Otimes__class_Otimes(X21388)),X21384),c_Groups_Oone__class_Oone(X21388)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21387,tc_HOL_Obool)),X21386),X21385))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__Un__Int])]) ).

fof(i_0_6711,plain,
    ! [X26759,X26760,X26761] : 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),X26761)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X26760))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26759))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26759),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26761),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26761),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26759),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X26760)))),
    inference(variable_rename,[status(thm)],[fact_arith__series__nat]) ).

fof(i_0_6712,plain,
    ! [X18123,X18124,X18125,X18126] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18126,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18126,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18126,tc_HOL_Obool)),X18125),X18124)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18126,tc_HOL_Obool)),X18124),X18123))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18126,tc_HOL_Obool)),X18123),X18125)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18126,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18126,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18126,tc_HOL_Obool)),X18125),X18124)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18126,tc_HOL_Obool)),X18124),X18123))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18126,tc_HOL_Obool)),X18123),X18125)),
    inference(variable_rename,[status(thm)],[fact_Un__Int__crazy]) ).

fof(i_0_6713,plain,
    ! [X30578,X30579,X30580,X30581,X30582,X30583] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30583,X30583)),hAPP(hAPP(c_Product__Type_OPair(X30583,X30583),X30582),X30581)),c_Transitive__Closure_Ortrancl(X30583,X30580)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30583),tc_List_Olist(X30583))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30583),tc_List_Olist(X30583)),X30579),X30578)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X30583),c_List_Olistrel1(X30583,X30580))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30583),tc_List_Olist(X30583))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30583),tc_List_Olist(X30583)),hAPP(hAPP(c_List_Olist_OCons(X30583),X30582),X30579)),hAPP(hAPP(c_List_Olist_OCons(X30583),X30581),X30578))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X30583),c_List_Olistrel1(X30583,X30580)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI2])]) ).

fof(i_0_6714,plain,
    ! [X18228,X18229,X18230,X18231,X18232] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18232,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18232,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18231,X18232,X18230),X18229)),hAPP(c_Set_Oimage(X18231,X18232,X18230),X18228))),hAPP(c_Set_Oimage(X18231,X18232,X18230),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18231,tc_HOL_Obool)),X18229),X18228)))),
    inference(variable_rename,[status(thm)],[fact_image__diff__subset]) ).

cnf(i_0_6715,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_5442]) ).

cnf(i_0_6716,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_5443]) ).

fof(i_0_6717,plain,
    ! [X18867,X18868,X18869,X18870,X18871,X18872] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X18872),X18871),X18870))
        | c_Map_Orestrict__map(X18872,X18869,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18872,tc_Option_Ooption(X18869)),X18868),X18871),X18867),X18870) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18872,tc_Option_Ooption(X18869)),c_Map_Orestrict__map(X18872,X18869,X18868,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18872,tc_HOL_Obool)),X18870),hAPP(hAPP(c_Set_Oinsert(X18872),X18871),c_Orderings_Obot__class_Obot(tc_fun(X18872,tc_HOL_Obool)))))),X18871),X18867) )
      & ( hBOOL(hAPP(hAPP(c_member(X18872),X18871),X18870))
        | c_Map_Orestrict__map(X18872,X18869,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18872,tc_Option_Ooption(X18869)),X18868),X18871),X18867),X18870) = c_Map_Orestrict__map(X18872,X18869,X18868,X18870) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5444])]) ).

fof(i_0_6718,plain,
    ! [X24551] : hAPP(c_Set_OCollect(tc_Nat_Onat),X24551) = 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),X24551),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J]) ).

fof(i_0_6719,plain,
    ! [X30531,X30532] : c_List_Olenlex(X30532,X30531) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(X30532)),tc_List_Olist(X30532)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(X30532),c_Wellfounded_Oless__than,c_List_Olex(X30532,X30531))),hAPP(hAPP(c_COMBS(tc_List_Olist(X30532),tc_List_Olist(X30532),tc_prod(tc_Nat_Onat,tc_List_Olist(X30532))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(X30532),tc_prod(tc_Nat_Onat,tc_List_Olist(X30532))),tc_List_Olist(X30532)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(X30532))),c_Nat_Osize__class_Osize(tc_List_Olist(X30532)))),c_COMBI(tc_List_Olist(X30532)))),
    inference(variable_rename,[status(thm)],[fact_lenlex__def]) ).

fof(i_0_6720,plain,
    ! [X28158,X28159,X28160] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28160),esk284_3(X28158,X28159,X28160)),X28158))
        | c_Relation_Orefl__on(X28160,X28158,X28159)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28160,X28160),tc_HOL_Obool)),X28159),hAPP(hAPP(c_Product__Type_OSigma(X28160,X28160),X28158),hAPP(c_COMBK(tc_fun(X28160,tc_HOL_Obool),X28160),X28158)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28160,X28160)),hAPP(hAPP(c_Product__Type_OPair(X28160,X28160),esk284_3(X28158,X28159,X28160)),esk284_3(X28158,X28159,X28160))),X28159))
        | c_Relation_Orefl__on(X28160,X28158,X28159)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28160,X28160),tc_HOL_Obool)),X28159),hAPP(hAPP(c_Product__Type_OSigma(X28160,X28160),X28158),hAPP(c_COMBK(tc_fun(X28160,tc_HOL_Obool),X28160),X28158)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onI])])])]) ).

fof(i_0_6721,plain,
    ! [X28116,X28117,X28118,X28119,X28120,X28121,X28122] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28118,X28118),tc_HOL_Obool)),X28116),hAPP(hAPP(c_Product__Type_OSigma(X28118,X28118),X28117),hAPP(c_COMBK(tc_fun(X28118,tc_HOL_Obool),X28118),X28117))))
        | ~ c_Relation_Orefl__on(X28118,X28117,X28116) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28118),X28119),X28117))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28118,X28118)),hAPP(hAPP(c_Product__Type_OPair(X28118,X28118),X28119),X28119)),X28116))
        | ~ c_Relation_Orefl__on(X28118,X28117,X28116) )
      & ( hBOOL(hAPP(hAPP(c_member(X28122),esk281_3(X28120,X28121,X28122)),X28121))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28122,X28122),tc_HOL_Obool)),X28120),hAPP(hAPP(c_Product__Type_OSigma(X28122,X28122),X28121),hAPP(c_COMBK(tc_fun(X28122,tc_HOL_Obool),X28122),X28121))))
        | c_Relation_Orefl__on(X28122,X28121,X28120) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28122,X28122)),hAPP(hAPP(c_Product__Type_OPair(X28122,X28122),esk281_3(X28120,X28121,X28122)),esk281_3(X28120,X28121,X28122))),X28120))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28122,X28122),tc_HOL_Obool)),X28120),hAPP(hAPP(c_Product__Type_OSigma(X28122,X28122),X28121),hAPP(c_COMBK(tc_fun(X28122,tc_HOL_Obool),X28122),X28121))))
        | c_Relation_Orefl__on(X28122,X28121,X28120) ) ),
    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_6722,plain,
    ! [X30362,X30363,X30364,X30365] :
      ( hAPP(c_List_Oset(X30365),X30364) != c_Map_Odom(X30365,X30363,X30362)
      | hAPP(c_Map_Omap__of(X30365,X30363),hAPP(hAPP(c_List_Omap(X30365,tc_prod(X30365,X30363)),hAPP(hAPP(c_COMBS(X30365,X30363,tc_prod(X30365,X30363)),c_Product__Type_OPair(X30365,X30363)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X30363),X30363,X30365),c_Option_Othe(X30363)),X30362))),X30364)) = X30362 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__map__keys])]) ).

fof(i_0_6723,plain,
    ! [X17242,X17243,X17244] : hAPP(hAPP(c_Set_Oinsert(X17244),X17243),X17242) = hAPP(c_Set_OCollect(X17244),hAPP(hAPP(c_COMBS(X17244,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17244),c_fdisj),hAPP(hAPP(c_COMBC(X17244,X17244,tc_HOL_Obool),c_fequal),X17243))),hAPP(hAPP(c_COMBC(X17244,tc_fun(X17244,tc_HOL_Obool),tc_HOL_Obool),c_member(X17244)),X17242))),
    inference(variable_rename,[status(thm)],[fact_insert__compr__raw]) ).

fof(i_0_6724,plain,
    ! [X17239,X17240,X17241] : hAPP(hAPP(c_Set_Oinsert(X17241),X17240),X17239) = hAPP(c_Set_OCollect(X17241),hAPP(hAPP(c_COMBS(X17241,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17241),c_fdisj),hAPP(hAPP(c_COMBC(X17241,X17241,tc_HOL_Obool),c_fequal),X17240))),hAPP(hAPP(c_COMBC(X17241,tc_fun(X17241,tc_HOL_Obool),tc_HOL_Obool),c_member(X17241)),X17239))),
    inference(variable_rename,[status(thm)],[fact_insert__compr]) ).

cnf(i_0_6725,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk348_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_5422]) ).

fof(i_0_6726,plain,
    ! [X30704,X30705,X30706,X30707,X30708,X30709] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30709,X30709)),hAPP(hAPP(c_Product__Type_OPair(X30709,X30709),X30708),X30707)),X30706))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30709),tc_List_Olist(X30709))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30709),tc_List_Olist(X30709)),X30705),X30704)),c_List_Olistrel(X30709,X30706)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30709),tc_List_Olist(X30709))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30709),tc_List_Olist(X30709)),hAPP(hAPP(c_List_Olist_OCons(X30709),X30708),X30705)),hAPP(hAPP(c_List_Olist_OCons(X30709),X30707),X30704))),c_List_Olistrel(X30709,X30706))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel_OCons])]) ).

cnf(i_0_6727,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk347_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_5421]) ).

fof(i_0_6728,plain,
    ! [X19057,X19058,X19059,X19060,X19061] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19061,X19061,X19060,X19059,X19058),X19057))
      | hBOOL(hAPP(hAPP(c_member(X19061),X19059),X19058))
      | hBOOL(hAPP(c_Finite__Set_Ofold1Set(X19061,X19060,hAPP(hAPP(c_Set_Oinsert(X19061),X19059),X19058)),X19057)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5445])]) ).

cnf(i_0_6729,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_5446]) ).

fof(i_0_6730,plain,
    ! [X19264,X19265,X19266] : c_Map_Odom(X19266,X19265,X19264) = hAPP(c_Set_OCollect(X19266),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X19266),c_fNot),hAPP(hAPP(c_COMBC(X19266,tc_Option_Ooption(X19265),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X19265),tc_fun(tc_Option_Ooption(X19265),tc_HOL_Obool),X19266),c_fequal),X19264)),c_Option_Ooption_ONone(X19265)))),
    inference(variable_rename,[status(thm)],[fact_dom__def]) ).

cnf(i_0_6731,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_5447]) ).

cnf(i_0_6732,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_5448]) ).

fof(i_0_6733,plain,
    ! [X24499] :
      ( X24499 = 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)),X24499),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_6734,plain,
    ! [X25594,X25595] : 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),X25595),X25594)),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),X25594),X25595)),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_6735,plain,
    ! [X24519] : 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)),X24519),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_6736,plain,
    ! [X29190,X29191,X29192,X29193,X29194,X29195] :
      ( ~ c_Finite__Set_Ofun__left__comm(X29195,X29194,X29193)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X29195,X29194,X29193,X29192,X29191),X29190))
      | hAPP(hAPP(c_Finite__Set_Ofold(X29195,X29194,X29193),X29192),X29191) = X29190 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__equality])]) ).

fof(i_0_6737,plain,
    ! [X19133,X19134,X19135,X19136,X19137] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19137,X19136,X19135,X19134,c_Orderings_Obot__class_Obot(tc_fun(X19137,tc_HOL_Obool))),X19133))
      | X19133 = X19134 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__fold__graphE])]) ).

fof(i_0_6738,plain,
    ! [X19854,X19855,X19856,X19857,X19858] :
      ( ~ c_Equiv__Relations_Oequiv(X19858,X19857,X19856)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19858,tc_HOL_Obool)),hAPP(c_Relation_OImage(X19858,X19858,X19856),hAPP(hAPP(c_Set_Oinsert(X19858),X19855),c_Orderings_Obot__class_Obot(tc_fun(X19858,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X19858,X19858,X19856),hAPP(hAPP(c_Set_Oinsert(X19858),X19854),c_Orderings_Obot__class_Obot(tc_fun(X19858,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(X19858),X19855),X19857))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X19858,X19858)),hAPP(hAPP(c_Product__Type_OPair(X19858,X19858),X19854),X19855)),X19856)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__equiv__class])]) ).

fof(i_0_6739,plain,
    ! [X20937,X20938,X20939,X20940,X20941,X20942] :
      ( ( hBOOL(hAPP(hAPP(X20940,X20938),X20941))
        | ~ hBOOL(hAPP(hAPP(c_member(X20942),X20941),c_SetInterval_Oord_OatLeastLessThan(X20942,X20940,X20939,X20938,X20937))) )
      & ( hBOOL(hAPP(hAPP(X20939,X20941),X20937))
        | ~ hBOOL(hAPP(hAPP(c_member(X20942),X20941),c_SetInterval_Oord_OatLeastLessThan(X20942,X20940,X20939,X20938,X20937))) )
      & ( ~ hBOOL(hAPP(hAPP(X20940,X20938),X20941))
        | ~ hBOOL(hAPP(hAPP(X20939,X20941),X20937))
        | hBOOL(hAPP(hAPP(c_member(X20942),X20941),c_SetInterval_Oord_OatLeastLessThan(X20942,X20940,X20939,X20938,X20937))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastLessThan__iff])])]) ).

fof(i_0_6740,plain,
    ! [X20931,X20932,X20933,X20934,X20935,X20936] :
      ( ( hBOOL(hAPP(hAPP(X20933,X20932),X20935))
        | ~ hBOOL(hAPP(hAPP(c_member(X20936),X20935),c_SetInterval_Oord_OgreaterThanAtMost(X20936,X20934,X20933,X20932,X20931))) )
      & ( hBOOL(hAPP(hAPP(X20934,X20935),X20931))
        | ~ hBOOL(hAPP(hAPP(c_member(X20936),X20935),c_SetInterval_Oord_OgreaterThanAtMost(X20936,X20934,X20933,X20932,X20931))) )
      & ( ~ hBOOL(hAPP(hAPP(X20933,X20932),X20935))
        | ~ hBOOL(hAPP(hAPP(X20934,X20935),X20931))
        | hBOOL(hAPP(hAPP(c_member(X20936),X20935),c_SetInterval_Oord_OgreaterThanAtMost(X20936,X20934,X20933,X20932,X20931))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanAtMost__iff])])]) ).

fof(i_0_6741,plain,
    ! [X27255,X27256,X27257,X27258,X27259] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk254_5(X27255,X27256,X27257,X27258,X27259)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X27259),X27256),X27258) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X27259),X27255),X27257)
        | ~ c_Nat__Transfer_Onat__set(X27257)
        | X27258 != X27257
        | ~ class_Groups_Ocomm__monoid__add(X27259)
        | ~ class_Groups_Ocomm__monoid__mult(X27259) )
      & ( hAPP(X27256,esk254_5(X27255,X27256,X27257,X27258,X27259)) != hAPP(X27255,esk254_5(X27255,X27256,X27257,X27258,X27259))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X27259),X27256),X27258) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X27259),X27255),X27257)
        | ~ c_Nat__Transfer_Onat__set(X27257)
        | X27258 != X27257
        | ~ class_Groups_Ocomm__monoid__add(X27259)
        | ~ class_Groups_Ocomm__monoid__mult(X27259) ) ),
    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_6742,plain,
    ! [X26962,X26963,X26964,X26965,X26966] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk251_5(X26962,X26963,X26964,X26965,X26966)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X26966),X26963),X26965) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X26966),X26962),X26964)
        | ~ c_Nat__Transfer_Onat__set(X26964)
        | X26965 != X26964
        | ~ class_Groups_Ocomm__monoid__add(X26966)
        | ~ class_Groups_Ocomm__monoid__mult(X26966) )
      & ( hAPP(X26963,esk251_5(X26962,X26963,X26964,X26965,X26966)) != hAPP(X26962,esk251_5(X26962,X26963,X26964,X26965,X26966))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X26966),X26963),X26965) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X26966),X26962),X26964)
        | ~ c_Nat__Transfer_Onat__set(X26964)
        | X26965 != X26964
        | ~ class_Groups_Ocomm__monoid__add(X26966)
        | ~ class_Groups_Ocomm__monoid__mult(X26966) ) ),
    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_6743,plain,
    ! [X32383,X32384] : c_Random_Oselect__weight(X32384,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X32384),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X32384,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X32384,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X32384)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X32383)) = c_Random_Oselect__weight(X32384,X32383),
    inference(variable_rename,[status(thm)],[fact_select__weigth__drop__zero]) ).

fof(i_0_6744,plain,
    ! [X32381,X32382] : c_Random_Opick(X32382,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X32382),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X32382,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X32382,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X32382)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X32381)) = c_Random_Opick(X32382,X32381),
    inference(variable_rename,[status(thm)],[fact_pick__drop__zero]) ).

cnf(i_0_6745,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_6746,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]) ).

cnf(i_0_6747,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_5449]) ).

cnf(i_0_6748,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_5450]) ).

fof(i_0_6749,plain,
    ! [X27631,X27632,X27633,X27634] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27634,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X27634,X27633),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27634,X27633),tc_HOL_Obool)),X27632),X27631))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27634,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X27634,X27633),X27632)),hAPP(c_Relation_ODomain(X27634,X27633),X27631)))),
    inference(variable_rename,[status(thm)],[fact_Domain__Int__subset]) ).

fof(i_0_6750,plain,
    ! [X27553,X27554,X27555,X27556] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27556,tc_HOL_Obool)),hAPP(c_Relation_ORange(X27555,X27556),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27555,X27556),tc_HOL_Obool)),X27554),X27553))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27556,tc_HOL_Obool)),hAPP(c_Relation_ORange(X27555,X27556),X27554)),hAPP(c_Relation_ORange(X27555,X27556),X27553)))),
    inference(variable_rename,[status(thm)],[fact_Range__Int__subset]) ).

fof(i_0_6751,plain,
    ! [X26500,X26501,X26502,X26503,X26504] :
      ( ~ class_Groups_Ocomm__monoid__add(X26504)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26503),X26502))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26503,X26504),hAPP(hAPP(c_COMBS(X26503,X26504,X26504),hAPP(hAPP(c_COMBB(X26504,tc_fun(X26504,X26504),X26503),c_Groups_Oplus__class_Oplus(X26504)),X26501)),X26500)),X26502) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26504),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26503,X26504),X26501),X26502)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26503,X26504),X26500),X26502)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Odistrib])]) ).

fof(i_0_6752,plain,
    ! [X24188,X24189,X24190,X24191,X24192] :
      ( ~ class_Fields_Ofield__inverse__zero(X24192)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24191),X24190))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24191,X24192),hAPP(hAPP(c_COMBS(X24191,X24192,X24192),hAPP(hAPP(c_COMBB(X24192,tc_fun(X24192,X24192),X24191),c_Rings_Oinverse__class_Odivide(X24192)),X24189)),X24188)),X24190) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24192),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24191,X24192),X24189),X24190)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24191,X24192),X24188),X24190)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__dividef])]) ).

fof(i_0_6753,plain,
    ! [X23065,X23066,X23067,X23068,X23069] :
      ( ~ class_Groups_Ocomm__monoid__mult(X23069)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23068),X23067))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23068,X23069),hAPP(hAPP(c_COMBS(X23068,X23069,X23069),hAPP(hAPP(c_COMBB(X23069,tc_fun(X23069,X23069),X23068),c_Groups_Otimes__class_Otimes(X23069)),X23066)),X23065)),X23067) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23069),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23068,X23069),X23066),X23067)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23068,X23069),X23065),X23067)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Odistrib])]) ).

fof(i_0_6754,plain,
    ! [X20484,X20485,X20486,X20487,X20488,X20489] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X20489,X20488,X20487,X20486,X20485),X20484))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20489),X20485)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__graph__imp__finite])]) ).

fof(i_0_6755,plain,
    ! [X31749,X31750] : hAPP(c_List_Orotate1(X31750),X31749) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X31750),X31750,c_List_Olist_ONil(X31750),hAPP(hAPP(c_COMBB(tc_List_Olist(X31750),tc_fun(tc_List_Olist(X31750),tc_List_Olist(X31750)),X31750),hAPP(c_COMBC(tc_List_Olist(X31750),tc_List_Olist(X31750),tc_List_Olist(X31750)),c_List_Oappend(X31750))),hAPP(hAPP(c_COMBC(X31750,tc_List_Olist(X31750),tc_List_Olist(X31750)),c_List_Olist_OCons(X31750)),c_List_Olist_ONil(X31750)))),X31749),
    inference(variable_rename,[status(thm)],[fact_rotate1__def]) ).

fof(i_0_6756,plain,
    ! [X26449,X26450,X26451,X26452,X26453] :
      ( ~ class_Groups_Ocomm__monoid__add(X26453)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26452,X26453),hAPP(hAPP(c_COMBS(X26452,X26453,X26453),hAPP(hAPP(c_COMBB(X26453,tc_fun(X26453,X26453),X26452),c_Groups_Oplus__class_Oplus(X26453)),X26451)),X26450)),X26449) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26453),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26452,X26453),X26451),X26449)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26452,X26453),X26450),X26449)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__addf])]) ).

fof(i_0_6757,plain,
    ! [X26477,X26478,X26479,X26480,X26481] :
      ( ~ class_Groups_Oab__group__add(X26481)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26480,X26481),hAPP(hAPP(c_COMBS(X26480,X26481,X26481),hAPP(hAPP(c_COMBB(X26481,tc_fun(X26481,X26481),X26480),c_Groups_Ominus__class_Ominus(X26481)),X26479)),X26478)),X26477) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26481),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26480,X26481),X26479),X26477)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26480,X26481),X26478),X26477)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__subtractf])]) ).

fof(i_0_6758,plain,
    ! [X23002,X23003,X23004,X23005,X23006] :
      ( ~ class_Groups_Ocomm__monoid__mult(X23006)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23005,X23006),hAPP(hAPP(c_COMBS(X23005,X23006,X23006),hAPP(hAPP(c_COMBB(X23006,tc_fun(X23006,X23006),X23005),c_Groups_Otimes__class_Otimes(X23006)),X23004)),X23003)),X23002) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23006),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23005,X23006),X23004),X23002)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23005,X23006),X23003),X23002)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__timesf])]) ).

fof(i_0_6759,plain,
    ! [X23717,X23718,X23719,X23720,X23721] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23721,X23720),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X23719),X23718)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23720))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23717))
      | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23721,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23720),X23717)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23719),X23717)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23720),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23719,X23717))),X23718)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__mult2__eq])]) ).

fof(i_0_6760,plain,
    ! [X33154,X33155,X33156] : c_List_Olistsp(X33156,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33156,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X33156,tc_fun(X33156,tc_HOL_Obool),tc_HOL_Obool),c_member(X33156)),X33155)),hAPP(hAPP(c_COMBC(X33156,tc_fun(X33156,tc_HOL_Obool),tc_HOL_Obool),c_member(X33156)),X33154))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X33156),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(X33156),tc_fun(tc_List_Olist(X33156),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X33156))),c_List_Olists(X33156,X33155))),hAPP(hAPP(c_COMBC(tc_List_Olist(X33156),tc_fun(tc_List_Olist(X33156),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X33156))),c_List_Olists(X33156,X33154))),
    inference(variable_rename,[status(thm)],[fact_lists__Int__eq]) ).

fof(i_0_6761,plain,
    ! [X30415,X30416] : c_Random_Oselect__weight(X30416,X30415) = 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(X30416,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,X30416),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X30416)),X30415)))),hAPP(hAPP(c_COMBB(X30416,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X30416,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X30416,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X30416,X30415))),
    inference(variable_rename,[status(thm)],[fact_select__weight__def]) ).

fof(i_0_6762,plain,
    ! [X27850,X27851,X27852,X27853,X27854,X27855] : hAPP(hAPP(c_Product__Type_OSigma(X27855,X27854),hAPP(hAPP(c_Set_Oinsert(X27855),X27853),X27852)),hAPP(c_COMBK(tc_fun(X27854,tc_HOL_Obool),X27855),hAPP(hAPP(c_Set_Oinsert(X27854),X27851),X27850))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(X27855,X27854)),hAPP(hAPP(c_Product__Type_OPair(X27855,X27854),X27853),X27851)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27855,X27854),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27855,X27854),X27852),hAPP(c_COMBK(tc_fun(X27854,tc_HOL_Obool),X27855),hAPP(hAPP(c_Set_Oinsert(X27854),X27851),X27850)))),hAPP(hAPP(c_Product__Type_OSigma(X27855,X27854),hAPP(hAPP(c_Set_Oinsert(X27855),X27853),X27852)),hAPP(c_COMBK(tc_fun(X27854,tc_HOL_Obool),X27855),X27850)))),
    inference(variable_rename,[status(thm)],[fact_insert__times__insert]) ).

fof(i_0_6763,plain,
    ! [X26444,X26445,X26446,X26447,X26448] :
      ( ~ class_Fields_Ofield(X26448)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X26448),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26447,X26448),X26446),X26445)),X26444) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26447,X26448),hAPP(hAPP(c_COMBC(X26447,X26448,X26448),hAPP(hAPP(c_COMBB(X26448,tc_fun(X26448,X26448),X26447),c_Rings_Oinverse__class_Odivide(X26448)),X26446)),X26444)),X26445) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__divide__distrib])]) ).

fof(i_0_6764,plain,
    ! [X26461,X26462,X26463,X26464,X26465] :
      ( ~ class_Rings_Osemiring__0(X26465)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26465),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26464,X26465),X26463),X26462)),X26461) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26464,X26465),hAPP(hAPP(c_COMBC(X26464,X26465,X26465),hAPP(hAPP(c_COMBB(X26465,tc_fun(X26465,X26465),X26464),c_Groups_Otimes__class_Otimes(X26465)),X26463)),X26461)),X26462) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__left__distrib])]) ).

fof(i_0_6765,plain,
    ! [X23263,X23264,X23265,X23266,X23267] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X23267,X23266),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X23265),X23264)))
      | X23266 = 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)),X23263))
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X23267,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23266),X23263)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23265),X23263)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23266),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23265,X23263))),X23264)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma])]) ).

fof(i_0_6766,plain,
    ! [X30682,X30683,X30684,X30685,X30686] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30686),tc_List_Olist(X30686))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30686),tc_List_Olist(X30686)),X30685),X30684)),c_List_Olistrel(X30686,c_Transitive__Closure_Ortrancl(X30686,X30683))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30686),tc_List_Olist(X30686))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30686),tc_List_Olist(X30686)),X30684),X30682)),c_List_Olistrel(X30686,c_Transitive__Closure_Ortrancl(X30686,X30683))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30686),tc_List_Olist(X30686))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30686),tc_List_Olist(X30686)),X30685),X30682)),c_List_Olistrel(X30686,c_Transitive__Closure_Ortrancl(X30686,X30683)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__rtrancl__trans])]) ).

cnf(i_0_6767,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_5451]) ).

cnf(i_0_6768,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_5452]) ).

fof(i_0_6769,plain,
    ! [X17597,X17598,X17599] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17599,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X17599,tc_fun(X17599,tc_HOL_Obool),tc_HOL_Obool),c_member(X17599)),X17598)),hAPP(hAPP(c_COMBC(X17599,tc_fun(X17599,tc_HOL_Obool),tc_HOL_Obool),c_member(X17599)),X17597)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17599,tc_HOL_Obool)),X17598),X17597)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17599,tc_HOL_Obool)),X17598),X17597))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17599,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X17599,tc_fun(X17599,tc_HOL_Obool),tc_HOL_Obool),c_member(X17599)),X17598)),hAPP(hAPP(c_COMBC(X17599,tc_fun(X17599,tc_HOL_Obool),tc_HOL_Obool),c_member(X17599)),X17597))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq])]) ).

fof(i_0_6770,plain,
    ! [X30867,X30868,X30869,X30870,X30871,X30872,X30873,X30874] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30874)),X30873) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30872)),X30871)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30874)),X30870) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30872)),X30871)
      | hBOOL(hAPP(hAPP(c_member(X30872),X30869),hAPP(c_List_Oset(X30872),X30871)))
      | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X30872,tc_Option_Ooption(X30874)),hAPP(c_Map_Omap__of(X30872,X30874),hAPP(hAPP(c_List_Ozip(X30872,X30874),X30871),X30873))),X30869),hAPP(c_Option_Ooption_OSome(X30874),X30868)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X30872,tc_Option_Ooption(X30874)),hAPP(c_Map_Omap__of(X30872,X30874),hAPP(hAPP(c_List_Ozip(X30872,X30874),X30871),X30870))),X30869),hAPP(c_Option_Ooption_OSome(X30874),X30867))
      | hAPP(c_Map_Omap__of(X30872,X30874),hAPP(hAPP(c_List_Ozip(X30872,X30874),X30871),X30873)) = hAPP(c_Map_Omap__of(X30872,X30874),hAPP(hAPP(c_List_Ozip(X30872,X30874),X30871),X30870)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5453])]) ).

cnf(i_0_6771,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_5454]) ).

cnf(i_0_6772,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_5455]) ).

fof(i_0_6773,plain,
    ! [X30024,X30025,X30026,X30027] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X30027)),hAPP(c_Set_Oimage(X30026,tc_Option_Ooption(X30027),X30025),c_Orderings_Otop__class_Otop(tc_fun(X30026,tc_HOL_Obool)))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X30027)),hAPP(c_Set_Oimage(X30026,tc_Option_Ooption(X30027),c_Map_Omap__add(X30026,X30027,X30025,hAPP(c_Map_Omap__of(X30026,X30027),X30024))),c_Orderings_Otop__class_Otop(tc_fun(X30026,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__map__of__map__add])]) ).

fof(i_0_6774,plain,
    ! [X27477,X27478,X27479,X27480] :
      ( ~ c_FunDef_Oreduction__pair(X27480,X27479)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27480,X27480),tc_HOL_Obool)),X27478),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X27480,X27480),tc_HOL_Obool),tc_fun(tc_prod(X27480,X27480),tc_HOL_Obool)),X27479)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27480,X27480),tc_HOL_Obool)),X27477),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X27480,X27480),tc_HOL_Obool),tc_fun(tc_prod(X27480,X27480),tc_HOL_Obool)),X27479)))
      | ~ c_Wellfounded_Owf(X27480,X27477)
      | c_Wellfounded_Owf(X27480,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27480,X27480),tc_HOL_Obool)),X27478),X27477)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduction__pair__lemma])]) ).

fof(i_0_6775,plain,
    ! [X29779,X29780,X29781] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29781,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29781,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X29781,tc_HOL_Obool),tc_HOL_Obool)),X29780),X29779))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29781,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29781,tc_HOL_Obool),X29780)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29781,tc_HOL_Obool),X29779)))),
    inference(variable_rename,[status(thm)],[fact_Union__Int__subset]) ).

fof(i_0_6776,plain,
    ! [X28798,X28799,X28800,X28801,X28802] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28802,tc_HOL_Obool)),hAPP(c_Relation_OImage(X28801,X28802,X28800),X28799)),X28798))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28801,tc_HOL_Obool)),X28799),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28801,tc_HOL_Obool)),hAPP(c_Relation_OImage(X28802,X28801,hAPP(c_Relation_Oconverse(X28801,X28802),X28800)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28802,tc_HOL_Obool)),X28798))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28801,tc_HOL_Obool)),X28799),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28801,tc_HOL_Obool)),hAPP(c_Relation_OImage(X28802,X28801,hAPP(c_Relation_Oconverse(X28801,X28802),X28800)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28802,tc_HOL_Obool)),X28798)))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28802,tc_HOL_Obool)),hAPP(c_Relation_OImage(X28801,X28802,X28800),X28799)),X28798)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__subset__eq])]) ).

cnf(i_0_6777,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_5456]) ).

cnf(i_0_6778,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_5457]) ).

fof(i_0_6779,plain,
    ! [X19536,X19537,X19538,X19539] : hAPP(c_Set_Oimage(X19539,X19538,X19537),X19536) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19539,tc_fun(X19538,tc_HOL_Obool)),X19536),hAPP(hAPP(c_COMBC(X19539,tc_fun(X19538,tc_HOL_Obool),tc_fun(X19538,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X19538,tc_fun(tc_fun(X19538,tc_HOL_Obool),tc_fun(X19538,tc_HOL_Obool)),X19539),c_Set_Oinsert(X19538)),X19537)),c_Orderings_Obot__class_Obot(tc_fun(X19538,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_image__eq__UN]) ).

fof(i_0_6780,plain,
    ! [X17175,X17176,X17177] :
      ( ( ~ hBOOL(hAPP(X17177,X17176))
        | hAPP(c_Set_OCollect(X17175),hAPP(hAPP(c_COMBS(X17175,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17175),c_fconj),hAPP(hAPP(c_COMBC(X17175,X17175,tc_HOL_Obool),c_fequal),X17176))),X17177)) = hAPP(hAPP(c_Set_Oinsert(X17175),X17176),c_Orderings_Obot__class_Obot(tc_fun(X17175,tc_HOL_Obool))) )
      & ( hBOOL(hAPP(X17177,X17176))
        | hAPP(c_Set_OCollect(X17175),hAPP(hAPP(c_COMBS(X17175,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17175),c_fconj),hAPP(hAPP(c_COMBC(X17175,X17175,tc_HOL_Obool),c_fequal),X17176))),X17177)) = c_Orderings_Obot__class_Obot(tc_fun(X17175,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5458])]) ).

fof(i_0_6781,plain,
    ! [X34220,X34221,X34222,X34223,X34224,X34225,X34226] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(X34226),tc_Option_Ooption(X34225),tc_sum(X34224,X34223),hAPP(c_Option_Omap(X34226,X34225),X34222)),c_Sum__Type_Osum_Osum__case(X34224,tc_Option_Ooption(X34226),X34223,X34221,X34220)) = c_Sum__Type_Osum_Osum__case(X34224,tc_Option_Ooption(X34225),X34223,hAPP(c_Fun_Ocomp(tc_Option_Ooption(X34226),tc_Option_Ooption(X34225),X34224,hAPP(c_Option_Omap(X34226,X34225),X34222)),X34221),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X34226),tc_Option_Ooption(X34225),X34223,hAPP(c_Option_Omap(X34226,X34225),X34222)),X34220)),
    inference(variable_rename,[status(thm)],[fact_option__map__o__sum__case]) ).

fof(i_0_6782,plain,
    ! [X30609,X30610,X30611,X30612,X30613] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30613),tc_List_Olist(X30613))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30613),tc_List_Olist(X30613)),X30612),X30611)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X30613),c_List_Olistrel1(X30613,X30610))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30613),tc_List_Olist(X30613))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30613),tc_List_Olist(X30613)),hAPP(hAPP(c_List_Olist_OCons(X30613),X30609),X30612)),hAPP(hAPP(c_List_Olist_OCons(X30613),X30609),X30611))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X30613),c_List_Olistrel1(X30613,X30610)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI1])]) ).

fof(i_0_6783,plain,
    ! [X30223,X30224,X30225,X30226,X30227,X30228,X30229] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(X30229),tc_Option_Ooption(X30228),X30227,hAPP(c_Option_Omap(X30229,X30228),X30226)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X30227,tc_Option_Ooption(X30229)),X30225),X30224),hAPP(c_Option_Ooption_OSome(X30229),X30223))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X30227,tc_Option_Ooption(X30228)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X30229),tc_Option_Ooption(X30228),X30227,hAPP(c_Option_Omap(X30229,X30228),X30226)),X30225)),X30224),hAPP(c_Option_Ooption_OSome(X30228),hAPP(X30226,X30223))),
    inference(variable_rename,[status(thm)],[fact_option__map__o__map__upd]) ).

fof(i_0_6784,plain,
    ! [X24476,X24477,X24478,X24479] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24479),X24478))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24477),X24476))
      | 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),X24479),X24477)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X24478),X24476))),c_FunDef_Opair__leq)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__leqI2])]) ).

fof(i_0_6785,plain,
    ! [X24111,X24112,X24113,X24114] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24114),X24113))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24112),X24111))
      | 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),X24114),X24112)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X24113),X24111))),c_FunDef_Opair__less)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__lessI2])]) ).

fof(i_0_6786,plain,
    ! [X28559,X28560,X28561] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28561,X28561),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28561,X28561),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X28561,X28560)),c_Transitive__Closure_Ortrancl(X28561,X28559))),c_Transitive__Closure_Ortrancl(X28561,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28561,X28561),tc_HOL_Obool)),X28560),X28559)))),
    inference(variable_rename,[status(thm)],[fact_rtrancl__Un__subset]) ).

fof(i_0_6787,plain,
    ! [X19334,X19335,X19336,X19337,X19338] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19338,tc_HOL_Obool)),hAPP(c_Relation_OImage(X19337,X19338,X19336),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19337,tc_HOL_Obool)),X19335),X19334))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19338,tc_HOL_Obool)),hAPP(c_Relation_OImage(X19337,X19338,X19336),X19335)),hAPP(c_Relation_OImage(X19337,X19338,X19336),X19334)))),
    inference(variable_rename,[status(thm)],[fact_Image__Int__subset]) ).

fof(i_0_6788,plain,
    ! [X18245,X18246,X18247,X18248,X18249] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18249,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18248,X18249,X18247),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18248,tc_HOL_Obool)),X18246),X18245))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18249,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18248,X18249,X18247),X18246)),hAPP(c_Set_Oimage(X18248,X18249,X18247),X18245)))),
    inference(variable_rename,[status(thm)],[fact_image__Int__subset]) ).

fof(i_0_6789,plain,
    ! [X29933,X29934] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk386_2(X29933,X29934)))
        | 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)))),X29934)) = 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)))),X29933)) )
      & ( ~ hBOOL(hAPP(X29934,esk386_2(X29933,X29934)))
        | ~ hBOOL(hAPP(X29933,esk386_2(X29933,X29934)))
        | 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)))),X29934)) = 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)))),X29933)) )
      & ( hBOOL(hAPP(X29934,esk386_2(X29933,X29934)))
        | hBOOL(hAPP(X29933,esk386_2(X29933,X29934)))
        | 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)))),X29934)) = 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)))),X29933)) ) ),
    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_6790,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_5459]) ).

fof(i_0_6791,plain,
    ! [X24488,X24489,X24490,X24491] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24491),X24490))
      | 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),X24491),X24489)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X24490),X24488))),c_FunDef_Opair__leq)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__leqI1])]) ).

fof(i_0_6792,plain,
    ! [X24236,X24237,X24238,X24239] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24239),X24238))
      | 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),X24239),X24237)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X24238),X24236))),c_FunDef_Opair__less)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__lessI1])]) ).

fof(i_0_6793,plain,
    ! [X31028,X31029] : c_List_Olists(X31029,X31028) = hAPP(c_Set_OCollect(tc_List_Olist(X31029)),hAPP(hAPP(c_COMBC(tc_List_Olist(X31029),tc_fun(X31029,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X31029,tc_HOL_Obool),tc_fun(tc_fun(X31029,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X31029)),c_Orderings_Oord__class_Oless__eq(tc_fun(X31029,tc_HOL_Obool))),c_List_Oset(X31029))),X31028)),
    inference(variable_rename,[status(thm)],[fact_lists__eq__set]) ).

fof(i_0_6794,plain,
    ! [X31675,X31676,X31677,X31678,X31679,X31680] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31680),tc_List_Olist(X31680))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31680),tc_List_Olist(X31680)),X31679),X31678)),c_List_Olistrel1(X31680,X31677)))
        | X31676 != X31675
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31680),tc_List_Olist(X31680))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31680),tc_List_Olist(X31680)),hAPP(hAPP(c_List_Oappend(X31680),X31679),X31676)),hAPP(hAPP(c_List_Oappend(X31680),X31678),X31675))),c_List_Olistrel1(X31680,X31677))) )
      & ( X31679 != X31678
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31680),tc_List_Olist(X31680))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31680),tc_List_Olist(X31680)),X31676),X31675)),c_List_Olistrel1(X31680,X31677)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31680),tc_List_Olist(X31680))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31680),tc_List_Olist(X31680)),hAPP(hAPP(c_List_Oappend(X31680),X31679),X31676)),hAPP(hAPP(c_List_Oappend(X31680),X31678),X31675))),c_List_Olistrel1(X31680,X31677))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__listrel1I])])]) ).

fof(i_0_6795,plain,
    ! [X31681,X31682,X31683,X31684,X31685] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31685),tc_List_Olist(X31685))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31685),tc_List_Olist(X31685)),X31684),X31683)),c_List_Olexord(X31685,X31682)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31685),tc_List_Olist(X31685))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31685),tc_List_Olist(X31685)),hAPP(hAPP(c_List_Oappend(X31685),X31681),X31684)),hAPP(hAPP(c_List_Oappend(X31685),X31681),X31683))),c_List_Olexord(X31685,X31682))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__leftI])]) ).

fof(i_0_6796,plain,
    ! [X30604,X30605,X30606,X30607,X30608] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30608),tc_List_Olist(X30608))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30608),tc_List_Olist(X30608)),X30607),X30606)),c_List_Olistrel1(X30608,X30605)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30608),tc_List_Olist(X30608))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30608),tc_List_Olist(X30608)),hAPP(hAPP(c_List_Olist_OCons(X30608),X30604),X30607)),hAPP(hAPP(c_List_Olist_OCons(X30608),X30604),X30606))),c_List_Olistrel1(X30608,X30605))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I2])]) ).

cnf(i_0_6797,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_5460]) ).

fof(i_0_6798,plain,
    ! [X25523] : 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)))),X25523))),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J]) ).

fof(i_0_6799,plain,
    ! [X20310,X20311,X20312,X20313,X20314] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X20314)),hAPP(c_Set_Oimage(X20313,tc_Option_Ooption(X20314),X20312),c_Orderings_Otop__class_Otop(tc_fun(X20313,tc_HOL_Obool)))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X20314)),hAPP(c_Set_Oimage(X20313,tc_Option_Ooption(X20314),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X20313,tc_Option_Ooption(X20314)),X20312),X20311),hAPP(c_Option_Ooption_OSome(X20314),X20310))),c_Orderings_Otop__class_Otop(tc_fun(X20313,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__updI])]) ).

fof(i_0_6800,plain,
    ! [X30849,X30850,X30851,X30852,X30853,X30854] : hAPP(hAPP(c_List_Ozip(X30854,X30853),hAPP(hAPP(c_List_Omap(X30852,X30854),X30851),X30850)),X30849) = hAPP(hAPP(c_List_Omap(tc_prod(X30852,X30853),tc_prod(X30854,X30853)),hAPP(c_Product__Type_Oprod_Oprod__case(X30852,X30853,tc_prod(X30854,X30853)),hAPP(hAPP(c_COMBB(X30854,tc_fun(X30853,tc_prod(X30854,X30853)),X30852),c_Product__Type_OPair(X30854,X30853)),X30851))),hAPP(hAPP(c_List_Ozip(X30852,X30853),X30850),X30849)),
    inference(variable_rename,[status(thm)],[fact_zip__map1]) ).

fof(i_0_6801,plain,
    ! [X25699,X25700,X25701] : c_Wellfounded_Omlex__prod(X25701,X25700,X25699) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X25701),X25701),c_Wellfounded_Olex__prod(tc_Nat_Onat,X25701,c_Wellfounded_Oless__than,X25699)),hAPP(hAPP(c_COMBS(X25701,X25701,tc_prod(tc_Nat_Onat,X25701)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X25701,tc_prod(tc_Nat_Onat,X25701)),X25701),c_Product__Type_OPair(tc_Nat_Onat,X25701)),X25700)),c_COMBI(X25701))),
    inference(variable_rename,[status(thm)],[fact_mlex__prod__def]) ).

fof(i_0_6802,plain,
    ! [X21112,X21113,X21114] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X21114),esk92_3(X21112,X21113,X21114)))
        | hBOOL(hAPP(X21112,c_Orderings_Obot__class_Obot(tc_fun(X21114,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X21112,X21113))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21114),X21113)) )
      & ( hBOOL(hAPP(hAPP(c_member(X21114),esk91_3(X21112,X21113,X21114)),esk92_3(X21112,X21113,X21114)))
        | hBOOL(hAPP(X21112,c_Orderings_Obot__class_Obot(tc_fun(X21114,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X21112,X21113))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21114),X21113)) )
      & ( hBOOL(hAPP(X21112,esk92_3(X21112,X21113,X21114)))
        | hBOOL(hAPP(X21112,c_Orderings_Obot__class_Obot(tc_fun(X21114,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X21112,X21113))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21114),X21113)) )
      & ( ~ hBOOL(hAPP(X21112,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21114,tc_HOL_Obool)),esk92_3(X21112,X21113,X21114)),hAPP(hAPP(c_Set_Oinsert(X21114),esk91_3(X21112,X21113,X21114)),c_Orderings_Obot__class_Obot(tc_fun(X21114,tc_HOL_Obool))))))
        | hBOOL(hAPP(X21112,c_Orderings_Obot__class_Obot(tc_fun(X21114,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X21112,X21113))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21114),X21113)) ) ),
    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_6803,plain,
    ! [X27814,X27815,X27816,X27817,X27818,X27819] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27816,X27819),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27816,X27819),X27815),hAPP(c_COMBK(tc_fun(X27819,tc_HOL_Obool),X27816),X27817))),hAPP(hAPP(c_Product__Type_OSigma(X27816,X27819),X27814),hAPP(c_COMBK(tc_fun(X27819,tc_HOL_Obool),X27816),X27817))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27816,tc_HOL_Obool)),X27815),X27814))
        | ~ hBOOL(hAPP(hAPP(c_member(X27819),X27818),X27817)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27816,tc_HOL_Obool)),X27815),X27814))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27816,X27819),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27816,X27819),X27815),hAPP(c_COMBK(tc_fun(X27819,tc_HOL_Obool),X27816),X27817))),hAPP(hAPP(c_Product__Type_OSigma(X27816,X27819),X27814),hAPP(c_COMBK(tc_fun(X27819,tc_HOL_Obool),X27816),X27817))))
        | ~ hBOOL(hAPP(hAPP(c_member(X27819),X27818),X27817)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__subset__cancel2])])]) ).

cnf(i_0_6804,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_5461]) ).

fof(i_0_6805,plain,
    ! [X28898,X28899,X28900,X28901,X28902,X28903] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28903,X28903)),hAPP(hAPP(c_Product__Type_OPair(X28903,X28903),X28902),X28901)),X28900))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28903,X28903)),hAPP(hAPP(c_Product__Type_OPair(X28903,X28903),X28901),X28899)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28903,X28903),tc_HOL_Obool),X28898),X28900)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28903,X28903)),hAPP(hAPP(c_Product__Type_OPair(X28903,X28903),X28902),X28899)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28903,X28903),tc_HOL_Obool),hAPP(c_Nat_OSuc,X28898)),X28900))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__I2])]) ).

fof(i_0_6806,plain,
    ! [X28904,X28905,X28906,X28907,X28908,X28909] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28909,X28909)),hAPP(hAPP(c_Product__Type_OPair(X28909,X28909),X28908),X28907)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28909,X28909),tc_HOL_Obool),X28906),X28905)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28909,X28909)),hAPP(hAPP(c_Product__Type_OPair(X28909,X28909),X28907),X28904)),X28905))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28909,X28909)),hAPP(hAPP(c_Product__Type_OPair(X28909,X28909),X28908),X28904)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28909,X28909),tc_HOL_Obool),hAPP(c_Nat_OSuc,X28906)),X28905))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__I])]) ).

fof(i_0_6807,plain,
    ! [X17742,X17743,X17744,X17745,X17746] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17746,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17745,X17746,X17744),X17743)),X17742))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X17746,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(X17745,tc_HOL_Obool),tc_fun(X17746,tc_HOL_Obool),c_Set_Oimage(X17745,X17746,X17744)),hAPP(c_Set_OPow(X17745),X17743))),hAPP(c_Set_OPow(X17746),X17742))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Pow__mono])]) ).

fof(i_0_6808,plain,
    ! [X23597,X23598] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23597),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Nitpick_Onorm__frac(X23598,X23597) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23598),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23597))
        | ~ 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),X23598),X23597))) )
      & ( X23598 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X23598,X23597) = 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),X23597),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),X23598),X23597))) )
      & ( X23597 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X23598,X23597) = 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),X23597),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),X23598),X23597))) )
      & ( X23598 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X23597 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X23598,X23597) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X23598),X23597)),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),X23598))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23597)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23597),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),X23598),X23597))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5462])])]) ).

cnf(i_0_6809,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_5463]) ).

fof(i_0_6810,plain,
    ! [X30417,X30418,X30419] :
      ( ~ 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,X30419),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X30419)),X30418))))
      | hBOOL(hAPP(hAPP(c_member(X30419),hAPP(c_Product__Type_Ofst(X30419,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X30419,X30418),X30417))),hAPP(c_List_Oset(X30419),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X30419),X30419),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X30419)),X30418)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_select__weight__member])]) ).

fof(i_0_6811,plain,
    ! [X27001,X27002,X27003,X27004] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27004)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27004),hAPP(c_Groups_Oabs__class_Oabs(X27004),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27003,X27004),X27002),X27001))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27003,X27004),hAPP(hAPP(c_COMBB(X27004,X27004,X27003),c_Groups_Oabs__class_Oabs(X27004)),X27002)),X27001))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__abs])]) ).

fof(i_0_6812,plain,
    ! [X32305,X32306,X32307] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X32307,tc_HOL_Obool)),hAPP(c_List_Oset(X32307),X32306)),hAPP(hAPP(c_Set_Oinsert(X32307),X32305),c_Orderings_Obot__class_Obot(tc_fun(X32307,tc_HOL_Obool)))) = hAPP(c_List_Oset(X32307),hAPP(c_List_Ofilter(X32307,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32307),c_fNot),hAPP(hAPP(c_COMBC(X32307,X32307,tc_HOL_Obool),c_fequal),X32305))),X32306)),
    inference(variable_rename,[status(thm)],[fact_set__minus__filter__out]) ).

fof(i_0_6813,plain,
    ! [X32282,X32283,X32284,X32285] : hAPP(c_List_Ofilter(X32285,X32284),hAPP(c_List_Ofilter(X32285,X32283),X32282)) = hAPP(c_List_Ofilter(X32285,hAPP(hAPP(c_COMBS(X32285,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X32285),c_fconj),X32283)),X32284)),X32282),
    inference(variable_rename,[status(thm)],[fact_filter__filter]) ).

fof(i_0_6814,plain,
    ! [X27635,X27636,X27637,X27638] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27638,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27638,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X27638,X27637),X27636)),hAPP(c_Relation_ODomain(X27638,X27637),X27635))),hAPP(c_Relation_ODomain(X27638,X27637),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X27638,X27637),tc_HOL_Obool)),X27636),X27635)))),
    inference(variable_rename,[status(thm)],[fact_Domain__Diff__subset]) ).

fof(i_0_6815,plain,
    ! [X27519,X27520,X27521,X27522] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27522,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27522,tc_HOL_Obool)),hAPP(c_Relation_ORange(X27521,X27522),X27520)),hAPP(c_Relation_ORange(X27521,X27522),X27519))),hAPP(c_Relation_ORange(X27521,X27522),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X27521,X27522),tc_HOL_Obool)),X27520),X27519)))),
    inference(variable_rename,[status(thm)],[fact_Range__Diff__subset]) ).

fof(i_0_6816,plain,
    ! [X18333,X18334,X18335,X18336] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X18336),X18334),X18333))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),X18335),X18333))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),X18335),hAPP(hAPP(c_Set_Oinsert(X18336),X18334),X18333))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18336),X18334),X18335))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18336,tc_HOL_Obool)),X18335),hAPP(hAPP(c_Set_Oinsert(X18336),X18334),c_Orderings_Obot__class_Obot(tc_fun(X18336,tc_HOL_Obool))))),X18333))
        | hBOOL(hAPP(hAPP(c_member(X18336),X18334),X18333))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),X18335),hAPP(hAPP(c_Set_Oinsert(X18336),X18334),X18333))) )
      & ( hBOOL(hAPP(hAPP(c_member(X18336),X18334),X18335))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18336,tc_HOL_Obool)),X18335),X18333))
        | hBOOL(hAPP(hAPP(c_member(X18336),X18334),X18333))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),X18335),hAPP(hAPP(c_Set_Oinsert(X18336),X18334),X18333))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18336),X18334),X18333))
        | hBOOL(hAPP(hAPP(c_member(X18336),X18334),X18333))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),X18335),hAPP(hAPP(c_Set_Oinsert(X18336),X18334),X18333))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18336),X18334),X18335))
        | hBOOL(hAPP(hAPP(c_member(X18336),X18334),X18335))
        | hBOOL(hAPP(hAPP(c_member(X18336),X18334),X18333))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),X18335),hAPP(hAPP(c_Set_Oinsert(X18336),X18334),X18333))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18336,tc_HOL_Obool)),X18335),X18333))
        | hBOOL(hAPP(hAPP(c_member(X18336),X18334),X18335))
        | hBOOL(hAPP(hAPP(c_member(X18336),X18334),X18333))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),X18335),hAPP(hAPP(c_Set_Oinsert(X18336),X18334),X18333))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18336),X18334),X18335))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18336,tc_HOL_Obool)),X18335),hAPP(hAPP(c_Set_Oinsert(X18336),X18334),c_Orderings_Obot__class_Obot(tc_fun(X18336,tc_HOL_Obool))))),X18333))
        | hBOOL(hAPP(hAPP(c_member(X18336),X18334),X18333))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),X18335),hAPP(hAPP(c_Set_Oinsert(X18336),X18334),X18333))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18336,tc_HOL_Obool)),X18335),X18333))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18336,tc_HOL_Obool)),X18335),hAPP(hAPP(c_Set_Oinsert(X18336),X18334),c_Orderings_Obot__class_Obot(tc_fun(X18336,tc_HOL_Obool))))),X18333))
        | hBOOL(hAPP(hAPP(c_member(X18336),X18334),X18333))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),X18335),hAPP(hAPP(c_Set_Oinsert(X18336),X18334),X18333))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18336),X18334),X18333))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),X18335),X18333))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),X18335),hAPP(hAPP(c_Set_Oinsert(X18336),X18334),X18333))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18336),X18334),X18335))
        | hBOOL(hAPP(hAPP(c_member(X18336),X18334),X18335))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),X18335),X18333))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),X18335),hAPP(hAPP(c_Set_Oinsert(X18336),X18334),X18333))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18336,tc_HOL_Obool)),X18335),X18333))
        | hBOOL(hAPP(hAPP(c_member(X18336),X18334),X18335))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),X18335),X18333))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),X18335),hAPP(hAPP(c_Set_Oinsert(X18336),X18334),X18333))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18336),X18334),X18335))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18336,tc_HOL_Obool)),X18335),hAPP(hAPP(c_Set_Oinsert(X18336),X18334),c_Orderings_Obot__class_Obot(tc_fun(X18336,tc_HOL_Obool))))),X18333))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),X18335),X18333))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),X18335),hAPP(hAPP(c_Set_Oinsert(X18336),X18334),X18333))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18336,tc_HOL_Obool)),X18335),X18333))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18336,tc_HOL_Obool)),X18335),hAPP(hAPP(c_Set_Oinsert(X18336),X18334),c_Orderings_Obot__class_Obot(tc_fun(X18336,tc_HOL_Obool))))),X18333))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),X18335),X18333))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18336,tc_HOL_Obool)),X18335),hAPP(hAPP(c_Set_Oinsert(X18336),X18334),X18333))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5464])])]) ).

fof(i_0_6817,plain,
    ! [X32142,X32143,X32144] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32144,X32144)),hAPP(hAPP(c_Product__Type_OPair(X32144,X32144),esk437_3(X32142,X32143,X32144)),esk437_3(X32142,X32143,X32144))),X32143))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32144),tc_List_Olist(X32144))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32144),tc_List_Olist(X32144)),X32142),X32142)),c_List_Olexord(X32144,X32143))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5465])])]) ).

fof(i_0_6818,plain,
    ! [X18856] : c_Finite__Set_Ofun__left__comm__idem(X18856,tc_fun(X18856,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X18856,tc_HOL_Obool),tc_fun(tc_fun(X18856,tc_HOL_Obool),tc_fun(X18856,tc_HOL_Obool)),X18856),hAPP(c_COMBC(tc_fun(X18856,tc_HOL_Obool),tc_fun(X18856,tc_HOL_Obool),tc_fun(X18856,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X18856,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X18856,tc_fun(X18856,tc_HOL_Obool),tc_fun(X18856,tc_HOL_Obool)),c_Set_Oinsert(X18856)),c_Orderings_Obot__class_Obot(tc_fun(X18856,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_fun__left__comm__idem__remove]) ).

cnf(i_0_6819,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_5466]) ).

fof(i_0_6820,plain,
    ! [X21166,X21167,X21168] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21168),X21167))
      | ~ hBOOL(hAPP(hAPP(c_member(X21168),X21166),X21167))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21168),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21168,tc_HOL_Obool)),X21167),hAPP(hAPP(c_Set_Oinsert(X21168),X21166),c_Orderings_Obot__class_Obot(tc_fun(X21168,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X21168),X21167))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff1__less])]) ).

fof(i_0_6821,plain,
    ! [X23806,X23807,X23808,X23809,X23810,X23811] : hAPP(hAPP(c_COMBS(tc_prod(X23811,X23810),X23810,X23809),hAPP(hAPP(c_COMBB(X23808,tc_fun(X23810,X23809),tc_prod(X23811,X23810)),X23807),hAPP(hAPP(c_COMBB(X23811,X23808,tc_prod(X23811,X23810)),X23806),c_Product__Type_Ofst(X23811,X23810)))),c_Product__Type_Osnd(X23811,X23810)) = hAPP(c_Product__Type_Oprod_Oprod__case(X23811,X23810,X23809),hAPP(hAPP(c_COMBB(X23808,tc_fun(X23810,X23809),X23811),X23807),X23806)),
    inference(variable_rename,[status(thm)],[fact_split__comp__eq]) ).

fof(i_0_6822,plain,
    ! [X32711,X32712,X32713,X32714,X32715] :
      ( ~ class_Orderings_Olinorder(X32715)
      | ~ hBOOL(hAPP(hAPP(c_member(X32714),X32713),hAPP(c_List_Oset(X32714),X32712)))
      | ~ c_List_Olinorder__class_Osorted(X32715,hAPP(hAPP(c_List_Omap(X32714,X32715),X32711),X32712))
      | hAPP(c_List_Ohd(X32714),hAPP(c_List_Ofilter(X32714,hAPP(hAPP(c_COMBB(X32715,tc_HOL_Obool,X32714),hAPP(c_fequal,hAPP(X32711,X32713))),X32711)),X32712)) != X32713
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32714,X32715,X32711),X32713),c_List_Oremove1(X32714,X32713,X32712)) = X32712 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__key__remove1])]) ).

fof(i_0_6823,plain,
    ! [X25560,X25561] :
      ( ( 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)),X25561),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)),X25560),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)),X25561),X25560)),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)),X25561),X25560)),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)),X25561),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)),X25560),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_6824,plain,
    ! [X34136,X34137,X34138,X34139] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X34138,tc_HOL_Obool)),esk526_4(X34136,X34137,X34138,X34139)),X34137))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136),c_Complete__Lattice_OSup__class_OSup(tc_fun(X34138,tc_HOL_Obool),X34137)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X34138,tc_HOL_Obool),X34139),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136)),X34137)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X34138,tc_HOL_Obool)),esk525_4(X34136,X34137,X34138,X34139)),X34137))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X34138,tc_HOL_Obool)),X34137))
        | ~ class_Groups_Ocomm__monoid__add(X34139) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X34138,tc_HOL_Obool)),esk527_4(X34136,X34137,X34138,X34139)),X34137))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136),c_Complete__Lattice_OSup__class_OSup(tc_fun(X34138,tc_HOL_Obool),X34137)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X34138,tc_HOL_Obool),X34139),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136)),X34137)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X34138,tc_HOL_Obool)),esk525_4(X34136,X34137,X34138,X34139)),X34137))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X34138,tc_HOL_Obool)),X34137))
        | ~ class_Groups_Ocomm__monoid__add(X34139) )
      & ( esk526_4(X34136,X34137,X34138,X34139) != esk527_4(X34136,X34137,X34138,X34139)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136),c_Complete__Lattice_OSup__class_OSup(tc_fun(X34138,tc_HOL_Obool),X34137)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X34138,tc_HOL_Obool),X34139),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136)),X34137)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X34138,tc_HOL_Obool)),esk525_4(X34136,X34137,X34138,X34139)),X34137))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X34138,tc_HOL_Obool)),X34137))
        | ~ class_Groups_Ocomm__monoid__add(X34139) )
      & ( hBOOL(hAPP(hAPP(c_member(X34138),esk528_4(X34136,X34137,X34138,X34139)),esk526_4(X34136,X34137,X34138,X34139)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136),c_Complete__Lattice_OSup__class_OSup(tc_fun(X34138,tc_HOL_Obool),X34137)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X34138,tc_HOL_Obool),X34139),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136)),X34137)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X34138,tc_HOL_Obool)),esk525_4(X34136,X34137,X34138,X34139)),X34137))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X34138,tc_HOL_Obool)),X34137))
        | ~ class_Groups_Ocomm__monoid__add(X34139) )
      & ( hBOOL(hAPP(hAPP(c_member(X34138),esk528_4(X34136,X34137,X34138,X34139)),esk527_4(X34136,X34137,X34138,X34139)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136),c_Complete__Lattice_OSup__class_OSup(tc_fun(X34138,tc_HOL_Obool),X34137)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X34138,tc_HOL_Obool),X34139),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136)),X34137)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X34138,tc_HOL_Obool)),esk525_4(X34136,X34137,X34138,X34139)),X34137))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X34138,tc_HOL_Obool)),X34137))
        | ~ class_Groups_Ocomm__monoid__add(X34139) )
      & ( hAPP(X34136,esk528_4(X34136,X34137,X34138,X34139)) != c_Groups_Ozero__class_Ozero(X34139)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136),c_Complete__Lattice_OSup__class_OSup(tc_fun(X34138,tc_HOL_Obool),X34137)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X34138,tc_HOL_Obool),X34139),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136)),X34137)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X34138,tc_HOL_Obool)),esk525_4(X34136,X34137,X34138,X34139)),X34137))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X34138,tc_HOL_Obool)),X34137))
        | ~ class_Groups_Ocomm__monoid__add(X34139) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X34138,tc_HOL_Obool)),esk526_4(X34136,X34137,X34138,X34139)),X34137))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136),c_Complete__Lattice_OSup__class_OSup(tc_fun(X34138,tc_HOL_Obool),X34137)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X34138,tc_HOL_Obool),X34139),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136)),X34137)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34138),esk525_4(X34136,X34137,X34138,X34139)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X34138,tc_HOL_Obool)),X34137))
        | ~ class_Groups_Ocomm__monoid__add(X34139) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X34138,tc_HOL_Obool)),esk527_4(X34136,X34137,X34138,X34139)),X34137))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136),c_Complete__Lattice_OSup__class_OSup(tc_fun(X34138,tc_HOL_Obool),X34137)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X34138,tc_HOL_Obool),X34139),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136)),X34137)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34138),esk525_4(X34136,X34137,X34138,X34139)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X34138,tc_HOL_Obool)),X34137))
        | ~ class_Groups_Ocomm__monoid__add(X34139) )
      & ( esk526_4(X34136,X34137,X34138,X34139) != esk527_4(X34136,X34137,X34138,X34139)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136),c_Complete__Lattice_OSup__class_OSup(tc_fun(X34138,tc_HOL_Obool),X34137)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X34138,tc_HOL_Obool),X34139),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136)),X34137)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34138),esk525_4(X34136,X34137,X34138,X34139)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X34138,tc_HOL_Obool)),X34137))
        | ~ class_Groups_Ocomm__monoid__add(X34139) )
      & ( hBOOL(hAPP(hAPP(c_member(X34138),esk528_4(X34136,X34137,X34138,X34139)),esk526_4(X34136,X34137,X34138,X34139)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136),c_Complete__Lattice_OSup__class_OSup(tc_fun(X34138,tc_HOL_Obool),X34137)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X34138,tc_HOL_Obool),X34139),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136)),X34137)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34138),esk525_4(X34136,X34137,X34138,X34139)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X34138,tc_HOL_Obool)),X34137))
        | ~ class_Groups_Ocomm__monoid__add(X34139) )
      & ( hBOOL(hAPP(hAPP(c_member(X34138),esk528_4(X34136,X34137,X34138,X34139)),esk527_4(X34136,X34137,X34138,X34139)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136),c_Complete__Lattice_OSup__class_OSup(tc_fun(X34138,tc_HOL_Obool),X34137)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X34138,tc_HOL_Obool),X34139),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136)),X34137)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34138),esk525_4(X34136,X34137,X34138,X34139)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X34138,tc_HOL_Obool)),X34137))
        | ~ class_Groups_Ocomm__monoid__add(X34139) )
      & ( hAPP(X34136,esk528_4(X34136,X34137,X34138,X34139)) != c_Groups_Ozero__class_Ozero(X34139)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136),c_Complete__Lattice_OSup__class_OSup(tc_fun(X34138,tc_HOL_Obool),X34137)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X34138,tc_HOL_Obool),X34139),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X34138,X34139),X34136)),X34137)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34138),esk525_4(X34136,X34137,X34138,X34139)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X34138,tc_HOL_Obool)),X34137))
        | ~ class_Groups_Ocomm__monoid__add(X34139) ) ),
    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_6825,plain,
    ! [X18486,X18487,X18488,X18489] : c_Nitpick_Ofold__graph_H(X18489,X18488,X18487,X18486,c_Orderings_Obot__class_Obot(tc_fun(X18489,tc_HOL_Obool)),X18486),
    inference(variable_rename,[status(thm)],[fact_fold__graph_H_Ointros_I1_J]) ).

fof(i_0_6826,plain,
    ! [X18482,X18483,X18484,X18485] : c_Nitpick_Ofold__graph_H(X18485,X18484,X18483,X18482,c_Orderings_Obot__class_Obot(tc_fun(X18485,tc_HOL_Obool)),X18482),
    inference(variable_rename,[status(thm)],[fact_fold__graph_H_Oequations_I1_J]) ).

fof(i_0_6827,plain,
    ! [X18672,X18673,X18674,X18675,X18676] :
      ( ( c_Fun_Oinj__on(X18676,X18675,X18674,X18672)
        | ~ c_Fun_Oinj__on(X18676,X18675,X18674,hAPP(hAPP(c_Set_Oinsert(X18676),X18673),X18672)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18675),hAPP(X18674,X18673)),hAPP(c_Set_Oimage(X18676,X18675,X18674),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18676,tc_HOL_Obool)),X18672),hAPP(hAPP(c_Set_Oinsert(X18676),X18673),c_Orderings_Obot__class_Obot(tc_fun(X18676,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(X18676,X18675,X18674,hAPP(hAPP(c_Set_Oinsert(X18676),X18673),X18672)) )
      & ( ~ c_Fun_Oinj__on(X18676,X18675,X18674,X18672)
        | hBOOL(hAPP(hAPP(c_member(X18675),hAPP(X18674,X18673)),hAPP(c_Set_Oimage(X18676,X18675,X18674),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18676,tc_HOL_Obool)),X18672),hAPP(hAPP(c_Set_Oinsert(X18676),X18673),c_Orderings_Obot__class_Obot(tc_fun(X18676,tc_HOL_Obool)))))))
        | c_Fun_Oinj__on(X18676,X18675,X18674,hAPP(hAPP(c_Set_Oinsert(X18676),X18673),X18672)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5467])])]) ).

fof(i_0_6828,plain,
    ! [X28076,X28077] : c_Product__Type_Omap__pair(X28077,X28077,X28076,X28076,c_Fun_Oid(X28077),c_Fun_Oid(X28076)) = c_Fun_Oid(tc_prod(X28077,X28076)),
    inference(variable_rename,[status(thm)],[fact_map__pair_Oid]) ).

cnf(i_0_6829,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_5468]) ).

fof(i_0_6830,plain,
    ! [X28066,X28067] : c_Product__Type_Omap__pair(X28067,X28067,X28066,X28066,c_COMBI(X28067),c_COMBI(X28066)) = c_Fun_Oid(tc_prod(X28067,X28066)),
    inference(variable_rename,[status(thm)],[fact_map__pair_Oidentity]) ).

cnf(i_0_6831,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_5469]) ).

fof(i_0_6832,plain,
    ! [X29196,X29197,X29198,X29199,X29200] :
      ( ~ c_Finite__Set_Ofun__left__comm(X29200,X29199,X29198)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29200),X29197))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X29200,X29199,X29198,X29196,X29197),hAPP(hAPP(c_Finite__Set_Ofold(X29200,X29199,X29198),X29196),X29197))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__fold])]) ).

cnf(i_0_6833,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_6834,plain,
    ! [X21300,X21301,X21302] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21302),X21301))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21302),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21302,tc_HOL_Obool)),X21301),hAPP(hAPP(c_Set_Oinsert(X21302),X21300),c_Orderings_Obot__class_Obot(tc_fun(X21302,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X21302),X21301))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff1__le])]) ).

fof(i_0_6835,plain,
    ! [X27292,X27293,X27294,X27295,X27296,X27297,X27298] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27298,X27297),tc_HOL_Obool)),X27296),X27295))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27297,X27294),tc_HOL_Obool)),X27293),X27292))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27298,X27294),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27298,X27297,X27294),X27296),X27293)),hAPP(hAPP(c_Relation_Orel__comp(X27298,X27297,X27294),X27295),X27292))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__comp__mono])]) ).

fof(i_0_6836,plain,
    ! [X19885,X19886,X19887,X19888,X19889] :
      ( ~ c_Equiv__Relations_Oequiv(X19889,X19888,X19887)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X19889,X19889)),hAPP(hAPP(c_Product__Type_OPair(X19889,X19889),X19886),X19885)),X19887))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19889,tc_HOL_Obool)),hAPP(c_Relation_OImage(X19889,X19889,X19887),hAPP(hAPP(c_Set_Oinsert(X19889),X19886),c_Orderings_Obot__class_Obot(tc_fun(X19889,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X19889,X19889,X19887),hAPP(hAPP(c_Set_Oinsert(X19889),X19885),c_Orderings_Obot__class_Obot(tc_fun(X19889,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__subset])]) ).

fof(i_0_6837,plain,
    ! [X18782,X18783,X18784,X18785,X18786,X18787] :
      ( ~ c_Fun_Oinj__on(X18787,X18786,X18785,X18784)
      | ~ hBOOL(hAPP(hAPP(c_member(X18786),X18783),hAPP(c_Set_Oimage(X18787,X18786,X18785),X18784)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18787,tc_HOL_Obool)),X18784),X18782))
      | hBOOL(hAPP(hAPP(c_member(X18787),hAPP(c_Fun_Othe__inv__into(X18787,X18786,X18784,X18785),X18783)),X18782)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__into])]) ).

fof(i_0_6838,plain,
    ! [X20565,X20566,X20567,X20568,X20569] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20569),hAPP(c_Set_Oimage(X20568,X20569,X20567),c_Orderings_Otop__class_Otop(tc_fun(X20568,tc_HOL_Obool)))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20566),hAPP(c_Set_Oimage(X20568,X20566,hAPP(hAPP(c_COMBB(X20569,X20566,X20568),X20565),X20567)),c_Orderings_Otop__class_Otop(tc_fun(X20568,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__imageI])]) ).

fof(i_0_6839,plain,
    ! [X29785,X29786,X29787] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29787,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29787,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X29787,tc_HOL_Obool),X29786)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X29787,tc_HOL_Obool),X29785))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X29787,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X29787,tc_HOL_Obool),tc_HOL_Obool)),X29786),X29785)))),
    inference(variable_rename,[status(thm)],[fact_Inter__Un__subset]) ).

fof(i_0_6840,plain,
    ! [X30929,X30930,X30931] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30931,X30931),tc_HOL_Obool)),X30930),hAPP(hAPP(c_Product__Type_OSigma(X30931,X30931),X30929),hAPP(c_COMBK(tc_fun(X30931,tc_HOL_Obool),X30931),X30929))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X30931),tc_List_Olist(X30931)),tc_HOL_Obool)),c_List_Olistrel(X30931,X30930)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(X30931),tc_List_Olist(X30931)),c_List_Olists(X30931,X30929)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X30931),tc_HOL_Obool),tc_List_Olist(X30931)),c_List_Olists(X30931,X30929))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__subset])]) ).

fof(i_0_6841,plain,
    ! [X21314,X21315,X21316,X21317,X21318,X21319,X21320] :
      ( ~ class_Groups_Oab__semigroup__mult(X21320)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21319),X21318))
      | ~ c_Fun_Oinj__on(X21319,X21317,X21316,X21318)
      | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21320,X21317,c_Groups_Otimes__class_Otimes(X21320)),X21315),X21314),hAPP(c_Set_Oimage(X21319,X21317,X21316),X21318)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21320,X21319,c_Groups_Otimes__class_Otimes(X21320)),hAPP(c_Fun_Ocomp(X21317,X21320,X21319,X21315),X21316)),X21314),X21318) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__reindex])]) ).

fof(i_0_6842,plain,
    ! [X23551,X23552,X23553,X23554] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23554))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23553))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23553),X23552))
      | 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),X23552),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23551,X23554))),X23553)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23552),X23554))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux4])]) ).

fof(i_0_6843,plain,
    ! [X31267,X31268,X31269,X31270,X31271,X31272] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31272)),X31271) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31270)),X31269)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31272,tc_HOL_Obool)),hAPP(c_List_Oset(X31272),X31271)),X31268))
      | c_Map_Orestrict__map(X31272,X31270,c_Map_Omap__upds(X31272,X31270,X31267,X31271,X31269),X31268) = c_Map_Omap__upds(X31272,X31270,c_Map_Orestrict__map(X31272,X31270,X31267,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31272,tc_HOL_Obool)),X31268),hAPP(c_List_Oset(X31272),X31271))),X31271,X31269) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_restrict__map__upds])]) ).

fof(i_0_6844,plain,
    ! [X29855,X29856,X29857,X29858] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29858),esk377_4(X29855,X29856,X29857,X29858)),X29857))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29858),hAPP(hAPP(c_Finite__Set_Ofold(X29858,X29858,c_Orderings_Oord__class_Omax(X29858)),X29855),X29857)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X29858),X29856),X29855)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29858),X29857))
        | ~ class_Orderings_Olinorder(X29858) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29858),esk377_4(X29855,X29856,X29857,X29858)),X29856))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29858),hAPP(hAPP(c_Finite__Set_Ofold(X29858,X29858,c_Orderings_Oord__class_Omax(X29858)),X29855),X29857)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X29858),X29856),X29855)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29858),X29857))
        | ~ class_Orderings_Olinorder(X29858) ) ),
    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_6845,plain,
    ! [X29874,X29875,X29876,X29877] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29877),esk381_4(X29874,X29875,X29876,X29877)),X29876))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29877),hAPP(hAPP(c_Finite__Set_Ofold(X29877,X29877,c_Lattices_Osemilattice__sup__class_Osup(X29877)),X29874),X29876)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X29877),X29875),X29874)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29877),X29876))
        | ~ class_Lattices_Osemilattice__sup(X29877) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29877),esk381_4(X29874,X29875,X29876,X29877)),X29875))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29877),hAPP(hAPP(c_Finite__Set_Ofold(X29877,X29877,c_Lattices_Osemilattice__sup__class_Osup(X29877)),X29874),X29876)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X29877),X29875),X29874)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29877),X29876))
        | ~ class_Lattices_Osemilattice__sup(X29877) ) ),
    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_6846,plain,
    ! [X33416,X33417,X33418,X33419] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33419),esk479_4(X33416,X33417,X33418,X33419)),hAPP(c_List_Oset(X33419),hAPP(hAPP(c_List_Omap(tc_prod(X33419,X33418),X33419),c_Product__Type_Ofst(X33419,X33418)),X33417))))
        | hAPP(c_Map_Omap__of(X33419,X33418),X33417) = hAPP(c_Map_Omap__of(X33419,X33418),X33416)
        | hAPP(c_List_Oset(X33419),hAPP(hAPP(c_List_Omap(tc_prod(X33419,X33418),X33419),c_Product__Type_Ofst(X33419,X33418)),X33417)) != hAPP(c_List_Oset(X33419),hAPP(hAPP(c_List_Omap(tc_prod(X33419,X33418),X33419),c_Product__Type_Ofst(X33419,X33418)),X33416)) )
      & ( hAPP(hAPP(c_Map_Omap__of(X33419,X33418),X33417),esk479_4(X33416,X33417,X33418,X33419)) != hAPP(hAPP(c_Map_Omap__of(X33419,X33418),X33416),esk479_4(X33416,X33417,X33418,X33419))
        | hAPP(c_Map_Omap__of(X33419,X33418),X33417) = hAPP(c_Map_Omap__of(X33419,X33418),X33416)
        | hAPP(c_List_Oset(X33419),hAPP(hAPP(c_List_Omap(tc_prod(X33419,X33418),X33419),c_Product__Type_Ofst(X33419,X33418)),X33417)) != hAPP(c_List_Oset(X33419),hAPP(hAPP(c_List_Omap(tc_prod(X33419,X33418),X33419),c_Product__Type_Ofst(X33419,X33418)),X33416)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__eqI])])])]) ).

cnf(i_0_6847,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_5470]) ).

fof(i_0_6848,plain,
    ! [X17747,X17748,X17749,X17750] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17750),X17748),X17749))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17750,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17750,tc_HOL_Obool)),X17749),hAPP(hAPP(c_Set_Oinsert(X17750),X17748),c_Orderings_Obot__class_Obot(tc_fun(X17750,tc_HOL_Obool))))),X17747))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17750,tc_HOL_Obool)),X17749),hAPP(hAPP(c_Set_Oinsert(X17750),X17748),X17747))) )
      & ( hBOOL(hAPP(hAPP(c_member(X17750),X17748),X17749))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17750,tc_HOL_Obool)),X17749),X17747))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17750,tc_HOL_Obool)),X17749),hAPP(hAPP(c_Set_Oinsert(X17750),X17748),X17747))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17750),X17748),X17749))
        | hBOOL(hAPP(hAPP(c_member(X17750),X17748),X17749))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17750,tc_HOL_Obool)),X17749),hAPP(hAPP(c_Set_Oinsert(X17750),X17748),X17747))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17750,tc_HOL_Obool)),X17749),X17747))
        | hBOOL(hAPP(hAPP(c_member(X17750),X17748),X17749))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17750,tc_HOL_Obool)),X17749),hAPP(hAPP(c_Set_Oinsert(X17750),X17748),X17747))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17750),X17748),X17749))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17750,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17750,tc_HOL_Obool)),X17749),hAPP(hAPP(c_Set_Oinsert(X17750),X17748),c_Orderings_Obot__class_Obot(tc_fun(X17750,tc_HOL_Obool))))),X17747))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17750,tc_HOL_Obool)),X17749),hAPP(hAPP(c_Set_Oinsert(X17750),X17748),X17747))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17750,tc_HOL_Obool)),X17749),X17747))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17750,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17750,tc_HOL_Obool)),X17749),hAPP(hAPP(c_Set_Oinsert(X17750),X17748),c_Orderings_Obot__class_Obot(tc_fun(X17750,tc_HOL_Obool))))),X17747))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17750,tc_HOL_Obool)),X17749),hAPP(hAPP(c_Set_Oinsert(X17750),X17748),X17747))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5471])])]) ).

fof(i_0_6849,plain,
    ! [X30636,X30637,X30638,X30639,X30640] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30640,X30640)),hAPP(hAPP(c_Product__Type_OPair(X30640,X30640),X30639),X30638)),X30637))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30640),tc_List_Olist(X30640))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30640),tc_List_Olist(X30640)),hAPP(hAPP(c_List_Olist_OCons(X30640),X30639),X30636)),hAPP(hAPP(c_List_Olist_OCons(X30640),X30638),X30636))),c_List_Olistrel1(X30640,X30637))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I1])]) ).

cnf(i_0_6850,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_5472]) ).

cnf(i_0_6851,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_5473]) ).

fof(i_0_6852,plain,
    ! [X32857,X32858,X32859] :
      ( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X32859),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X32859))),X32858)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32857),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32859))),X32858)))
      | hAPP(hAPP(c_List_Omap(tc_List_Olist(X32859),X32859),hAPP(hAPP(c_COMBC(tc_List_Olist(X32859),tc_Nat_Onat,X32859),c_List_Onth(X32859)),X32857)),hAPP(c_List_Ofilter(tc_List_Olist(X32859),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X32859)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32857)),c_Nat_Osize__class_Osize(tc_List_Olist(X32859)))),c_List_Otranspose(X32859,X32858))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(X32859)),X32858),X32857) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose__column])]) ).

fof(i_0_6853,plain,
    ! [X28317,X28318,X28319] : c_Hilbert__Choice_OEps(tc_prod(X28319,X28318),X28317) = c_Hilbert__Choice_OEps(tc_prod(X28319,X28318),hAPP(c_Product__Type_Oprod_Oprod__case(X28319,X28318,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X28318,tc_prod(X28319,X28318)),tc_fun(X28318,tc_HOL_Obool),X28319),hAPP(c_COMBB(tc_prod(X28319,X28318),tc_HOL_Obool,X28318),X28317)),c_Product__Type_OPair(X28319,X28318)))),
    inference(variable_rename,[status(thm)],[fact_split__paired__Eps]) ).

fof(i_0_6854,plain,
    ! [X23843,X23844,X23845] : c_HOL_OThe(tc_prod(X23845,X23844),X23843) = c_HOL_OThe(tc_prod(X23845,X23844),hAPP(c_Product__Type_Oprod_Oprod__case(X23845,X23844,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X23844,tc_prod(X23845,X23844)),tc_fun(X23844,tc_HOL_Obool),X23845),hAPP(c_COMBB(tc_prod(X23845,X23844),tc_HOL_Obool,X23844),X23843)),c_Product__Type_OPair(X23845,X23844)))),
    inference(variable_rename,[status(thm)],[fact_split__paired__The]) ).

fof(i_0_6855,plain,
    ! [X28811,X28812,X28813,X28814,X28815,X28816,X28817,X28818] :
      ( ( ~ c_Relation_Ototal__on(X28813,X28812,X28811)
        | ~ hBOOL(hAPP(hAPP(c_member(X28813),X28814),X28812))
        | ~ hBOOL(hAPP(hAPP(c_member(X28813),X28815),X28812))
        | X28814 = X28815
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28813,X28813)),hAPP(hAPP(c_Product__Type_OPair(X28813,X28813),X28814),X28815)),X28811))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28813,X28813)),hAPP(hAPP(c_Product__Type_OPair(X28813,X28813),X28815),X28814)),X28811)) )
      & ( hBOOL(hAPP(hAPP(c_member(X28818),esk328_3(X28816,X28817,X28818)),X28817))
        | c_Relation_Ototal__on(X28818,X28817,X28816) )
      & ( hBOOL(hAPP(hAPP(c_member(X28818),esk329_3(X28816,X28817,X28818)),X28817))
        | c_Relation_Ototal__on(X28818,X28817,X28816) )
      & ( esk328_3(X28816,X28817,X28818) != esk329_3(X28816,X28817,X28818)
        | c_Relation_Ototal__on(X28818,X28817,X28816) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28818,X28818)),hAPP(hAPP(c_Product__Type_OPair(X28818,X28818),esk328_3(X28816,X28817,X28818)),esk329_3(X28816,X28817,X28818))),X28816))
        | c_Relation_Ototal__on(X28818,X28817,X28816) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28818,X28818)),hAPP(hAPP(c_Product__Type_OPair(X28818,X28818),esk329_3(X28816,X28817,X28818)),esk328_3(X28816,X28817,X28818))),X28816))
        | c_Relation_Ototal__on(X28818,X28817,X28816) ) ),
    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_6856,plain,
    ! [X23681,X23682,X23683,X23684] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23684))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23683),X23682))
      | 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),X23682),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23681,X23684))),X23683)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23682),X23684))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__lemma])]) ).

fof(i_0_6857,plain,
    ! [X30055,X30056,X30057] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30056),X30055))
        | c_Smallcheck_Osmall_H(X30057,X30056,X30055) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X30057),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X30056),X30055)))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30056),X30055))
        | c_Smallcheck_Osmall_H(X30057,X30056,X30055) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X30057,X30056,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X30055),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X30057,X30055))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X30057),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X30056),X30055)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5474])])]) ).

fof(i_0_6858,plain,
    ! [X28947,X28948,X28949,X28950,X28951] :
      ( ~ c_Relation_Osingle__valued(X28951,X28951,X28950)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28951,X28951)),hAPP(hAPP(c_Product__Type_OPair(X28951,X28951),X28949),X28948)),c_Transitive__Closure_Ortrancl(X28951,X28950)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28951,X28951)),hAPP(hAPP(c_Product__Type_OPair(X28951,X28951),X28949),X28947)),c_Transitive__Closure_Ortrancl(X28951,X28950)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28951,X28951)),hAPP(hAPP(c_Product__Type_OPair(X28951,X28951),X28948),X28947)),c_Transitive__Closure_Ortrancl(X28951,X28950)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28951,X28951)),hAPP(hAPP(c_Product__Type_OPair(X28951,X28951),X28947),X28948)),c_Transitive__Closure_Ortrancl(X28951,X28950))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__confluent])]) ).

fof(i_0_6859,plain,
    ! [X27361,X27362,X27363] :
      ( ~ c_Wellfounded_Owf(X27363,X27362)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27363,X27363),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27363,X27363,X27363),X27362),X27361)),X27362))
      | c_FunDef_Oreduction__pair(X27363,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X27363,X27363),tc_HOL_Obool),tc_fun(tc_prod(X27363,X27363),tc_HOL_Obool)),X27362),X27361)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduction__pairI])]) ).

fof(i_0_6860,plain,
    ! [X23543,X23544,X23545,X23546] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23546))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23545),X23544))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23544),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),X23545),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23543,X23546))),X23544)),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_6861,plain,
    ! [X31278,X31279] : c_Random_Oselect(X31279,X31278) = 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(X31279,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(X31279)),X31278)))),hAPP(hAPP(c_COMBB(X31279,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X31279,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X31279,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X31279,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X31279),X31278)),c_Code__Numeral_Onat__of))),
    inference(variable_rename,[status(thm)],[fact_select__def]) ).

fof(i_0_6862,plain,
    ! [X23249,X23250] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23250),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Nitpick_Onorm__frac(X23249,X23250) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23249),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23250)) )
      & ( X23249 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X23249,X23250) = 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),X23250),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( X23250 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X23249,X23250) = 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),X23250),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( X23249 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X23250 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X23249,X23250) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X23249),X23250)),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),X23249))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23250)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23250),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5475])])]) ).

fof(i_0_6863,plain,
    ! [X25579,X25580,X25581] :
      ( ~ class_Rings_Oring__1(X25581)
      | hAPP(c_Int_Oring__1__class_Oof__int(X25581),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),X25580),X25579)),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(X25581),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25581),X25580)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25581),X25579)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int])]) ).

fof(i_0_6864,plain,
    ! [X30170,X30171,X30172,X30173,X30174] : c_Map_Odom(X30174,X30173,hAPP(hAPP(c_COMBS(X30174,tc_Option_Ooption(X30172),tc_Option_Ooption(X30173)),hAPP(hAPP(c_COMBB(tc_fun(X30172,X30173),tc_fun(tc_Option_Ooption(X30172),tc_Option_Ooption(X30173)),X30174),c_Option_Omap(X30172,X30173)),X30171)),X30170)) = c_Map_Odom(X30174,X30172,X30170),
    inference(variable_rename,[status(thm)],[fact_dom__option__map]) ).

cnf(i_0_6865,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk464_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_5476]) ).

cnf(i_0_6866,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_5477]) ).

cnf(i_0_6867,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_5478]) ).

fof(i_0_6868,plain,
    ! [X17751,X17752,X17753,X17754] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17754,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17754,tc_HOL_Obool)),X17753),hAPP(hAPP(c_Set_Oinsert(X17754),X17752),c_Orderings_Obot__class_Obot(tc_fun(X17754,tc_HOL_Obool))))),X17751))
      | ~ hBOOL(hAPP(hAPP(c_member(X17754),X17752),X17753))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17754,tc_HOL_Obool)),X17753),hAPP(hAPP(c_Set_Oinsert(X17754),X17752),X17751))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__single__insert])]) ).

fof(i_0_6869,plain,
    ! [X25601,X25602] : 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),X25602),X25601)),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),X25602),X25601),
    inference(variable_rename,[status(thm)],[fact_nat]) ).

cnf(i_0_6870,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_5479]) ).

cnf(i_0_6871,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_5480]) ).

cnf(i_0_6872,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_5481]) ).

fof(i_0_6873,plain,
    ! [X18667,X18668,X18669,X18670,X18671] :
      ( ( c_Fun_Oinj__on(X18671,X18670,X18669,X18668)
        | ~ c_Fun_Oinj__on(X18671,X18670,X18669,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18671,tc_HOL_Obool)),X18668),X18667)) )
      & ( c_Fun_Oinj__on(X18671,X18670,X18669,X18667)
        | ~ c_Fun_Oinj__on(X18671,X18670,X18669,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18671,tc_HOL_Obool)),X18668),X18667)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18670,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18671,X18670,X18669),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18671,tc_HOL_Obool)),X18668),X18667))),hAPP(c_Set_Oimage(X18671,X18670,X18669),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18671,tc_HOL_Obool)),X18667),X18668))) = c_Orderings_Obot__class_Obot(tc_fun(X18670,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(X18671,X18670,X18669,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18671,tc_HOL_Obool)),X18668),X18667)) )
      & ( ~ c_Fun_Oinj__on(X18671,X18670,X18669,X18668)
        | ~ c_Fun_Oinj__on(X18671,X18670,X18669,X18667)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18670,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18671,X18670,X18669),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18671,tc_HOL_Obool)),X18668),X18667))),hAPP(c_Set_Oimage(X18671,X18670,X18669),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18671,tc_HOL_Obool)),X18667),X18668))) != c_Orderings_Obot__class_Obot(tc_fun(X18670,tc_HOL_Obool))
        | c_Fun_Oinj__on(X18671,X18670,X18669,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18671,tc_HOL_Obool)),X18668),X18667)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Un])])]) ).

fof(i_0_6874,plain,
    ! [X22836,X22837,X22838] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22838,tc_HOL_Obool)),X22837),X22836))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X22838,tc_HOL_Obool),tc_fun(X22838,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X22838,tc_HOL_Obool),tc_fun(X22838,tc_HOL_Obool)),X22837),X22836)),c_Wellfounded_Ofinite__psubset(X22838))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X22838),X22836))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X22838,tc_HOL_Obool),tc_fun(X22838,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X22838,tc_HOL_Obool),tc_fun(X22838,tc_HOL_Obool)),X22837),X22836)),c_Wellfounded_Ofinite__psubset(X22838))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22838,tc_HOL_Obool)),X22837),X22836))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22838),X22836))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X22838,tc_HOL_Obool),tc_fun(X22838,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X22838,tc_HOL_Obool),tc_fun(X22838,tc_HOL_Obool)),X22837),X22836)),c_Wellfounded_Ofinite__psubset(X22838))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__finite__psubset])])]) ).

fof(i_0_6875,plain,
    ! [X27648,X27649,X27650,X27651] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X27651),X27650),hAPP(c_Relation_ODomain(X27651,X27649),X27648)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X27651,X27649)),hAPP(hAPP(c_Product__Type_OPair(X27651,X27649),X27650),esk269_4(X27648,X27649,X27650,X27651))),X27648)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5482])])]) ).

fof(i_0_6876,plain,
    ! [X27616,X27617,X27618,X27619,X27621,X27622,X27623,X27624,X27625] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X27619),X27618),hAPP(c_Relation_ODomain(X27619,X27617),X27616)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X27619,X27617)),hAPP(hAPP(c_Product__Type_OPair(X27619,X27617),X27618),esk268_4(X27616,X27617,X27618,X27619))),X27616)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27624,X27622)),hAPP(hAPP(c_Product__Type_OPair(X27624,X27622),X27623),X27625)),X27621))
        | hBOOL(hAPP(hAPP(c_member(X27624),X27623),hAPP(c_Relation_ODomain(X27624,X27622),X27621))) ) ),
    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_6877,plain,
    ! [X18292,X18293,X18294] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X18294,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X18294,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X18294),X18293)),hAPP(c_Set_OPow(X18294),X18292))),hAPP(c_Set_OPow(X18294),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18294,tc_HOL_Obool)),X18293),X18292)))),
    inference(variable_rename,[status(thm)],[fact_Un__Pow__subset]) ).

fof(i_0_6878,plain,
    ! [X19107,X19108,X19109,X19110,X19111] :
      ( ~ c_Fun_Oinj__on(X19111,X19110,X19109,c_Orderings_Otop__class_Otop(tc_fun(X19111,tc_HOL_Obool)))
      | hAPP(c_Fun_Ocomp(X19110,X19108,X19111,hAPP(c_Fun_Ocomp(X19111,X19108,X19110,X19107),c_Hilbert__Choice_Oinv__into(X19111,X19110,c_Orderings_Otop__class_Otop(tc_fun(X19111,tc_HOL_Obool)),X19109))),X19109) = X19107 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__inv__o__cancel])]) ).

fof(i_0_6879,plain,
    ! [X21963,X21964,X21965,X21966,X21967] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21967),X21966))
      | 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),X21966),X21965)),X21964)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21967),X21965)),X21963)) = 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),X21966),X21967)),X21965)),X21964)),X21963) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq1])]) ).

cnf(i_0_6880,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_5483]) ).

fof(i_0_6881,plain,
    ! [X30380,X30381,X30382] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X30382),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X30381),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X30381)),X30380))))
      | hBOOL(hAPP(hAPP(c_member(X30381),hAPP(c_Random_Opick(X30381,X30380),X30382)),hAPP(c_List_Oset(X30381),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X30381),X30381),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X30381)),X30380)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pick__member])]) ).

fof(i_0_6882,plain,
    ! [X27269,X27270,X27271,X27272,X27273,X27274,X27275,X27276] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27276,X27275)),hAPP(hAPP(c_Product__Type_OPair(X27276,X27275),X27274),X27273)),X27272))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27275,X27271)),hAPP(hAPP(c_Product__Type_OPair(X27275,X27271),X27273),X27270)),X27269))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X27276,X27271)),hAPP(hAPP(c_Product__Type_OPair(X27276,X27271),X27274),X27270)),hAPP(hAPP(c_Relation_Orel__comp(X27276,X27275,X27271),X27272),X27269))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__compI])]) ).

fof(i_0_6883,plain,
    ! [X32738,X32739,X32740,X32741,X32742] :
      ( ~ class_Orderings_Olinorder(X32742)
      | ~ c_List_Olinorder__class_Osorted(X32742,hAPP(hAPP(c_List_Omap(X32741,X32742),X32740),X32739))
      | c_List_Olinorder__class_Osorted(X32742,hAPP(hAPP(c_List_Omap(X32741,X32742),X32740),c_List_Olinorder__class_Oinsort__insert__key(X32741,X32742,X32740,X32738,X32739))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort__insert__key])]) ).

fof(i_0_6884,plain,
    ! [X18634,X18635,X18636,X18637] :
      ( ( hBOOL(hAPP(hAPP(c_member(X18637),esk27_4(X18634,X18635,X18636,X18637)),hAPP(X18635,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18637,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X18637,tc_HOL_Obool),X18635)),hAPP(c_Set_OCollect(X18637),X18634)))))
        | hBOOL(hAPP(X18634,X18636))
        | ~ c_Orderings_Oorder__class_Omono(tc_fun(X18637,tc_HOL_Obool),tc_fun(X18637,tc_HOL_Obool),X18635)
        | ~ hBOOL(hAPP(hAPP(c_member(X18637),X18636),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X18637,tc_HOL_Obool),X18635))) )
      & ( ~ hBOOL(hAPP(X18634,esk27_4(X18634,X18635,X18636,X18637)))
        | hBOOL(hAPP(X18634,X18636))
        | ~ c_Orderings_Oorder__class_Omono(tc_fun(X18637,tc_HOL_Obool),tc_fun(X18637,tc_HOL_Obool),X18635)
        | ~ hBOOL(hAPP(hAPP(c_member(X18637),X18636),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X18637,tc_HOL_Obool),X18635))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lfp__induct__set])])])]) ).

fof(i_0_6885,plain,
    ! [X33273,X33274,X33275,X33276,X33277,X33278,X33279] :
      ( ( c_List_Olist__all2(X33279,X33277,X33275,X33278,X33276)
        | ~ c_List_Olist__all2(X33279,X33277,X33275,hAPP(hAPP(c_List_Oappend(X33279),X33278),X33274),hAPP(hAPP(c_List_Oappend(X33277),X33276),X33273))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33279)),X33278) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33277)),X33276) )
      & ( c_List_Olist__all2(X33279,X33277,X33275,X33274,X33273)
        | ~ c_List_Olist__all2(X33279,X33277,X33275,hAPP(hAPP(c_List_Oappend(X33279),X33278),X33274),hAPP(hAPP(c_List_Oappend(X33277),X33276),X33273))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33279)),X33278) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33277)),X33276) )
      & ( ~ c_List_Olist__all2(X33279,X33277,X33275,X33278,X33276)
        | ~ c_List_Olist__all2(X33279,X33277,X33275,X33274,X33273)
        | c_List_Olist__all2(X33279,X33277,X33275,hAPP(hAPP(c_List_Oappend(X33279),X33278),X33274),hAPP(hAPP(c_List_Oappend(X33277),X33276),X33273))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33279)),X33278) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33277)),X33276) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__append])])]) ).

fof(i_0_6886,plain,
    ! [X17364,X17365,X17366,X17367,X17368,X17371,X17372,X17373,X17374,X17375,X17376] :
      ( ( hBOOL(hAPP(hAPP(c_member(X17367),esk14_4(X17364,X17365,X17366,X17367)),X17365))
        | hBOOL(hAPP(hAPP(c_member(X17367),esk13_4(X17364,X17365,X17366,X17367)),X17366))
        | ~ hBOOL(hAPP(hAPP(c_member(X17367),X17368),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17367,tc_HOL_Obool)),X17366),X17365)))
        | ~ hBOOL(hAPP(X17364,X17368)) )
      & ( hBOOL(hAPP(X17364,esk14_4(X17364,X17365,X17366,X17367)))
        | hBOOL(hAPP(hAPP(c_member(X17367),esk13_4(X17364,X17365,X17366,X17367)),X17366))
        | ~ hBOOL(hAPP(hAPP(c_member(X17367),X17368),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17367,tc_HOL_Obool)),X17366),X17365)))
        | ~ hBOOL(hAPP(X17364,X17368)) )
      & ( hBOOL(hAPP(hAPP(c_member(X17367),esk14_4(X17364,X17365,X17366,X17367)),X17365))
        | hBOOL(hAPP(X17364,esk13_4(X17364,X17365,X17366,X17367)))
        | ~ hBOOL(hAPP(hAPP(c_member(X17367),X17368),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17367,tc_HOL_Obool)),X17366),X17365)))
        | ~ hBOOL(hAPP(X17364,X17368)) )
      & ( hBOOL(hAPP(X17364,esk14_4(X17364,X17365,X17366,X17367)))
        | hBOOL(hAPP(X17364,esk13_4(X17364,X17365,X17366,X17367)))
        | ~ hBOOL(hAPP(hAPP(c_member(X17367),X17368),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17367,tc_HOL_Obool)),X17366),X17365)))
        | ~ hBOOL(hAPP(X17364,X17368)) )
      & ( hBOOL(hAPP(hAPP(c_member(X17374),esk15_4(X17371,X17372,X17373,X17374)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17374,tc_HOL_Obool)),X17373),X17372)))
        | ~ hBOOL(hAPP(hAPP(c_member(X17374),X17375),X17373))
        | ~ hBOOL(hAPP(X17371,X17375)) )
      & ( hBOOL(hAPP(X17371,esk15_4(X17371,X17372,X17373,X17374)))
        | ~ hBOOL(hAPP(hAPP(c_member(X17374),X17375),X17373))
        | ~ hBOOL(hAPP(X17371,X17375)) )
      & ( hBOOL(hAPP(hAPP(c_member(X17374),esk15_4(X17371,X17372,X17373,X17374)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17374,tc_HOL_Obool)),X17373),X17372)))
        | ~ hBOOL(hAPP(hAPP(c_member(X17374),X17376),X17372))
        | ~ hBOOL(hAPP(X17371,X17376)) )
      & ( hBOOL(hAPP(X17371,esk15_4(X17371,X17372,X17373,X17374)))
        | ~ hBOOL(hAPP(hAPP(c_member(X17374),X17376),X17372))
        | ~ hBOOL(hAPP(X17371,X17376)) ) ),
    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_6887,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_5484]) ).

fof(i_0_6888,plain,
    ! [X17350,X17351,X17352,X17353,X17355,X17356,X17357,X17358,X17359,X17360,X17363] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17353),X17355),X17352))
        | hBOOL(hAPP(X17350,X17355))
        | hBOOL(hAPP(hAPP(c_member(X17353),esk10_4(X17350,X17351,X17352,X17353)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17353,tc_HOL_Obool)),X17352),X17351))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17353),X17356),X17351))
        | hBOOL(hAPP(X17350,X17356))
        | hBOOL(hAPP(hAPP(c_member(X17353),esk10_4(X17350,X17351,X17352,X17353)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17353,tc_HOL_Obool)),X17352),X17351))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17353),X17355),X17352))
        | hBOOL(hAPP(X17350,X17355))
        | ~ hBOOL(hAPP(X17350,esk10_4(X17350,X17351,X17352,X17353))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17353),X17356),X17351))
        | hBOOL(hAPP(X17350,X17356))
        | ~ hBOOL(hAPP(X17350,esk10_4(X17350,X17351,X17352,X17353))) )
      & ( hBOOL(hAPP(hAPP(c_member(X17360),esk12_4(X17357,X17358,X17359,X17360)),X17358))
        | hBOOL(hAPP(hAPP(c_member(X17360),esk11_4(X17357,X17358,X17359,X17360)),X17359))
        | ~ hBOOL(hAPP(hAPP(c_member(X17360),X17363),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17360,tc_HOL_Obool)),X17359),X17358)))
        | hBOOL(hAPP(X17357,X17363)) )
      & ( ~ hBOOL(hAPP(X17357,esk12_4(X17357,X17358,X17359,X17360)))
        | hBOOL(hAPP(hAPP(c_member(X17360),esk11_4(X17357,X17358,X17359,X17360)),X17359))
        | ~ hBOOL(hAPP(hAPP(c_member(X17360),X17363),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17360,tc_HOL_Obool)),X17359),X17358)))
        | hBOOL(hAPP(X17357,X17363)) )
      & ( hBOOL(hAPP(hAPP(c_member(X17360),esk12_4(X17357,X17358,X17359,X17360)),X17358))
        | ~ hBOOL(hAPP(X17357,esk11_4(X17357,X17358,X17359,X17360)))
        | ~ hBOOL(hAPP(hAPP(c_member(X17360),X17363),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17360,tc_HOL_Obool)),X17359),X17358)))
        | hBOOL(hAPP(X17357,X17363)) )
      & ( ~ hBOOL(hAPP(X17357,esk12_4(X17357,X17358,X17359,X17360)))
        | ~ hBOOL(hAPP(X17357,esk11_4(X17357,X17358,X17359,X17360)))
        | ~ hBOOL(hAPP(hAPP(c_member(X17360),X17363),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17360,tc_HOL_Obool)),X17359),X17358)))
        | hBOOL(hAPP(X17357,X17363)) ) ),
    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_6889,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_5485]) ).

cnf(i_0_6890,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_5486]) ).

cnf(i_0_6891,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_5447]) ).

fof(i_0_6892,plain,
    ! [X29257,X29258,X29259,X29260,X29261,X29262,X29263,X29264] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29264,tc_fun(X29263,tc_fun(X29262,tc_HOL_Obool))),X29261),X29260),X29259),X29258))
      | ~ hBOOL(hAPP(hAPP(c_member(X29264),X29257),X29261))
      | hBOOL(hAPP(hAPP(hAPP(X29260,X29257),X29259),X29258)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF2__D])]) ).

fof(i_0_6893,plain,
    ! [X29249,X29250,X29251,X29252,X29253,X29254,X29255,X29256] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29256,tc_fun(X29255,tc_fun(X29254,tc_HOL_Obool))),X29253),X29252),X29251),X29250))
      | hBOOL(hAPP(hAPP(hAPP(X29252,X29249),X29251),X29250))
      | ~ hBOOL(hAPP(hAPP(c_member(X29256),X29249),X29253)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5487])]) ).

cnf(i_0_6894,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_5488]) ).

cnf(i_0_6895,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_5489]) ).

cnf(i_0_6896,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_5490]) ).

cnf(i_0_6897,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_5491]) ).

cnf(i_0_6898,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_5448]) ).

cnf(i_0_6899,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_5447]) ).

fof(i_0_6900,plain,
    ! [X33266,X33267,X33268,X33269,X33270,X33271,X33272] :
      ( ~ c_List_Olist__all2(X33272,X33271,X33270,X33269,X33268)
      | ~ c_List_Olist__all2(X33272,X33271,X33270,X33267,X33266)
      | c_List_Olist__all2(X33272,X33271,X33270,hAPP(hAPP(c_List_Oappend(X33272),X33269),X33267),hAPP(hAPP(c_List_Oappend(X33271),X33268),X33266)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__appendI])]) ).

cnf(i_0_6901,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_6902,plain,
    ! [X18962,X18963,X18964,X18965,X18966,X18967,X18968] : hAPP(c_Fun_Ocomp(X18968,X18967,X18966,X18965),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18966,X18968),X18964),X18963),X18962)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18966,X18967),hAPP(c_Fun_Ocomp(X18968,X18967,X18966,X18965),X18964)),X18963),hAPP(X18965,X18962)),
    inference(variable_rename,[status(thm)],[fact_fun__upd__comp]) ).

cnf(i_0_6903,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_6904,plain,
    ! [X19486,X19487,X19488,X19489] : hAPP(c_Set_Ovimage(X19489,X19488,X19487),X19486) = hAPP(c_Set_OCollect(X19489),hAPP(hAPP(c_COMBC(X19489,tc_fun(X19488,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X19488,tc_fun(tc_fun(X19488,tc_HOL_Obool),tc_HOL_Obool),X19489),c_member(X19488)),X19487)),X19486)),
    inference(variable_rename,[status(thm)],[fact_vimage__def]) ).

fof(i_0_6905,plain,
    ! [X31869,X31870,X31871,X31872,X31873] : hAPP(hAPP(c_List_Ozip(X31873,X31872),X31871),hAPP(hAPP(c_List_Oappend(X31872),X31870),X31869)) = hAPP(hAPP(c_List_Oappend(tc_prod(X31873,X31872)),hAPP(hAPP(c_List_Ozip(X31873,X31872),hAPP(hAPP(c_List_Otake(X31873),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31872)),X31870)),X31871)),X31870)),hAPP(hAPP(c_List_Ozip(X31873,X31872),hAPP(hAPP(c_List_Odrop(X31873),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31872)),X31870)),X31871)),X31869)),
    inference(variable_rename,[status(thm)],[fact_zip__append2]) ).

fof(i_0_6906,plain,
    ! [X30622,X30623,X30624,X30625] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30625),tc_List_Olist(X30625))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30625),tc_List_Olist(X30625)),X30624),X30623)),c_List_Olistrel1(X30625,hAPP(c_Relation_Oconverse(X30625,X30625),X30622))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30625),tc_List_Olist(X30625))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30625),tc_List_Olist(X30625)),X30624),X30623)),hAPP(c_Relation_Oconverse(tc_List_Olist(X30625),tc_List_Olist(X30625)),c_List_Olistrel1(X30625,X30622)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30625),tc_List_Olist(X30625))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30625),tc_List_Olist(X30625)),X30624),X30623)),hAPP(c_Relation_Oconverse(tc_List_Olist(X30625),tc_List_Olist(X30625)),c_List_Olistrel1(X30625,X30622))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30625),tc_List_Olist(X30625))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30625),tc_List_Olist(X30625)),X30624),X30623)),c_List_Olistrel1(X30625,hAPP(c_Relation_Oconverse(X30625,X30625),X30622)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__listrel1__converse])]) ).

fof(i_0_6907,plain,
    ! [X32367,X32368,X32369,X32370,X32371] : c_List_Omap__filter(X32371,X32370,X32369,hAPP(hAPP(c_List_Olist_OCons(X32371),X32368),X32367)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(X32370),X32370,c_List_Omap__filter(X32371,X32370,X32369,X32367),hAPP(hAPP(c_COMBC(X32370,tc_List_Olist(X32370),tc_List_Olist(X32370)),c_List_Olist_OCons(X32370)),c_List_Omap__filter(X32371,X32370,X32369,X32367))),hAPP(X32369,X32368)),
    inference(variable_rename,[status(thm)],[fact_map__filter__simps_I1_J]) ).

fof(i_0_6908,plain,
    ! [X31513,X31514,X31515,X31516,X31517,X31519,X31520,X31521,X31522,X31523,X31524] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(X31517),X31516),esk424_5(X31513,X31514,X31515,X31516,X31517)) = X31514
        | X31514 = c_List_Olist_ONil(X31517)
        | hAPP(hAPP(c_List_Olist_OCons(X31517),X31516),X31515) != hAPP(hAPP(c_List_Oappend(X31517),X31514),X31513) )
      & ( X31515 = hAPP(hAPP(c_List_Oappend(X31517),esk424_5(X31513,X31514,X31515,X31516,X31517)),X31513)
        | X31514 = c_List_Olist_ONil(X31517)
        | hAPP(hAPP(c_List_Olist_OCons(X31517),X31516),X31515) != hAPP(hAPP(c_List_Oappend(X31517),X31514),X31513) )
      & ( hAPP(hAPP(c_List_Olist_OCons(X31517),X31516),esk424_5(X31513,X31514,X31515,X31516,X31517)) = X31514
        | hAPP(hAPP(c_List_Olist_OCons(X31517),X31516),X31515) = X31513
        | hAPP(hAPP(c_List_Olist_OCons(X31517),X31516),X31515) != hAPP(hAPP(c_List_Oappend(X31517),X31514),X31513) )
      & ( X31515 = hAPP(hAPP(c_List_Oappend(X31517),esk424_5(X31513,X31514,X31515,X31516,X31517)),X31513)
        | hAPP(hAPP(c_List_Olist_OCons(X31517),X31516),X31515) = X31513
        | hAPP(hAPP(c_List_Olist_OCons(X31517),X31516),X31515) != hAPP(hAPP(c_List_Oappend(X31517),X31514),X31513) )
      & ( X31520 != c_List_Olist_ONil(X31523)
        | hAPP(hAPP(c_List_Olist_OCons(X31523),X31522),X31521) != X31519
        | hAPP(hAPP(c_List_Olist_OCons(X31523),X31522),X31521) = hAPP(hAPP(c_List_Oappend(X31523),X31520),X31519) )
      & ( hAPP(hAPP(c_List_Olist_OCons(X31523),X31522),X31524) != X31520
        | X31521 != hAPP(hAPP(c_List_Oappend(X31523),X31524),X31519)
        | hAPP(hAPP(c_List_Olist_OCons(X31523),X31522),X31521) = hAPP(hAPP(c_List_Oappend(X31523),X31520),X31519) ) ),
    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_6909,plain,
    ! [X31525,X31526,X31527,X31528,X31529,X31531,X31532,X31533,X31534,X31535,X31536] :
      ( ( X31528 = hAPP(hAPP(c_List_Olist_OCons(X31529),X31526),esk425_5(X31525,X31526,X31527,X31528,X31529))
        | X31528 = c_List_Olist_ONil(X31529)
        | hAPP(hAPP(c_List_Oappend(X31529),X31528),X31527) != hAPP(hAPP(c_List_Olist_OCons(X31529),X31526),X31525) )
      & ( hAPP(hAPP(c_List_Oappend(X31529),esk425_5(X31525,X31526,X31527,X31528,X31529)),X31527) = X31525
        | X31528 = c_List_Olist_ONil(X31529)
        | hAPP(hAPP(c_List_Oappend(X31529),X31528),X31527) != hAPP(hAPP(c_List_Olist_OCons(X31529),X31526),X31525) )
      & ( X31528 = hAPP(hAPP(c_List_Olist_OCons(X31529),X31526),esk425_5(X31525,X31526,X31527,X31528,X31529))
        | X31527 = hAPP(hAPP(c_List_Olist_OCons(X31529),X31526),X31525)
        | hAPP(hAPP(c_List_Oappend(X31529),X31528),X31527) != hAPP(hAPP(c_List_Olist_OCons(X31529),X31526),X31525) )
      & ( hAPP(hAPP(c_List_Oappend(X31529),esk425_5(X31525,X31526,X31527,X31528,X31529)),X31527) = X31525
        | X31527 = hAPP(hAPP(c_List_Olist_OCons(X31529),X31526),X31525)
        | hAPP(hAPP(c_List_Oappend(X31529),X31528),X31527) != hAPP(hAPP(c_List_Olist_OCons(X31529),X31526),X31525) )
      & ( X31534 != c_List_Olist_ONil(X31535)
        | X31533 != hAPP(hAPP(c_List_Olist_OCons(X31535),X31532),X31531)
        | hAPP(hAPP(c_List_Oappend(X31535),X31534),X31533) = hAPP(hAPP(c_List_Olist_OCons(X31535),X31532),X31531) )
      & ( X31534 != hAPP(hAPP(c_List_Olist_OCons(X31535),X31532),X31536)
        | hAPP(hAPP(c_List_Oappend(X31535),X31536),X31533) != X31531
        | hAPP(hAPP(c_List_Oappend(X31535),X31534),X31533) = hAPP(hAPP(c_List_Olist_OCons(X31535),X31532),X31531) ) ),
    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_6910,plain,
    ! [X19214,X19215,X19216,X19217,X19218] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X19218),X19217),hAPP(c_Set_Oimage(X19216,X19218,X19215),X19214)))
      | hBOOL(hAPP(hAPP(c_member(X19216),hAPP(c_Hilbert__Choice_Oinv__into(X19216,X19218,X19214,X19215),X19217)),X19214)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__into])]) ).

fof(i_0_6911,plain,
    ! [X26009,X26010] :
      ( ~ class_Orderings_Olinorder(X26010)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26010),X26009))
      | X26009 = c_Orderings_Obot__class_Obot(tc_fun(X26010,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X26010),hAPP(hAPP(c_Orderings_Oord__class_Omax(X26010),esk171_2(X26009,X26010)),esk172_2(X26009,X26010))),hAPP(hAPP(c_Set_Oinsert(X26010),esk171_2(X26009,X26010)),hAPP(hAPP(c_Set_Oinsert(X26010),esk172_2(X26009,X26010)),c_Orderings_Obot__class_Obot(tc_fun(X26010,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X26010),c_Big__Operators_Olattice_OSup__fin(X26010,c_Orderings_Oord__class_Omax(X26010),X26009)),X26009)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oclosed])])]) ).

fof(i_0_6912,plain,
    ! [X25702,X25703] :
      ( ~ class_Orderings_Olinorder(X25703)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25703),X25702))
      | X25702 = c_Orderings_Obot__class_Obot(tc_fun(X25703,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X25703),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25703),esk169_2(X25702,X25703)),esk170_2(X25702,X25703))),hAPP(hAPP(c_Set_Oinsert(X25703),esk169_2(X25702,X25703)),hAPP(hAPP(c_Set_Oinsert(X25703),esk170_2(X25702,X25703)),c_Orderings_Obot__class_Obot(tc_fun(X25703,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X25703),c_Big__Operators_Olattice_OInf__fin(X25703,c_Orderings_Oord__class_Omin(X25703),X25702)),X25702)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oclosed])])]) ).

fof(i_0_6913,plain,
    ! [X27966,X27967,X27968,X27969] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27969),esk275_4(X27966,X27967,X27968,X27969)),X27968))
        | hAPP(c_Finite__Set_Ocard(tc_prod(X27969,X27967)),hAPP(hAPP(c_Product__Type_OSigma(X27969,X27967),X27968),X27966)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27969,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X27967,tc_HOL_Obool),tc_Nat_Onat,X27969),c_Finite__Set_Ocard(X27967)),X27966)),X27968)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27969),X27968)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27967),hAPP(X27966,esk275_4(X27966,X27967,X27968,X27969))))
        | hAPP(c_Finite__Set_Ocard(tc_prod(X27969,X27967)),hAPP(hAPP(c_Product__Type_OSigma(X27969,X27967),X27968),X27966)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27969,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X27967,tc_HOL_Obool),tc_Nat_Onat,X27969),c_Finite__Set_Ocard(X27967)),X27966)),X27968)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27969),X27968)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__SigmaI])])])]) ).

fof(i_0_6914,plain,
    ! [X19142,X19143,X19144,X19145] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19145,X19144,X19143,X19142,c_Orderings_Obot__class_Obot(tc_fun(X19145,tc_HOL_Obool))),X19142)),
    inference(variable_rename,[status(thm)],[fact_fold__graph_Oequations_I1_J]) ).

fof(i_0_6915,plain,
    ! [X19138,X19139,X19140,X19141] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19141,X19140,X19139,X19138,c_Orderings_Obot__class_Obot(tc_fun(X19141,tc_HOL_Obool))),X19138)),
    inference(variable_rename,[status(thm)],[fact_fold__graph_OemptyI]) ).

fof(i_0_6916,plain,
    ! [X27471,X27472,X27473] :
      ( ~ c_Wellfounded_Owf(X27473,X27472)
      | ~ c_Wellfounded_Owf(X27473,X27471)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27473,X27473),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27473,X27473,X27473),X27472),X27471)),X27472))
      | c_Wellfounded_Owf(X27473,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27473,X27473),tc_HOL_Obool)),X27472),X27471)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__union__compatible])]) ).

fof(i_0_6917,plain,
    ! [X30257,X30258,X30259,X30260] : hAPP(c_Map_Omap__of(X30260,X30259),hAPP(hAPP(c_List_Omap(X30260,tc_prod(X30260,X30259)),hAPP(hAPP(c_COMBS(X30260,X30259,tc_prod(X30260,X30259)),c_Product__Type_OPair(X30260,X30259)),X30258)),X30257)) = c_Map_Orestrict__map(X30260,X30259,hAPP(c_Fun_Ocomp(X30259,tc_Option_Ooption(X30259),X30260,c_Option_Ooption_OSome(X30259)),X30258),hAPP(c_List_Oset(X30260),X30257)),
    inference(variable_rename,[status(thm)],[fact_map__of__map__restrict]) ).

fof(i_0_6918,plain,
    ! [X21332,X21333] :
      ( ~ class_Groups_Oab__semigroup__mult(X21333)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21333),X21332))
      | X21332 = c_Orderings_Obot__class_Obot(tc_fun(X21333,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X21333),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21333),esk102_2(X21332,X21333)),esk103_2(X21332,X21333))),hAPP(hAPP(c_Set_Oinsert(X21333),esk102_2(X21332,X21333)),hAPP(hAPP(c_Set_Oinsert(X21333),esk103_2(X21332,X21333)),c_Orderings_Obot__class_Obot(tc_fun(X21333,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X21333),hAPP(c_Finite__Set_Ofold1(X21333,c_Groups_Otimes__class_Otimes(X21333)),X21332)),X21332)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__in])])]) ).

cnf(i_0_6919,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_5492]) ).

fof(i_0_6920,plain,
    ! [X22920,X22921,X22922,X22923,X22924] :
      ( ~ 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),X22924),X22923)),X22922)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22924),X22921)),X22920)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22922))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22922),X22924))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22920),X22924))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22923),X22921)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma])]) ).

fof(i_0_6921,plain,
    ! [X22945,X22946,X22947,X22948,X22949] :
      ( ~ 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),X22949),X22948)),X22947)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22949),X22946)),X22945)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22945),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22949),X22945))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22949),X22947))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22946),X22948)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg])]) ).

fof(i_0_6922,plain,
    ! [X32777,X32778,X32779,X32780,X32781] :
      ( ~ class_Orderings_Olinorder(X32781)
      | ~ hBOOL(hAPP(c_List_Odistinct(X32780),X32779))
      | hBOOL(hAPP(c_List_Odistinct(X32780),c_List_Olinorder__class_Oinsort__insert__key(X32780,X32781,X32778,X32777,X32779))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__insort__insert])]) ).

fof(i_0_6923,plain,
    ! [X32314,X32315,X32316] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32316),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32315))),c_List_Otranspose(X32315,X32314))))
      | hAPP(hAPP(c_List_Onth(tc_List_Olist(X32315)),c_List_Otranspose(X32315,X32314)),X32316) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X32315),X32315),hAPP(hAPP(c_COMBC(tc_List_Olist(X32315),tc_Nat_Onat,X32315),c_List_Onth(X32315)),X32316)),hAPP(c_List_Ofilter(tc_List_Olist(X32315),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X32315)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32316)),c_Nat_Osize__class_Osize(tc_List_Olist(X32315)))),X32314)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__transpose])]) ).

fof(i_0_6924,plain,
    ! [X17767,X17768,X17769] :
      ( ( ~ hBOOL(hAPP(c_Predicate_OPowp(X17769,hAPP(hAPP(c_COMBC(X17769,tc_fun(X17769,tc_HOL_Obool),tc_HOL_Obool),c_member(X17769)),X17768)),X17767))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X17769,tc_HOL_Obool)),X17767),hAPP(c_Set_OPow(X17769),X17768))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X17769,tc_HOL_Obool)),X17767),hAPP(c_Set_OPow(X17769),X17768)))
        | hBOOL(hAPP(c_Predicate_OPowp(X17769,hAPP(hAPP(c_COMBC(X17769,tc_fun(X17769,tc_HOL_Obool),tc_HOL_Obool),c_member(X17769)),X17768)),X17767)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Powp__Pow__eq])]) ).

fof(i_0_6925,plain,
    ! [X21262,X21263,X21264,X21265,X21266,X21267] :
      ( ~ c_Fun_Oinj__on(X21267,X21266,X21265,X21264)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21266,tc_HOL_Obool)),hAPP(c_Set_Oimage(X21267,X21266,X21265),X21264)),X21263))
      | ~ c_Fun_Oinj__on(X21266,X21267,X21262,X21263)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21267,tc_HOL_Obool)),hAPP(c_Set_Oimage(X21266,X21267,X21262),X21263)),X21264))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21267),X21264))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21266),X21263))
      | hAPP(c_Finite__Set_Ocard(X21267),X21264) = hAPP(c_Finite__Set_Ocard(X21266),X21263) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij__eq])]) ).

fof(i_0_6926,plain,
    ! [X28291,X28292,X28293] : c_Hilbert__Choice_OEps(tc_prod(X28293,X28292),hAPP(c_Product__Type_Oprod_Oprod__case(X28293,X28292,tc_HOL_Obool),X28291)) = c_Hilbert__Choice_OEps(tc_prod(X28293,X28292),hAPP(hAPP(c_COMBS(tc_prod(X28293,X28292),X28292,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X28293,tc_fun(X28292,tc_HOL_Obool),tc_prod(X28293,X28292)),X28291),c_Product__Type_Ofst(X28293,X28292))),c_Product__Type_Osnd(X28293,X28292))),
    inference(variable_rename,[status(thm)],[fact_Eps__split]) ).

fof(i_0_6927,plain,
    ! [X23856,X23857,X23858] : c_HOL_OThe(tc_prod(X23858,X23857),hAPP(c_Product__Type_Oprod_Oprod__case(X23858,X23857,tc_HOL_Obool),X23856)) = c_HOL_OThe(tc_prod(X23858,X23857),hAPP(hAPP(c_COMBS(tc_prod(X23858,X23857),X23857,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X23858,tc_fun(X23857,tc_HOL_Obool),tc_prod(X23858,X23857)),X23856),c_Product__Type_Ofst(X23858,X23857))),c_Product__Type_Osnd(X23858,X23857))),
    inference(variable_rename,[status(thm)],[fact_The__split]) ).

fof(i_0_6928,plain,
    ! [X33397,X33398,X33399,X33400,X33401] :
      ( ( hAPP(X33398,X33400) = hAPP(X33398,X33399)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X33398,X33400)),hAPP(X33398,X33399)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33401,X33401)),hAPP(hAPP(c_Product__Type_OPair(X33401,X33401),X33400),X33399)),c_List_Omeasures(X33401,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X33401,tc_Nat_Onat)),X33398),X33397)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33401,X33401)),hAPP(hAPP(c_Product__Type_OPair(X33401,X33401),X33400),X33399)),c_List_Omeasures(X33401,X33397)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X33398,X33400)),hAPP(X33398,X33399)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33401,X33401)),hAPP(hAPP(c_Product__Type_OPair(X33401,X33401),X33400),X33399)),c_List_Omeasures(X33401,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X33401,tc_Nat_Onat)),X33398),X33397)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X33398,X33400)),hAPP(X33398,X33399)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X33401,X33401)),hAPP(hAPP(c_Product__Type_OPair(X33401,X33401),X33400),X33399)),c_List_Omeasures(X33401,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X33401,tc_Nat_Onat)),X33398),X33397)))) )
      & ( hAPP(X33398,X33400) != hAPP(X33398,X33399)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33401,X33401)),hAPP(hAPP(c_Product__Type_OPair(X33401,X33401),X33400),X33399)),c_List_Omeasures(X33401,X33397)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X33401,X33401)),hAPP(hAPP(c_Product__Type_OPair(X33401,X33401),X33400),X33399)),c_List_Omeasures(X33401,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X33401,tc_Nat_Onat)),X33398),X33397)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measures_I2_J])])]) ).

fof(i_0_6929,plain,
    ! [X23457,X23458,X23459,X23460] :
      ( ~ class_Divides_Osemiring__div(X23460)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23460),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23460),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23460),X23459),X23458)),X23458)),c_Divides_Odiv__class_Omod(X23460,X23459,X23458))),X23457) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23460),X23459),X23457) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mod__equality])]) ).

fof(i_0_6930,plain,
    ! [X21389,X21390,X21391,X21392,X21393] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21393)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21392),X21391))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21392),X21390))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21392,tc_HOL_Obool)),X21391),X21390) != c_Orderings_Obot__class_Obot(tc_fun(X21392,tc_HOL_Obool))
      | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21393,X21392,c_Groups_Otimes__class_Otimes(X21393)),X21389),c_Groups_Oone__class_Oone(X21393)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21392,tc_HOL_Obool)),X21391),X21390)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21393),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21393,X21392,c_Groups_Otimes__class_Otimes(X21393)),X21389),c_Groups_Oone__class_Oone(X21393)),X21391)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21393,X21392,c_Groups_Otimes__class_Otimes(X21393)),X21389),c_Groups_Oone__class_Oone(X21393)),X21390)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__Un__disjoint])]) ).

cnf(i_0_6931,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_5493]) ).

fof(i_0_6932,plain,
    ! [X30411,X30412,X30413,X30414] :
      ( ~ class_Groups_Oab__group__add(X30414)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X30414),hAPP(c_List_Omonoid__add__class_Olistsum(X30414),hAPP(hAPP(c_List_Omap(X30413,X30414),X30412),X30411))) = hAPP(c_List_Omonoid__add__class_Olistsum(X30414),hAPP(hAPP(c_List_Omap(X30413,X30414),hAPP(c_Fun_Ocomp(X30414,X30414,X30413,c_Groups_Ouminus__class_Ouminus(X30414)),X30412)),X30411)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__listsum__map])]) ).

fof(i_0_6933,plain,
    ! [X33815,X33816,X33817,X33818] : c_New__Random__Sequence_Oneg__map(X33818,X33817,X33816,X33815) = c_New__Random__Sequence_Oneg__bind(X33818,X33817,X33815,hAPP(c_Fun_Ocomp(X33817,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(X33817)))))),X33818,c_New__Random__Sequence_Oneg__single(X33817)),X33816)),
    inference(variable_rename,[status(thm)],[fact_neg__map__def]) ).

fof(i_0_6934,plain,
    ! [X33151,X33152,X33153] :
      ( ( ~ hBOOL(hAPP(c_List_Olistsp(X33153,hAPP(hAPP(c_COMBC(X33153,tc_fun(X33153,tc_HOL_Obool),tc_HOL_Obool),c_member(X33153)),X33152)),X33151))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33153)),X33151),c_List_Olists(X33153,X33152))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33153)),X33151),c_List_Olists(X33153,X33152)))
        | hBOOL(hAPP(c_List_Olistsp(X33153,hAPP(hAPP(c_COMBC(X33153,tc_fun(X33153,tc_HOL_Obool),tc_HOL_Obool),c_member(X33153)),X33152)),X33151)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__lists__eq])]) ).

fof(i_0_6935,plain,
    ! [X27005,X27006,X27007,X27008] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27008)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27008),c_Groups_Ozero__class_Ozero(X27008)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27007,X27008),hAPP(hAPP(c_COMBB(X27008,X27008,X27007),c_Groups_Oabs__class_Oabs(X27008)),X27006)),X27005))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__abs__ge__zero])]) ).

fof(i_0_6936,plain,
    ! [X20347,X20348] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20348),X20347))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X20348,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(X20348,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X20348,tc_HOL_Obool),tc_fun(X20348,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X20348,tc_HOL_Obool))),X20347)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__subsets])]) ).

fof(i_0_6937,plain,
    ! [X22107,X22108,X22109] :
      ( ( X22108 = c_Groups_Ozero__class_Ozero(X22109)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22109),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22109),X22108),X22108)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22109),X22107),X22107))),c_Groups_Ozero__class_Ozero(X22109)))
        | ~ class_Rings_Olinordered__ring__strict(X22109) )
      & ( X22107 = c_Groups_Ozero__class_Ozero(X22109)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22109),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22109),X22108),X22108)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22109),X22107),X22107))),c_Groups_Ozero__class_Ozero(X22109)))
        | ~ class_Rings_Olinordered__ring__strict(X22109) )
      & ( X22108 != c_Groups_Ozero__class_Ozero(X22109)
        | X22107 != c_Groups_Ozero__class_Ozero(X22109)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22109),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22109),X22108),X22108)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22109),X22107),X22107))),c_Groups_Ozero__class_Ozero(X22109)))
        | ~ class_Rings_Olinordered__ring__strict(X22109) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff])])]) ).

fof(i_0_6938,plain,
    ! [X25533,X25534] :
      ( ~ class_Orderings_Olinorder(X25534)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25534),X25533))
      | X25533 = c_Orderings_Obot__class_Obot(tc_fun(X25534,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X25534),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25534),esk164_2(X25533,X25534)),esk165_2(X25533,X25534))),hAPP(hAPP(c_Set_Oinsert(X25534),esk164_2(X25533,X25534)),hAPP(hAPP(c_Set_Oinsert(X25534),esk165_2(X25533,X25534)),c_Orderings_Obot__class_Obot(tc_fun(X25534,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X25534),c_Big__Operators_Olinorder__class_OMin(X25534,X25533)),X25533)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oclosed])])]) ).

fof(i_0_6939,plain,
    ! [X26013,X26014] :
      ( ~ class_Orderings_Olinorder(X26014)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26014),X26013))
      | X26013 = c_Orderings_Obot__class_Obot(tc_fun(X26014,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X26014),hAPP(hAPP(c_Orderings_Oord__class_Omax(X26014),esk173_2(X26013,X26014)),esk174_2(X26013,X26014))),hAPP(hAPP(c_Set_Oinsert(X26014),esk173_2(X26013,X26014)),hAPP(hAPP(c_Set_Oinsert(X26014),esk174_2(X26013,X26014)),c_Orderings_Obot__class_Obot(tc_fun(X26014,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X26014),c_Big__Operators_Olinorder__class_OMax(X26014,X26013)),X26013)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oclosed])])]) ).

fof(i_0_6940,plain,
    ! [X20901,X20902] :
      ( ~ class_Lattices_Olattice(X20902)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20902),X20901))
      | X20901 = c_Orderings_Obot__class_Obot(tc_fun(X20902,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X20902),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20902),esk82_2(X20901,X20902)),esk83_2(X20901,X20902))),hAPP(hAPP(c_Set_Oinsert(X20902),esk82_2(X20901,X20902)),hAPP(hAPP(c_Set_Oinsert(X20902),esk83_2(X20901,X20902)),c_Orderings_Obot__class_Obot(tc_fun(X20902,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X20902),c_Big__Operators_Olattice__class_OSup__fin(X20902,X20901)),X20901)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oclosed])])]) ).

fof(i_0_6941,plain,
    ! [X20897,X20898] :
      ( ~ class_Lattices_Olattice(X20898)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20898),X20897))
      | X20897 = c_Orderings_Obot__class_Obot(tc_fun(X20898,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X20898),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20898),esk80_2(X20897,X20898)),esk81_2(X20897,X20898))),hAPP(hAPP(c_Set_Oinsert(X20898),esk80_2(X20897,X20898)),hAPP(hAPP(c_Set_Oinsert(X20898),esk81_2(X20897,X20898)),c_Orderings_Obot__class_Obot(tc_fun(X20898,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X20898),c_Big__Operators_Olattice__class_OInf__fin(X20898,X20897)),X20897)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oclosed])])]) ).

fof(i_0_6942,plain,
    ! [X22116,X22117,X22118] :
      ( ~ class_Rings_Olinordered__ring(X22118)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22118),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22118),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22118),X22117),X22117)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22118),X22116),X22116))),c_Groups_Ozero__class_Ozero(X22118))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5494])]) ).

fof(i_0_6943,plain,
    ! [X20640,X20641,X20642,X20643,X20644,X20645,X20646,X20647] :
      ( ~ c_Finite__Set_Ofolding__image(X20647,X20646,X20645,X20644,X20643)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20646),X20642))
      | ~ c_Fun_Oinj__on(X20646,X20646,X20641,X20642)
      | hAPP(hAPP(X20643,X20640),hAPP(c_Set_Oimage(X20646,X20646,X20641),X20642)) = hAPP(hAPP(X20643,hAPP(c_Fun_Ocomp(X20646,X20647,X20646,X20640),X20641)),X20642) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image_Oreindex])]) ).

fof(i_0_6944,plain,
    ! [X32959,X32960,X32961] :
      ( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X32961),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X32961))),X32960)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32959),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32961))),X32960)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32961))),hAPP(c_List_Ofilter(tc_List_Olist(X32961),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X32961)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32959)),c_Nat_Osize__class_Osize(tc_List_Olist(X32961)))),c_List_Otranspose(X32961,X32960))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32961)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X32961)),X32960),X32959)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose__column__length])]) ).

fof(i_0_6945,plain,
    ! [X23782,X23783,X23784,X23785,X23786,X23787,X23788] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23788,X23787)),hAPP(hAPP(c_Product__Type_OPair(X23788,X23787),X23786),X23785)),X23784))
      | hBOOL(hAPP(hAPP(c_member(X23783),hAPP(hAPP(X23782,X23786),X23785)),hAPP(c_Set_Oimage(tc_prod(X23788,X23787),X23783,hAPP(c_Product__Type_Oprod_Oprod__case(X23788,X23787,X23783),X23782)),X23784))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__imageI])]) ).

fof(i_0_6946,plain,
    ! [X32250,X32251,X32252,X32253,X32254] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32254)),hAPP(c_List_Ofilter(X32254,X32253),hAPP(hAPP(c_List_Omap(X32252,X32254),X32251),X32250))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32252)),hAPP(c_List_Ofilter(X32252,hAPP(c_Fun_Ocomp(X32254,tc_HOL_Obool,X32252,X32253),X32251)),X32250)),
    inference(variable_rename,[status(thm)],[fact_length__filter__map]) ).

fof(i_0_6947,plain,
    ! [X32162,X32163,X32164,X32165,X32166] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32166,X32165)),hAPP(hAPP(c_Product__Type_OPair(X32166,X32165),X32164),X32163)),hAPP(c_List_Oset(tc_prod(X32166,X32165)),X32162)))
      | hAPP(hAPP(c_Map_Omap__of(X32166,X32165),X32162),X32164) = hAPP(c_Option_Ooption_OSome(X32165),esk442_5(X32162,X32163,X32164,X32165,X32166)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_weak__map__of__SomeI])])]) ).

cnf(i_0_6948,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_5495]) ).

fof(i_0_6949,plain,
    ! [X28689,X28690,X28691,X28692,X28693] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28693,X28693)),hAPP(hAPP(c_Product__Type_OPair(X28693,X28693),X28692),X28691)),c_Transitive__Closure_Ortrancl(X28693,X28690)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28693,X28693),tc_HOL_Obool)),X28690),hAPP(hAPP(c_Product__Type_OSigma(X28693,X28693),X28689),hAPP(c_COMBK(tc_fun(X28693,tc_HOL_Obool),X28693),X28689))))
      | X28692 = X28691
      | hBOOL(hAPP(hAPP(c_member(X28693),X28692),X28689)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma__aux])]) ).

fof(i_0_6950,plain,
    ! [X20117,X20118,X20119,X20120,X20121,X20122] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20122,tc_fun(X20121,tc_HOL_Obool))),X20120),X20119),X20118),X20117))
      | hBOOL(hAPP(hAPP(X20120,X20118),X20117))
      | hBOOL(hAPP(hAPP(X20119,X20118),X20117)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5496])]) ).

fof(i_0_6951,plain,
    ! [X32273,X32274,X32275] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32275)),hAPP(c_List_Ofilter(X32275,X32274),X32273))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32275)),hAPP(c_List_Ofilter(X32275,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32275),c_fNot),X32274)),X32273))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32275)),X32273),
    inference(variable_rename,[status(thm)],[fact_sum__length__filter__compl]) ).

fof(i_0_6952,plain,
    ! [X28596,X28597,X28598,X28599,X28600] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28600,X28600)),hAPP(hAPP(c_Product__Type_OPair(X28600,X28600),X28599),X28598)),c_Transitive__Closure_Ortrancl(X28600,X28597)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28600,X28600)),hAPP(hAPP(c_Product__Type_OPair(X28600,X28600),X28598),X28596)),c_Transitive__Closure_Ortrancl(X28600,X28597)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28600,X28600)),hAPP(hAPP(c_Product__Type_OPair(X28600,X28600),X28599),X28596)),c_Transitive__Closure_Ortrancl(X28600,X28597))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__trans])]) ).

cnf(i_0_6953,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_5497]) ).

cnf(i_0_6954,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_5498]) ).

fof(i_0_6955,plain,
    ! [X23441,X23442,X23443] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23443),X23442)),X23441) = 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),X23443),X23441)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23442),X23441))),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,X23443,X23441)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23442,X23441))),X23441)),
    inference(variable_rename,[status(thm)],[fact_zdiv__zadd1__eq]) ).

fof(i_0_6956,plain,
    ! [X23629,X23630,X23631] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23631),X23630)),X23629) = 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),X23631),X23629)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23630),X23629))),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,X23631,X23629)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23630,X23629))),X23629)),
    inference(variable_rename,[status(thm)],[fact_div__add1__eq]) ).

fof(i_0_6957,plain,
    ! [X20123,X20124,X20125,X20126,X20127,X20128] :
      ( ( hBOOL(hAPP(hAPP(X20126,X20124),X20123))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20128,tc_fun(X20127,tc_HOL_Obool))),X20126),X20125),X20124),X20123)) )
      & ( hBOOL(hAPP(hAPP(X20125,X20124),X20123))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20128,tc_fun(X20127,tc_HOL_Obool))),X20126),X20125),X20124),X20123)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5499])])]) ).

fof(i_0_6958,plain,
    ! [X20185,X20186,X20187,X20188,X20189,X20190] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20190,tc_fun(X20189,tc_HOL_Obool))),X20188),X20187),X20186),X20185))
      | hBOOL(hAPP(hAPP(X20188,X20186),X20185)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D1])]) ).

fof(i_0_6959,plain,
    ! [X20179,X20180,X20181,X20182,X20183,X20184] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20184,tc_fun(X20183,tc_HOL_Obool))),X20182),X20181),X20180),X20179))
      | hBOOL(hAPP(hAPP(X20181,X20180),X20179)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D2])]) ).

cnf(i_0_6960,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk451_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_5295]) ).

cnf(i_0_6961,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk450_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_5296]) ).

fof(i_0_6962,plain,
    ! [X33108,X33109,X33110,X33111] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk466_4(X33108,X33109,X33110,X33111)),X33111))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33111),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33109)),X33108)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33111),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33109)),c_List_OtakeWhile(X33109,X33110,X33108)))) )
      & ( ~ hBOOL(hAPP(X33110,hAPP(hAPP(c_List_Onth(X33109),X33108),esk466_4(X33108,X33109,X33110,X33111))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33111),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33109)),X33108)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33111),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33109)),c_List_OtakeWhile(X33109,X33110,X33108)))) ) ),
    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_6963,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5500]) ).

cnf(i_0_6964,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_5501]) ).

cnf(i_0_6965,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_5502]) ).

cnf(i_0_6966,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_5503]) ).

cnf(i_0_6967,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_5504]) ).

fof(i_0_6968,plain,
    ! [X28606,X28607,X28608,X28609,X28610] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28610,X28610)),hAPP(hAPP(c_Product__Type_OPair(X28610,X28610),X28609),X28608)),X28607))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28610,X28610)),hAPP(hAPP(c_Product__Type_OPair(X28610,X28610),X28608),X28606)),c_Transitive__Closure_Ortrancl(X28610,X28607)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28610,X28610)),hAPP(hAPP(c_Product__Type_OPair(X28610,X28610),X28609),X28606)),c_Transitive__Closure_Ortrancl(X28610,X28607))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__into__rtrancl])]) ).

fof(i_0_6969,plain,
    ! [X28601,X28602,X28603,X28604,X28605] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28605,X28605)),hAPP(hAPP(c_Product__Type_OPair(X28605,X28605),X28604),X28603)),c_Transitive__Closure_Ortrancl(X28605,X28602)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28605,X28605)),hAPP(hAPP(c_Product__Type_OPair(X28605,X28605),X28603),X28601)),X28602))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28605,X28605)),hAPP(hAPP(c_Product__Type_OPair(X28605,X28605),X28604),X28601)),c_Transitive__Closure_Ortrancl(X28605,X28602))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__into__rtrancl])]) ).

fof(i_0_6970,plain,
    ! [X30700,X30701,X30702,X30703] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30703),tc_List_Olist(X30703))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30703),tc_List_Olist(X30703)),X30702),X30701)),c_List_Olistrel(X30703,X30700)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30703),tc_List_Olist(X30703))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30703),tc_List_Olist(X30703)),X30702),X30701)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X30703),c_List_Olistrel1(X30703,X30700)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__if__listrel])]) ).

fof(i_0_6971,plain,
    ! [X20691,X20692,X20693,X20694,X20695,X20696,X20697,X20698,X20699,X20700,X20701] :
      ( ~ c_Finite__Set_Ofolding(X20701,X20700,X20699,X20698)
      | hAPP(c_Fun_Ocomp(X20697,X20696,X20695,X20694),hAPP(c_Fun_Ocomp(X20693,X20697,X20695,X20692),X20691)) = hAPP(c_Fun_Ocomp(X20693,X20696,X20695,hAPP(c_Fun_Ocomp(X20697,X20696,X20693,X20694),X20692)),X20691) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comps_I1_J])]) ).

cnf(i_0_6972,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_5505]) ).

fof(i_0_6973,plain,
    ! [X22939,X22940,X22941,X22942,X22943,X22944] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22944),X22943)),X22942) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22941),X22940)),X22939)
      | ~ 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),X22941),X22940)),X22939)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22942),X22944))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22939))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22941))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22941),X22944))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22940),X22943)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma])]) ).

fof(i_0_6974,plain,
    ! [X25277] : 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)))),X25277)) = 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),X25277),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_6975,plain,
    ! [X30691,X30692,X30693,X30694] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30694),tc_List_Olist(X30694))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30694),tc_List_Olist(X30694)),X30693),X30692)),c_List_Olistrel1(X30694,X30691)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30694),tc_List_Olist(X30694))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30694),tc_List_Olist(X30694)),X30693),X30692)),c_List_Olistrel(X30694,c_Transitive__Closure_Ortrancl(X30694,X30691)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__reflcl__if__listrel1])]) ).

fof(i_0_6976,plain,
    ! [X30574,X30575,X30576,X30577] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30577),tc_List_Olist(X30577))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30577),tc_List_Olist(X30577)),X30576),X30575)),c_List_Olexord(X30577,X30574)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30577),tc_List_Olist(X30577))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30577),tc_List_Olist(X30577)),X30576),X30575)),c_List_Olex(X30577,X30574))) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30577)),X30576) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30577)),X30575)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30577),tc_List_Olist(X30577))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30577),tc_List_Olist(X30577)),X30576),X30575)),c_List_Olex(X30577,X30574))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30577),tc_List_Olist(X30577))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30577),tc_List_Olist(X30577)),X30576),X30575)),c_List_Olexord(X30577,X30574)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30577)),X30576) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30577)),X30575)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30577),tc_List_Olist(X30577))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30577),tc_List_Olist(X30577)),X30576),X30575)),c_List_Olex(X30577,X30574))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__lex])])]) ).

fof(i_0_6977,plain,
    ! [X32255,X32256,X32257,X32258,X32259] : hAPP(c_List_Ofilter(X32259,X32258),hAPP(hAPP(c_List_Omap(X32257,X32259),X32256),X32255)) = hAPP(hAPP(c_List_Omap(X32257,X32259),X32256),hAPP(c_List_Ofilter(X32257,hAPP(c_Fun_Ocomp(X32259,tc_HOL_Obool,X32257,X32258),X32256)),X32255)),
    inference(variable_rename,[status(thm)],[fact_filter__map]) ).

fof(i_0_6978,plain,
    ! [X28260,X28261,X28262] :
      ( ( hAPP(X28261,esk301_3(X28260,X28261,X28262)) != hAPP(X28261,esk302_3(X28260,X28261,X28262))
        | c_Wellfounded_OwfP(X28262,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28260,tc_fun(X28262,tc_fun(X28262,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X28260,tc_HOL_Obool))),X28261))
        | ~ c_Wellfounded_OwfP(X28262,hAPP(X28261,esk300_3(X28260,X28261,X28262))) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28262,tc_HOL_Obool)),c_Predicate_ODomainP(X28262,X28262,hAPP(X28261,esk301_3(X28260,X28261,X28262)))),c_Predicate_ORangeP(X28262,X28262,hAPP(X28261,esk302_3(X28260,X28261,X28262)))) != c_Orderings_Obot__class_Obot(tc_fun(X28262,tc_HOL_Obool))
        | c_Wellfounded_OwfP(X28262,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28260,tc_fun(X28262,tc_fun(X28262,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X28260,tc_HOL_Obool))),X28261))
        | ~ c_Wellfounded_OwfP(X28262,hAPP(X28261,esk300_3(X28260,X28261,X28262))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__SUP])])])]) ).

fof(i_0_6979,plain,
    ! [X32622,X32623,X32624] : c_List_Opartition(X32624,X32623,X32622) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32624),tc_List_Olist(X32624)),hAPP(c_List_Ofilter(X32624,X32623),X32622)),hAPP(c_List_Ofilter(X32624,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X32624,c_fNot),X32623)),X32622)),
    inference(variable_rename,[status(thm)],[fact_partition__filter__conv]) ).

cnf(i_0_6980,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_5506]) ).

fof(i_0_6981,plain,
    ! [X31497,X31498,X31499] :
      ( ( 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),esk422_3(X31497,X31498,X31499)),esk423_3(X31497,X31498,X31499))))
        | hBOOL(hAPP(hAPP(X31497,X31499),X31498))
        | ~ 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),X31499),X31498))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk422_3(X31497,X31498,X31499)),esk423_3(X31497,X31498,X31499)))
        | hBOOL(hAPP(hAPP(X31497,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk422_3(X31497,X31498,X31499)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk423_3(X31497,X31498,X31499)))
        | hBOOL(hAPP(hAPP(X31497,X31499),X31498))
        | ~ 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),X31499),X31498))) )
      & ( ~ hBOOL(hAPP(hAPP(X31497,esk422_3(X31497,X31498,X31499)),esk423_3(X31497,X31498,X31499)))
        | hBOOL(hAPP(hAPP(X31497,X31499),X31498))
        | ~ 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),X31499),X31498))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upto_Opinduct])])])]) ).

fof(i_0_6982,plain,
    ! [X33224,X33225,X33226,X33227,X33228,X33229,X33230] :
      ( ( ~ c_List_Olist__all2(X33230,X33229,X33228,hAPP(hAPP(c_List_Omap(X33227,X33230),X33226),X33225),X33224)
        | c_List_Olist__all2(X33227,X33229,hAPP(hAPP(c_COMBB(X33230,tc_fun(X33229,tc_HOL_Obool),X33227),X33228),X33226),X33225,X33224) )
      & ( ~ c_List_Olist__all2(X33227,X33229,hAPP(hAPP(c_COMBB(X33230,tc_fun(X33229,tc_HOL_Obool),X33227),X33228),X33226),X33225,X33224)
        | c_List_Olist__all2(X33230,X33229,X33228,hAPP(hAPP(c_List_Omap(X33227,X33230),X33226),X33225),X33224) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__map1])]) ).

fof(i_0_6983,plain,
    ! [X31240,X31241,X31242,X31243,X31244,X31245] : c_Map_Omap__add(X31245,X31244,X31243,c_Map_Omap__upds(X31245,X31244,X31242,X31241,X31240)) = c_Map_Omap__upds(X31245,X31244,c_Map_Omap__add(X31245,X31244,X31243,X31242),X31241,X31240),
    inference(variable_rename,[status(thm)],[fact_map__add__upds]) ).

cnf(i_0_6984,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_5507]) ).

fof(i_0_6985,plain,
    ! [X33380,X33381,X33382,X33383,X33384] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X33384,X33383)),hAPP(X33384,X33382)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33381,X33381)),hAPP(hAPP(c_Product__Type_OPair(X33381,X33381),X33383),X33382)),c_List_Omeasures(X33381,X33380)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X33381,X33381)),hAPP(hAPP(c_Product__Type_OPair(X33381,X33381),X33383),X33382)),c_List_Omeasures(X33381,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X33381,tc_Nat_Onat)),X33384),X33380)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_measures__lesseq])]) ).

fof(i_0_6986,plain,
    ! [X22826,X22827] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22827),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22827),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22827),c_Groups_Oone__class_Oone(X22827)),X22826)),X22826)),c_Groups_Ozero__class_Ozero(X22827)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22827),X22826),c_Groups_Ozero__class_Ozero(X22827)))
        | ~ hBOOL(hAPP(hAPP(c_member(X22827),X22826),c_Int_Oring__1__class_OInts(X22827)))
        | ~ class_Rings_Olinordered__idom(X22827) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22827),X22826),c_Groups_Ozero__class_Ozero(X22827)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22827),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22827),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22827),c_Groups_Oone__class_Oone(X22827)),X22826)),X22826)),c_Groups_Ozero__class_Ozero(X22827)))
        | ~ hBOOL(hAPP(hAPP(c_member(X22827),X22826),c_Int_Oring__1__class_OInts(X22827)))
        | ~ class_Rings_Olinordered__idom(X22827) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__less__0])])]) ).

cnf(i_0_6987,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_5508]) ).

fof(i_0_6988,plain,
    ! [X23497,X23498,X23499] : 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),X23499),X23498)),X23498)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23499,X23498))),X23497) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23499),X23497),
    inference(variable_rename,[status(thm)],[fact_zdiv__zmod__equality2]) ).

cnf(i_0_6989,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk480_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_5509]) ).

fof(i_0_6990,plain,
    ! [X31273,X31274,X31275,X31276,X31277] : c_Map_Odom(X31277,X31276,c_Map_Omap__upds(X31277,X31276,X31275,X31274,X31273)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31277,tc_HOL_Obool)),hAPP(c_List_Oset(X31277),hAPP(hAPP(c_List_Otake(X31277),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31276)),X31273)),X31274))),c_Map_Odom(X31277,X31276,X31275)),
    inference(variable_rename,[status(thm)],[fact_dom__map__upds]) ).

cnf(i_0_6991,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_5510]) ).

fof(i_0_6992,plain,
    ! [X33023,X33024,X33025] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33025)),c_List_OtakeWhile(X33025,X33024,X33023))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33025)),X33023)))
      | ~ hBOOL(hAPP(X33024,hAPP(hAPP(c_List_Onth(X33025),X33023),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33025)),c_List_OtakeWhile(X33025,X33024,X33023))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5511])]) ).

cnf(i_0_6993,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_5512]) ).

cnf(i_0_6994,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk335_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_5513]) ).

fof(i_0_6995,plain,
    ! [X32078,X32079,X32080,X32081] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X32081)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X32080,X32081),hAPP(c_List_Oset(X32080),X32079)),X32078) = hAPP(c_List_Ofoldl(X32081,X32080,hAPP(c_COMBC(X32080,X32081,X32081),hAPP(hAPP(c_COMBB(X32081,tc_fun(X32081,X32081),X32080),c_Lattices_Osemilattice__inf__class_Oinf(X32081)),X32078)),c_Orderings_Otop__class_Otop(X32081)),X32079) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__set__fold])]) ).

fof(i_0_6996,plain,
    ! [X32074,X32075,X32076,X32077] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X32077)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X32076,X32077),hAPP(c_List_Oset(X32076),X32075)),X32074) = hAPP(c_List_Ofoldl(X32077,X32076,hAPP(c_COMBC(X32076,X32077,X32077),hAPP(hAPP(c_COMBB(X32077,tc_fun(X32077,X32077),X32076),c_Lattices_Osemilattice__sup__class_Osup(X32077)),X32074)),c_Orderings_Obot__class_Obot(X32077)),X32075) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUPR__set__fold])]) ).

cnf(i_0_6997,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_5514]) ).

fof(i_0_6998,plain,
    ! [X28252,X28253,X28254,X28255] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28255),esk298_4(X28252,X28253,X28254,X28255)),X28254))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X28253),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28255,tc_fun(X28253,tc_HOL_Obool)),X28254),X28252)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28255),X28254)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28253),hAPP(X28252,esk298_4(X28252,X28253,X28254,X28255))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X28253),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28255,tc_fun(X28253,tc_HOL_Obool)),X28254),X28252)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28255),X28254)) ) ),
    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_6999,plain,
    ! [X20478,X20479,X20480,X20481,X20482] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20479),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20481,tc_fun(X20479,tc_HOL_Obool)),X20480),X20478)))
        | ~ hBOOL(hAPP(hAPP(c_member(X20481),X20482),X20480))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20479),hAPP(X20478,X20482)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20481),X20480)) )
      & ( hBOOL(hAPP(hAPP(c_member(X20481),esk75_4(X20478,X20479,X20480,X20481)),X20480))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20479),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20481,tc_fun(X20479,tc_HOL_Obool)),X20480),X20478)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20481),X20480)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20479),hAPP(X20478,esk75_4(X20478,X20479,X20480,X20481))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20479),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20481,tc_fun(X20479,tc_HOL_Obool)),X20480),X20478)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20481),X20480)) ) ),
    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_7000,plain,
    ! [X27311,X27312,X27313,X27314,X27315,X27316,X27317] : hAPP(hAPP(c_Relation_Orel__comp(X27317,X27316,X27315),X27314),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27313,tc_fun(tc_prod(X27316,X27315),tc_HOL_Obool)),X27312),X27311)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27313,tc_fun(tc_prod(X27317,X27315),tc_HOL_Obool)),X27312),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X27316,X27315),tc_HOL_Obool),tc_fun(tc_prod(X27317,X27315),tc_HOL_Obool),X27313),hAPP(c_Relation_Orel__comp(X27317,X27316,X27315),X27314)),X27311)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__UNION__distrib]) ).

fof(i_0_7001,plain,
    ! [X18254,X18255,X18256,X18257,X18258,X18259] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X18259),X18258),X18257))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18256,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18259,X18256,X18255),X18257)),hAPP(X18254,hAPP(c_Set_Oimage(X18259,X18256,X18255),X18257))))
      | hBOOL(hAPP(hAPP(c_member(X18256),hAPP(X18255,X18258)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X18256,tc_HOL_Obool),X18254))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_weak__coinduct__image])]) ).

fof(i_0_7002,plain,
    ! [X18877,X18878,X18879,X18880,X18881,X18882,X18883] : hAPP(c_Fun_Ocomp(X18883,X18882,X18881,X18880),hAPP(c_Fun_Ocomp(X18879,X18883,X18881,X18878),X18877)) = hAPP(c_Fun_Ocomp(X18879,X18882,X18881,hAPP(c_Fun_Ocomp(X18883,X18882,X18879,X18880),X18878)),X18877),
    inference(variable_rename,[status(thm)],[fact_o__assoc]) ).

fof(i_0_7003,plain,
    ! [X20573,X20574,X20575,X20576] :
      ( hAPP(c_Set_Oimage(X20576,X20575,X20574),c_Orderings_Otop__class_Otop(tc_fun(X20576,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X20575,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20575,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20575,tc_HOL_Obool)),hAPP(c_Set_Oimage(X20576,X20575,X20574),X20573))),hAPP(c_Set_Oimage(X20576,X20575,X20574),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20576,tc_HOL_Obool)),X20573)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__Compl__image__subset])]) ).

fof(i_0_7004,plain,
    ! [X24081,X24082,X24083,X24084,X24085,X24086] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24086,X24086)),hAPP(hAPP(c_Product__Type_OPair(X24086,X24086),X24085),X24084)),hAPP(hAPP(c_Relation_Oinv__image(X24083,X24086),X24082),X24081)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X24083,X24083)),hAPP(hAPP(c_Product__Type_OPair(X24083,X24083),hAPP(X24081,X24085)),hAPP(X24081,X24084))),X24082)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24083,X24083)),hAPP(hAPP(c_Product__Type_OPair(X24083,X24083),hAPP(X24081,X24085)),hAPP(X24081,X24084))),X24082))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X24086,X24086)),hAPP(hAPP(c_Product__Type_OPair(X24086,X24086),X24085),X24084)),hAPP(hAPP(c_Relation_Oinv__image(X24083,X24086),X24082),X24081))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__inv__image])]) ).

fof(i_0_7005,plain,
    ! [X20621,X20622,X20623,X20624,X20625,X20626] :
      ( ~ c_Finite__Set_Ofolding(X20626,X20625,X20624,X20623)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20626),X20622))
      | ~ hBOOL(hAPP(hAPP(c_member(X20626),X20621),X20622))
      | hAPP(X20623,X20622) = hAPP(c_Fun_Ocomp(X20625,X20625,X20625,hAPP(X20623,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20626,tc_HOL_Obool)),X20622),hAPP(hAPP(c_Set_Oinsert(X20626),X20621),c_Orderings_Obot__class_Obot(tc_fun(X20626,tc_HOL_Obool)))))),hAPP(X20624,X20621)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oremove])]) ).

fof(i_0_7006,plain,
    ! [X27820,X27821,X27822,X27823,X27824,X27825] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27825,X27824),tc_HOL_Obool)),X27823),hAPP(hAPP(c_Product__Type_OSigma(X27825,X27824),X27822),hAPP(c_COMBK(tc_fun(X27824,tc_HOL_Obool),X27825),X27821))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27824,tc_HOL_Obool)),hAPP(c_Relation_OImage(X27825,X27824,X27823),X27820)),X27821)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__subset])]) ).

fof(i_0_7007,plain,
    ! [X31967,X31968,X31969] : hAPP(c_List_Otl(X31969),hAPP(hAPP(c_List_Oappend(X31969),X31968),X31967)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X31969),X31969,hAPP(c_List_Otl(X31969),X31967),hAPP(c_COMBK(tc_fun(tc_List_Olist(X31969),tc_List_Olist(X31969)),X31969),hAPP(hAPP(c_COMBC(tc_List_Olist(X31969),tc_List_Olist(X31969),tc_List_Olist(X31969)),c_List_Oappend(X31969)),X31967))),X31968),
    inference(variable_rename,[status(thm)],[fact_tl__append]) ).

fof(i_0_7008,plain,
    ! [X33775,X33776,X33777,X33778] : c_New__Random__Sequence_Opos__map(X33778,X33777,X33776,X33775) = c_New__Random__Sequence_Opos__bind(X33778,X33777,X33775,hAPP(c_Fun_Ocomp(X33777,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(X33777))))),X33778,c_New__Random__Sequence_Opos__single(X33777)),X33776)),
    inference(variable_rename,[status(thm)],[fact_pos__map__def]) ).

fof(i_0_7009,plain,
    ! [X20603,X20604,X20605,X20606] :
      ( ~ c_Fun_Oinj__on(X20606,X20605,X20604,c_Orderings_Otop__class_Otop(tc_fun(X20606,tc_HOL_Obool)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20605,tc_HOL_Obool)),hAPP(c_Set_Oimage(X20606,X20605,X20604),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20606,tc_HOL_Obool)),X20603))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20605,tc_HOL_Obool)),hAPP(c_Set_Oimage(X20606,X20605,X20604),X20603)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__Compl__subset])]) ).

fof(i_0_7010,plain,
    ! [X20654,X20655,X20656,X20657,X20658,X20659] :
      ( ~ c_Finite__Set_Ofolding(X20659,X20658,X20657,X20656)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20659),X20655))
      | hAPP(X20656,hAPP(hAPP(c_Set_Oinsert(X20659),X20654),X20655)) = hAPP(c_Fun_Ocomp(X20658,X20658,X20658,hAPP(X20656,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20659,tc_HOL_Obool)),X20655),hAPP(hAPP(c_Set_Oinsert(X20659),X20654),c_Orderings_Obot__class_Obot(tc_fun(X20659,tc_HOL_Obool)))))),hAPP(X20657,X20654)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oinsert__remove])]) ).

fof(i_0_7011,plain,
    ! [X33177,X33178,X33179,X33180,X33181,X33182,X33183,X33184] :
      ( ~ c_List_Olist__all2(X33184,X33183,X33182,X33181,X33180)
      | ~ hBOOL(hAPP(hAPP(X33182,X33179),X33178))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33177),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33183)),X33180)))
      | c_List_Olist__all2(X33184,X33183,X33182,hAPP(hAPP(c_List_Olist__update(X33184,X33181),X33177),X33179),hAPP(hAPP(c_List_Olist__update(X33183,X33180),X33177),X33178)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__update__cong2])]) ).

fof(i_0_7012,plain,
    ! [X33185,X33186,X33187,X33188,X33189,X33190,X33191,X33192] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33192),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33191)),X33190)))
      | ~ c_List_Olist__all2(X33191,X33189,X33188,X33190,X33187)
      | ~ hBOOL(hAPP(hAPP(X33188,X33186),X33185))
      | c_List_Olist__all2(X33191,X33189,X33188,hAPP(hAPP(c_List_Olist__update(X33191,X33190),X33192),X33186),hAPP(hAPP(c_List_Olist__update(X33189,X33187),X33192),X33185)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__update__cong])]) ).

fof(i_0_7013,plain,
    ! [X31125,X31126,X31127,X31128] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31128),X31127))
      | hBOOL(hAPP(hAPP(c_member(X31128),X31126),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31128,tc_HOL_Obool)),hAPP(c_List_Oset(X31128),X31127)),hAPP(hAPP(c_Set_Oinsert(X31128),hAPP(hAPP(c_List_Onth(X31128),X31127),X31125)),c_Orderings_Obot__class_Obot(tc_fun(X31128,tc_HOL_Obool))))))
      | hBOOL(hAPP(c_List_Odistinct(X31128),hAPP(hAPP(c_List_Olist__update(X31128,X31127),X31125),X31126))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5515])]) ).

fof(i_0_7014,plain,
    ! [X21245,X21246,X21247,X21248] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21248),hAPP(c_Set_Oimage(X21247,X21248,X21246),X21245))),hAPP(c_Finite__Set_Ocard(X21247),X21245)))
      | ~ c_Fun_Oinj__on(X21247,X21248,X21246,X21245) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5516])]) ).

fof(i_0_7015,plain,
    ! [X33572,X33573,X33574,X33575] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33574),esk501_4(X33572,X33573,X33574,X33575)),X33573))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X33575),c_Groups_Ozero__class_Ozero(X33575)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X33574,X33575),X33572),X33573)))
        | ~ class_Rings_Olinordered__semidom(X33575) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X33575),c_Groups_Ozero__class_Ozero(X33575)),hAPP(X33572,esk501_4(X33572,X33573,X33574,X33575))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X33575),c_Groups_Ozero__class_Ozero(X33575)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X33574,X33575),X33572),X33573)))
        | ~ class_Rings_Olinordered__semidom(X33575) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__pos])])])]) ).

fof(i_0_7016,plain,
    ! [X33653,X33654,X33655,X33656] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33655),esk510_4(X33653,X33654,X33655,X33656)),X33654))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33656),c_Groups_Ozero__class_Ozero(X33656)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X33655,X33656),X33653),X33654)))
        | ~ class_Rings_Olinordered__semidom(X33656) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33656),c_Groups_Ozero__class_Ozero(X33656)),hAPP(X33653,esk510_4(X33653,X33654,X33655,X33656))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33656),c_Groups_Ozero__class_Ozero(X33656)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X33655,X33656),X33653),X33654)))
        | ~ class_Rings_Olinordered__semidom(X33656) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__nonneg])])])]) ).

fof(i_0_7017,plain,
    ! [X33892,X33893,X33894,X33895,X33896] : c_Predicate_Oconversep(X33896,X33895,c_Predicate_Opred__comp(X33896,X33894,X33895,X33893,X33892)) = c_Predicate_Opred__comp(X33895,X33894,X33896,c_Predicate_Oconversep(X33894,X33895,X33892),c_Predicate_Oconversep(X33896,X33894,X33893)),
    inference(variable_rename,[status(thm)],[fact_converse__pred__comp]) ).

cnf(i_0_7018,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]) ).

cnf(i_0_7019,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_5517]) ).

fof(i_0_7020,plain,
    ! [X20716,X20717,X20718,X20719,X20720,X20721,X20722,X20723] :
      ( ~ c_Finite__Set_Ofolding(X20723,X20722,X20721,X20720)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20723),X20719))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20723),X20718))
      | hAPP(c_Fun_Ocomp(X20722,X20722,X20717,hAPP(X20720,X20718)),hAPP(c_Fun_Ocomp(X20722,X20722,X20717,hAPP(X20720,X20719)),X20716)) = hAPP(c_Fun_Ocomp(X20722,X20722,X20717,hAPP(X20720,X20719)),hAPP(c_Fun_Ocomp(X20722,X20722,X20717,hAPP(X20720,X20718)),X20716)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp_H_H])]) ).

fof(i_0_7021,plain,
    ! [X28329,X28330,X28331,X28332] : hAPP(c_Hilbert__Choice_Oinv__into(X28332,X28331,c_Orderings_Otop__class_Otop(tc_fun(X28332,tc_HOL_Obool)),X28330),X28329) = c_Hilbert__Choice_OEps(X28332,hAPP(hAPP(c_COMBC(X28332,X28331,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X28331,tc_fun(X28331,tc_HOL_Obool),X28332),c_fequal),X28330)),X28329)),
    inference(variable_rename,[status(thm)],[fact_inv__def]) ).

fof(i_0_7022,plain,
    ! [X27971,X27972,X27973,X27974] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27974),esk276_4(X27971,X27972,X27973,X27974)),X27973))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27974,X27972)),hAPP(hAPP(c_Product__Type_OSigma(X27974,X27972),X27973),X27971)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27974),X27973)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27972),hAPP(X27971,esk276_4(X27971,X27972,X27973,X27974))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27974,X27972)),hAPP(hAPP(c_Product__Type_OSigma(X27974,X27972),X27973),X27971)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27974),X27973)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__SigmaI])])])]) ).

fof(i_0_7023,plain,
    ! [X22540,X22541,X22542,X22543,X22544,X22545] :
      ( ~ class_Rings_Olinordered__semiring__1__strict(X22545)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22545),X22544),X22543))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22545),X22542),X22543))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22545),c_Groups_Ozero__class_Ozero(X22545)),X22541))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22545),c_Groups_Ozero__class_Ozero(X22545)),X22540))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22545),X22541),X22540) != c_Groups_Oone__class_Oone(X22545)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22545),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22545),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22545),X22541),X22544)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22545),X22540),X22542))),X22543)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__lt])]) ).

fof(i_0_7024,plain,
    ! [X22520,X22521,X22522,X22523,X22524,X22525] :
      ( ~ class_Rings_Olinordered__semiring__1(X22525)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22525),X22524),X22523))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22525),X22522),X22523))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22525),c_Groups_Ozero__class_Ozero(X22525)),X22521))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22525),c_Groups_Ozero__class_Ozero(X22525)),X22520))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22525),X22521),X22520) != c_Groups_Oone__class_Oone(X22525)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22525),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22525),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22525),X22521),X22524)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22525),X22520),X22522))),X22523)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__le])]) ).

fof(i_0_7025,plain,
    ! [X26283,X26284,X26285,X26286] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk192_4(X26283,X26284,X26285,X26286)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26285)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26286),X26284))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26286),X26285)),X26284))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26284),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26283))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26285)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk193_4(X26283,X26284,X26285,X26286)),X26283))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26286),X26284))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26286),X26285)),X26284))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26284),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26283))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26285)) )
      & ( X26286 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk193_4(X26283,X26284,X26285,X26286)),esk192_4(X26283,X26284,X26285,X26286))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26286),X26284))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26286),X26285)),X26284))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26284),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26283))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26285)) ) ),
    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_7026,plain,
    ! [X30464,X30465,X30466,X30467,X30468] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30468),hAPP(hAPP(c_List_Omap(tc_prod(X30468,X30467),X30468),c_Product__Type_Ofst(X30468,X30467)),X30466)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30468,X30467)),hAPP(hAPP(c_Product__Type_OPair(X30468,X30467),X30465),X30464)),hAPP(c_List_Oset(tc_prod(X30468,X30467)),X30466)))
      | hAPP(hAPP(c_Map_Omap__of(X30468,X30467),X30466),X30465) = hAPP(c_Option_Ooption_OSome(X30467),X30464) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__is__SomeI])]) ).

fof(i_0_7027,plain,
    ! [X30459,X30460,X30461,X30462,X30463] :
      ( ( hAPP(hAPP(c_Map_Omap__of(X30463,X30462),X30461),X30460) != hAPP(c_Option_Ooption_OSome(X30462),X30459)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X30463,X30462)),hAPP(hAPP(c_Product__Type_OPair(X30463,X30462),X30460),X30459)),hAPP(c_List_Oset(tc_prod(X30463,X30462)),X30461)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30463),hAPP(hAPP(c_List_Omap(tc_prod(X30463,X30462),X30463),c_Product__Type_Ofst(X30463,X30462)),X30461))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30463,X30462)),hAPP(hAPP(c_Product__Type_OPair(X30463,X30462),X30460),X30459)),hAPP(c_List_Oset(tc_prod(X30463,X30462)),X30461)))
        | hAPP(hAPP(c_Map_Omap__of(X30463,X30462),X30461),X30460) = hAPP(c_Option_Ooption_OSome(X30462),X30459)
        | ~ hBOOL(hAPP(c_List_Odistinct(X30463),hAPP(hAPP(c_List_Omap(tc_prod(X30463,X30462),X30463),c_Product__Type_Ofst(X30463,X30462)),X30461))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__eq__Some__iff])])]) ).

fof(i_0_7028,plain,
    ! [X30454,X30455,X30456,X30457,X30458] :
      ( ( hAPP(c_Option_Ooption_OSome(X30457),X30455) != hAPP(hAPP(c_Map_Omap__of(X30458,X30457),X30456),X30454)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X30458,X30457)),hAPP(hAPP(c_Product__Type_OPair(X30458,X30457),X30454),X30455)),hAPP(c_List_Oset(tc_prod(X30458,X30457)),X30456)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30458),hAPP(hAPP(c_List_Omap(tc_prod(X30458,X30457),X30458),c_Product__Type_Ofst(X30458,X30457)),X30456))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30458,X30457)),hAPP(hAPP(c_Product__Type_OPair(X30458,X30457),X30454),X30455)),hAPP(c_List_Oset(tc_prod(X30458,X30457)),X30456)))
        | hAPP(c_Option_Ooption_OSome(X30457),X30455) = hAPP(hAPP(c_Map_Omap__of(X30458,X30457),X30456),X30454)
        | ~ hBOOL(hAPP(c_List_Odistinct(X30458),hAPP(hAPP(c_List_Omap(tc_prod(X30458,X30457),X30458),c_Product__Type_Ofst(X30458,X30457)),X30456))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Some__eq__map__of__iff])])]) ).

fof(i_0_7029,plain,
    ! [X33103,X33104,X33105,X33106] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33106),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33105)),X33104)))
        | c_List_OtakeWhile(X33105,X33103,X33104) = hAPP(hAPP(c_List_Otake(X33105),X33106),X33104)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk465_4(X33103,X33104,X33105,X33106)),X33106)) )
      & ( hBOOL(hAPP(X33103,hAPP(hAPP(c_List_Onth(X33105),X33104),X33106)))
        | c_List_OtakeWhile(X33105,X33103,X33104) = hAPP(hAPP(c_List_Otake(X33105),X33106),X33104)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk465_4(X33103,X33104,X33105,X33106)),X33106)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33106),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33105)),X33104)))
        | c_List_OtakeWhile(X33105,X33103,X33104) = hAPP(hAPP(c_List_Otake(X33105),X33106),X33104)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk465_4(X33103,X33104,X33105,X33106)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33105)),X33104))) )
      & ( hBOOL(hAPP(X33103,hAPP(hAPP(c_List_Onth(X33105),X33104),X33106)))
        | c_List_OtakeWhile(X33105,X33103,X33104) = hAPP(hAPP(c_List_Otake(X33105),X33106),X33104)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk465_4(X33103,X33104,X33105,X33106)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33105)),X33104))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33106),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33105)),X33104)))
        | c_List_OtakeWhile(X33105,X33103,X33104) = hAPP(hAPP(c_List_Otake(X33105),X33106),X33104)
        | ~ hBOOL(hAPP(X33103,hAPP(hAPP(c_List_Onth(X33105),X33104),esk465_4(X33103,X33104,X33105,X33106)))) )
      & ( hBOOL(hAPP(X33103,hAPP(hAPP(c_List_Onth(X33105),X33104),X33106)))
        | c_List_OtakeWhile(X33105,X33103,X33104) = hAPP(hAPP(c_List_Otake(X33105),X33106),X33104)
        | ~ hBOOL(hAPP(X33103,hAPP(hAPP(c_List_Onth(X33105),X33104),esk465_4(X33103,X33104,X33105,X33106)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5518])])])]) ).

fof(i_0_7030,plain,
    ! [X17775,X17776,X17777,X17778] :
      ( ~ c_Orderings_Oorder__class_Omono(tc_fun(X17778,tc_HOL_Obool),tc_fun(X17778,tc_HOL_Obool),X17777)
      | ~ hBOOL(hAPP(hAPP(c_member(X17778),X17776),X17775))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17778,tc_HOL_Obool)),X17775),hAPP(X17777,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17778,tc_HOL_Obool)),X17775),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X17778,tc_HOL_Obool),X17777)))))
      | hBOOL(hAPP(hAPP(c_member(X17778),X17776),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X17778,tc_HOL_Obool),X17777))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coinduct__set])]) ).

fof(i_0_7031,plain,
    ! [X20730,X20731,X20732,X20733,X20734,X20735,X20736,X20737] :
      ( ~ c_Finite__Set_Ofolding(X20737,X20736,X20735,X20734)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20737),X20733))
      | hAPP(c_Fun_Ocomp(X20736,X20736,X20732,hAPP(X20735,X20731)),hAPP(c_Fun_Ocomp(X20736,X20736,X20732,hAPP(X20734,X20733)),X20730)) = hAPP(c_Fun_Ocomp(X20736,X20736,X20732,hAPP(X20734,X20733)),hAPP(c_Fun_Ocomp(X20736,X20736,X20732,hAPP(X20735,X20731)),X20730)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp_H])]) ).

fof(i_0_7032,plain,
    ! [X31707,X31708,X31709,X31710,X31711,X31712,X31713,X31714] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31714,X31714)),hAPP(hAPP(c_Product__Type_OPair(X31714,X31714),X31713),X31712)),X31711))
      | X31710 != hAPP(hAPP(c_List_Oappend(X31714),X31709),hAPP(hAPP(c_List_Olist_OCons(X31714),X31713),X31708))
      | X31707 != hAPP(hAPP(c_List_Oappend(X31714),X31709),hAPP(hAPP(c_List_Olist_OCons(X31714),X31712),X31708))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31714),tc_List_Olist(X31714))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31714),tc_List_Olist(X31714)),X31710),X31707)),c_List_Olistrel1(X31714,X31711))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I])]) ).

cnf(i_0_7033,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_5519]) ).

fof(i_0_7034,plain,
    ! [X33296,X33297,X33298,X33299] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk474_4(X33296,X33297,X33298,X33299)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33299)),X33298)))
        | ~ hBOOL(hAPP(hAPP(c_member(X33299),X33296),hAPP(c_List_Oset(X33299),X33298)))
        | hBOOL(hAPP(X33297,X33296)) )
      & ( ~ hBOOL(hAPP(X33297,hAPP(hAPP(c_List_Onth(X33299),X33298),esk474_4(X33296,X33297,X33298,X33299))))
        | ~ hBOOL(hAPP(hAPP(c_member(X33299),X33296),hAPP(c_List_Oset(X33299),X33298)))
        | hBOOL(hAPP(X33297,X33296)) ) ),
    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_7035,plain,
    ! [X34232,X34233,X34234,X34235,X34236,X34237,X34238] :
      ( ( X34235 = X34233
        | c_Sum__Type_Osum_Osum__case(X34238,X34237,X34236,X34235,X34234) != c_Sum__Type_Osum_Osum__case(X34238,X34237,X34236,X34233,X34232) )
      & ( X34234 = X34232
        | c_Sum__Type_Osum_Osum__case(X34238,X34237,X34236,X34235,X34234) != c_Sum__Type_Osum_Osum__case(X34238,X34237,X34236,X34233,X34232) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__case__inject])])]) ).

fof(i_0_7036,plain,
    ! [X29869,X29870,X29871,X29872] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29872),esk380_4(X29869,X29870,X29871,X29872)),X29871))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29872),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X29872),X29870),X29869)),hAPP(hAPP(c_Finite__Set_Ofold(X29872,X29872,c_Lattices_Osemilattice__inf__class_Oinf(X29872)),X29869),X29871)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29872),X29871))
        | ~ class_Lattices_Osemilattice__inf(X29872) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29872),X29870),esk380_4(X29869,X29870,X29871,X29872)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29872),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X29872),X29870),X29869)),hAPP(hAPP(c_Finite__Set_Ofold(X29872,X29872,c_Lattices_Osemilattice__inf__class_Oinf(X29872)),X29869),X29871)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29872),X29871))
        | ~ class_Lattices_Osemilattice__inf(X29872) ) ),
    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_7037,plain,
    ! [X29860,X29861,X29862,X29863] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29863),esk378_4(X29860,X29861,X29862,X29863)),X29862))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29863),hAPP(hAPP(c_Orderings_Oord__class_Omin(X29863),X29861),X29860)),hAPP(hAPP(c_Finite__Set_Ofold(X29863,X29863,c_Orderings_Oord__class_Omin(X29863)),X29860),X29862)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29863),X29862))
        | ~ class_Orderings_Olinorder(X29863) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29863),X29861),esk378_4(X29860,X29861,X29862,X29863)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29863),hAPP(hAPP(c_Orderings_Oord__class_Omin(X29863),X29861),X29860)),hAPP(hAPP(c_Finite__Set_Ofold(X29863,X29863,c_Orderings_Oord__class_Omin(X29863)),X29860),X29862)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29863),X29862))
        | ~ class_Orderings_Olinorder(X29863) ) ),
    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_7038,plain,
    ! [X26509,X26510,X26511,X26512,X26513] :
      ( ~ class_Groups_Ocomm__monoid__add(X26513)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26513),X26512),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26511),X26510)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26509),X26510))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26513),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X26513,tc_Nat_Onat),X26512),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X26510))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26511),X26509)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__nat__ivl])]) ).

fof(i_0_7039,plain,
    ! [X28583,X28584,X28585,X28586] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28586,X28586)),X28585),c_Transitive__Closure_Ortrancl(X28586,X28584)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28586,X28586)),X28585),c_Transitive__Closure_Ortrancl(X28586,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28586,X28586),tc_HOL_Obool)),X28584),X28583)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28586,X28586)),X28585),c_Transitive__Closure_Ortrancl(X28586,X28583)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28586,X28586)),X28585),c_Transitive__Closure_Ortrancl(X28586,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28586,X28586),tc_HOL_Obool)),X28584),X28583)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rtrancl__UnI])])]) ).

fof(i_0_7040,plain,
    ! [X20677,X20678,X20679,X20680,X20681,X20682,X20683,X20684] :
      ( ~ c_Finite__Set_Ofolding(X20684,X20683,X20682,X20681)
      | hAPP(c_Fun_Ocomp(X20683,X20683,X20680,hAPP(X20682,X20679)),hAPP(c_Fun_Ocomp(X20683,X20683,X20680,hAPP(X20682,X20678)),X20677)) = hAPP(c_Fun_Ocomp(X20683,X20683,X20680,hAPP(X20682,X20678)),hAPP(c_Fun_Ocomp(X20683,X20683,X20680,hAPP(X20682,X20679)),X20677)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp])]) ).

cnf(i_0_7041,plain,
    ( c_List_OdropWhile(X4,X1,hAPP(hAPP(c_List_Oappend(X4),X3),X2)) = c_List_OdropWhile(X4,X1,X2)
    | ~ hBOOL(hAPP(X1,esk480_4(X2,X1,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_5509]) ).

fof(i_0_7042,plain,
    ! [X18263,X18264,X18265,X18266,X18267] :
      ( ~ c_Orderings_Oorder__class_Omono(tc_fun(X18267,tc_HOL_Obool),tc_fun(X18266,tc_HOL_Obool),X18265)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18266,tc_HOL_Obool)),hAPP(X18265,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18267,tc_HOL_Obool)),X18264),X18263))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18266,tc_HOL_Obool)),hAPP(X18265,X18264)),hAPP(X18265,X18263)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mono__Int])]) ).

fof(i_0_7043,plain,
    ! [X19289,X19290,X19291,X19292,X19294,X19295] :
      ( ( X19289 = hAPP(X19290,esk40_4(X19289,X19290,X19291,X19292))
        | ~ hBOOL(hAPP(hAPP(c_member(X19291),X19289),hAPP(c_Set_Oimage(X19292,X19291,X19290),c_Orderings_Otop__class_Otop(tc_fun(X19292,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X19292,X19291,X19290,c_Orderings_Otop__class_Otop(tc_fun(X19292,tc_HOL_Obool))) )
      & ( X19289 != hAPP(X19290,X19294)
        | X19294 = esk40_4(X19289,X19290,X19291,X19292)
        | ~ hBOOL(hAPP(hAPP(c_member(X19291),X19289),hAPP(c_Set_Oimage(X19292,X19291,X19290),c_Orderings_Otop__class_Otop(tc_fun(X19292,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X19292,X19291,X19290,c_Orderings_Otop__class_Otop(tc_fun(X19292,tc_HOL_Obool))) )
      & ( X19289 = hAPP(X19290,esk41_5(X19289,X19290,X19291,X19292,X19295))
        | X19289 != hAPP(X19290,X19295)
        | hBOOL(hAPP(hAPP(c_member(X19291),X19289),hAPP(c_Set_Oimage(X19292,X19291,X19290),c_Orderings_Otop__class_Otop(tc_fun(X19292,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X19292,X19291,X19290,c_Orderings_Otop__class_Otop(tc_fun(X19292,tc_HOL_Obool))) )
      & ( esk41_5(X19289,X19290,X19291,X19292,X19295) != X19295
        | X19289 != hAPP(X19290,X19295)
        | hBOOL(hAPP(hAPP(c_member(X19291),X19289),hAPP(c_Set_Oimage(X19292,X19291,X19290),c_Orderings_Otop__class_Otop(tc_fun(X19292,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X19292,X19291,X19290,c_Orderings_Otop__class_Otop(tc_fun(X19292,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_7044,plain,
    ! [X26633,X26634,X26635,X26636,X26637] :
      ( ~ class_Groups_Oab__group__add(X26637)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26636),X26635))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26636),X26634))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26636,X26637),X26633),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26636,tc_HOL_Obool)),X26635),X26634)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26637),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26637),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26636,X26637),X26633),X26635)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26636,X26637),X26633),X26634))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26636,X26637),X26633),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26636,tc_HOL_Obool)),X26635),X26634))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un])]) ).

fof(i_0_7045,plain,
    ! [X32946,X32947,X32948,X32949] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32949),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32948)),X32947)))
      | hAPP(c_List_Orev(X32948),hAPP(hAPP(c_List_Olist__update(X32948,X32947),X32949),X32946)) = hAPP(hAPP(c_List_Olist__update(X32948,hAPP(c_List_Orev(X32948),X32947)),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(X32948)),X32947)),X32949)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X32946) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__update])]) ).

cnf(i_0_7046,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_5473]) ).

cnf(i_0_7047,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_5472]) ).

fof(i_0_7048,plain,
    ! [X20560,X20561,X20562] : hAPP(c_Set_OCollect(X20562),hAPP(hAPP(c_COMBS(X20562,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X20562),c_fimplies),X20561)),X20560)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20562,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20562,tc_HOL_Obool)),hAPP(c_Set_OCollect(X20562),X20561))),hAPP(c_Set_OCollect(X20562),X20560)),
    inference(variable_rename,[status(thm)],[fact_Collect__imp__eq]) ).

fof(i_0_7049,plain,
    ! [X24220,X24221,X24222,X24223] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),c_Groups_Ozero__class_Ozero(X24223)),X24221))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),X24222),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24223),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)),X24221)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24223),X24222),X24221)),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24223)
        | ~ class_Int_Onumber(X24223) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),X24221),c_Groups_Ozero__class_Ozero(X24223)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24223),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)),X24221)),X24222))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),c_Groups_Ozero__class_Ozero(X24223)),X24221))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24223),X24222),X24221)),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24223)
        | ~ class_Int_Onumber(X24223) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),X24221),c_Groups_Ozero__class_Ozero(X24223)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),c_Groups_Ozero__class_Ozero(X24223)),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),c_Groups_Ozero__class_Ozero(X24223)),X24221))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24223),X24222),X24221)),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24223)
        | ~ class_Int_Onumber(X24223) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),c_Groups_Ozero__class_Ozero(X24223)),X24221))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),c_Groups_Ozero__class_Ozero(X24223)),X24221))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24223),X24222),X24221)),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24223)
        | ~ class_Int_Onumber(X24223) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),X24221),c_Groups_Ozero__class_Ozero(X24223)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),X24221),c_Groups_Ozero__class_Ozero(X24223)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),c_Groups_Ozero__class_Ozero(X24223)),X24221))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24223),X24222),X24221)),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24223)
        | ~ class_Int_Onumber(X24223) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),c_Groups_Ozero__class_Ozero(X24223)),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),X24221),c_Groups_Ozero__class_Ozero(X24223)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),c_Groups_Ozero__class_Ozero(X24223)),X24221))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24223),X24222),X24221)),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24223)
        | ~ class_Int_Onumber(X24223) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),X24221),c_Groups_Ozero__class_Ozero(X24223)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24223),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)),X24221)),X24222))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),c_Groups_Ozero__class_Ozero(X24223)),X24221))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24223),X24222),X24221)),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24223)
        | ~ class_Int_Onumber(X24223) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),c_Groups_Ozero__class_Ozero(X24223)),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24223),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)),X24221)),X24222))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),c_Groups_Ozero__class_Ozero(X24223)),X24221))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24223),X24222),X24221)),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24223)
        | ~ class_Int_Onumber(X24223) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),c_Groups_Ozero__class_Ozero(X24223)),X24221))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),X24222),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24223),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)),X24221)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24223),X24222),X24221)),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24223)
        | ~ class_Int_Onumber(X24223) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),X24221),c_Groups_Ozero__class_Ozero(X24223)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),X24221),c_Groups_Ozero__class_Ozero(X24223)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),X24222),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24223),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)),X24221)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24223),X24222),X24221)),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24223)
        | ~ class_Int_Onumber(X24223) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),c_Groups_Ozero__class_Ozero(X24223)),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),X24221),c_Groups_Ozero__class_Ozero(X24223)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),X24222),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24223),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)),X24221)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24223),X24222),X24221)),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24223)
        | ~ class_Int_Onumber(X24223) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),X24221),c_Groups_Ozero__class_Ozero(X24223)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24223),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)),X24221)),X24222))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),X24222),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24223),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)),X24221)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24223),X24222),X24221)),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24223)
        | ~ class_Int_Onumber(X24223) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),c_Groups_Ozero__class_Ozero(X24223)),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24223),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)),X24221)),X24222))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),X24222),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24223),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)),X24221)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24223),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24223),X24222),X24221)),hAPP(c_Int_Onumber__class_Onumber__of(X24223),X24220)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24223)
        | ~ class_Int_Onumber(X24223) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5520])])]) ).

fof(i_0_7050,plain,
    ! [X24248,X24249,X24250,X24251] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24251),c_Groups_Ozero__class_Ozero(X24251)),X24249))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),X24250),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24251),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)),X24249)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24251),X24250),X24249)),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24251)
        | ~ class_Int_Onumber(X24251) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24251),X24249),c_Groups_Ozero__class_Ozero(X24251)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24251),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)),X24249)),X24250))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24251),c_Groups_Ozero__class_Ozero(X24251)),X24249))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24251),X24250),X24249)),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24251)
        | ~ class_Int_Onumber(X24251) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24251),X24249),c_Groups_Ozero__class_Ozero(X24251)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),c_Groups_Ozero__class_Ozero(X24251)),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24251),c_Groups_Ozero__class_Ozero(X24251)),X24249))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24251),X24250),X24249)),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24251)
        | ~ class_Int_Onumber(X24251) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24251),c_Groups_Ozero__class_Ozero(X24251)),X24249))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24251),c_Groups_Ozero__class_Ozero(X24251)),X24249))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24251),X24250),X24249)),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24251)
        | ~ class_Int_Onumber(X24251) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24251),X24249),c_Groups_Ozero__class_Ozero(X24251)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24251),X24249),c_Groups_Ozero__class_Ozero(X24251)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24251),c_Groups_Ozero__class_Ozero(X24251)),X24249))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24251),X24250),X24249)),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24251)
        | ~ class_Int_Onumber(X24251) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),c_Groups_Ozero__class_Ozero(X24251)),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24251),X24249),c_Groups_Ozero__class_Ozero(X24251)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24251),c_Groups_Ozero__class_Ozero(X24251)),X24249))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24251),X24250),X24249)),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24251)
        | ~ class_Int_Onumber(X24251) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24251),X24249),c_Groups_Ozero__class_Ozero(X24251)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24251),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)),X24249)),X24250))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24251),c_Groups_Ozero__class_Ozero(X24251)),X24249))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24251),X24250),X24249)),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24251)
        | ~ class_Int_Onumber(X24251) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),c_Groups_Ozero__class_Ozero(X24251)),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24251),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)),X24249)),X24250))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24251),c_Groups_Ozero__class_Ozero(X24251)),X24249))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24251),X24250),X24249)),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24251)
        | ~ class_Int_Onumber(X24251) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24251),c_Groups_Ozero__class_Ozero(X24251)),X24249))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),X24250),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24251),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)),X24249)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24251),X24250),X24249)),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24251)
        | ~ class_Int_Onumber(X24251) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24251),X24249),c_Groups_Ozero__class_Ozero(X24251)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24251),X24249),c_Groups_Ozero__class_Ozero(X24251)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),X24250),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24251),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)),X24249)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24251),X24250),X24249)),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24251)
        | ~ class_Int_Onumber(X24251) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),c_Groups_Ozero__class_Ozero(X24251)),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24251),X24249),c_Groups_Ozero__class_Ozero(X24251)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),X24250),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24251),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)),X24249)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24251),X24250),X24249)),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24251)
        | ~ class_Int_Onumber(X24251) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24251),X24249),c_Groups_Ozero__class_Ozero(X24251)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24251),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)),X24249)),X24250))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),X24250),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24251),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)),X24249)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24251),X24250),X24249)),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24251)
        | ~ class_Int_Onumber(X24251) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),c_Groups_Ozero__class_Ozero(X24251)),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24251),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)),X24249)),X24250))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),X24250),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24251),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)),X24249)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24251),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24251),X24250),X24249)),hAPP(c_Int_Onumber__class_Onumber__of(X24251),X24248)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24251)
        | ~ class_Int_Onumber(X24251) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5521])])]) ).

fof(i_0_7051,plain,
    ! [X28917,X28918,X28919,X28920,X28921,X28922,X28923,X28924,X28925] :
      ( ( ~ c_Relation_Osingle__valued(X28919,X28918,X28917)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28919,X28918)),hAPP(hAPP(c_Product__Type_OPair(X28919,X28918),X28920),X28921)),X28917))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28919,X28918)),hAPP(hAPP(c_Product__Type_OPair(X28919,X28918),X28920),X28922)),X28917))
        | X28921 = X28922 )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28925,X28924)),hAPP(hAPP(c_Product__Type_OPair(X28925,X28924),esk332_3(X28923,X28924,X28925)),esk333_3(X28923,X28924,X28925))),X28923))
        | c_Relation_Osingle__valued(X28925,X28924,X28923) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28925,X28924)),hAPP(hAPP(c_Product__Type_OPair(X28925,X28924),esk332_3(X28923,X28924,X28925)),esk334_3(X28923,X28924,X28925))),X28923))
        | c_Relation_Osingle__valued(X28925,X28924,X28923) )
      & ( esk333_3(X28923,X28924,X28925) != esk334_3(X28923,X28924,X28925)
        | c_Relation_Osingle__valued(X28925,X28924,X28923) ) ),
    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_7052,plain,
    ! [X24224,X24225,X24226,X24227] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),c_Groups_Ozero__class_Ozero(X24227)),X24224))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),X24224)),X24225))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24227),X24225),X24224)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24227)
        | ~ class_Int_Onumber(X24227) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),X24224),c_Groups_Ozero__class_Ozero(X24227)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),X24225),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),X24224)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),c_Groups_Ozero__class_Ozero(X24227)),X24224))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24227),X24225),X24224)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24227)
        | ~ class_Int_Onumber(X24227) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),X24224),c_Groups_Ozero__class_Ozero(X24227)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),c_Groups_Ozero__class_Ozero(X24227)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),c_Groups_Ozero__class_Ozero(X24227)),X24224))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24227),X24225),X24224)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24227)
        | ~ class_Int_Onumber(X24227) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),c_Groups_Ozero__class_Ozero(X24227)),X24224))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),c_Groups_Ozero__class_Ozero(X24227)),X24224))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24227),X24225),X24224)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24227)
        | ~ class_Int_Onumber(X24227) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),X24224),c_Groups_Ozero__class_Ozero(X24227)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),X24224),c_Groups_Ozero__class_Ozero(X24227)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),c_Groups_Ozero__class_Ozero(X24227)),X24224))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24227),X24225),X24224)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24227)
        | ~ class_Int_Onumber(X24227) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),c_Groups_Ozero__class_Ozero(X24227)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),X24224),c_Groups_Ozero__class_Ozero(X24227)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),c_Groups_Ozero__class_Ozero(X24227)),X24224))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24227),X24225),X24224)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24227)
        | ~ class_Int_Onumber(X24227) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),X24224),c_Groups_Ozero__class_Ozero(X24227)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),X24225),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),X24224)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),c_Groups_Ozero__class_Ozero(X24227)),X24224))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24227),X24225),X24224)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24227)
        | ~ class_Int_Onumber(X24227) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),c_Groups_Ozero__class_Ozero(X24227)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),X24225),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),X24224)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),c_Groups_Ozero__class_Ozero(X24227)),X24224))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24227),X24225),X24224)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24227)
        | ~ class_Int_Onumber(X24227) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),c_Groups_Ozero__class_Ozero(X24227)),X24224))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),X24224)),X24225))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24227),X24225),X24224)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24227)
        | ~ class_Int_Onumber(X24227) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),X24224),c_Groups_Ozero__class_Ozero(X24227)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),X24224),c_Groups_Ozero__class_Ozero(X24227)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),X24224)),X24225))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24227),X24225),X24224)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24227)
        | ~ class_Int_Onumber(X24227) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),c_Groups_Ozero__class_Ozero(X24227)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),X24224),c_Groups_Ozero__class_Ozero(X24227)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),X24224)),X24225))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24227),X24225),X24224)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24227)
        | ~ class_Int_Onumber(X24227) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),X24224),c_Groups_Ozero__class_Ozero(X24227)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),X24225),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),X24224)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),X24224)),X24225))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24227),X24225),X24224)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24227)
        | ~ class_Int_Onumber(X24227) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),c_Groups_Ozero__class_Ozero(X24227)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),X24225),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),X24224)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),X24224)),X24225))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24227),hAPP(c_Int_Onumber__class_Onumber__of(X24227),X24226)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24227),X24225),X24224)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24227)
        | ~ class_Int_Onumber(X24227) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5522])])]) ).

fof(i_0_7053,plain,
    ! [X24244,X24245,X24246,X24247] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24247),c_Groups_Ozero__class_Ozero(X24247)),X24244))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),X24244)),X24245))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24247),X24245),X24244)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24247)
        | ~ class_Int_Onumber(X24247) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24247),X24244),c_Groups_Ozero__class_Ozero(X24247)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),X24245),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),X24244)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24247),c_Groups_Ozero__class_Ozero(X24247)),X24244))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24247),X24245),X24244)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24247)
        | ~ class_Int_Onumber(X24247) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24247),X24244),c_Groups_Ozero__class_Ozero(X24247)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),c_Groups_Ozero__class_Ozero(X24247)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24247),c_Groups_Ozero__class_Ozero(X24247)),X24244))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24247),X24245),X24244)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24247)
        | ~ class_Int_Onumber(X24247) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24247),c_Groups_Ozero__class_Ozero(X24247)),X24244))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24247),c_Groups_Ozero__class_Ozero(X24247)),X24244))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24247),X24245),X24244)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24247)
        | ~ class_Int_Onumber(X24247) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24247),X24244),c_Groups_Ozero__class_Ozero(X24247)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24247),X24244),c_Groups_Ozero__class_Ozero(X24247)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24247),c_Groups_Ozero__class_Ozero(X24247)),X24244))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24247),X24245),X24244)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24247)
        | ~ class_Int_Onumber(X24247) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),c_Groups_Ozero__class_Ozero(X24247)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24247),X24244),c_Groups_Ozero__class_Ozero(X24247)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24247),c_Groups_Ozero__class_Ozero(X24247)),X24244))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24247),X24245),X24244)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24247)
        | ~ class_Int_Onumber(X24247) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24247),X24244),c_Groups_Ozero__class_Ozero(X24247)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),X24245),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),X24244)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24247),c_Groups_Ozero__class_Ozero(X24247)),X24244))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24247),X24245),X24244)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24247)
        | ~ class_Int_Onumber(X24247) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),c_Groups_Ozero__class_Ozero(X24247)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),X24245),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),X24244)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24247),c_Groups_Ozero__class_Ozero(X24247)),X24244))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24247),X24245),X24244)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24247)
        | ~ class_Int_Onumber(X24247) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24247),c_Groups_Ozero__class_Ozero(X24247)),X24244))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),X24244)),X24245))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24247),X24245),X24244)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24247)
        | ~ class_Int_Onumber(X24247) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24247),X24244),c_Groups_Ozero__class_Ozero(X24247)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24247),X24244),c_Groups_Ozero__class_Ozero(X24247)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),X24244)),X24245))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24247),X24245),X24244)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24247)
        | ~ class_Int_Onumber(X24247) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),c_Groups_Ozero__class_Ozero(X24247)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24247),X24244),c_Groups_Ozero__class_Ozero(X24247)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),X24244)),X24245))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24247),X24245),X24244)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24247)
        | ~ class_Int_Onumber(X24247) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24247),X24244),c_Groups_Ozero__class_Ozero(X24247)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),X24245),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),X24244)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),X24244)),X24245))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24247),X24245),X24244)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24247)
        | ~ class_Int_Onumber(X24247) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),c_Groups_Ozero__class_Ozero(X24247)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),X24245),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),X24244)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),X24244)),X24245))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24247),hAPP(c_Int_Onumber__class_Onumber__of(X24247),X24246)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24247),X24245),X24244)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24247)
        | ~ class_Int_Onumber(X24247) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5523])])]) ).

fof(i_0_7054,plain,
    ! [X23789,X23790,X23791,X23792,X23793] : c_Product__Type_Oprod_Oprod__size(X23793,X23792,X23791,X23790,X23789) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X23791,hAPP(c_Product__Type_Ofst(X23793,X23792),X23789))),hAPP(X23790,hAPP(c_Product__Type_Osnd(X23793,X23792),X23789)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_prod__size__simp]) ).

fof(i_0_7055,plain,
    ! [X26518,X26519,X26520,X26521,X26522] :
      ( ~ class_Groups_Ocomm__monoid__add(X26522)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26522),X26521),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26520),X26519),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26518),X26519))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26522),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X26522,tc_Nat_Onat),X26521),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X26519))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26520,X26518)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__nat__ivl])]) ).

fof(i_0_7056,plain,
    ! [X26277,X26278,X26279,X26280] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk190_4(X26277,X26278,X26279,X26280)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26279)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26278),X26280))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26278),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26280),X26279)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26278),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26277))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26279)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk191_4(X26277,X26278,X26279,X26280)),X26277))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26278),X26280))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26278),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26280),X26279)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26278),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26277))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26279)) )
      & ( X26280 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk191_4(X26277,X26278,X26279,X26280)),esk190_4(X26277,X26278,X26279,X26280))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26278),X26280))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26278),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26280),X26279)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26278),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26277))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26279)) ) ),
    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_7057,plain,
    ! [X27856,X27857,X27858,X27859] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27859),X27858))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27859,X27859),tc_HOL_Obool)),X27857),hAPP(hAPP(c_Product__Type_OSigma(X27859,X27859),X27858),hAPP(c_COMBK(tc_fun(X27859,tc_HOL_Obool),X27859),X27858))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27859,tc_HOL_Obool)),X27856),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27859),X27858),X27857)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27859),X27856)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__equiv__class])]) ).

fof(i_0_7058,plain,
    ! [X20035,X20036,X20037,X20038,X20039,X20040,X20041] :
      ( ~ c_Equiv__Relations_Oequiv(X20041,X20040,X20039)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X20041,tc_HOL_Obool)),X20038),hAPP(hAPP(c_Equiv__Relations_Oquotient(X20041),X20040),X20039)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X20041,tc_HOL_Obool)),X20037),hAPP(hAPP(c_Equiv__Relations_Oquotient(X20041),X20040),X20039)))
      | ~ hBOOL(hAPP(hAPP(c_member(X20041),X20036),X20038))
      | ~ hBOOL(hAPP(hAPP(c_member(X20041),X20035),X20037))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20041,X20041)),hAPP(hAPP(c_Product__Type_OPair(X20041,X20041),X20036),X20035)),X20039))
      | X20038 = X20037 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__eqI])]) ).

fof(i_0_7059,plain,
    ! [X20042,X20043,X20044,X20045,X20046,X20047,X20048] :
      ( ( X20045 != X20044
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X20048,X20048)),hAPP(hAPP(c_Product__Type_OPair(X20048,X20048),X20043),X20042)),X20046))
        | ~ hBOOL(hAPP(hAPP(c_member(X20048),X20042),X20044))
        | ~ hBOOL(hAPP(hAPP(c_member(X20048),X20043),X20045))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X20048,tc_HOL_Obool)),X20044),hAPP(hAPP(c_Equiv__Relations_Oquotient(X20048),X20047),X20046)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X20048,tc_HOL_Obool)),X20045),hAPP(hAPP(c_Equiv__Relations_Oquotient(X20048),X20047),X20046)))
        | ~ c_Equiv__Relations_Oequiv(X20048,X20047,X20046) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20048,X20048)),hAPP(hAPP(c_Product__Type_OPair(X20048,X20048),X20043),X20042)),X20046))
        | X20045 = X20044
        | ~ hBOOL(hAPP(hAPP(c_member(X20048),X20042),X20044))
        | ~ hBOOL(hAPP(hAPP(c_member(X20048),X20043),X20045))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X20048,tc_HOL_Obool)),X20044),hAPP(hAPP(c_Equiv__Relations_Oquotient(X20048),X20047),X20046)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X20048,tc_HOL_Obool)),X20045),hAPP(hAPP(c_Equiv__Relations_Oquotient(X20048),X20047),X20046)))
        | ~ c_Equiv__Relations_Oequiv(X20048,X20047,X20046) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__eq__iff])])]) ).

fof(i_0_7060,plain,
    ! [X26958,X26959,X26960] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26960),c_Groups_Ozero__class_Ozero(X26960)),esk250_3(X26958,X26959,X26960)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26960),X26959),X26958))
        | ~ class_Fields_Olinordered__field__inverse__zero(X26960) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26960),esk250_3(X26958,X26959,X26960)),c_Groups_Oone__class_Oone(X26960)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26960),X26959),X26958))
        | ~ class_Fields_Olinordered__field__inverse__zero(X26960) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26960),esk250_3(X26958,X26959,X26960)),X26959)),X26958))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26960),X26959),X26958))
        | ~ class_Fields_Olinordered__field__inverse__zero(X26960) ) ),
    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_7061,plain,
    ! [X33948,X33949] : c_Predicate_Opred__comp(X33949,X33949,X33949,c_fequal,c_Predicate_Opred__comp(X33949,X33949,X33949,X33948,c_fequal)) = X33948,
    inference(variable_rename,[status(thm)],[fact_eq__comp__r]) ).

fof(i_0_7062,plain,
    ! [X19532,X19533,X19534,X19535] : hAPP(c_Set_Ovimage(X19535,X19534,X19533),X19532) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19534,tc_fun(X19535,tc_HOL_Obool)),X19532),hAPP(hAPP(c_COMBB(tc_fun(X19534,tc_HOL_Obool),tc_fun(X19535,tc_HOL_Obool),X19534),c_Set_Ovimage(X19535,X19534,X19533)),hAPP(hAPP(c_COMBC(X19534,tc_fun(X19534,tc_HOL_Obool),tc_fun(X19534,tc_HOL_Obool)),c_Set_Oinsert(X19534)),c_Orderings_Obot__class_Obot(tc_fun(X19534,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_vimage__eq__UN]) ).

fof(i_0_7063,plain,
    ! [X19482,X19483,X19484,X19485] : hAPP(c_Relation_OImage(X19485,X19484,X19483),X19482) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19485,tc_fun(X19484,tc_HOL_Obool)),X19482),hAPP(hAPP(c_COMBB(tc_fun(X19485,tc_HOL_Obool),tc_fun(X19484,tc_HOL_Obool),X19485),c_Relation_OImage(X19485,X19484,X19483)),hAPP(hAPP(c_COMBC(X19485,tc_fun(X19485,tc_HOL_Obool),tc_fun(X19485,tc_HOL_Obool)),c_Set_Oinsert(X19485)),c_Orderings_Obot__class_Obot(tc_fun(X19485,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_Image__eq__UN]) ).

fof(i_0_7064,plain,
    ! [X25856,X25857,X25858,X25859] :
      ( ~ class_Orderings_Olinorder(X25859)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25859),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25859),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25859),X25858),X25857)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25859),X25858),X25856))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25859),X25858),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25859),X25857),X25856)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Odistrib__inf__le])]) ).

fof(i_0_7065,plain,
    ! [X18181,X18182,X18183,X18184] :
      ( ~ class_Lattices_Olattice(X18184)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18184),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18184),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18184),X18183),X18182)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18184),X18183),X18181))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18184),X18183),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18184),X18182),X18181)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distrib__inf__le])]) ).

fof(i_0_7066,plain,
    ! [X19900,X19901,X19902,X19903,X19904,X19905,X19906,X19907] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X19907),X19906),X19905))
      | ~ hBOOL(hAPP(hAPP(hAPP(X19904,X19906),X19903),X19902))
      | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19907,tc_fun(X19901,tc_fun(X19900,tc_HOL_Obool))),X19905),X19904),X19903),X19902)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP2__I])]) ).

fof(i_0_7067,plain,
    ! [X30450,X30451,X30452,X30453] :
      ( ( hAPP(c_Map_Omap__of(X30453,X30452),X30451) != hAPP(c_Map_Omap__of(X30453,X30452),X30450)
        | hAPP(c_List_Oset(tc_prod(X30453,X30452)),X30451) = hAPP(c_List_Oset(tc_prod(X30453,X30452)),X30450)
        | ~ hBOOL(hAPP(c_List_Odistinct(X30453),hAPP(hAPP(c_List_Omap(tc_prod(X30453,X30452),X30453),c_Product__Type_Ofst(X30453,X30452)),X30450)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30453),hAPP(hAPP(c_List_Omap(tc_prod(X30453,X30452),X30453),c_Product__Type_Ofst(X30453,X30452)),X30451))) )
      & ( hAPP(c_List_Oset(tc_prod(X30453,X30452)),X30451) != hAPP(c_List_Oset(tc_prod(X30453,X30452)),X30450)
        | hAPP(c_Map_Omap__of(X30453,X30452),X30451) = hAPP(c_Map_Omap__of(X30453,X30452),X30450)
        | ~ hBOOL(hAPP(c_List_Odistinct(X30453),hAPP(hAPP(c_List_Omap(tc_prod(X30453,X30452),X30453),c_Product__Type_Ofst(X30453,X30452)),X30450)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30453),hAPP(hAPP(c_List_Omap(tc_prod(X30453,X30452),X30453),c_Product__Type_Ofst(X30453,X30452)),X30451))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__inject__set])])]) ).

fof(i_0_7068,plain,
    ! [X23834,X23835,X23836,X23837,X23838,X23839,X23840] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X23840,X23839,tc_fun(X23838,tc_HOL_Obool)),X23837),hAPP(hAPP(c_Product__Type_OPair(X23840,X23839),X23836),X23835)),X23834))
      | hBOOL(hAPP(hAPP(hAPP(X23837,X23836),X23835),X23834)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitD_H])]) ).

fof(i_0_7069,plain,
    ! [X27305,X27306,X27307,X27308,X27309,X27310] : hAPP(hAPP(c_Relation_Orel__comp(X27310,X27309,X27308),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27310,X27309),tc_HOL_Obool)),X27307),X27306)),X27305) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27310,X27308),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27310,X27309,X27308),X27307),X27305)),hAPP(hAPP(c_Relation_Orel__comp(X27310,X27309,X27308),X27306),X27305)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__distrib2]) ).

fof(i_0_7070,plain,
    ! [X29562,X29563,X29564,X29565,X29566] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29566)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29565),X29564))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X29566),X29563),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29565,X29566),X29564),X29562)) = hAPP(hAPP(c_Finite__Set_Ofold(X29565,X29566,hAPP(hAPP(c_COMBB(X29566,tc_fun(X29566,X29566),X29565),c_Lattices_Osemilattice__inf__class_Oinf(X29566)),X29562)),X29563),X29564) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__INFI__fold__inf])]) ).

fof(i_0_7071,plain,
    ! [X29074,X29075,X29076,X29077,X29078] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29078)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29077),X29076))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X29078),X29075),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29077,X29078),X29076),X29074)) = hAPP(hAPP(c_Finite__Set_Ofold(X29077,X29078,hAPP(hAPP(c_COMBB(X29078,tc_fun(X29078,X29078),X29077),c_Lattices_Osemilattice__sup__class_Osup(X29078)),X29074)),X29075),X29076) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__SUPR__fold__sup])]) ).

fof(i_0_7072,plain,
    ! [X18379,X18380,X18381,X18382,X18383,X18384,X18385] :
      ( X18385 = X18384
      | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18383,X18382),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18383,X18382),X18381),X18385),X18380)),X18384),X18379) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18383,X18382),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18383,X18382),X18381),X18384),X18379)),X18385),X18380) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__twist])]) ).

fof(i_0_7073,plain,
    ! [X26752,X26753,X26754,X26755] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26755),X26754))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26755),X26753))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26755,tc_Nat_Onat),X26752),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26755,tc_HOL_Obool)),X26754),X26753)) = 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(X26755,tc_Nat_Onat),X26752),X26754)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26755,tc_Nat_Onat),X26752),X26753))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26755,tc_Nat_Onat),X26752),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26755,tc_HOL_Obool)),X26754),X26753))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un__nat])]) ).

fof(i_0_7074,plain,
    ! [X20563,X20564] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20564),hAPP(c_Set_OCollect(X20564),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X20564),c_fNot),X20563))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20564),c_Orderings_Otop__class_Otop(tc_fun(X20564,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20564),hAPP(c_Set_OCollect(X20564),X20563))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20564),c_Orderings_Otop__class_Otop(tc_fun(X20564,tc_HOL_Obool))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20564),hAPP(c_Set_OCollect(X20564),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X20564),c_fNot),X20563))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20564),hAPP(c_Set_OCollect(X20564),X20563))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__not])])]) ).

fof(i_0_7075,plain,
    ! [X23547,X23548,X23549,X23550] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23550))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23549),X23548))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23548),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),X23549),X23550)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23549),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23547,X23550))),X23548))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux1])]) ).

fof(i_0_7076,plain,
    ! [X21978,X21979,X21980,X21981,X21982] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21982),X21981))
      | 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),X21982),X21980)),X21979)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21981),X21980)),X21978)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21979),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),X21981),X21982)),X21980)),X21978)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq2])]) ).

fof(i_0_7077,plain,
    ! [X27024,X27025,X27026,X27027] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27027)
      | hAPP(c_Groups_Oabs__class_Oabs(X27027),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27026,X27027),hAPP(hAPP(c_COMBB(X27027,X27027,X27026),c_Groups_Oabs__class_Oabs(X27027)),X27025)),X27024)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27026,X27027),hAPP(hAPP(c_COMBB(X27027,X27027,X27026),c_Groups_Oabs__class_Oabs(X27027)),X27025)),X27024) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__setsum__abs])]) ).

fof(i_0_7078,plain,
    ! [X31253,X31254,X31255,X31256,X31257,X31258,X31259] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31259)),X31258)),X31257))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31257),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31256)),X31255)))
      | c_Map_Omap__upds(X31259,X31256,X31254,X31258,hAPP(hAPP(c_List_Olist__update(X31256,X31255),X31257),X31253)) = c_Map_Omap__upds(X31259,X31256,X31254,X31258,X31255) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__upds__list__update2__drop])]) ).

fof(i_0_7079,plain,
    ! [X19302,X19303,X19304,X19305,X19306] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19305,tc_HOL_Obool)),hAPP(c_Set_Oimage(X19306,X19305,X19304),X19303)),hAPP(c_Set_Oimage(X19306,X19305,X19304),X19302)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19306,tc_HOL_Obool)),X19303),X19302))
        | ~ c_Fun_Oinj__on(X19306,X19305,X19304,c_Orderings_Otop__class_Otop(tc_fun(X19306,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19306,tc_HOL_Obool)),X19303),X19302))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19305,tc_HOL_Obool)),hAPP(c_Set_Oimage(X19306,X19305,X19304),X19303)),hAPP(c_Set_Oimage(X19306,X19305,X19304),X19302)))
        | ~ c_Fun_Oinj__on(X19306,X19305,X19304,c_Orderings_Otop__class_Otop(tc_fun(X19306,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__subset__iff])])]) ).

fof(i_0_7080,plain,
    ! [X30887,X30888,X30889,X30890] :
      ( ~ class_Enum_Oenum(X30890)
      | ~ class_Enum_Oenum(X30889)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30889)),X30888) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30890)),c_Enum_Oenum__class_Oenum(X30890))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30889)),X30887) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30890)),c_Enum_Oenum__class_Oenum(X30890))
      | hAPP(c_Fun_Ocomp(tc_Option_Ooption(X30889),X30889,X30890,c_Option_Othe(X30889)),hAPP(c_Map_Omap__of(X30890,X30889),hAPP(hAPP(c_List_Ozip(X30890,X30889),c_Enum_Oenum__class_Oenum(X30890)),X30888))) != hAPP(c_Fun_Ocomp(tc_Option_Ooption(X30889),X30889,X30890,c_Option_Othe(X30889)),hAPP(c_Map_Omap__of(X30890,X30889),hAPP(hAPP(c_List_Ozip(X30890,X30889),c_Enum_Oenum__class_Oenum(X30890)),X30887)))
      | X30888 = X30887 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__zip__enum__inject])]) ).

cnf(i_0_7081,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oconcat(X1,X2)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk475_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),esk476_2(X2,X1))),hAPP(c_List_Oset(X1),esk477_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_5524]) ).

fof(i_0_7082,plain,
    ! [X24450,X24451,X24452] :
      ( ~ class_Fields_Olinordered__field(X24452)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24452),X24451),X24450))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24452),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24452),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24452),X24451),X24450)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24452),c_Groups_Oone__class_Oone(X24452)),c_Groups_Oone__class_Oone(X24452)))),X24450)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gt__half__sum])]) ).

fof(i_0_7083,plain,
    ! [X19219,X19220,X19221,X19222,X19223,X19224] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(X19224,X19223,X19222,X19221),X19220) != hAPP(c_Hilbert__Choice_Oinv__into(X19224,X19223,X19222,X19221),X19219)
      | ~ hBOOL(hAPP(hAPP(c_member(X19223),X19220),hAPP(c_Set_Oimage(X19224,X19223,X19221),X19222)))
      | ~ hBOOL(hAPP(hAPP(c_member(X19223),X19219),hAPP(c_Set_Oimage(X19224,X19223,X19221),X19222)))
      | X19220 = X19219 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__injective])]) ).

fof(i_0_7084,plain,
    ! [X33259,X33260,X33261,X33262,X33263,X33264,X33265] :
      ( ( hBOOL(hAPP(hAPP(X33263,X33262),X33260))
        | ~ c_List_Olist__all2(X33265,X33264,X33263,hAPP(hAPP(c_List_Olist_OCons(X33265),X33262),X33261),hAPP(hAPP(c_List_Olist_OCons(X33264),X33260),X33259)) )
      & ( c_List_Olist__all2(X33265,X33264,X33263,X33261,X33259)
        | ~ c_List_Olist__all2(X33265,X33264,X33263,hAPP(hAPP(c_List_Olist_OCons(X33265),X33262),X33261),hAPP(hAPP(c_List_Olist_OCons(X33264),X33260),X33259)) )
      & ( ~ hBOOL(hAPP(hAPP(X33263,X33262),X33260))
        | ~ c_List_Olist__all2(X33265,X33264,X33263,X33261,X33259)
        | c_List_Olist__all2(X33265,X33264,X33263,hAPP(hAPP(c_List_Olist_OCons(X33265),X33262),X33261),hAPP(hAPP(c_List_Olist_OCons(X33264),X33260),X33259)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__Cons])])]) ).

fof(i_0_7085,plain,
    ! [X22917,X22918,X22919] :
      ( ~ 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),X22919),X22918)),X22917)),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)),X22917))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22919))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22918),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_7086,plain,
    ! [X17178,X17179,X17180] :
      ( ( ~ hBOOL(hAPP(X17180,X17179))
        | hAPP(c_Set_OCollect(X17178),hAPP(hAPP(c_COMBS(X17178,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17178),c_fconj),hAPP(c_fequal,X17179))),X17180)) = hAPP(hAPP(c_Set_Oinsert(X17178),X17179),c_Orderings_Obot__class_Obot(tc_fun(X17178,tc_HOL_Obool))) )
      & ( hBOOL(hAPP(X17180,X17179))
        | hAPP(c_Set_OCollect(X17178),hAPP(hAPP(c_COMBS(X17178,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17178),c_fconj),hAPP(c_fequal,X17179))),X17180)) = c_Orderings_Obot__class_Obot(tc_fun(X17178,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5525])]) ).

cnf(i_0_7087,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_5526]) ).

cnf(i_0_7088,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_5527]) ).

fof(i_0_7089,plain,
    ! [X30809,X30810,X30811,X30812] :
      ( ( hBOOL(hAPP(hAPP(c_member(X30812),X30811),hAPP(c_List_Oset(X30812),X30809)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30812,X30812)),hAPP(hAPP(c_Product__Type_OPair(X30812,X30812),X30811),X30810)),hAPP(c_List_Oset(tc_prod(X30812,X30812)),hAPP(hAPP(c_List_Ozip(X30812,X30812),X30809),X30809)))) )
      & ( X30811 = X30810
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30812,X30812)),hAPP(hAPP(c_Product__Type_OPair(X30812,X30812),X30811),X30810)),hAPP(c_List_Oset(tc_prod(X30812,X30812)),hAPP(hAPP(c_List_Ozip(X30812,X30812),X30809),X30809)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X30812),X30811),hAPP(c_List_Oset(X30812),X30809)))
        | X30811 != X30810
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X30812,X30812)),hAPP(hAPP(c_Product__Type_OPair(X30812,X30812),X30811),X30810)),hAPP(c_List_Oset(tc_prod(X30812,X30812)),hAPP(hAPP(c_List_Ozip(X30812,X30812),X30809),X30809)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__same])])]) ).

fof(i_0_7090,plain,
    ! [X30825,X30826,X30827,X30828,X30829,X30830] :
      ( ( hBOOL(hAPP(hAPP(c_member(X30830),X30828),hAPP(c_List_Oset(X30830),X30826)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30830,X30829)),hAPP(hAPP(c_Product__Type_OPair(X30830,X30829),X30828),X30827)),hAPP(c_List_Oset(tc_prod(X30830,X30829)),hAPP(hAPP(c_List_Ozip(X30830,X30829),X30826),X30825)))) )
      & ( hBOOL(hAPP(hAPP(c_member(X30829),X30827),hAPP(c_List_Oset(X30829),X30825)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30830,X30829)),hAPP(hAPP(c_Product__Type_OPair(X30830,X30829),X30828),X30827)),hAPP(c_List_Oset(tc_prod(X30830,X30829)),hAPP(hAPP(c_List_Ozip(X30830,X30829),X30826),X30825)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5528])])]) ).

fof(i_0_7091,plain,
    ! [X30813,X30814,X30815,X30816,X30817,X30818] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30818,X30817)),hAPP(hAPP(c_Product__Type_OPair(X30818,X30817),X30816),X30815)),hAPP(c_List_Oset(tc_prod(X30818,X30817)),hAPP(hAPP(c_List_Ozip(X30818,X30817),X30814),X30813))))
      | hBOOL(hAPP(hAPP(c_member(X30818),X30816),hAPP(c_List_Oset(X30818),X30814))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__zip__leftD])]) ).

fof(i_0_7092,plain,
    ! [X30819,X30820,X30821,X30822,X30823,X30824] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30824,X30823)),hAPP(hAPP(c_Product__Type_OPair(X30824,X30823),X30822),X30821)),hAPP(c_List_Oset(tc_prod(X30824,X30823)),hAPP(hAPP(c_List_Ozip(X30824,X30823),X30820),X30819))))
      | hBOOL(hAPP(hAPP(c_member(X30823),X30821),hAPP(c_List_Oset(X30823),X30819))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__zip__rightD])]) ).

fof(i_0_7093,plain,
    ! [X20770,X20771,X20772,X20773,X20774,X20775] :
      ( ~ c_Finite__Set_Ofolding(X20775,X20774,X20773,X20772)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20775),X20771))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20775),X20770))
      | hAPP(c_Fun_Ocomp(X20774,X20774,X20774,hAPP(X20772,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20775,tc_HOL_Obool)),X20771),X20770))),hAPP(X20772,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20775,tc_HOL_Obool)),X20771),X20770))) = hAPP(c_Fun_Ocomp(X20774,X20774,X20774,hAPP(X20772,X20771)),hAPP(X20772,X20770)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ounion__inter])]) ).

fof(i_0_7094,plain,
    ! [X17429,X17430,X17431,X17432,X17433] :
      ( ~ c_Orderings_Oorder__class_Omono(tc_fun(X17433,tc_HOL_Obool),tc_fun(X17432,tc_HOL_Obool),X17431)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17432,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17432,tc_HOL_Obool)),hAPP(X17431,X17430)),hAPP(X17431,X17429))),hAPP(X17431,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17433,tc_HOL_Obool)),X17430),X17429)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mono__Un])]) ).

fof(i_0_7095,plain,
    ! [X27062,X27063,X27064] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27064)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27064),hAPP(c_Groups_Oabs__class_Oabs(X27064),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27064),hAPP(c_Groups_Oabs__class_Oabs(X27064),X27063)),hAPP(c_Groups_Oabs__class_Oabs(X27064),X27062)))),hAPP(c_Groups_Oabs__class_Oabs(X27064),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27064),X27063),X27062)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq3])]) ).

cnf(i_0_7096,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_5529]) ).

fof(i_0_7097,plain,
    ! [X22839] :
      ( ( ~ 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)),X22839)),X22839)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22839),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22839),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)),X22839)),X22839)),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_7098,plain,
    ! [X29940,X29941,X29942,X29943,X29944,X29945] :
      ( hBOOL(hAPP(hAPP(c_member(X29945),X29944),c_Map_Odom(X29945,X29943,X29942)))
      | c_Map_Omap__add(X29945,X29943,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X29945,tc_Option_Ooption(X29943)),X29941),X29944),hAPP(c_Option_Ooption_OSome(X29943),X29940)),X29942) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X29945,tc_Option_Ooption(X29943)),c_Map_Omap__add(X29945,X29943,X29941,X29942)),X29944),hAPP(c_Option_Ooption_OSome(X29943),X29940)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5530])]) ).

fof(i_0_7099,plain,
    ! [X29221,X29222,X29223,X29224] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29224)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29223),X29222))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29223,X29224),X29222),X29221) = hAPP(hAPP(c_Finite__Set_Ofold(X29223,X29224,hAPP(hAPP(c_COMBB(X29224,tc_fun(X29224,X29224),X29223),c_Lattices_Osemilattice__inf__class_Oinf(X29224)),X29221)),c_Orderings_Otop__class_Otop(X29224)),X29222) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__fold__inf])]) ).

fof(i_0_7100,plain,
    ! [X29129,X29130,X29131,X29132] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29132)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29131),X29130))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29131,X29132),X29130),X29129) = hAPP(hAPP(c_Finite__Set_Ofold(X29131,X29132,hAPP(hAPP(c_COMBB(X29132,tc_fun(X29132,X29132),X29131),c_Lattices_Osemilattice__sup__class_Osup(X29132)),X29129)),c_Orderings_Obot__class_Obot(X29132)),X29130) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUPR__fold__sup])]) ).

fof(i_0_7101,plain,
    ! [X28678,X28679,X28680,X28681] :
      ( ( c_Wellfounded_Oacyclic(X28681,X28678)
        | ~ c_Wellfounded_Oacyclic(X28681,hAPP(hAPP(c_Set_Oinsert(tc_prod(X28681,X28681)),hAPP(hAPP(c_Product__Type_OPair(X28681,X28681),X28680),X28679)),X28678)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28681,X28681)),hAPP(hAPP(c_Product__Type_OPair(X28681,X28681),X28679),X28680)),c_Transitive__Closure_Ortrancl(X28681,X28678)))
        | ~ c_Wellfounded_Oacyclic(X28681,hAPP(hAPP(c_Set_Oinsert(tc_prod(X28681,X28681)),hAPP(hAPP(c_Product__Type_OPair(X28681,X28681),X28680),X28679)),X28678)) )
      & ( ~ c_Wellfounded_Oacyclic(X28681,X28678)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28681,X28681)),hAPP(hAPP(c_Product__Type_OPair(X28681,X28681),X28679),X28680)),c_Transitive__Closure_Ortrancl(X28681,X28678)))
        | c_Wellfounded_Oacyclic(X28681,hAPP(hAPP(c_Set_Oinsert(tc_prod(X28681,X28681)),hAPP(hAPP(c_Product__Type_OPair(X28681,X28681),X28680),X28679)),X28678)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5531])])]) ).

fof(i_0_7102,plain,
    ! [X28674,X28675,X28676,X28677] :
      ( ( c_Wellfounded_Owf(X28677,X28674)
        | ~ c_Wellfounded_Owf(X28677,hAPP(hAPP(c_Set_Oinsert(tc_prod(X28677,X28677)),hAPP(hAPP(c_Product__Type_OPair(X28677,X28677),X28676),X28675)),X28674)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28677,X28677)),hAPP(hAPP(c_Product__Type_OPair(X28677,X28677),X28675),X28676)),c_Transitive__Closure_Ortrancl(X28677,X28674)))
        | ~ c_Wellfounded_Owf(X28677,hAPP(hAPP(c_Set_Oinsert(tc_prod(X28677,X28677)),hAPP(hAPP(c_Product__Type_OPair(X28677,X28677),X28676),X28675)),X28674)) )
      & ( ~ c_Wellfounded_Owf(X28677,X28674)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28677,X28677)),hAPP(hAPP(c_Product__Type_OPair(X28677,X28677),X28675),X28676)),c_Transitive__Closure_Ortrancl(X28677,X28674)))
        | c_Wellfounded_Owf(X28677,hAPP(hAPP(c_Set_Oinsert(tc_prod(X28677,X28677)),hAPP(hAPP(c_Product__Type_OPair(X28677,X28677),X28676),X28675)),X28674)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5532])])]) ).

cnf(i_0_7103,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_5533]) ).

fof(i_0_7104,plain,
    ! [X28929,X28930,X28931,X28932,X28933,X28934] :
      ( ~ c_Relation_Osingle__valued(X28934,X28933,X28932)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28934,X28933)),hAPP(hAPP(c_Product__Type_OPair(X28934,X28933),X28931),X28930)),X28932))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28934,X28933)),hAPP(hAPP(c_Product__Type_OPair(X28934,X28933),X28931),X28929)),X28932))
      | X28930 = X28929 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valuedD])]) ).

fof(i_0_7105,plain,
    ! [X17576,X17577,X17578] : hAPP(c_Set_OCollect(X17578),hAPP(hAPP(c_COMBS(X17578,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17578),c_fdisj),X17577)),X17576)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17578,tc_HOL_Obool)),hAPP(c_Set_OCollect(X17578),X17577)),hAPP(c_Set_OCollect(X17578),X17576)),
    inference(variable_rename,[status(thm)],[fact_Collect__disj__eq]) ).

fof(i_0_7106,plain,
    ! [X18168,X18169,X18170] : hAPP(c_Set_OCollect(X18170),hAPP(hAPP(c_COMBS(X18170,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X18170),c_fconj),X18169)),X18168)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18170,tc_HOL_Obool)),hAPP(c_Set_OCollect(X18170),X18169)),hAPP(c_Set_OCollect(X18170),X18168)),
    inference(variable_rename,[status(thm)],[fact_Collect__conj__eq]) ).

fof(i_0_7107,plain,
    ! [X29882,X29883,X29884,X29885,X29887,X29888,X29889,X29892] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29883),esk382_3(X29882,X29883,X29884)),X29884))
        | ~ hBOOL(hAPP(hAPP(c_member(X29883),X29885),X29884))
        | ~ c_Wellfounded_Owf(X29883,X29882) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29883,X29883)),hAPP(hAPP(c_Product__Type_OPair(X29883,X29883),X29887),esk382_3(X29882,X29883,X29884))),X29882))
        | ~ hBOOL(hAPP(hAPP(c_member(X29883),X29887),X29884))
        | ~ hBOOL(hAPP(hAPP(c_member(X29883),X29885),X29884))
        | ~ c_Wellfounded_Owf(X29883,X29882) )
      & ( hBOOL(hAPP(hAPP(c_member(X29889),esk384_2(X29888,X29889)),esk383_2(X29888,X29889)))
        | c_Wellfounded_Owf(X29889,X29888) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29889,X29889)),hAPP(hAPP(c_Product__Type_OPair(X29889,X29889),esk385_3(X29888,X29889,X29892)),X29892)),X29888))
        | ~ hBOOL(hAPP(hAPP(c_member(X29889),X29892),esk383_2(X29888,X29889)))
        | c_Wellfounded_Owf(X29889,X29888) )
      & ( hBOOL(hAPP(hAPP(c_member(X29889),esk385_3(X29888,X29889,X29892)),esk383_2(X29888,X29889)))
        | ~ hBOOL(hAPP(hAPP(c_member(X29889),X29892),esk383_2(X29888,X29889)))
        | c_Wellfounded_Owf(X29889,X29888) ) ),
    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_5534])])])])])]) ).

cnf(i_0_7108,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_5535]) ).

cnf(i_0_7109,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_5536]) ).

cnf(i_0_7110,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_5537]) ).

cnf(i_0_7111,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_5538]) ).

fof(i_0_7112,plain,
    ! [X19006,X19007,X19008,X19009,X19010] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X19010),X19009),X19008))
        | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X19010,tc_Option_Ooption(X19007)),c_Map_Orestrict__map(X19010,X19007,X19006,X19008)),X19009),c_Option_Ooption_ONone(X19007)) = c_Map_Orestrict__map(X19010,X19007,X19006,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19010,tc_HOL_Obool)),X19008),hAPP(hAPP(c_Set_Oinsert(X19010),X19009),c_Orderings_Obot__class_Obot(tc_fun(X19010,tc_HOL_Obool))))) )
      & ( hBOOL(hAPP(hAPP(c_member(X19010),X19009),X19008))
        | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X19010,tc_Option_Ooption(X19007)),c_Map_Orestrict__map(X19010,X19007,X19006,X19008)),X19009),c_Option_Ooption_ONone(X19007)) = c_Map_Orestrict__map(X19010,X19007,X19006,X19008) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5539])]) ).

cnf(i_0_7113,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_5540]) ).

cnf(i_0_7114,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_5541]) ).

cnf(i_0_7115,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_5542]) ).

fof(i_0_7116,plain,
    ! [X33239,X33240,X33241,X33242,X33243,X33244] :
      ( ~ c_List_Olist__all2(X33244,X33243,X33242,X33241,X33240)
      | c_List_Olist__all2(X33244,X33243,X33242,hAPP(hAPP(c_List_Odrop(X33244),X33239),X33241),hAPP(hAPP(c_List_Odrop(X33243),X33239),X33240)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__dropI])]) ).

fof(i_0_7117,plain,
    ! [X33253,X33254,X33255,X33256,X33257,X33258] :
      ( ~ c_List_Olist__all2(X33258,X33257,X33256,X33255,X33254)
      | c_List_Olist__all2(X33258,X33257,X33256,hAPP(hAPP(c_List_Otake(X33258),X33253),X33255),hAPP(hAPP(c_List_Otake(X33257),X33253),X33254)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__takeI])]) ).

fof(i_0_7118,plain,
    ! [X28786,X28787,X28788,X28789] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28789,X28789)),hAPP(hAPP(c_Product__Type_OPair(X28789,X28789),X28788),X28787)),c_Transitive__Closure_Ortrancl(X28789,hAPP(c_Relation_Oconverse(X28789,X28789),X28786))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28789,X28789)),hAPP(hAPP(c_Product__Type_OPair(X28789,X28789),X28787),X28788)),c_Transitive__Closure_Ortrancl(X28789,X28786))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__converseD])]) ).

fof(i_0_7119,plain,
    ! [X27437,X27438,X27439,X27440] :
      ( ~ c_Wellfounded_Owf(X27440,X27439)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27440,X27440)),hAPP(hAPP(c_Product__Type_OPair(X27440,X27440),X27438),X27437)),X27439))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27440,X27440)),hAPP(hAPP(c_Product__Type_OPair(X27440,X27440),X27437),X27438)),X27439)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5543])]) ).

fof(i_0_7120,plain,
    ! [X27433,X27434,X27435,X27436] :
      ( ~ c_Wellfounded_Owf(X27436,X27435)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27436,X27436)),hAPP(hAPP(c_Product__Type_OPair(X27436,X27436),X27434),X27433)),X27435))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27436,X27436)),hAPP(hAPP(c_Product__Type_OPair(X27436,X27436),X27433),X27434)),X27435)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5544])]) ).

fof(i_0_7121,plain,
    ! [X30394,X30395,X30396,X30397,X30398] :
      ( ~ class_Rings_Osemiring__0(X30398)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30398),hAPP(hAPP(c_List_Omap(X30397,X30398),hAPP(hAPP(c_COMBB(X30398,X30398,X30397),hAPP(c_Groups_Otimes__class_Otimes(X30398),X30396)),X30395)),X30394)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X30398),X30396),hAPP(c_List_Omonoid__add__class_Olistsum(X30398),hAPP(hAPP(c_List_Omap(X30397,X30398),X30395),X30394))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__const__mult])]) ).

fof(i_0_7122,plain,
    ! [X19354,X19355,X19356,X19357,X19358,X19359] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X19359,X19358),tc_HOL_Obool)),X19357),X19356))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19359,tc_HOL_Obool)),X19355),X19354))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19358,tc_HOL_Obool)),hAPP(c_Relation_OImage(X19359,X19358,X19357),X19355)),hAPP(c_Relation_OImage(X19359,X19358,X19356),X19354))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__mono])]) ).

fof(i_0_7123,plain,
    ! [X23859,X23860,X23861] :
      ( ( X23861 = 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),X23859)),X23860)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859))
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23861,X23860),X23859)) )
      & ( X23860 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X23859) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23861,X23860),X23859)) )
      & ( 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),X23859)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23860))
        | X23860 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23861,X23860),X23859)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859)),X23860))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23860))
        | X23860 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23861,X23860),X23859)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23860),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23860))
        | X23860 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23861,X23860),X23859)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859)),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)),X23860))
        | X23860 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23861,X23860),X23859)) )
      & ( X23860 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X23860 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X23861 != 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),X23859)),X23860)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23861,X23860),X23859)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23860))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23860))
        | X23860 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X23861 != 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),X23859)),X23860)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23861,X23860),X23859)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23860),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859)),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)),X23860))
        | X23860 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X23861 != 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),X23859)),X23860)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23861,X23860),X23859)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23860))
        | ~ 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),X23859)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859)),X23860))
        | X23860 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X23861 != 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),X23859)),X23860)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23861,X23860),X23859)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23860),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859)),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),X23859)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859)),X23860))
        | X23860 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X23861 != 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),X23859)),X23860)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23861,X23860),X23859)) )
      & ( X23860 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X23859) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X23861 != 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),X23859)),X23860)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23861,X23860),X23859)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23860))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23860))
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X23859) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X23861 != 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),X23859)),X23860)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23861,X23860),X23859)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23860),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859)),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)),X23860))
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X23859) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X23861 != 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),X23859)),X23860)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23861,X23860),X23859)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23860))
        | ~ 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),X23859)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859)),X23860))
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X23859) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X23861 != 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),X23859)),X23860)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23861,X23860),X23859)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23860),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859)),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),X23859)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859)),X23860))
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X23859) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X23861 != 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),X23859)),X23860)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X23859))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23861,X23860),X23859)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5545])])]) ).

fof(i_0_7124,plain,
    ! [X22777,X22778,X22779,X22780,X22781] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X22781,X22780)),hAPP(X22781,X22779)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22778,X22778)),hAPP(hAPP(c_Product__Type_OPair(X22778,X22778),X22780),X22779)),X22777))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X22778,X22778)),hAPP(hAPP(c_Product__Type_OPair(X22778,X22778),X22780),X22779)),c_Wellfounded_Omlex__prod(X22778,X22781,X22777))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__leq])]) ).

fof(i_0_7125,plain,
    ! [X24216,X24217,X24218,X24219] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),c_Groups_Ozero__class_Ozero(X24219)),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),X24218),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24219),X24216),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24219),X24218),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))),X24216))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24219)
        | ~ class_Int_Onumber(X24219) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217)),c_Groups_Ozero__class_Ozero(X24219)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24219),X24216),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))),X24218))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),c_Groups_Ozero__class_Ozero(X24219)),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24219),X24218),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))),X24216))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24219)
        | ~ class_Int_Onumber(X24219) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217)),c_Groups_Ozero__class_Ozero(X24219)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),c_Groups_Ozero__class_Ozero(X24219)),X24216))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),c_Groups_Ozero__class_Ozero(X24219)),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24219),X24218),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))),X24216))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24219)
        | ~ class_Int_Onumber(X24219) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),c_Groups_Ozero__class_Ozero(X24219)),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),c_Groups_Ozero__class_Ozero(X24219)),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24219),X24218),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))),X24216))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24219)
        | ~ class_Int_Onumber(X24219) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217)),c_Groups_Ozero__class_Ozero(X24219)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217)),c_Groups_Ozero__class_Ozero(X24219)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),c_Groups_Ozero__class_Ozero(X24219)),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24219),X24218),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))),X24216))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24219)
        | ~ class_Int_Onumber(X24219) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),c_Groups_Ozero__class_Ozero(X24219)),X24216))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217)),c_Groups_Ozero__class_Ozero(X24219)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),c_Groups_Ozero__class_Ozero(X24219)),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24219),X24218),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))),X24216))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24219)
        | ~ class_Int_Onumber(X24219) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217)),c_Groups_Ozero__class_Ozero(X24219)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24219),X24216),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))),X24218))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),c_Groups_Ozero__class_Ozero(X24219)),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24219),X24218),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))),X24216))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24219)
        | ~ class_Int_Onumber(X24219) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),c_Groups_Ozero__class_Ozero(X24219)),X24216))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24219),X24216),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))),X24218))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),c_Groups_Ozero__class_Ozero(X24219)),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24219),X24218),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))),X24216))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24219)
        | ~ class_Int_Onumber(X24219) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),c_Groups_Ozero__class_Ozero(X24219)),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),X24218),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24219),X24216),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24219),X24218),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))),X24216))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24219)
        | ~ class_Int_Onumber(X24219) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217)),c_Groups_Ozero__class_Ozero(X24219)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217)),c_Groups_Ozero__class_Ozero(X24219)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),X24218),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24219),X24216),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24219),X24218),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))),X24216))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24219)
        | ~ class_Int_Onumber(X24219) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),c_Groups_Ozero__class_Ozero(X24219)),X24216))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217)),c_Groups_Ozero__class_Ozero(X24219)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),X24218),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24219),X24216),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24219),X24218),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))),X24216))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24219)
        | ~ class_Int_Onumber(X24219) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217)),c_Groups_Ozero__class_Ozero(X24219)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24219),X24216),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))),X24218))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),X24218),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24219),X24216),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24219),X24218),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))),X24216))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24219)
        | ~ class_Int_Onumber(X24219) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),c_Groups_Ozero__class_Ozero(X24219)),X24216))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24219),X24216),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))),X24218))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),X24218),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24219),X24216),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24219),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24219),X24218),hAPP(c_Int_Onumber__class_Onumber__of(X24219),X24217))),X24216))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24219)
        | ~ class_Int_Onumber(X24219) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5546])])]) ).

fof(i_0_7126,plain,
    ! [X24252,X24253,X24254,X24255] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),c_Groups_Ozero__class_Ozero(X24255)),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),X24254),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24255),X24252),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24255),X24254),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))),X24252))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24255)
        | ~ class_Int_Onumber(X24255) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253)),c_Groups_Ozero__class_Ozero(X24255)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24255),X24252),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))),X24254))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),c_Groups_Ozero__class_Ozero(X24255)),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24255),X24254),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))),X24252))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24255)
        | ~ class_Int_Onumber(X24255) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253)),c_Groups_Ozero__class_Ozero(X24255)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),c_Groups_Ozero__class_Ozero(X24255)),X24252))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),c_Groups_Ozero__class_Ozero(X24255)),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24255),X24254),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))),X24252))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24255)
        | ~ class_Int_Onumber(X24255) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),c_Groups_Ozero__class_Ozero(X24255)),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),c_Groups_Ozero__class_Ozero(X24255)),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24255),X24254),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))),X24252))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24255)
        | ~ class_Int_Onumber(X24255) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253)),c_Groups_Ozero__class_Ozero(X24255)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253)),c_Groups_Ozero__class_Ozero(X24255)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),c_Groups_Ozero__class_Ozero(X24255)),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24255),X24254),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))),X24252))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24255)
        | ~ class_Int_Onumber(X24255) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),c_Groups_Ozero__class_Ozero(X24255)),X24252))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253)),c_Groups_Ozero__class_Ozero(X24255)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),c_Groups_Ozero__class_Ozero(X24255)),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24255),X24254),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))),X24252))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24255)
        | ~ class_Int_Onumber(X24255) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253)),c_Groups_Ozero__class_Ozero(X24255)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24255),X24252),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))),X24254))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),c_Groups_Ozero__class_Ozero(X24255)),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24255),X24254),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))),X24252))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24255)
        | ~ class_Int_Onumber(X24255) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),c_Groups_Ozero__class_Ozero(X24255)),X24252))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24255),X24252),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))),X24254))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),c_Groups_Ozero__class_Ozero(X24255)),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24255),X24254),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))),X24252))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24255)
        | ~ class_Int_Onumber(X24255) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),c_Groups_Ozero__class_Ozero(X24255)),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),X24254),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24255),X24252),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24255),X24254),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))),X24252))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24255)
        | ~ class_Int_Onumber(X24255) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253)),c_Groups_Ozero__class_Ozero(X24255)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253)),c_Groups_Ozero__class_Ozero(X24255)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),X24254),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24255),X24252),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24255),X24254),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))),X24252))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24255)
        | ~ class_Int_Onumber(X24255) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),c_Groups_Ozero__class_Ozero(X24255)),X24252))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253)),c_Groups_Ozero__class_Ozero(X24255)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),X24254),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24255),X24252),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24255),X24254),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))),X24252))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24255)
        | ~ class_Int_Onumber(X24255) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24255),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253)),c_Groups_Ozero__class_Ozero(X24255)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24255),X24252),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))),X24254))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),X24254),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24255),X24252),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24255),X24254),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))),X24252))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24255)
        | ~ class_Int_Onumber(X24255) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),c_Groups_Ozero__class_Ozero(X24255)),X24252))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24255),X24252),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))),X24254))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),X24254),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24255),X24252),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24255),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24255),X24254),hAPP(c_Int_Onumber__class_Onumber__of(X24255),X24253))),X24252))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24255)
        | ~ class_Int_Onumber(X24255) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5547])])]) ).

cnf(i_0_7127,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_5513]) ).

fof(i_0_7128,plain,
    ! [X27731,X27732,X27733,X27734] : hAPP(c_Set_Oimage(tc_prod(X27734,X27733),tc_prod(X27733,X27734),hAPP(c_Product__Type_Oprod_Oprod__case(X27734,X27733,tc_prod(X27733,X27734)),hAPP(c_COMBC(X27733,X27734,tc_prod(X27733,X27734)),c_Product__Type_OPair(X27733,X27734)))),hAPP(hAPP(c_Product__Type_OSigma(X27734,X27733),X27732),hAPP(c_COMBK(tc_fun(X27733,tc_HOL_Obool),X27734),X27731))) = hAPP(hAPP(c_Product__Type_OSigma(X27733,X27734),X27731),hAPP(c_COMBK(tc_fun(X27734,tc_HOL_Obool),X27733),X27732)),
    inference(variable_rename,[status(thm)],[fact_swap__product]) ).

cnf(i_0_7129,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_5548]) ).

fof(i_0_7130,plain,
    ! [X30836,X30837,X30838,X30839,X30840,X30842] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X30840),X30836),hAPP(c_List_Oset(X30840),X30839)))
        | hAPP(hAPP(c_Map_Omap__of(X30840,X30838),hAPP(hAPP(c_List_Ozip(X30840,X30838),X30839),X30837)),X30836) = hAPP(c_Option_Ooption_OSome(X30838),esk405_5(X30836,X30837,X30838,X30839,X30840))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30840)),X30839) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30838)),X30837) )
      & ( hAPP(hAPP(c_Map_Omap__of(X30840,X30838),hAPP(hAPP(c_List_Ozip(X30840,X30838),X30839),X30837)),X30836) != hAPP(c_Option_Ooption_OSome(X30838),X30842)
        | hBOOL(hAPP(hAPP(c_member(X30840),X30836),hAPP(c_List_Oset(X30840),X30839)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30840)),X30839) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30838)),X30837) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__zip__is__Some])])])])]) ).

fof(i_0_7131,plain,
    ! [X19014,X19015,X19016,X19017] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X19017),X19016),X19015))
      | hBOOL(hAPP(hAPP(c_member(tc_fun(X19017,tc_HOL_Obool)),hAPP(c_Relation_OImage(X19017,X19017,X19014),hAPP(hAPP(c_Set_Oinsert(X19017),X19016),c_Orderings_Obot__class_Obot(tc_fun(X19017,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X19017),X19015),X19014))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotientI])]) ).

fof(i_0_7132,plain,
    ! [X20025,X20026,X20027,X20028,X20029] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20029),X20028),hAPP(c_Relation_OImage(X20027,X20029,X20026),hAPP(hAPP(c_Set_Oinsert(X20027),X20025),c_Orderings_Obot__class_Obot(tc_fun(X20027,tc_HOL_Obool))))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X20027,X20029)),hAPP(hAPP(c_Product__Type_OPair(X20027,X20029),X20025),X20028)),X20026)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20027,X20029)),hAPP(hAPP(c_Product__Type_OPair(X20027,X20029),X20025),X20028)),X20026))
        | hBOOL(hAPP(hAPP(c_member(X20029),X20028),hAPP(c_Relation_OImage(X20027,X20029,X20026),hAPP(hAPP(c_Set_Oinsert(X20027),X20025),c_Orderings_Obot__class_Obot(tc_fun(X20027,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__singleton__iff])]) ).

cnf(i_0_7133,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2))),
    inference(split_conjunct,[status(thm)],[i_0_5549]) ).

fof(i_0_7134,plain,
    ! [X18350,X18351,X18352] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X18352)
      | ~ c_Orderings_Oorder__class_Omono(X18352,X18352,X18351)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18352),hAPP(X18351,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18352),c_Inductive_Ocomplete__lattice__class_Olfp(X18352,X18351)),X18350))),X18350))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18352),c_Inductive_Ocomplete__lattice__class_Olfp(X18352,X18351)),X18350)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lfp__induct])]) ).

fof(i_0_7135,plain,
    ! [X33280,X33281,X33282,X33283,X33284] :
      ( ( ~ c_List_Olist__all2(X33284,X33283,X33282,hAPP(c_List_Orev(X33284),X33281),hAPP(c_List_Orev(X33283),X33280))
        | c_List_Olist__all2(X33284,X33283,X33282,X33281,X33280) )
      & ( ~ c_List_Olist__all2(X33284,X33283,X33282,X33281,X33280)
        | c_List_Olist__all2(X33284,X33283,X33282,hAPP(c_List_Orev(X33284),X33281),hAPP(c_List_Orev(X33283),X33280)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__rev])]) ).

cnf(i_0_7136,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),esk476_2(X2,X1))),hAPP(c_List_Oset(X1),esk477_2(X2,X1))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),esk475_2(X2,X1)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5524]) ).

fof(i_0_7137,plain,
    ! [X23707,X23708,X23709] :
      ( ( 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),esk136_3(X23707,X23708,X23709)),esk137_3(X23707,X23708,X23709))))
        | hBOOL(hAPP(hAPP(X23707,X23709),X23708))
        | ~ 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),X23709),X23708))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk137_3(X23707,X23708,X23709)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(X23707,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk136_3(X23707,X23708,X23709))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk137_3(X23707,X23708,X23709))))
        | hBOOL(hAPP(hAPP(X23707,X23709),X23708))
        | ~ 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),X23709),X23708))) )
      & ( ~ hBOOL(hAPP(hAPP(X23707,esk136_3(X23707,X23708,X23709)),esk137_3(X23707,X23708,X23709)))
        | hBOOL(hAPP(hAPP(X23707,X23709),X23708))
        | ~ 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),X23709),X23708))) ) ),
    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_7138,plain,
    ! [X26331,X26332,X26333,X26334] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk206_4(X26331,X26332,X26333,X26334)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26333)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26334),X26332))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26334),X26333)),X26332))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26332),X26331))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26333)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk207_4(X26331,X26332,X26333,X26334)),X26331))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26334),X26332))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26334),X26333)),X26332))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26332),X26331))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26333)) )
      & ( X26334 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk207_4(X26331,X26332,X26333,X26334)),esk206_4(X26331,X26332,X26333,X26334))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26334),X26332))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26334),X26333)),X26332))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26332),X26331))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26333)) ) ),
    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_7139,plain,
    ! [X23453,X23454,X23455,X23456] :
      ( ~ class_Divides_Osemiring__div(X23456)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23456),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23456),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23456),X23455),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23456),X23454),X23455))),c_Divides_Odiv__class_Omod(X23456,X23454,X23455))),X23453) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23456),X23454),X23453) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mod__equality2])]) ).

fof(i_0_7140,plain,
    ! [X33285,X33286,X33287,X33288,X33289] :
      ( ( ~ c_List_Olist__all2(X33289,X33288,X33287,hAPP(c_List_Orev(X33289),X33286),X33285)
        | c_List_Olist__all2(X33289,X33288,X33287,X33286,hAPP(c_List_Orev(X33288),X33285)) )
      & ( ~ c_List_Olist__all2(X33289,X33288,X33287,X33286,hAPP(c_List_Orev(X33288),X33285))
        | c_List_Olist__all2(X33289,X33288,X33287,hAPP(c_List_Orev(X33289),X33286),X33285) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__rev1])]) ).

fof(i_0_7141,plain,
    ! [X31246,X31247,X31248,X31249,X31250,X31251,X31252] : c_Map_Omap__upds(X31252,X31251,X31250,hAPP(hAPP(c_List_Olist_OCons(X31252),X31249),X31248),hAPP(hAPP(c_List_Olist_OCons(X31251),X31247),X31246)) = c_Map_Omap__upds(X31252,X31251,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X31252,tc_Option_Ooption(X31251)),X31250),X31249),hAPP(c_Option_Ooption_OSome(X31251),X31247)),X31248,X31246),
    inference(variable_rename,[status(thm)],[fact_map__upds__Cons]) ).

fof(i_0_7142,plain,
    ! [X32089,X32090,X32091,X32094,X32095,X32096,X32097,X32098] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32091),tc_List_Olist(X32091))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32091),tc_List_Olist(X32091)),c_List_Olist_ONil(X32091)),X32090)),c_List_Olexord(X32091,X32089)))
        | X32090 = hAPP(hAPP(c_List_Olist_OCons(X32091),esk434_3(X32089,X32090,X32091)),esk435_3(X32089,X32090,X32091)) )
      & ( X32095 != hAPP(hAPP(c_List_Olist_OCons(X32096),X32097),X32098)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32096),tc_List_Olist(X32096))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32096),tc_List_Olist(X32096)),c_List_Olist_ONil(X32096)),X32095)),c_List_Olexord(X32096,X32094))) ) ),
    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_7143,plain,
    ! [X19470,X19471,X19472,X19473] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19473,tc_HOL_Obool)),hAPP(c_Set_Oimage(X19472,X19473,X19471),hAPP(c_Set_Ovimage(X19472,X19473,X19471),X19470))),X19470)),
    inference(variable_rename,[status(thm)],[fact_image__vimage__subset]) ).

fof(i_0_7144,plain,
    ! [X32844,X32845,X32846,X32847,X32848] :
      ( ~ class_Orderings_Olinorder(X32848)
      | ~ c_Fun_Oinj__on(X32847,X32848,X32846,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X32847,tc_HOL_Obool)),hAPP(c_List_Oset(X32847),X32845)),hAPP(c_List_Oset(X32847),X32844)))
      | ~ c_List_Olinorder__class_Osorted(X32848,hAPP(hAPP(c_List_Omap(X32847,X32848),X32846),X32845))
      | ~ hBOOL(hAPP(c_List_Odistinct(X32848),hAPP(hAPP(c_List_Omap(X32847,X32848),X32846),X32845)))
      | ~ c_List_Olinorder__class_Osorted(X32848,hAPP(hAPP(c_List_Omap(X32847,X32848),X32846),X32844))
      | ~ hBOOL(hAPP(c_List_Odistinct(X32848),hAPP(hAPP(c_List_Omap(X32847,X32848),X32846),X32844)))
      | hAPP(c_List_Oset(X32847),X32845) != hAPP(c_List_Oset(X32847),X32844)
      | X32845 = X32844 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__sorted__distinct__set__unique])]) ).

fof(i_0_7145,plain,
    ! [X23555,X23556,X23557,X23558] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23558))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23557))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23557),X23556))
      | 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),X23556),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23555,X23558))),X23557))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux3])]) ).

fof(i_0_7146,plain,
    ! [X27878,X27879,X27880] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27880),X27879))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27880,X27880),tc_HOL_Obool)),X27878),hAPP(hAPP(c_Product__Type_OSigma(X27880,X27880),X27879),hAPP(c_COMBK(tc_fun(X27880,tc_HOL_Obool),X27880),X27879))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X27880,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27880),X27879),X27878))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__quotient])]) ).

fof(i_0_7147,plain,
    ! [X32029,X32030,X32031,X32032,X32033,X32034] : hAPP(c_List_Ofoldl(X32034,X32033,X32032,X32031),hAPP(hAPP(c_List_Oappend(X32033),X32030),X32029)) = hAPP(c_List_Ofoldl(X32034,X32033,X32032,hAPP(c_List_Ofoldl(X32034,X32033,X32032,X32031),X32030)),X32029),
    inference(variable_rename,[status(thm)],[fact_foldl__append]) ).

cnf(i_0_7148,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk477_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)),esk475_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_5524]) ).

cnf(i_0_7149,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk476_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)),esk475_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_5524]) ).

fof(i_0_7150,plain,
    ! [X28782,X28783,X28784,X28785] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28785,X28785)),hAPP(hAPP(c_Product__Type_OPair(X28785,X28785),X28784),X28783)),c_Transitive__Closure_Ortrancl(X28785,X28782)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28785,X28785)),hAPP(hAPP(c_Product__Type_OPair(X28785,X28785),X28783),X28784)),c_Transitive__Closure_Ortrancl(X28785,hAPP(c_Relation_Oconverse(X28785,X28785),X28782)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__converseI])]) ).

fof(i_0_7151,plain,
    ! [X33851,X33852,X33853] :
      ( ( 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),esk515_3(X33851,X33852,X33853)),esk516_3(X33851,X33852,X33853))))
        | hBOOL(hAPP(hAPP(X33851,X33853),X33852))
        | ~ 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),X33853),X33852))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk515_3(X33851,X33852,X33853)),esk516_3(X33851,X33852,X33853)))
        | hBOOL(hAPP(hAPP(X33851,esk515_3(X33851,X33852,X33853)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk516_3(X33851,X33852,X33853)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(X33851,X33853),X33852))
        | ~ 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),X33853),X33852))) )
      & ( ~ hBOOL(hAPP(hAPP(X33851,esk515_3(X33851,X33852,X33853)),esk516_3(X33851,X33852,X33853)))
        | hBOOL(hAPP(hAPP(X33851,X33853),X33852))
        | ~ 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),X33853),X33852))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5550])])])]) ).

fof(i_0_7152,plain,
    ! [X31874,X31875,X31876,X31877,X31878] : hAPP(hAPP(c_List_Ozip(X31878,X31877),hAPP(hAPP(c_List_Oappend(X31878),X31876),X31875)),X31874) = hAPP(hAPP(c_List_Oappend(tc_prod(X31878,X31877)),hAPP(hAPP(c_List_Ozip(X31878,X31877),X31876),hAPP(hAPP(c_List_Otake(X31877),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31878)),X31876)),X31874))),hAPP(hAPP(c_List_Ozip(X31878,X31877),X31875),hAPP(hAPP(c_List_Odrop(X31877),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31878)),X31876)),X31874))),
    inference(variable_rename,[status(thm)],[fact_zip__append1]) ).

fof(i_0_7153,plain,
    ! [X18238,X18239,X18240,X18241] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18241,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18241,tc_HOL_Obool)),X18240),X18239)),X18238))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18241,tc_HOL_Obool)),X18240),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18241,tc_HOL_Obool)),X18239),X18238))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18241,tc_HOL_Obool)),X18240),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18241,tc_HOL_Obool)),X18239),X18238)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18241,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18241,tc_HOL_Obool)),X18240),X18239)),X18238)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__subset__conv])]) ).

cnf(i_0_7154,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_5551]) ).

fof(i_0_7155,plain,
    ! [X19339,X19340,X19341,X19342] :
      ( ( X19341 = hAPP(c_Relation_OImage(X19342,X19342,X19339),hAPP(hAPP(c_Set_Oinsert(X19342),esk42_4(X19339,X19340,X19341,X19342)),c_Orderings_Obot__class_Obot(tc_fun(X19342,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X19342,tc_HOL_Obool)),X19341),hAPP(hAPP(c_Equiv__Relations_Oquotient(X19342),X19340),X19339))) )
      & ( hBOOL(hAPP(hAPP(c_member(X19342),esk42_4(X19339,X19340,X19341,X19342)),X19340))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X19342,tc_HOL_Obool)),X19341),hAPP(hAPP(c_Equiv__Relations_Oquotient(X19342),X19340),X19339))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5552])])])]) ).

cnf(i_0_7156,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_5553]) ).

cnf(i_0_7157,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_5554]) ).

cnf(i_0_7158,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_5555]) ).

fof(i_0_7159,plain,
    ! [X30010,X30011,X30012,X30013,X30014,X30015] : c_Map_Omap__add(X30015,X30014,X30013,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X30015,tc_Option_Ooption(X30014)),X30012),X30011),hAPP(c_Option_Ooption_OSome(X30014),X30010))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X30015,tc_Option_Ooption(X30014)),c_Map_Omap__add(X30015,X30014,X30013,X30012)),X30011),hAPP(c_Option_Ooption_OSome(X30014),X30010)),
    inference(variable_rename,[status(thm)],[fact_map__add__upd]) ).

fof(i_0_7160,plain,
    ! [X19074,X19075,X19076,X19077] :
      ( hAPP(c_Set_Oimage(X19077,X19076,X19075),c_Orderings_Otop__class_Otop(tc_fun(X19077,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X19076,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(X19077,X19076,X19075),hAPP(c_Set_Oimage(X19076,X19077,c_Hilbert__Choice_Oinv__into(X19077,X19076,c_Orderings_Otop__class_Otop(tc_fun(X19077,tc_HOL_Obool)),X19075)),X19074)) = X19074 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__surj__f__inv__f])]) ).

fof(i_0_7161,plain,
    ! [X26386,X26387,X26388,X26389] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk225_4(X26386,X26387,X26388,X26389)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26388)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26389),X26386))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26389),X26388)),X26386))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26388)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk226_4(X26386,X26387,X26388,X26389)),X26387))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26389),X26386))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26389),X26388)),X26386))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26388)) )
      & ( X26389 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk226_4(X26386,X26387,X26388,X26389)),esk225_4(X26386,X26387,X26388,X26389))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26389),X26386))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26389),X26388)),X26386))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26388)) ) ),
    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_7162,plain,
    ! [X26361,X26362,X26363,X26364] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk216_4(X26361,X26362,X26363,X26364)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26363)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26364),X26361))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26364),X26363)),X26361))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26363)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk217_4(X26361,X26362,X26363,X26364)),X26362))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26364),X26361))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26364),X26363)),X26361))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26363)) )
      & ( X26364 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk217_4(X26361,X26362,X26363,X26364)),esk216_4(X26361,X26362,X26363,X26364))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26364),X26361))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26364),X26363)),X26361))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26363)) ) ),
    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_7163,plain,
    ! [X31847,X31848,X31849,X31850,X31851] :
      ( ( X31850 = hAPP(hAPP(c_List_Otake(X31851),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31850)),X31848)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31850)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31848)))
        | hAPP(hAPP(c_List_Oappend(X31851),X31850),X31849) != hAPP(hAPP(c_List_Oappend(X31851),X31848),X31847) )
      & ( X31849 = hAPP(hAPP(c_List_Oappend(X31851),hAPP(hAPP(c_List_Odrop(X31851),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31850)),X31848)),X31847)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31850)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31848)))
        | hAPP(hAPP(c_List_Oappend(X31851),X31850),X31849) != hAPP(hAPP(c_List_Oappend(X31851),X31848),X31847) )
      & ( hAPP(hAPP(c_List_Otake(X31851),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31848)),X31850) = X31848
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31850)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31848)))
        | hAPP(hAPP(c_List_Oappend(X31851),X31850),X31849) != hAPP(hAPP(c_List_Oappend(X31851),X31848),X31847) )
      & ( hAPP(hAPP(c_List_Oappend(X31851),hAPP(hAPP(c_List_Odrop(X31851),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31848)),X31850)),X31849) = X31847
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31850)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31848)))
        | hAPP(hAPP(c_List_Oappend(X31851),X31850),X31849) != hAPP(hAPP(c_List_Oappend(X31851),X31848),X31847) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31850)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31848)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31850)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31848)))
        | hAPP(hAPP(c_List_Oappend(X31851),X31850),X31849) = hAPP(hAPP(c_List_Oappend(X31851),X31848),X31847) )
      & ( hAPP(hAPP(c_List_Otake(X31851),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31848)),X31850) != X31848
        | hAPP(hAPP(c_List_Oappend(X31851),hAPP(hAPP(c_List_Odrop(X31851),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31848)),X31850)),X31849) != X31847
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31850)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31848)))
        | hAPP(hAPP(c_List_Oappend(X31851),X31850),X31849) = hAPP(hAPP(c_List_Oappend(X31851),X31848),X31847) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31850)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31848)))
        | X31850 != hAPP(hAPP(c_List_Otake(X31851),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31850)),X31848)
        | X31849 != hAPP(hAPP(c_List_Oappend(X31851),hAPP(hAPP(c_List_Odrop(X31851),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31850)),X31848)),X31847)
        | hAPP(hAPP(c_List_Oappend(X31851),X31850),X31849) = hAPP(hAPP(c_List_Oappend(X31851),X31848),X31847) )
      & ( hAPP(hAPP(c_List_Otake(X31851),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31848)),X31850) != X31848
        | hAPP(hAPP(c_List_Oappend(X31851),hAPP(hAPP(c_List_Odrop(X31851),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31848)),X31850)),X31849) != X31847
        | X31850 != hAPP(hAPP(c_List_Otake(X31851),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31850)),X31848)
        | X31849 != hAPP(hAPP(c_List_Oappend(X31851),hAPP(hAPP(c_List_Odrop(X31851),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31851)),X31850)),X31848)),X31847)
        | hAPP(hAPP(c_List_Oappend(X31851),X31850),X31849) = hAPP(hAPP(c_List_Oappend(X31851),X31848),X31847) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5556])])]) ).

fof(i_0_7164,plain,
    ! [X26573,X26574,X26575,X26576,X26577] :
      ( ~ class_Groups_Ocomm__monoid__add(X26577)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26576),X26575))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26576),X26574))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26577),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26576,X26577),X26573),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26576,tc_HOL_Obool)),X26575),X26574))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26576,X26577),X26573),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26576,tc_HOL_Obool)),X26575),X26574))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26577),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26576,X26577),X26573),X26575)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26576,X26577),X26573),X26574)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un__Int])]) ).

fof(i_0_7165,plain,
    ! [X23190,X23191,X23192,X23193,X23194] :
      ( ~ class_Groups_Ocomm__monoid__mult(X23194)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23193),X23192))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23193),X23191))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23194),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23193,X23194),X23190),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23193,tc_HOL_Obool)),X23192),X23191))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23193,X23194),X23190),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23193,tc_HOL_Obool)),X23192),X23191))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23194),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23193,X23194),X23190),X23192)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23193,X23194),X23190),X23191)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__inter])]) ).

fof(i_0_7166,plain,
    ! [X23185,X23186,X23187,X23188,X23189] :
      ( ~ class_Groups_Ocomm__monoid__mult(X23189)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23188),X23187))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23188),X23186))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23189),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23188,X23189),X23185),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23188,tc_HOL_Obool)),X23187),X23186))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23188,X23189),X23185),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23188,tc_HOL_Obool)),X23187),X23186))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23189),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23188,X23189),X23185),X23187)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23188,X23189),X23185),X23186)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Un__Int])]) ).

cnf(i_0_7167,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OMin)) ),
    inference(split_conjunct,[status(thm)],[i_0_5557]) ).

cnf(i_0_7168,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_5558]) ).

cnf(i_0_7169,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_5559]) ).

cnf(i_0_7170,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_5560]) ).

cnf(i_0_7171,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_5561]) ).

cnf(i_0_7172,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_5562]) ).

fof(i_0_7173,plain,
    ! [X20129,X20130,X20131,X20132,X20133,X20134] :
      ( ~ hBOOL(hAPP(hAPP(X20134,X20133),X20132))
      | ~ hBOOL(hAPP(hAPP(X20131,X20133),X20132))
      | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20130,tc_fun(X20129,tc_HOL_Obool))),X20134),X20131),X20133),X20132)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2I])]) ).

fof(i_0_7174,plain,
    ! [X19500,X19501,X19502,X19503,X19504] :
      ( hAPP(c_Set_Oimage(X19504,X19503,X19502),c_Orderings_Otop__class_Otop(tc_fun(X19504,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X19503,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19504,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X19504,X19503,X19502),X19501)),X19500))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19503,tc_HOL_Obool)),X19501),hAPP(c_Set_Oimage(X19504,X19503,X19502),X19500))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__subsetD])]) ).

fof(i_0_7175,plain,
    ! [X26337,X26338,X26339,X26340] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk208_4(X26337,X26338,X26339,X26340)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26339)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26338),X26340))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26338),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26340),X26339)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26338),X26337))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26339)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk209_4(X26337,X26338,X26339,X26340)),X26337))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26338),X26340))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26338),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26340),X26339)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26338),X26337))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26339)) )
      & ( X26340 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk209_4(X26337,X26338,X26339,X26340)),esk208_4(X26337,X26338,X26339,X26340))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26338),X26340))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26338),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26340),X26339)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26338),X26337))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26339)) ) ),
    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_7176,plain,
    ! [X22925,X22926,X22927,X22928,X22929,X22930] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22930),X22929)),X22928) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22927),X22926)),X22925)
      | ~ 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),X22927),X22926)),X22925)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22925),X22927))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22928))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22927))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22927),X22930))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22929),X22926)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma])]) ).

fof(i_0_7177,plain,
    ! [X29469,X29470,X29471,X29472,X29473] : hAPP(c_Relation_Oconverse(X29473,X29472),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29471,tc_fun(tc_prod(X29473,X29472),tc_HOL_Obool)),X29470),X29469)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29471,tc_fun(tc_prod(X29472,X29473),tc_HOL_Obool)),X29470),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X29473,X29472),tc_HOL_Obool),tc_fun(tc_prod(X29472,X29473),tc_HOL_Obool),X29471),c_Relation_Oconverse(X29473,X29472)),X29469)),
    inference(variable_rename,[status(thm)],[fact_converse__INTER]) ).

fof(i_0_7178,plain,
    ! [X28759,X28760,X28761,X28762,X28763] : hAPP(c_Relation_Oconverse(X28763,X28762),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28761,tc_fun(tc_prod(X28763,X28762),tc_HOL_Obool)),X28760),X28759)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28761,tc_fun(tc_prod(X28762,X28763),tc_HOL_Obool)),X28760),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X28763,X28762),tc_HOL_Obool),tc_fun(tc_prod(X28762,X28763),tc_HOL_Obool),X28761),c_Relation_Oconverse(X28763,X28762)),X28759)),
    inference(variable_rename,[status(thm)],[fact_converse__UNION]) ).

fof(i_0_7179,plain,
    ! [X25609] : X25609 = 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),esk167_1(X25609)),esk168_1(X25609))),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_7180,plain,
    ! [X17755,X17756,X17757,X17758,X17759] :
      ( ( X17758 = hAPP(X17756,esk21_4(X17755,X17756,X17757,X17758))
        | ~ hBOOL(hAPP(hAPP(c_member(X17759),X17758),hAPP(c_Set_Oimage(X17757,X17759,X17756),X17755))) )
      & ( hBOOL(hAPP(hAPP(c_member(X17757),esk21_4(X17755,X17756,X17757,X17758)),X17755))
        | ~ hBOOL(hAPP(hAPP(c_member(X17759),X17758),hAPP(c_Set_Oimage(X17757,X17759,X17756),X17755))) ) ),
    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_5563])])])])])]) ).

fof(i_0_7181,plain,
    ! [X17395,X17396,X17397,X17398,X17399,X17401,X17402,X17403,X17404,X17405,X17406] :
      ( ( hBOOL(hAPP(hAPP(c_member(X17397),esk16_4(X17395,X17396,X17397,X17398)),X17395))
        | ~ hBOOL(hAPP(hAPP(c_member(X17399),X17398),hAPP(c_Set_Oimage(X17397,X17399,X17396),X17395))) )
      & ( X17398 = hAPP(X17396,esk16_4(X17395,X17396,X17397,X17398))
        | ~ hBOOL(hAPP(hAPP(c_member(X17399),X17398),hAPP(c_Set_Oimage(X17397,X17399,X17396),X17395))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17403),X17405),X17401))
        | X17404 != hAPP(X17402,X17405)
        | hBOOL(hAPP(hAPP(c_member(X17406),X17404),hAPP(c_Set_Oimage(X17403,X17406,X17402),X17401))) ) ),
    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_7182,plain,
    ! [X19880,X19881,X19882,X19883,X19884] :
      ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X19884),hAPP(hAPP(c_Set_Oinsert(X19884),X19881),c_Orderings_Obot__class_Obot(tc_fun(X19884,tc_HOL_Obool)))),X19882) != hAPP(hAPP(c_Equiv__Relations_Oquotient(X19884),hAPP(hAPP(c_Set_Oinsert(X19884),X19880),c_Orderings_Obot__class_Obot(tc_fun(X19884,tc_HOL_Obool)))),X19882)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X19884,X19884)),hAPP(hAPP(c_Product__Type_OPair(X19884,X19884),X19881),X19880)),X19882))
        | ~ hBOOL(hAPP(hAPP(c_member(X19884),X19880),X19883))
        | ~ hBOOL(hAPP(hAPP(c_member(X19884),X19881),X19883))
        | ~ c_Equiv__Relations_Oequiv(X19884,X19883,X19882) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X19884,X19884)),hAPP(hAPP(c_Product__Type_OPair(X19884,X19884),X19881),X19880)),X19882))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(X19884),hAPP(hAPP(c_Set_Oinsert(X19884),X19881),c_Orderings_Obot__class_Obot(tc_fun(X19884,tc_HOL_Obool)))),X19882) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X19884),hAPP(hAPP(c_Set_Oinsert(X19884),X19880),c_Orderings_Obot__class_Obot(tc_fun(X19884,tc_HOL_Obool)))),X19882)
        | ~ hBOOL(hAPP(hAPP(c_member(X19884),X19880),X19883))
        | ~ hBOOL(hAPP(hAPP(c_member(X19884),X19881),X19883))
        | ~ c_Equiv__Relations_Oequiv(X19884,X19883,X19882) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff2])])]) ).

fof(i_0_7183,plain,
    ! [X19246,X19247,X19248,X19249,X19250,X19251] :
      ( hAPP(c_Set_Oimage(X19251,X19250,X19249),X19248) != X19247
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19250,tc_HOL_Obool)),X19246),X19247))
      | hAPP(c_Set_Oimage(X19251,X19250,X19249),hAPP(c_Set_Oimage(X19250,X19251,c_Hilbert__Choice_Oinv__into(X19251,X19250,X19248,X19249)),X19246)) = X19246 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__into__cancel])]) ).

fof(i_0_7184,plain,
    ! [X27949,X27950,X27951] :
      ( ( ~ c_Fun_Oinj__on(X27951,X27950,X27949,c_Orderings_Otop__class_Otop(tc_fun(X27951,tc_HOL_Obool)))
        | hAPP(c_Fun_Ocomp(X27950,X27951,X27951,c_Hilbert__Choice_Oinv__into(X27951,X27950,c_Orderings_Otop__class_Otop(tc_fun(X27951,tc_HOL_Obool)),X27949)),X27949) = c_Fun_Oid(X27951) )
      & ( hAPP(c_Fun_Ocomp(X27950,X27951,X27951,c_Hilbert__Choice_Oinv__into(X27951,X27950,c_Orderings_Otop__class_Otop(tc_fun(X27951,tc_HOL_Obool)),X27949)),X27949) != c_Fun_Oid(X27951)
        | c_Fun_Oinj__on(X27951,X27950,X27949,c_Orderings_Otop__class_Otop(tc_fun(X27951,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__iff])]) ).

cnf(i_0_7185,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_5564]) ).

fof(i_0_7186,plain,
    ! [X23794,X23795,X23796,X23797,X23798,X23799,X23800] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X23800,X23799,X23798),hAPP(c_Fun_Ocomp(X23797,tc_fun(X23799,X23798),X23800,X23796),X23795)),X23794) = hAPP(hAPP(X23796,hAPP(X23795,hAPP(c_Product__Type_Ofst(X23800,X23799),X23794))),hAPP(c_Product__Type_Osnd(X23800,X23799),X23794)),
    inference(variable_rename,[status(thm)],[fact_split__comp]) ).

cnf(i_0_7187,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OPls)),
    inference(split_conjunct,[status(thm)],[i_0_5565]) ).

cnf(i_0_7188,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_5566]) ).

cnf(i_0_7189,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_5567]) ).

fof(i_0_7190,plain,
    ! [X25299,X25300] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X25300),X25299))
        | 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)),X25300)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25299))) )
      & ( ~ 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)),X25300)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25299)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X25300),X25299)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I4_J])]) ).

fof(i_0_7191,plain,
    ! [X25295,X25296] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X25296),X25295))
        | 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)),X25296)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25295))) )
      & ( ~ 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)),X25296)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25295)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X25296),X25295)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I5_J])]) ).

fof(i_0_7192,plain,
    ! [X26017,X26018,X26019] :
      ( ~ class_Orderings_Olinorder(X26019)
      | hAPP(X26018,hAPP(hAPP(c_Orderings_Oord__class_Omax(X26019),esk175_3(X26017,X26018,X26019)),esk176_3(X26017,X26018,X26019))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X26019),hAPP(X26018,esk175_3(X26017,X26018,X26019))),hAPP(X26018,esk176_3(X26017,X26018,X26019)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26019),X26017))
      | X26017 = c_Orderings_Obot__class_Obot(tc_fun(X26019,tc_HOL_Obool))
      | hAPP(X26018,c_Big__Operators_Olattice_OSup__fin(X26019,c_Orderings_Oord__class_Omax(X26019),X26017)) = c_Big__Operators_Olattice_OSup__fin(X26019,c_Orderings_Oord__class_Omax(X26019),hAPP(c_Set_Oimage(X26019,X26019,X26018),X26017)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ohom__commute])])]) ).

fof(i_0_7193,plain,
    ! [X26022,X26023,X26024] :
      ( ~ class_Orderings_Olinorder(X26024)
      | hAPP(X26023,hAPP(hAPP(c_Orderings_Oord__class_Omin(X26024),esk177_3(X26022,X26023,X26024)),esk178_3(X26022,X26023,X26024))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X26024),hAPP(X26023,esk177_3(X26022,X26023,X26024))),hAPP(X26023,esk178_3(X26022,X26023,X26024)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26024),X26022))
      | X26022 = c_Orderings_Obot__class_Obot(tc_fun(X26024,tc_HOL_Obool))
      | hAPP(X26023,c_Big__Operators_Olattice_OInf__fin(X26024,c_Orderings_Oord__class_Omin(X26024),X26022)) = c_Big__Operators_Olattice_OInf__fin(X26024,c_Orderings_Oord__class_Omin(X26024),hAPP(c_Set_Oimage(X26024,X26024,X26023),X26022)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ohom__commute])])]) ).

fof(i_0_7194,plain,
    ! [X33205,X33206,X33207,X33208,X33209,X33210] :
      ( ~ c_List_Olist__all2(X33210,X33209,X33208,X33207,X33206)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33205),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33210)),X33207)))
      | hBOOL(hAPP(hAPP(X33208,hAPP(hAPP(c_List_Onth(X33210),X33207),X33205)),hAPP(hAPP(c_List_Onth(X33209),X33206),X33205))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__nthD])]) ).

fof(i_0_7195,plain,
    ! [X33211,X33212,X33213,X33214,X33215,X33216] :
      ( ~ c_List_Olist__all2(X33216,X33215,X33214,X33213,X33212)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33211),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33215)),X33212)))
      | hBOOL(hAPP(hAPP(X33214,hAPP(hAPP(c_List_Onth(X33216),X33213),X33211)),hAPP(hAPP(c_List_Onth(X33215),X33212),X33211))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__nthD2])]) ).

fof(i_0_7196,plain,
    ! [X19517,X19518,X19519,X19520,X19521] :
      ( ~ c_Fun_Oinj__on(X19521,X19520,X19519,c_Orderings_Otop__class_Otop(tc_fun(X19521,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19520,tc_HOL_Obool)),X19518),hAPP(c_Set_Oimage(X19521,X19520,X19519),X19517)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19521,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X19521,X19520,X19519),X19518)),X19517)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__subsetI])]) ).

cnf(i_0_7197,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5500]) ).

cnf(i_0_7198,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_5501]) ).

cnf(i_0_7199,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_5502]) ).

cnf(i_0_7200,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_5503]) ).

cnf(i_0_7201,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_5504]) ).

fof(i_0_7202,plain,
    ! [X24228,X24229,X24230,X24231] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),c_Groups_Ozero__class_Ozero(X24231)),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24231),X24230),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))),X24229))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24230),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24231),X24229),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24231)
        | ~ class_Int_Onumber(X24231) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228)),c_Groups_Ozero__class_Ozero(X24231)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24229),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24231),X24230),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),c_Groups_Ozero__class_Ozero(X24231)),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24230),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24231),X24229),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24231)
        | ~ class_Int_Onumber(X24231) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228)),c_Groups_Ozero__class_Ozero(X24231)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24230),c_Groups_Ozero__class_Ozero(X24231)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),c_Groups_Ozero__class_Ozero(X24231)),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24230),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24231),X24229),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24231)
        | ~ class_Int_Onumber(X24231) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),c_Groups_Ozero__class_Ozero(X24231)),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),c_Groups_Ozero__class_Ozero(X24231)),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24230),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24231),X24229),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24231)
        | ~ class_Int_Onumber(X24231) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228)),c_Groups_Ozero__class_Ozero(X24231)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228)),c_Groups_Ozero__class_Ozero(X24231)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),c_Groups_Ozero__class_Ozero(X24231)),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24230),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24231),X24229),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24231)
        | ~ class_Int_Onumber(X24231) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24230),c_Groups_Ozero__class_Ozero(X24231)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228)),c_Groups_Ozero__class_Ozero(X24231)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),c_Groups_Ozero__class_Ozero(X24231)),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24230),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24231),X24229),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24231)
        | ~ class_Int_Onumber(X24231) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228)),c_Groups_Ozero__class_Ozero(X24231)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24229),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24231),X24230),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),c_Groups_Ozero__class_Ozero(X24231)),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24230),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24231),X24229),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24231)
        | ~ class_Int_Onumber(X24231) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24230),c_Groups_Ozero__class_Ozero(X24231)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24229),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24231),X24230),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),c_Groups_Ozero__class_Ozero(X24231)),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24230),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24231),X24229),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24231)
        | ~ class_Int_Onumber(X24231) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),c_Groups_Ozero__class_Ozero(X24231)),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24231),X24230),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))),X24229))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24230),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24231),X24229),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24231)
        | ~ class_Int_Onumber(X24231) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228)),c_Groups_Ozero__class_Ozero(X24231)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228)),c_Groups_Ozero__class_Ozero(X24231)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24231),X24230),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))),X24229))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24230),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24231),X24229),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24231)
        | ~ class_Int_Onumber(X24231) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24230),c_Groups_Ozero__class_Ozero(X24231)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228)),c_Groups_Ozero__class_Ozero(X24231)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24231),X24230),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))),X24229))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24230),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24231),X24229),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24231)
        | ~ class_Int_Onumber(X24231) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228)),c_Groups_Ozero__class_Ozero(X24231)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24229),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24231),X24230),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24231),X24230),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))),X24229))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24230),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24231),X24229),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24231)
        | ~ class_Int_Onumber(X24231) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24230),c_Groups_Ozero__class_Ozero(X24231)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24229),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24231),X24230),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24231),X24230),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))),X24229))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24231),X24230),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24231),X24229),hAPP(c_Int_Onumber__class_Onumber__of(X24231),X24228))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24231)
        | ~ class_Int_Onumber(X24231) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5568])])]) ).

fof(i_0_7203,plain,
    ! [X24240,X24241,X24242,X24243] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24243),c_Groups_Ozero__class_Ozero(X24243)),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24243),X24242),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))),X24241))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24242),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24243),X24241),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24243)
        | ~ class_Int_Onumber(X24243) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24243),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240)),c_Groups_Ozero__class_Ozero(X24243)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24241),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24243),X24242),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24243),c_Groups_Ozero__class_Ozero(X24243)),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24242),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24243),X24241),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24243)
        | ~ class_Int_Onumber(X24243) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24243),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240)),c_Groups_Ozero__class_Ozero(X24243)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24242),c_Groups_Ozero__class_Ozero(X24243)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24243),c_Groups_Ozero__class_Ozero(X24243)),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24242),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24243),X24241),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24243)
        | ~ class_Int_Onumber(X24243) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24243),c_Groups_Ozero__class_Ozero(X24243)),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24243),c_Groups_Ozero__class_Ozero(X24243)),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24242),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24243),X24241),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24243)
        | ~ class_Int_Onumber(X24243) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24243),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240)),c_Groups_Ozero__class_Ozero(X24243)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24243),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240)),c_Groups_Ozero__class_Ozero(X24243)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24243),c_Groups_Ozero__class_Ozero(X24243)),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24242),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24243),X24241),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24243)
        | ~ class_Int_Onumber(X24243) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24242),c_Groups_Ozero__class_Ozero(X24243)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24243),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240)),c_Groups_Ozero__class_Ozero(X24243)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24243),c_Groups_Ozero__class_Ozero(X24243)),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24242),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24243),X24241),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24243)
        | ~ class_Int_Onumber(X24243) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24243),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240)),c_Groups_Ozero__class_Ozero(X24243)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24241),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24243),X24242),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24243),c_Groups_Ozero__class_Ozero(X24243)),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24242),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24243),X24241),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24243)
        | ~ class_Int_Onumber(X24243) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24242),c_Groups_Ozero__class_Ozero(X24243)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24241),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24243),X24242),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24243),c_Groups_Ozero__class_Ozero(X24243)),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24242),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24243),X24241),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24243)
        | ~ class_Int_Onumber(X24243) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24243),c_Groups_Ozero__class_Ozero(X24243)),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24243),X24242),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))),X24241))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24242),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24243),X24241),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24243)
        | ~ class_Int_Onumber(X24243) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24243),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240)),c_Groups_Ozero__class_Ozero(X24243)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24243),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240)),c_Groups_Ozero__class_Ozero(X24243)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24243),X24242),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))),X24241))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24242),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24243),X24241),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24243)
        | ~ class_Int_Onumber(X24243) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24242),c_Groups_Ozero__class_Ozero(X24243)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24243),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240)),c_Groups_Ozero__class_Ozero(X24243)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24243),X24242),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))),X24241))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24242),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24243),X24241),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24243)
        | ~ class_Int_Onumber(X24243) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24243),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240)),c_Groups_Ozero__class_Ozero(X24243)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24241),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24243),X24242),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24243),X24242),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))),X24241))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24242),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24243),X24241),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24243)
        | ~ class_Int_Onumber(X24243) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24242),c_Groups_Ozero__class_Ozero(X24243)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24241),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24243),X24242),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24243),X24242),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))),X24241))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24243),X24242),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24243),X24241),hAPP(c_Int_Onumber__class_Onumber__of(X24243),X24240))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24243)
        | ~ class_Int_Onumber(X24243) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5569])])]) ).

fof(i_0_7204,plain,
    ! [X28721,X28722,X28723,X28724,X28725] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28725,X28724)),hAPP(hAPP(c_Product__Type_OPair(X28725,X28724),X28723),X28722)),hAPP(c_Relation_Oconverse(X28724,X28725),X28721)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28724,X28725)),hAPP(hAPP(c_Product__Type_OPair(X28724,X28725),X28722),X28723)),X28721)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converseD])]) ).

fof(i_0_7205,plain,
    ! [X28711,X28712,X28713,X28714,X28715] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28715,X28714)),hAPP(hAPP(c_Product__Type_OPair(X28715,X28714),X28713),X28712)),hAPP(c_Relation_Oconverse(X28714,X28715),X28711)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28714,X28715)),hAPP(hAPP(c_Product__Type_OPair(X28714,X28715),X28712),X28713)),X28711)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28714,X28715)),hAPP(hAPP(c_Product__Type_OPair(X28714,X28715),X28712),X28713)),X28711))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28715,X28714)),hAPP(hAPP(c_Product__Type_OPair(X28715,X28714),X28713),X28712)),hAPP(c_Relation_Oconverse(X28714,X28715),X28711))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__iff])]) ).

fof(i_0_7206,plain,
    ! [X20173,X20174,X20175,X20176,X20177,X20178] :
      ( ~ hBOOL(hAPP(hAPP(X20178,X20177),X20176))
      | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20175,tc_fun(X20174,tc_HOL_Obool))),X20178),X20173),X20177),X20176)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup2I1])]) ).

fof(i_0_7207,plain,
    ! [X20111,X20112,X20113,X20114,X20115,X20116] :
      ( ( ~ hBOOL(hAPP(hAPP(X20116,X20115),X20114))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20112,tc_fun(X20111,tc_HOL_Obool))),X20113),X20116),X20115),X20114)) )
      & ( ~ hBOOL(hAPP(hAPP(X20113,X20115),X20114))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20112,tc_fun(X20111,tc_HOL_Obool))),X20113),X20116),X20115),X20114)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5570])])]) ).

fof(i_0_7208,plain,
    ! [X20167,X20168,X20169,X20170,X20171,X20172] :
      ( ~ hBOOL(hAPP(hAPP(X20172,X20171),X20170))
      | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20169,tc_fun(X20168,tc_HOL_Obool))),X20167),X20172),X20171),X20170)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup2I2])]) ).

fof(i_0_7209,plain,
    ! [X18102,X18103,X18104,X18105,X18106] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18106,tc_HOL_Obool)),X18105),X18104))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18106,tc_HOL_Obool)),X18103),X18102))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18106,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18106,tc_HOL_Obool)),X18105),X18103)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18106,tc_HOL_Obool)),X18104),X18102))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__mono])]) ).

fof(i_0_7210,plain,
    ! [X18080,X18081,X18082,X18083,X18084] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18084,tc_HOL_Obool)),X18083),X18082))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18084,tc_HOL_Obool)),X18081),X18080))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18084,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18084,tc_HOL_Obool)),X18083),X18080)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18084,tc_HOL_Obool)),X18082),X18081))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__mono])]) ).

fof(i_0_7211,plain,
    ! [X17499,X17500,X17501,X17502,X17503] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17503,tc_HOL_Obool)),X17502),X17501))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17503,tc_HOL_Obool)),X17500),X17499))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17503,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17503,tc_HOL_Obool)),X17502),X17500)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17503,tc_HOL_Obool)),X17501),X17499))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__mono])]) ).

fof(i_0_7212,plain,
    ! [X21342,X21343,X21344] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X21344)
      | hAPP(X21343,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21344),esk104_3(X21342,X21343,X21344)),esk105_3(X21342,X21343,X21344))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21344),hAPP(X21343,esk104_3(X21342,X21343,X21344))),hAPP(X21343,esk105_3(X21342,X21343,X21344)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21344),X21342))
      | X21342 = c_Orderings_Obot__class_Obot(tc_fun(X21344,tc_HOL_Obool))
      | hAPP(X21343,hAPP(c_Finite__Set_Ofold1(X21344,c_Groups_Otimes__class_Otimes(X21344)),X21342)) = hAPP(c_Finite__Set_Ofold1(X21344,c_Groups_Otimes__class_Otimes(X21344)),hAPP(c_Set_Oimage(X21344,X21344,X21343),X21342)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hom__fold1__commute])])]) ).

fof(i_0_7213,plain,
    ! [X26583,X26584,X26585,X26586,X26587] :
      ( ~ class_Groups_Ocomm__monoid__add(X26587)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26586),X26585))
      | ~ c_Fun_Oinj__on(X26586,X26586,X26584,X26585)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26586,X26587),X26583),hAPP(c_Set_Oimage(X26586,X26586,X26584),X26585)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26586,X26587),hAPP(c_Fun_Ocomp(X26586,X26587,X26586,X26583),X26584)),X26585) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oreindex])]) ).

fof(i_0_7214,plain,
    ! [X23195,X23196,X23197,X23198,X23199] :
      ( ~ class_Groups_Ocomm__monoid__mult(X23199)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23198),X23197))
      | ~ c_Fun_Oinj__on(X23198,X23198,X23196,X23197)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23198,X23199),X23195),hAPP(c_Set_Oimage(X23198,X23198,X23196),X23197)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23198,X23199),hAPP(c_Fun_Ocomp(X23198,X23199,X23198,X23195),X23196)),X23197) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oreindex])]) ).

fof(i_0_7215,plain,
    ! [X28351,X28352,X28353] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28353,X28353)),hAPP(hAPP(c_Product__Type_OPair(X28353,X28353),esk314_3(X28351,X28352,X28353)),X28352)),X28351))
        | hBOOL(hAPP(hAPP(c_member(X28353),X28352),c_Wellfounded_Oacc(X28353,X28351))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28353),esk314_3(X28351,X28352,X28353)),c_Wellfounded_Oacc(X28353,X28351)))
        | hBOOL(hAPP(hAPP(c_member(X28353),X28352),c_Wellfounded_Oacc(X28353,X28351))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5571])])])]) ).

fof(i_0_7216,plain,
    ! [X28347,X28348,X28349] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28349,X28349)),hAPP(hAPP(c_Product__Type_OPair(X28349,X28349),esk313_3(X28347,X28348,X28349)),X28348)),X28347))
        | hBOOL(hAPP(hAPP(c_member(X28349),X28348),c_Wellfounded_Oacc(X28349,X28347))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28349),esk313_3(X28347,X28348,X28349)),c_Wellfounded_Oacc(X28349,X28347)))
        | hBOOL(hAPP(hAPP(c_member(X28349),X28348),c_Wellfounded_Oacc(X28349,X28347))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc_OaccI])])])]) ).

fof(i_0_7217,plain,
    ! [X27336,X27337,X27338,X27339,X27340,X27341,X27342] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X27338),X27337),c_Wellfounded_Oacc(X27338,X27336)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27338,X27338)),hAPP(hAPP(c_Product__Type_OPair(X27338,X27338),X27339),X27337)),X27336))
        | hBOOL(hAPP(hAPP(c_member(X27338),X27339),c_Wellfounded_Oacc(X27338,X27336))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X27342,X27342)),hAPP(hAPP(c_Product__Type_OPair(X27342,X27342),esk255_3(X27340,X27341,X27342)),X27341)),X27340))
        | hBOOL(hAPP(hAPP(c_member(X27342),X27341),c_Wellfounded_Oacc(X27342,X27340))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27342),esk255_3(X27340,X27341,X27342)),c_Wellfounded_Oacc(X27342,X27340)))
        | hBOOL(hAPP(hAPP(c_member(X27342),X27341),c_Wellfounded_Oacc(X27342,X27340))) ) ),
    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_7218,plain,
    ! [X30614,X30615,X30616,X30617] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30617),tc_List_Olist(X30617))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30617),tc_List_Olist(X30617)),X30616),X30615)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X30617),c_List_Olistrel1(X30617,X30614))))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30617)),X30616) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30617)),X30615) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__eq__len])]) ).

cnf(i_0_7219,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk477_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),esk475_2(X2,X1)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5524]) ).

cnf(i_0_7220,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk476_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),esk475_2(X2,X1)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5524]) ).

fof(i_0_7221,plain,
    ! [X31175,X31176,X31177,X31178,X31179] : hAPP(hAPP(c_List_Olist__update(X31179,hAPP(hAPP(c_List_Olist_OCons(X31179),X31178),X31177)),X31176),X31175) = c_Nat_Onat_Onat__case(tc_List_Olist(X31179),hAPP(hAPP(c_List_Olist_OCons(X31179),X31175),X31177),hAPP(hAPP(c_COMBB(tc_List_Olist(X31179),tc_List_Olist(X31179),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X31179),X31178)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X31179,tc_List_Olist(X31179)),c_List_Olist__update(X31179,X31177)),X31175)),X31176),
    inference(variable_rename,[status(thm)],[fact_list__update_Osimps_I2_J]) ).

fof(i_0_7222,plain,
    ! [X23933,X23934,X23935,X23936] : hAPP(c_Product__Type_Oprod_Oprod__case(X23936,X23935,X23934),hAPP(hAPP(c_COMBB(tc_fun(X23935,tc_prod(X23936,X23935)),tc_fun(X23935,X23934),X23936),hAPP(c_COMBB(tc_prod(X23936,X23935),X23934,X23935),X23933)),c_Product__Type_OPair(X23936,X23935))) = X23933,
    inference(variable_rename,[status(thm)],[fact_split__eta]) ).

fof(i_0_7223,plain,
    ! [X26380,X26381,X26382,X26383] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk223_4(X26380,X26381,X26382,X26383)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26382)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26380),X26383))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26380),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26383),X26382)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26382)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk224_4(X26380,X26381,X26382,X26383)),X26381))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26380),X26383))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26380),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26383),X26382)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26382)) )
      & ( X26383 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk224_4(X26380,X26381,X26382,X26383)),esk223_4(X26380,X26381,X26382,X26383))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26380),X26383))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26380),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26383),X26382)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26382)) ) ),
    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_7224,plain,
    ! [X26355,X26356,X26357,X26358] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk214_4(X26355,X26356,X26357,X26358)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26357)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26355),X26358))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26355),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26358),X26357)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26357)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk215_4(X26355,X26356,X26357,X26358)),X26356))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26355),X26358))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26355),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26358),X26357)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26357)) )
      & ( X26358 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk215_4(X26355,X26356,X26357,X26358)),esk214_4(X26355,X26356,X26357,X26358))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26355),X26358))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26355),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26358),X26357)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26357)) ) ),
    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_7225,plain,
    ! [X18301,X18302,X18303] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18303,tc_HOL_Obool)),X18302),hAPP(hAPP(c_Set_Oinsert(X18303),X18301),c_Orderings_Obot__class_Obot(tc_fun(X18303,tc_HOL_Obool)))))
        | c_Partial__Function_Oflat__lub(X18303,X18301,X18302) = X18301 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18303,tc_HOL_Obool)),X18302),hAPP(hAPP(c_Set_Oinsert(X18303),X18301),c_Orderings_Obot__class_Obot(tc_fun(X18303,tc_HOL_Obool)))))
        | c_Partial__Function_Oflat__lub(X18303,X18301,X18302) = c_HOL_OThe(X18303,hAPP(hAPP(c_COMBC(X18303,tc_fun(X18303,tc_HOL_Obool),tc_HOL_Obool),c_member(X18303)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18303,tc_HOL_Obool)),X18302),hAPP(hAPP(c_Set_Oinsert(X18303),X18301),c_Orderings_Obot__class_Obot(tc_fun(X18303,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5572])]) ).

fof(i_0_7226,plain,
    ! [X32222,X32223,X32224,X32225] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk444_4(X32222,X32223,X32224,X32225)),X32225))
        | hAPP(hAPP(c_List_Otake(X32224),X32225),X32223) = hAPP(hAPP(c_List_Otake(X32224),X32225),X32222)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32225),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32224)),X32222)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32225),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32224)),X32223))) )
      & ( hAPP(hAPP(c_List_Onth(X32224),X32223),esk444_4(X32222,X32223,X32224,X32225)) != hAPP(hAPP(c_List_Onth(X32224),X32222),esk444_4(X32222,X32223,X32224,X32225))
        | hAPP(hAPP(c_List_Otake(X32224),X32225),X32223) = hAPP(hAPP(c_List_Otake(X32224),X32225),X32222)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32225),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32224)),X32222)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32225),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32224)),X32223))) ) ),
    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_7227,plain,
    ! [X28894,X28895,X28896,X28897] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28897,X28897)),hAPP(hAPP(c_Product__Type_OPair(X28897,X28897),X28896),X28895)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28897,X28897),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28894)))
      | X28896 = X28895 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__0__E])]) ).

fof(i_0_7228,plain,
    ! [X23970,X23971,X23972,X23973,X23974] :
      ( ~ hBOOL(hAPP(hAPP(X23974,X23973),X23972))
      | hBOOL(hAPP(hAPP(X23974,hAPP(c_Product__Type_Osnd(X23971,X23970),hAPP(hAPP(c_Product__Type_OPair(X23971,X23970),X23972),X23973))),hAPP(c_Product__Type_Ofst(X23971,X23970),hAPP(hAPP(c_Product__Type_OPair(X23971,X23970),X23972),X23973)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exI__realizer])]) ).

fof(i_0_7229,plain,
    ! [X18977,X18978,X18979,X18980,X18981,X18982] :
      ( ( ~ c_Fun_Oinj__on(X18981,X18978,X18977,hAPP(c_Set_Oimage(X18982,X18981,X18980),X18979))
        | c_Fun_Oinj__on(X18982,X18978,hAPP(c_Fun_Ocomp(X18981,X18978,X18982,X18977),X18980),X18979)
        | ~ c_Fun_Oinj__on(X18982,X18981,X18980,X18979) )
      & ( ~ c_Fun_Oinj__on(X18982,X18978,hAPP(c_Fun_Ocomp(X18981,X18978,X18982,X18977),X18980),X18979)
        | c_Fun_Oinj__on(X18981,X18978,X18977,hAPP(c_Set_Oimage(X18982,X18981,X18980),X18979))
        | ~ c_Fun_Oinj__on(X18982,X18981,X18980,X18979) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__inj__on__iff])])]) ).

fof(i_0_7230,plain,
    ! [X19204,X19205,X19206,X19207,X19208] :
      ( hAPP(c_Set_Oimage(X19208,X19207,X19206),c_Orderings_Otop__class_Otop(tc_fun(X19208,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X19207,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(X19207,X19205,X19204),c_Orderings_Otop__class_Otop(tc_fun(X19207,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X19205,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(X19208,X19205,hAPP(c_Fun_Ocomp(X19207,X19205,X19208,X19204),X19206)),c_Orderings_Otop__class_Otop(tc_fun(X19208,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X19205,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__surj])]) ).

fof(i_0_7231,plain,
    ! [X23494,X23495,X23496] : 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),X23496),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23495),X23496))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23495,X23496))),X23494) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23495),X23494),
    inference(variable_rename,[status(thm)],[fact_zdiv__zmod__equality]) ).

fof(i_0_7232,plain,
    ! [X26523,X26524,X26525,X26526,X26527,X26528] :
      ( ~ class_Groups_Ocomm__monoid__add(X26528)
      | ~ c_Fun_Oinj__on(X26527,X26526,X26525,X26524)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26526,X26528),X26523),hAPP(c_Set_Oimage(X26527,X26526,X26525),X26524)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26527,X26528),hAPP(c_Fun_Ocomp(X26526,X26528,X26527,X26523),X26525)),X26524) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__reindex])]) ).

fof(i_0_7233,plain,
    ! [X23103,X23104,X23105,X23106,X23107,X23108] :
      ( ~ class_Groups_Ocomm__monoid__mult(X23108)
      | ~ c_Fun_Oinj__on(X23107,X23106,X23105,X23104)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23106,X23108),X23103),hAPP(c_Set_Oimage(X23107,X23106,X23105),X23104)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23107,X23108),hAPP(c_Fun_Ocomp(X23106,X23108,X23107,X23103),X23105)),X23104) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__reindex])]) ).

fof(i_0_7234,plain,
    ! [X25976,X25977,X25978] :
      ( ~ class_Orderings_Olinorder(X25978)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25978),X25977))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25978),X25976))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25978,tc_HOL_Obool)),X25977),X25976) = c_Orderings_Obot__class_Obot(tc_fun(X25978,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25978),c_Big__Operators_Olattice_OSup__fin(X25978,c_Orderings_Oord__class_Omax(X25978),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25978,tc_HOL_Obool)),X25977),X25976))),c_Big__Operators_Olattice_OSup__fin(X25978,c_Orderings_Oord__class_Omax(X25978),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25978,tc_HOL_Obool)),X25977),X25976))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25978),c_Big__Operators_Olattice_OSup__fin(X25978,c_Orderings_Oord__class_Omax(X25978),X25977)),c_Big__Operators_Olattice_OSup__fin(X25978,c_Orderings_Oord__class_Omax(X25978),X25976)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__inter])]) ).

fof(i_0_7235,plain,
    ! [X25693,X25694,X25695] :
      ( ~ class_Orderings_Olinorder(X25695)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25695),X25694))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25695),X25693))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25695,tc_HOL_Obool)),X25694),X25693) = c_Orderings_Obot__class_Obot(tc_fun(X25695,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25695),c_Big__Operators_Olattice_OInf__fin(X25695,c_Orderings_Oord__class_Omin(X25695),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25695,tc_HOL_Obool)),X25694),X25693))),c_Big__Operators_Olattice_OInf__fin(X25695,c_Orderings_Oord__class_Omin(X25695),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25695,tc_HOL_Obool)),X25694),X25693))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25695),c_Big__Operators_Olattice_OInf__fin(X25695,c_Orderings_Oord__class_Omin(X25695),X25694)),c_Big__Operators_Olattice_OInf__fin(X25695,c_Orderings_Oord__class_Omin(X25695),X25693)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__inter])]) ).

fof(i_0_7236,plain,
    ! [X30490,X30491,X30492,X30493,X30494] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30494)),X30493) = X30490
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30494),tc_List_Olist(X30494))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30494),tc_List_Olist(X30494)),X30493),X30492)),hAPP(c_List_Olexn(X30494,X30491),X30490))) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30494)),X30492) = X30490
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30494),tc_List_Olist(X30494))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30494),tc_List_Olist(X30494)),X30493),X30492)),hAPP(c_List_Olexn(X30494,X30491),X30490))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexn__length])])]) ).

fof(i_0_7237,plain,
    ! [X28716,X28717,X28718,X28719,X28720] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28720,X28719)),hAPP(hAPP(c_Product__Type_OPair(X28720,X28719),X28718),X28717)),X28716))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28719,X28720)),hAPP(hAPP(c_Product__Type_OPair(X28719,X28720),X28717),X28718)),hAPP(c_Relation_Oconverse(X28720,X28719),X28716))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converseI])]) ).

fof(i_0_7238,plain,
    ! [X17770,X17771,X17772,X17773,X17774] :
      ( X17774 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X17773,tc_HOL_Obool),X17772)
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(X17773,tc_HOL_Obool),tc_fun(X17773,tc_HOL_Obool),X17772)
      | ~ hBOOL(hAPP(hAPP(c_member(X17773),X17771),X17770))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17773,tc_HOL_Obool)),X17770),hAPP(X17772,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17773,tc_HOL_Obool)),X17770),X17774))))
      | hBOOL(hAPP(hAPP(c_member(X17773),X17771),X17774)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_def__coinduct__set])]) ).

fof(i_0_7239,plain,
    ! [X27299,X27300,X27301,X27302,X27303,X27304] : hAPP(hAPP(c_Relation_Orel__comp(X27304,X27303,X27302),X27301),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27303,X27302),tc_HOL_Obool)),X27300),X27299)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27304,X27302),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27304,X27303,X27302),X27301),X27300)),hAPP(hAPP(c_Relation_Orel__comp(X27304,X27303,X27302),X27301),X27299)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__distrib]) ).

cnf(i_0_7240,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_5573]) ).

fof(i_0_7241,plain,
    ! [X19908,X19909,X19910,X19911] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X19911,tc_fun(X19910,tc_HOL_Obool))),X19909),X19908))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X19911,X19910)),hAPP(hAPP(c_Product__Type_OPair(X19911,X19910),X19909),X19908)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X19911,X19910),tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X19911,X19910)),hAPP(hAPP(c_Product__Type_OPair(X19911,X19910),X19909),X19908)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X19911,X19910),tc_HOL_Obool))))
        | hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X19911,tc_fun(X19910,tc_HOL_Obool))),X19909),X19908)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__empty__eq2])]) ).

fof(i_0_7242,plain,
    ! [X32962,X32963] :
      ( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X32963),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X32963))),X32962)))
      | c_List_Otranspose(X32963,c_List_Otranspose(X32963,X32962)) = c_List_OtakeWhile(tc_List_Olist(X32963),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X32963)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X32963),tc_List_Olist(X32963),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X32963))),X32962) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose__transpose])]) ).

fof(i_0_7243,plain,
    ! [X26032,X26033,X26034] :
      ( ~ class_Orderings_Olinorder(X26034)
      | hAPP(X26033,hAPP(hAPP(c_Orderings_Oord__class_Omin(X26034),esk181_3(X26032,X26033,X26034)),esk182_3(X26032,X26033,X26034))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X26034),hAPP(X26033,esk181_3(X26032,X26033,X26034))),hAPP(X26033,esk182_3(X26032,X26033,X26034)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26034),X26032))
      | X26032 = c_Orderings_Obot__class_Obot(tc_fun(X26034,tc_HOL_Obool))
      | hAPP(X26033,c_Big__Operators_Olinorder__class_OMin(X26034,X26032)) = c_Big__Operators_Olinorder__class_OMin(X26034,hAPP(c_Set_Oimage(X26034,X26034,X26033),X26032)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Ohom__commute])])]) ).

fof(i_0_7244,plain,
    ! [X26027,X26028,X26029] :
      ( ~ class_Orderings_Olinorder(X26029)
      | hAPP(X26028,hAPP(hAPP(c_Orderings_Oord__class_Omax(X26029),esk179_3(X26027,X26028,X26029)),esk180_3(X26027,X26028,X26029))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X26029),hAPP(X26028,esk179_3(X26027,X26028,X26029))),hAPP(X26028,esk180_3(X26027,X26028,X26029)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26029),X26027))
      | X26027 = c_Orderings_Obot__class_Obot(tc_fun(X26029,tc_HOL_Obool))
      | hAPP(X26028,c_Big__Operators_Olinorder__class_OMax(X26029,X26027)) = c_Big__Operators_Olinorder__class_OMax(X26029,hAPP(c_Set_Oimage(X26029,X26029,X26028),X26027)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Ohom__commute])])]) ).

fof(i_0_7245,plain,
    ! [X21107,X21108,X21109] :
      ( ~ class_Lattices_Olattice(X21109)
      | hAPP(X21108,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X21109),esk89_3(X21107,X21108,X21109)),esk90_3(X21107,X21108,X21109))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X21109),hAPP(X21108,esk89_3(X21107,X21108,X21109))),hAPP(X21108,esk90_3(X21107,X21108,X21109)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21109),X21107))
      | X21107 = c_Orderings_Obot__class_Obot(tc_fun(X21109,tc_HOL_Obool))
      | hAPP(X21108,c_Big__Operators_Olattice__class_OSup__fin(X21109,X21107)) = c_Big__Operators_Olattice__class_OSup__fin(X21109,hAPP(c_Set_Oimage(X21109,X21109,X21108),X21107)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ohom__commute])])]) ).

fof(i_0_7246,plain,
    ! [X21102,X21103,X21104] :
      ( ~ class_Lattices_Olattice(X21104)
      | hAPP(X21103,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X21104),esk87_3(X21102,X21103,X21104)),esk88_3(X21102,X21103,X21104))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X21104),hAPP(X21103,esk87_3(X21102,X21103,X21104))),hAPP(X21103,esk88_3(X21102,X21103,X21104)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21104),X21102))
      | X21102 = c_Orderings_Obot__class_Obot(tc_fun(X21104,tc_HOL_Obool))
      | hAPP(X21103,c_Big__Operators_Olattice__class_OInf__fin(X21104,X21102)) = c_Big__Operators_Olattice__class_OInf__fin(X21104,hAPP(c_Set_Oimage(X21104,X21104,X21103),X21102)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ohom__commute])])]) ).

fof(i_0_7247,plain,
    ! [X26372,X26373,X26376,X26378] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk221_2(X26372,X26373)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26373)))
        | ~ hBOOL(hAPP(X26372,X26376))
        | ~ hBOOL(hAPP(X26372,esk219_2(X26372,X26373)))
        | ~ hBOOL(hAPP(X26372,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk219_2(X26372,X26373)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk220_2(X26372,X26373)),X26373))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26373)) )
      & ( hBOOL(hAPP(X26372,esk221_2(X26372,X26373)))
        | ~ hBOOL(hAPP(X26372,X26376))
        | ~ hBOOL(hAPP(X26372,esk219_2(X26372,X26373)))
        | ~ hBOOL(hAPP(X26372,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk219_2(X26372,X26373)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk220_2(X26372,X26373)),X26373))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26373)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26378),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26373)))
        | ~ hBOOL(hAPP(X26372,X26378))
        | hBOOL(hAPP(X26372,esk222_2(X26372,X26373)))
        | ~ hBOOL(hAPP(X26372,esk219_2(X26372,X26373)))
        | ~ hBOOL(hAPP(X26372,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk219_2(X26372,X26373)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk220_2(X26372,X26373)),X26373))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26373)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk221_2(X26372,X26373)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26373)))
        | ~ hBOOL(hAPP(X26372,X26376))
        | hBOOL(hAPP(X26372,esk219_2(X26372,X26373)))
        | hBOOL(hAPP(X26372,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk219_2(X26372,X26373)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk220_2(X26372,X26373)),X26373))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26373)) )
      & ( hBOOL(hAPP(X26372,esk221_2(X26372,X26373)))
        | ~ hBOOL(hAPP(X26372,X26376))
        | hBOOL(hAPP(X26372,esk219_2(X26372,X26373)))
        | hBOOL(hAPP(X26372,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk219_2(X26372,X26373)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk220_2(X26372,X26373)),X26373))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26373)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26378),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26373)))
        | ~ hBOOL(hAPP(X26372,X26378))
        | hBOOL(hAPP(X26372,esk222_2(X26372,X26373)))
        | hBOOL(hAPP(X26372,esk219_2(X26372,X26373)))
        | hBOOL(hAPP(X26372,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk219_2(X26372,X26373)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk220_2(X26372,X26373)),X26373))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26373)) ) ),
    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_7248,plain,
    ! [X31326,X31327,X31328] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31328),tc_List_Olist(X31328))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31328),tc_List_Olist(X31328)),c_List_Olist_ONil(X31328)),X31327)),c_List_Olistrel(X31328,X31326)))
      | X31327 = c_List_Olist_ONil(X31328) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__Nil1])]) ).

cnf(i_0_7249,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oconcat(X2,X1)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),esk475_2(X1,X2)),hAPP(c_List_Oset(tc_List_Olist(X2)),X1)))
    | esk476_2(X1,X2) != esk477_2(X1,X2)
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5524]) ).

fof(i_0_7250,plain,
    ! [X17173,X17174] : c_Set_Othe__elem(X17174,X17173) = c_HOL_OThe(X17174,hAPP(hAPP(c_COMBB(tc_fun(X17174,tc_HOL_Obool),tc_HOL_Obool,X17174),hAPP(c_fequal,X17173)),hAPP(hAPP(c_COMBC(X17174,tc_fun(X17174,tc_HOL_Obool),tc_fun(X17174,tc_HOL_Obool)),c_Set_Oinsert(X17174)),c_Orderings_Obot__class_Obot(tc_fun(X17174,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_the__elem__def]) ).

cnf(i_0_7251,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk330_2(X2,X1)),esk330_2(X2,X1))),c_Transitive__Closure_Otrancl(X1,X2)))
    | c_Wellfounded_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5574]) ).

cnf(i_0_7252,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk326_2(X2,X1)),esk326_2(X2,X1))),c_Transitive__Closure_Otrancl(X1,X2)))
    | c_Wellfounded_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5527]) ).

fof(i_0_7253,plain,
    ! [X31425,X31426,X31427] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31427),tc_List_Olist(X31427))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31427),tc_List_Olist(X31427)),c_List_Olist_ONil(X31427)),X31426)),c_List_Olistrel1(X31427,X31425))),
    inference(variable_rename,[status(thm)],[i_0_5575]) ).

fof(i_0_7254,plain,
    ! [X31436,X31437,X31438] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31438),tc_List_Olist(X31438))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31438),tc_List_Olist(X31438)),c_List_Olist_ONil(X31438)),X31437)),c_List_Olex(X31438,X31436))),
    inference(variable_rename,[status(thm)],[i_0_5576]) ).

fof(i_0_7255,plain,
    ! [X25515,X25516] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X25516),X25515))
        | 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),X25516)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25515)))
        | ~ c_Nat__Transfer_Onat__set(X25515)
        | ~ c_Nat__Transfer_Onat__set(X25516) )
      & ( ~ 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),X25516)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25515)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X25516),X25515))
        | ~ c_Nat__Transfer_Onat__set(X25515)
        | ~ c_Nat__Transfer_Onat__set(X25516) ) ),
    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_7256,plain,
    ! [X25519,X25520] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X25520),X25519))
        | 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),X25520)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25519)))
        | ~ c_Nat__Transfer_Onat__set(X25519)
        | ~ c_Nat__Transfer_Onat__set(X25520) )
      & ( ~ 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),X25520)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25519)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X25520),X25519))
        | ~ c_Nat__Transfer_Onat__set(X25519)
        | ~ c_Nat__Transfer_Onat__set(X25520) ) ),
    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_7257,plain,
    ! [X27329,X27330,X27331,X27332] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X27332,X27332,X27332),X27331),X27330) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27332,X27332),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(X27332,X27332,X27332),X27329),X27330) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27332,X27332),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(X27332,X27332,X27332),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27332,X27332),tc_HOL_Obool)),X27331),X27329)),X27330) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27332,X27332),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_union__comp__emptyL])]) ).

fof(i_0_7258,plain,
    ! [X25596] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25596) = 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),X25596),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_7259,plain,
    ! [X25852,X25853,X25854,X25855] :
      ( ~ class_Orderings_Olinorder(X25855)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25855),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25855),X25854),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25855),X25853),X25852))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25855),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25855),X25854),X25853)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25855),X25854),X25852)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Odistrib__sup__le])]) ).

fof(i_0_7260,plain,
    ! [X18177,X18178,X18179,X18180] :
      ( ~ class_Lattices_Olattice(X18180)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18180),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18180),X18179),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18180),X18178),X18177))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18180),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18180),X18179),X18178)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18180),X18179),X18177)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distrib__sup__le])]) ).

cnf(i_0_7261,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_5577]) ).

cnf(i_0_7262,plain,
    c_Lazy__Sequence_Ohb__bind(X1,X2,X3,X4) = c_Lazy__Sequence_Ohb__flat(X2,c_Lazy__Sequence_Ohb__map(X1,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)),X4,X3)),
    inference(split_conjunct,[status(thm)],[i_0_5578]) ).

fof(i_0_7263,plain,
    ! [X29092,X29093,X29094,X29095] :
      ( ~ class_Orderings_Olinorder(X29095)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29095),X29094))
      | ~ hBOOL(hAPP(hAPP(c_member(X29095),X29093),X29094))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29095),hAPP(hAPP(c_Finite__Set_Ofold(X29095,X29095,c_Orderings_Oord__class_Omin(X29095)),X29092),X29094)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X29095),X29093),X29092))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__le__inf])]) ).

fof(i_0_7264,plain,
    ! [X29088,X29089,X29090,X29091] :
      ( ~ class_Lattices_Osemilattice__inf(X29091)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29091),X29090))
      | ~ hBOOL(hAPP(hAPP(c_member(X29091),X29089),X29090))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29091),hAPP(hAPP(c_Finite__Set_Ofold(X29091,X29091,c_Lattices_Osemilattice__inf__class_Oinf(X29091)),X29088),X29090)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X29091),X29089),X29088))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__inf__le__inf])]) ).

fof(i_0_7265,plain,
    ! [X31189,X31190,X31191,X31192,X31193] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31193,tc_HOL_Obool)),hAPP(c_List_Oset(X31193),X31192)),X31191))
      | ~ hBOOL(hAPP(hAPP(c_member(X31193),X31190),X31191))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31193,tc_HOL_Obool)),hAPP(c_List_Oset(X31193),hAPP(hAPP(c_List_Olist__update(X31193,X31192),X31189),X31190))),X31191)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__update__subsetI])]) ).

fof(i_0_7266,plain,
    ! [X26650,X26651,X26652,X26653,X26654] :
      ( ~ class_Groups_Ocomm__monoid__add(X26654)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26653),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26652),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26654),X26651),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26653,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26652),X26650))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26654),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26654),X26651),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26653,X26652))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26654),X26651),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26652),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26652),X26650)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__ub__add__nat])]) ).

fof(i_0_7267,plain,
    ! [X18324,X18325,X18326,X18327,X18328,X18329] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X18329),X18328),X18327))
        | hAPP(c_Set_Oimage(X18329,X18326,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18329,X18326),X18325),X18328),X18324)),X18327) = hAPP(hAPP(c_Set_Oinsert(X18326),X18324),hAPP(c_Set_Oimage(X18329,X18326,X18325),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18329,tc_HOL_Obool)),X18327),hAPP(hAPP(c_Set_Oinsert(X18329),X18328),c_Orderings_Obot__class_Obot(tc_fun(X18329,tc_HOL_Obool)))))) )
      & ( hBOOL(hAPP(hAPP(c_member(X18329),X18328),X18327))
        | hAPP(c_Set_Oimage(X18329,X18326,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18329,X18326),X18325),X18328),X18324)),X18327) = hAPP(c_Set_Oimage(X18329,X18326,X18325),X18327) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5579])]) ).

fof(i_0_7268,plain,
    ! [X27747,X27748,X27749,X27750,X27751] : hAPP(hAPP(c_Product__Type_OSigma(X27751,X27750),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27751,tc_HOL_Obool)),X27749),X27748)),hAPP(c_COMBK(tc_fun(X27750,tc_HOL_Obool),X27751),X27747)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27751,X27750),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27751,X27750),X27749),hAPP(c_COMBK(tc_fun(X27750,tc_HOL_Obool),X27751),X27747))),hAPP(hAPP(c_Product__Type_OSigma(X27751,X27750),X27748),hAPP(c_COMBK(tc_fun(X27750,tc_HOL_Obool),X27751),X27747))),
    inference(variable_rename,[status(thm)],[fact_Times__Int__distrib1]) ).

fof(i_0_7269,plain,
    ! [X27764,X27765,X27766,X27767,X27768] : hAPP(hAPP(c_Product__Type_OSigma(X27768,X27767),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27768,tc_HOL_Obool)),X27766),X27765)),hAPP(c_COMBK(tc_fun(X27767,tc_HOL_Obool),X27768),X27764)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X27768,X27767),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27768,X27767),X27766),hAPP(c_COMBK(tc_fun(X27767,tc_HOL_Obool),X27768),X27764))),hAPP(hAPP(c_Product__Type_OSigma(X27768,X27767),X27765),hAPP(c_COMBK(tc_fun(X27767,tc_HOL_Obool),X27768),X27764))),
    inference(variable_rename,[status(thm)],[fact_Times__Diff__distrib1]) ).

fof(i_0_7270,plain,
    ! [X27713,X27714,X27715,X27716,X27717] : hAPP(hAPP(c_Product__Type_OSigma(X27717,X27716),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27717,tc_HOL_Obool)),X27715),X27714)),hAPP(c_COMBK(tc_fun(X27716,tc_HOL_Obool),X27717),X27713)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27717,X27716),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27717,X27716),X27715),hAPP(c_COMBK(tc_fun(X27716,tc_HOL_Obool),X27717),X27713))),hAPP(hAPP(c_Product__Type_OSigma(X27717,X27716),X27714),hAPP(c_COMBK(tc_fun(X27716,tc_HOL_Obool),X27717),X27713))),
    inference(variable_rename,[status(thm)],[fact_Times__Un__distrib1]) ).

fof(i_0_7271,plain,
    ! [X21303,X21304,X21305,X21306,X21307] :
      ( ~ c_Fun_Oinj__on(X21307,X21306,X21305,X21304)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21306,tc_HOL_Obool)),hAPP(c_Set_Oimage(X21307,X21306,X21305),X21304)),X21303))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21306),X21303))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21307),X21304)),hAPP(c_Finite__Set_Ocard(X21306),X21303))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj__on__le])]) ).

fof(i_0_7272,plain,
    ! [X28355,X28356,X28357,X28358] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28357),esk315_4(X28355,X28356,X28357,X28358)),X28356))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28358,X28357,c_Groups_Otimes__class_Otimes(X28358)),X28355),c_Groups_Oone__class_Oone(X28358)),X28356) = c_Groups_Oone__class_Oone(X28358)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28357),X28356))
        | ~ class_Groups_Ocomm__monoid__mult(X28358) )
      & ( hAPP(X28355,esk315_4(X28355,X28356,X28357,X28358)) != c_Groups_Oone__class_Oone(X28358)
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28358,X28357,c_Groups_Otimes__class_Otimes(X28358)),X28355),c_Groups_Oone__class_Oone(X28358)),X28356) = c_Groups_Oone__class_Oone(X28358)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28357),X28356))
        | ~ class_Groups_Ocomm__monoid__mult(X28358) ) ),
    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_7273,plain,
    ! [X33483,X33484,X33485,X33486] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33485),esk491_4(X33483,X33484,X33485,X33486)),hAPP(c_List_Oset(X33485),X33484)))
        | hBOOL(hAPP(X33483,hAPP(hAPP(c_List_Onth(X33485),X33484),X33486)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33486),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33485)),X33484))) )
      & ( ~ hBOOL(hAPP(X33483,esk491_4(X33483,X33484,X33485,X33486)))
        | hBOOL(hAPP(X33483,hAPP(hAPP(c_List_Onth(X33485),X33484),X33486)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33486),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33485)),X33484))) ) ),
    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_7274,plain,
    ! [X34227,X34228,X34229,X34230,X34231] : hAPP(c_Sum__Type_Osum_Osum__case(X34231,X34230,X34229,hAPP(c_COMBK(X34230,X34231),X34228),hAPP(c_COMBK(X34230,X34229),X34228)),X34227) = X34228,
    inference(variable_rename,[status(thm)],[fact_sum__case__KK]) ).

fof(i_0_7275,plain,
    ! [X31323,X31324,X31325] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31325),tc_List_Olist(X31325))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31325),tc_List_Olist(X31325)),X31324),c_List_Olist_ONil(X31325))),c_List_Olistrel(X31325,X31323)))
      | X31324 = c_List_Olist_ONil(X31325) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__Nil2])]) ).

fof(i_0_7276,plain,
    ! [X29346,X29347,X29348,X29349,X29350,X29351] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29351)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29350,X29351),X29349),hAPP(hAPP(c_COMBB(tc_fun(X29348,X29351),X29351,X29350),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29348,X29351),X29347)),X29346)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29348,X29351),X29347),hAPP(hAPP(c_COMBB(tc_fun(X29350,X29351),X29351,X29348),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29350,X29351),X29349)),hAPP(c_COMBC(X29350,X29348,X29351),X29346))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__commute])]) ).

fof(i_0_7277,plain,
    ! [X19595,X19596,X19597,X19598,X19599,X19600] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X19600)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19599,X19600),X19598),hAPP(hAPP(c_COMBB(tc_fun(X19597,X19600),X19600,X19599),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19597,X19600),X19596)),X19595)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19597,X19600),X19596),hAPP(hAPP(c_COMBB(tc_fun(X19599,X19600),X19600,X19597),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19599,X19600),X19598)),hAPP(c_COMBC(X19599,X19597,X19600),X19595))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__commute])]) ).

fof(i_0_7278,plain,
    ! [X31422,X31423,X31424] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31424),tc_List_Olist(X31424))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31424),tc_List_Olist(X31424)),X31423),c_List_Olist_ONil(X31424))),c_List_Olistrel1(X31424,X31422))),
    inference(variable_rename,[status(thm)],[i_0_5580]) ).

fof(i_0_7279,plain,
    ! [X31430,X31431,X31432] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31432),tc_List_Olist(X31432))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31432),tc_List_Olist(X31432)),X31431),c_List_Olist_ONil(X31432))),c_List_Olexord(X31432,X31430))),
    inference(variable_rename,[status(thm)],[i_0_5581]) ).

fof(i_0_7280,plain,
    ! [X31433,X31434,X31435] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31435),tc_List_Olist(X31435))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31435),tc_List_Olist(X31435)),X31434),c_List_Olist_ONil(X31435))),c_List_Olex(X31435,X31433))),
    inference(variable_rename,[status(thm)],[i_0_5582]) ).

fof(i_0_7281,plain,
    ! [X20058,X20059,X20060,X20061,X20062] :
      ( ( hAPP(c_Relation_OImage(X20062,X20062,X20060),hAPP(hAPP(c_Set_Oinsert(X20062),X20059),c_Orderings_Obot__class_Obot(tc_fun(X20062,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X20062,X20062,X20060),hAPP(hAPP(c_Set_Oinsert(X20062),X20058),c_Orderings_Obot__class_Obot(tc_fun(X20062,tc_HOL_Obool))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X20062,X20062)),hAPP(hAPP(c_Product__Type_OPair(X20062,X20062),X20059),X20058)),X20060))
        | ~ hBOOL(hAPP(hAPP(c_member(X20062),X20058),X20061))
        | ~ hBOOL(hAPP(hAPP(c_member(X20062),X20059),X20061))
        | ~ c_Equiv__Relations_Oequiv(X20062,X20061,X20060) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20062,X20062)),hAPP(hAPP(c_Product__Type_OPair(X20062,X20062),X20059),X20058)),X20060))
        | hAPP(c_Relation_OImage(X20062,X20062,X20060),hAPP(hAPP(c_Set_Oinsert(X20062),X20059),c_Orderings_Obot__class_Obot(tc_fun(X20062,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X20062,X20062,X20060),hAPP(hAPP(c_Set_Oinsert(X20062),X20058),c_Orderings_Obot__class_Obot(tc_fun(X20062,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(X20062),X20058),X20061))
        | ~ hBOOL(hAPP(hAPP(c_member(X20062),X20059),X20061))
        | ~ c_Equiv__Relations_Oequiv(X20062,X20061,X20060) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff])])]) ).

fof(i_0_7282,plain,
    ! [X26762,X26763,X26764] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26764),esk237_3(X26762,X26763,X26764)),X26763))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26764,tc_Int_Oint),X26762),X26763) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26764,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X26764),c_Int_Onat),X26762)),X26763)) )
      & ( ~ c_Nat__Transfer_Ois__nat(hAPP(X26762,esk237_3(X26762,X26763,X26764)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26764,tc_Int_Oint),X26762),X26763) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26764,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X26764),c_Int_Onat),X26762)),X26763)) ) ),
    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_7283,plain,
    ! [X25553,X25554,X25555] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25555),esk166_3(X25553,X25554,X25555)),X25554))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25555,tc_Int_Oint),X25553),X25554) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25555,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X25555),c_Int_Onat),X25553)),X25554)) )
      & ( ~ c_Nat__Transfer_Ois__nat(hAPP(X25553,esk166_3(X25553,X25554,X25555)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25555,tc_Int_Oint),X25553),X25554) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25555,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X25555),c_Int_Onat),X25553)),X25554)) ) ),
    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_7284,plain,
    ! [X18285,X18286,X18287] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X18287)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18287),X18286),hAPP(X18285,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18287),X18286),c_Inductive_Ocomplete__lattice__class_Ogfp(X18287,X18285)))))
      | ~ c_Orderings_Oorder__class_Omono(X18287,X18287,X18285)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18287),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18287),X18286),c_Inductive_Ocomplete__lattice__class_Ogfp(X18287,X18285))),hAPP(X18285,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18287),X18286),c_Inductive_Ocomplete__lattice__class_Ogfp(X18287,X18285))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coinduct__lemma])]) ).

fof(i_0_7285,plain,
    ! [X30678,X30679,X30680,X30681] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30681),tc_List_Olist(X30681))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30681),tc_List_Olist(X30681)),X30680),X30679)),c_List_Olistrel(X30681,X30678)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30681)),X30680) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30681)),X30679) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__eq__len])]) ).

fof(i_0_7286,plain,
    ! [X30618,X30619,X30620,X30621] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30621),tc_List_Olist(X30621))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30621),tc_List_Olist(X30621)),X30620),X30619)),c_List_Olistrel1(X30621,X30618)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30621)),X30620) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30621)),X30619) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__eq__len])]) ).

cnf(i_0_7287,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_5583]) ).

cnf(i_0_7288,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_5584]) ).

fof(i_0_7289,plain,
    ! [X33661,X33662,X33663] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X33663),esk513_3(X33661,X33662,X33663)))
        | hBOOL(hAPP(X33661,X33662))
        | ~ hBOOL(hAPP(X33661,c_Orderings_Obot__class_Obot(tc_fun(X33663,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33663),X33662)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X33663),esk512_3(X33661,X33662,X33663)),esk513_3(X33661,X33662,X33663)))
        | hBOOL(hAPP(X33661,X33662))
        | ~ hBOOL(hAPP(X33661,c_Orderings_Obot__class_Obot(tc_fun(X33663,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33663),X33662)) )
      & ( hBOOL(hAPP(X33661,esk513_3(X33661,X33662,X33663)))
        | hBOOL(hAPP(X33661,X33662))
        | ~ hBOOL(hAPP(X33661,c_Orderings_Obot__class_Obot(tc_fun(X33663,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33663),X33662)) )
      & ( ~ hBOOL(hAPP(X33661,hAPP(hAPP(c_Set_Oinsert(X33663),esk512_3(X33661,X33662,X33663)),esk513_3(X33661,X33662,X33663))))
        | hBOOL(hAPP(X33661,X33662))
        | ~ hBOOL(hAPP(X33661,c_Orderings_Obot__class_Obot(tc_fun(X33663,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33663),X33662)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5585])])])]) ).

fof(i_0_7290,plain,
    ! [X33037,X33038,X33039,X33040,X33041] :
      ( ~ class_Orderings_Olinorder(X33041)
      | ~ c_List_Olinorder__class_Osorted(X33041,hAPP(c_List_Orev(X33041),hAPP(hAPP(c_List_Omap(X33040,X33041),X33039),X33038)))
      | hAPP(c_List_Ofilter(X33040,hAPP(hAPP(c_COMBB(X33041,tc_HOL_Obool,X33040),hAPP(c_Orderings_Oord__class_Oless(X33041),X33037)),X33039)),X33038) = c_List_OtakeWhile(X33040,hAPP(hAPP(c_COMBB(X33041,tc_HOL_Obool,X33040),hAPP(c_Orderings_Oord__class_Oless(X33041),X33037)),X33039),X33038) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__equals__takeWhile__sorted__rev])]) ).

fof(i_0_7291,plain,
    ! [X29692,X29693,X29694,X29695] : hAPP(hAPP(c_Product__Type_OSigma(X29695,X29694),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29695,tc_HOL_Obool),X29693)),X29692) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X29695,tc_HOL_Obool),tc_fun(tc_prod(X29695,X29694),tc_HOL_Obool)),X29693),hAPP(hAPP(c_COMBC(tc_fun(X29695,tc_HOL_Obool),tc_fun(X29695,tc_fun(X29694,tc_HOL_Obool)),tc_fun(tc_prod(X29695,X29694),tc_HOL_Obool)),c_Product__Type_OSigma(X29695,X29694)),X29692)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Union]) ).

fof(i_0_7292,plain,
    ! [X26349,X26350,X26351,X26352] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk212_4(X26349,X26350,X26351,X26352)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26351)))
        | X26352 = X26350
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26352),X26351) != X26350
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26350),X26349))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26351)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk213_4(X26349,X26350,X26351,X26352)),X26349))
        | X26352 = X26350
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26352),X26351) != X26350
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26350),X26349))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26351)) )
      & ( X26352 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk213_4(X26349,X26350,X26351,X26352)),esk212_4(X26349,X26350,X26351,X26352))
        | X26352 = X26350
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26352),X26351) != X26350
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26350),X26349))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26351)) ) ),
    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_7293,plain,
    ! [X26343,X26344,X26345,X26346] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk210_4(X26343,X26344,X26345,X26346)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26345)))
        | X26346 = X26344
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26346),X26345) != X26344
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26344),X26343))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26345)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk211_4(X26343,X26344,X26345,X26346)),X26343))
        | X26346 = X26344
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26346),X26345) != X26344
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26344),X26343))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26345)) )
      & ( X26346 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk211_4(X26343,X26344,X26345,X26346)),esk210_4(X26343,X26344,X26345,X26346))
        | X26346 = X26344
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26346),X26345) != X26344
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26344),X26343))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26345)) ) ),
    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_7294,plain,
    ! [X29038,X29039,X29040,X29041,X29042] : hAPP(hAPP(c_Finite__Set_Ofold(X29042,X29041,X29040),X29039),X29038) = c_HOL_OThe(X29041,c_Finite__Set_Ofold__graph(X29042,X29041,X29040,X29039,X29038)),
    inference(variable_rename,[status(thm)],[fact_fold__def]) ).

fof(i_0_7295,plain,
    ! [X23874,X23875,X23876,X23878,X23879,X23880,X23881,X23882,X23885] :
      ( ( ~ hBOOL(hAPP(X23876,esk138_3(X23874,X23875,X23876)))
        | hBOOL(hAPP(X23876,hAPP(hAPP(c_Product__Type_OPair(X23875,X23874),X23878),X23879))) )
      & ( ~ hBOOL(hAPP(X23882,hAPP(hAPP(c_Product__Type_OPair(X23881,X23880),esk139_3(X23880,X23881,X23882)),esk140_3(X23880,X23881,X23882))))
        | hBOOL(hAPP(X23882,X23885)) ) ),
    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_7296,plain,
    ! [X21274,X21275,X21276] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21276),X21275))
      | 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(X21276),X21274)),hAPP(c_Finite__Set_Ocard(X21276),X21275))),hAPP(c_Finite__Set_Ocard(X21276),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21276,tc_HOL_Obool)),X21274),X21275)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__card__le__card__Diff])]) ).

fof(i_0_7297,plain,
    ! [X29831,X29832,X29833,X29834] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X29833,tc_HOL_Obool)),esk373_4(X29831,X29832,X29833,X29834)),X29834))
        | c_Fun_Oinj__on(X29833,X29832,X29831,c_Complete__Lattice_OInf__class_OInf(tc_fun(X29833,tc_HOL_Obool),X29834))
        | X29834 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X29833,tc_HOL_Obool),tc_HOL_Obool)) )
      & ( ~ c_Fun_Oinj__on(X29833,X29832,X29831,esk373_4(X29831,X29832,X29833,X29834))
        | c_Fun_Oinj__on(X29833,X29832,X29831,c_Complete__Lattice_OInf__class_OInf(tc_fun(X29833,tc_HOL_Obool),X29834))
        | X29834 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X29833,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_7298,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_5586]) ).

fof(i_0_7299,plain,
    ! [X32361,X32362,X32363,X32364,X32365,X32366] :
      ( hAPP(hAPP(c_Map_Omap__of(X32366,X32365),X32364),X32363) != hAPP(c_Option_Ooption_OSome(X32365),X32362)
      | ~ hBOOL(hAPP(hAPP(X32361,X32363),X32362))
      | hAPP(hAPP(c_Map_Omap__of(X32366,X32365),hAPP(c_List_Ofilter(tc_prod(X32366,X32365),hAPP(c_Product__Type_Oprod_Oprod__case(X32366,X32365,tc_HOL_Obool),X32361)),X32364)),X32363) = hAPP(c_Option_Ooption_OSome(X32365),X32362) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__filter__in])]) ).

fof(i_0_7300,plain,
    ! [X34004,X34005,X34006,X34007,X34008,X34009,X34010,X34011,X34012] :
      ( ( hBOOL(hAPP(X34004,X34005))
        | ~ hBOOL(hAPP(hAPP(c_member(X34007),X34008),hAPP(c_List_Oset(X34007),c_List_Oreplicate(X34007,X34006,X34005))))
        | ~ hBOOL(hAPP(X34004,X34008)) )
      & ( X34006 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X34007),X34008),hAPP(c_List_Oset(X34007),c_List_Oreplicate(X34007,X34006,X34005))))
        | ~ hBOOL(hAPP(X34004,X34008)) )
      & ( hBOOL(hAPP(hAPP(c_member(X34012),esk517_4(X34009,X34010,X34011,X34012)),hAPP(c_List_Oset(X34012),c_List_Oreplicate(X34012,X34011,X34010))))
        | ~ hBOOL(hAPP(X34009,X34010))
        | X34011 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(X34009,esk517_4(X34009,X34010,X34011,X34012)))
        | ~ hBOOL(hAPP(X34009,X34010))
        | X34011 = 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_7301,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_7302,plain,
    ! [X20068,X20069,X20070,X20071,X20072] :
      ( ( ~ c_Nitpick_Orefl_H(X20069,X20068)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X20069,X20069)),hAPP(hAPP(c_Product__Type_OPair(X20069,X20069),X20070),X20070)),X20068)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20072,X20072)),hAPP(hAPP(c_Product__Type_OPair(X20072,X20072),esk63_2(X20071,X20072)),esk63_2(X20071,X20072))),X20071))
        | c_Nitpick_Orefl_H(X20072,X20071) ) ),
    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_7303,plain,
    ! [X26044,X26045,X26046,X26048] :
      ( ( hBOOL(hAPP(X26045,esk185_3(X26044,X26045,X26046)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26044))
        | ~ hBOOL(hAPP(X26045,X26048))
        | hBOOL(hAPP(X26045,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26048),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26044),X26046))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26046)) )
      & ( ~ hBOOL(hAPP(X26045,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk185_3(X26044,X26045,X26046)),X26046)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26044))
        | ~ hBOOL(hAPP(X26045,X26048))
        | hBOOL(hAPP(X26045,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26048),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26044),X26046))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26046)) ) ),
    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_7304,plain,
    ! [X26037,X26038,X26039,X26041] :
      ( ( hBOOL(hAPP(X26038,esk183_3(X26037,X26038,X26039)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26037))
        | ~ hBOOL(hAPP(X26038,X26041))
        | hBOOL(hAPP(X26038,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26041),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26037),X26039))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26039)) )
      & ( ~ hBOOL(hAPP(X26038,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk183_3(X26037,X26038,X26039)),X26039)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26037))
        | ~ hBOOL(hAPP(X26038,X26041))
        | hBOOL(hAPP(X26038,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26041),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26037),X26039))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26039)) ) ),
    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_7305,plain,
    ! [X33392,X33393,X33394,X33395,X33396] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X33396,X33395)),hAPP(X33396,X33394)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X33393,X33393)),hAPP(hAPP(c_Product__Type_OPair(X33393,X33393),X33395),X33394)),c_List_Omeasures(X33393,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X33393,tc_Nat_Onat)),X33396),X33392)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_measures__less])]) ).

cnf(i_0_7306,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_7307,plain,
    ! [X21079,X21080,X21081,X21082,X21083,X21084,X21085] :
      ( ~ c_Finite__Set_Ofolding__idem(X21085,X21084,X21083,X21082)
      | hAPP(c_Fun_Ocomp(X21084,X21084,X21081,hAPP(X21083,X21080)),hAPP(c_Fun_Ocomp(X21084,X21084,X21081,hAPP(X21083,X21080)),X21079)) = hAPP(c_Fun_Ocomp(X21084,X21084,X21081,hAPP(X21083,X21080)),X21079) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__left__comp])]) ).

fof(i_0_7308,plain,
    ! [X23822,X23823,X23824,X23825,X23826,X23827,X23828] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X23828),X23827),hAPP(hAPP(X23826,X23825),X23824)))
      | hBOOL(hAPP(hAPP(c_member(X23828),X23827),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X23823,X23822,tc_fun(X23828,tc_HOL_Obool)),X23826),hAPP(hAPP(c_Product__Type_OPair(X23823,X23822),X23825),X23824)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__splitI])]) ).

fof(i_0_7309,plain,
    ! [X34014,X34015,X34016,X34017,X34019,X34020,X34021,X34022,X34023] :
      ( ( hBOOL(hAPP(hAPP(c_member(X34017),esk518_4(X34014,X34015,X34016,X34017)),hAPP(c_List_Oset(X34017),c_List_Oreplicate(X34017,X34016,X34015))))
        | hBOOL(hAPP(X34014,X34015))
        | X34016 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(X34014,esk518_4(X34014,X34015,X34016,X34017)))
        | hBOOL(hAPP(X34014,X34015))
        | X34016 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(X34019,X34020))
        | ~ hBOOL(hAPP(hAPP(c_member(X34022),X34023),hAPP(c_List_Oset(X34022),c_List_Oreplicate(X34022,X34021,X34020))))
        | hBOOL(hAPP(X34019,X34023)) )
      & ( X34021 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X34022),X34023),hAPP(c_List_Oset(X34022),c_List_Oreplicate(X34022,X34021,X34020))))
        | hBOOL(hAPP(X34019,X34023)) ) ),
    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_7310,plain,
    ! [X31234,X31235,X31236,X31237,X31238,X31239] :
      ( hBOOL(hAPP(hAPP(c_member(X31239),X31238),hAPP(c_List_Oset(X31239),X31237)))
      | hAPP(c_Map_Omap__upds(X31239,X31236,X31235,X31237,X31234),X31238) = hAPP(X31235,X31238) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5587])]) ).

fof(i_0_7311,plain,
    ! [X30358,X30359,X30360,X30361] :
      ( ( hAPP(hAPP(c_Map_Omap__of(X30361,X30360),X30359),X30358) != c_Option_Ooption_ONone(X30360)
        | ~ hBOOL(hAPP(hAPP(c_member(X30361),X30358),hAPP(c_Set_Oimage(tc_prod(X30361,X30360),X30361,c_Product__Type_Ofst(X30361,X30360)),hAPP(c_List_Oset(tc_prod(X30361,X30360)),X30359)))) )
      & ( hBOOL(hAPP(hAPP(c_member(X30361),X30358),hAPP(c_Set_Oimage(tc_prod(X30361,X30360),X30361,c_Product__Type_Ofst(X30361,X30360)),hAPP(c_List_Oset(tc_prod(X30361,X30360)),X30359))))
        | hAPP(hAPP(c_Map_Omap__of(X30361,X30360),X30359),X30358) = c_Option_Ooption_ONone(X30360) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5588])]) ).

fof(i_0_7312,plain,
    ! [X30650,X30651,X30652,X30653] : hAPP(c_Relation_OImage(tc_List_Olist(X30653),tc_List_Olist(X30653),c_List_Olistrel(X30653,X30652)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X30653)),hAPP(hAPP(c_List_Olist_OCons(X30653),X30651),X30650)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X30653),tc_HOL_Obool)))) = c_List_Oset__Cons(X30653,hAPP(c_Relation_OImage(X30653,X30653,X30652),hAPP(hAPP(c_Set_Oinsert(X30653),X30651),c_Orderings_Obot__class_Obot(tc_fun(X30653,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X30653),tc_List_Olist(X30653),c_List_Olistrel(X30653,X30652)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X30653)),X30650),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X30653),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_listrel__Cons]) ).

fof(i_0_7313,plain,
    ! [X26824,X26825,X26826,X26827] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26827,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X26826)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X26827,tc_HOL_Obool),tc_Nat_Onat),X26825),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X26824))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26827,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26824,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26826),X26824))),X26825),
    inference(variable_rename,[status(thm)],[fact_UN__le__add__shift]) ).

cnf(i_0_7314,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_7315,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_7316,plain,
    ! [X31562,X31563,X31564,X31565,X31566,X31567] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31567)),X31566) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31565)),X31564)
      | c_Map_Omap__upds(X31567,X31565,X31563,hAPP(hAPP(c_List_Oappend(X31567),X31566),X31562),X31564) = c_Map_Omap__upds(X31567,X31565,X31563,X31566,X31564) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upds__append__drop])]) ).

fof(i_0_7317,plain,
    ! [X31568,X31569,X31570,X31571,X31572,X31573] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31573)),X31572) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31571)),X31570)
      | c_Map_Omap__upds(X31573,X31571,X31569,X31572,hAPP(hAPP(c_List_Oappend(X31571),X31570),X31568)) = c_Map_Omap__upds(X31573,X31571,X31569,X31572,X31570) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upds__append2__drop])]) ).

cnf(i_0_7318,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_5589]) ).

fof(i_0_7319,plain,
    ! [X30146,X30147,X30148,X30149,X30150,X30152,X30153,X30154,X30155,X30156,X30157] :
      ( ( X30147 = hAPP(c_Option_Ooption_OSome(X30150),esk396_5(X30146,X30147,X30148,X30149,X30150))
        | hAPP(hAPP(c_Option_Omap(X30150,X30149),X30148),X30147) != hAPP(c_Option_Ooption_OSome(X30149),X30146) )
      & ( hAPP(X30148,esk396_5(X30146,X30147,X30148,X30149,X30150)) = X30146
        | hAPP(hAPP(c_Option_Omap(X30150,X30149),X30148),X30147) != hAPP(c_Option_Ooption_OSome(X30149),X30146) )
      & ( X30153 != hAPP(c_Option_Ooption_OSome(X30156),X30157)
        | hAPP(X30154,X30157) != X30152
        | hAPP(hAPP(c_Option_Omap(X30156,X30155),X30154),X30153) = hAPP(c_Option_Ooption_OSome(X30155),X30152) ) ),
    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_option__map__eq__Some])])])])])]) ).

fof(i_0_7320,plain,
    ! [X18822,X18823,X18824,X18825,X18826,X18827] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X18827),X18826),X18825))
      | hAPP(c_Fun_Ooverride__on(X18827,X18824,X18823,X18822,X18825),X18826) = hAPP(X18822,X18826) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_override__on__apply__in])]) ).

fof(i_0_7321,plain,
    ! [X18690,X18691,X18692,X18693,X18694,X18695] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X18695),X18694),X18693))
        | hAPP(c_Fun_Ooverride__on(X18695,X18692,X18691,X18690,X18693),X18694) = hAPP(X18690,X18694) )
      & ( hBOOL(hAPP(hAPP(c_member(X18695),X18694),X18693))
        | hAPP(c_Fun_Ooverride__on(X18695,X18692,X18691,X18690,X18693),X18694) = hAPP(X18691,X18694) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5590])]) ).

fof(i_0_7322,plain,
    ! [X18937,X18938,X18939,X18940,X18941] : c_Map_Orestrict__map(X18941,X18940,X18939,hAPP(hAPP(c_Set_Oinsert(X18941),X18938),X18937)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18941,tc_Option_Ooption(X18940)),c_Map_Orestrict__map(X18941,X18940,X18939,X18937)),X18938),hAPP(X18939,X18938)),
    inference(variable_rename,[status(thm)],[fact_restrict__map__insert]) ).

cnf(i_0_7323,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_5591]) ).

fof(i_0_7324,plain,
    ! [X31993,X31994,X31995,X31996,X31997,X31998] :
      ( X31996 != hAPP(hAPP(c_List_Olist_OCons(X31995),X31997),X31998)
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31995),tc_List_Olist(X31995))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31995),tc_List_Olist(X31995)),X31994),hAPP(hAPP(c_List_Oappend(X31995),X31994),X31996))),c_List_Olexord(X31995,X31993))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__rightI])])]) ).

fof(i_0_7325,plain,
    ! [X30801,X30802,X30803,X30804,X30805,X30806,X30807] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30801)),X30803) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30801)),X30802)
        | X30803 != X30802 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30801,X30801)),X30804),hAPP(c_List_Oset(tc_prod(X30801,X30801)),hAPP(hAPP(c_List_Ozip(X30801,X30801),X30803),X30802))))
        | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X30801,X30801,tc_HOL_Obool),c_fequal),X30804))
        | X30803 != X30802 )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30805,X30805)),esk404_3(X30805,X30806,X30807)),hAPP(c_List_Oset(tc_prod(X30805,X30805)),hAPP(hAPP(c_List_Ozip(X30805,X30805),X30807),X30806))))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30805)),X30807) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30805)),X30806)
        | X30807 = X30806 )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X30805,X30805,tc_HOL_Obool),c_fequal),esk404_3(X30805,X30806,X30807)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30805)),X30807) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30805)),X30806)
        | X30807 = X30806 ) ),
    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_7326,plain,
    ! [X27200,X27201,X27202] :
      ( ( 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),esk252_3(X27200,X27201,X27202)),esk253_3(X27200,X27201,X27202))))
        | hBOOL(hAPP(hAPP(X27200,X27202),X27201))
        | ~ 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),X27202),X27201))) )
      & ( esk253_3(X27200,X27201,X27202) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(X27200,esk253_3(X27200,X27201,X27202)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,esk252_3(X27200,X27201,X27202),esk253_3(X27200,X27201,X27202))))
        | hBOOL(hAPP(hAPP(X27200,X27202),X27201))
        | ~ 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),X27202),X27201))) )
      & ( ~ hBOOL(hAPP(hAPP(X27200,esk252_3(X27200,X27201,X27202)),esk253_3(X27200,X27201,X27202)))
        | hBOOL(hAPP(hAPP(X27200,X27202),X27201))
        | ~ 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),X27202),X27201))) ) ),
    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_7327,plain,
    ! [X18793,X18794,X18795,X18796,X18797] :
      ( ~ c_Fun_Oinj__on(X18797,X18796,X18795,X18794)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18797,tc_HOL_Obool)),X18793),X18794))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18796,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18797,X18796,X18795),X18793)),hAPP(c_Set_Oimage(X18797,X18796,X18795),X18794))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__strict__subset])]) ).

fof(i_0_7328,plain,
    ! [X18798,X18799,X18800,X18801,X18802,X18803] :
      ( ~ c_Fun_Oinj__on(X18803,X18802,X18801,X18800)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18803,tc_HOL_Obool)),X18799),X18800))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18803,tc_HOL_Obool)),X18798),X18800))
      | hAPP(c_Set_Oimage(X18803,X18802,X18801),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18803,tc_HOL_Obool)),X18799),X18798)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18802,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18803,X18802,X18801),X18799)),hAPP(c_Set_Oimage(X18803,X18802,X18801),X18798)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__image__Int])]) ).

fof(i_0_7329,plain,
    ! [X18804,X18805,X18806,X18807,X18808,X18809] :
      ( ~ c_Fun_Oinj__on(X18809,X18808,X18807,X18806)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18809,tc_HOL_Obool)),X18805),X18806))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18809,tc_HOL_Obool)),X18804),X18806))
      | hAPP(c_Set_Oimage(X18809,X18808,X18807),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18809,tc_HOL_Obool)),X18805),X18804)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18808,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18809,X18808,X18807),X18805)),hAPP(c_Set_Oimage(X18809,X18808,X18807),X18804)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__image__set__diff])]) ).

fof(i_0_7330,plain,
    ! [X32308,X32309,X32310] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X32310),X32309))
      | hAPP(c_List_Ofilter(X32310,hAPP(hAPP(c_COMBC(X32310,tc_fun(X32310,tc_HOL_Obool),tc_HOL_Obool),c_member(X32310)),hAPP(c_List_Oset(X32310),c_List_Osublist(X32310,X32309,X32308)))),X32309) = c_List_Osublist(X32310,X32309,X32308) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__in__sublist])]) ).

cnf(i_0_7331,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_5592]) ).

cnf(i_0_7332,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk335_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_5513]) ).

cnf(i_0_7333,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oconcat(X2,X1)))
    | esk476_2(X1,X2) != esk477_2(X1,X2)
    | ~ hBOOL(hAPP(c_List_Odistinct(X2),esk475_2(X1,X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5524]) ).

fof(i_0_7334,plain,
    ! [X19062,X19063,X19064,X19065,X19066,X19067,X19068] :
      ( ( hAPP(c_Set_Oimage(X19064,X19063,X19062),c_Orderings_Otop__class_Otop(tc_fun(X19064,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X19063,tc_HOL_Obool))
        | hAPP(X19062,hAPP(c_Hilbert__Choice_Oinv__into(X19064,X19063,c_Orderings_Otop__class_Otop(tc_fun(X19064,tc_HOL_Obool)),X19062),X19065)) = X19065 )
      & ( hAPP(X19066,hAPP(c_Hilbert__Choice_Oinv__into(X19068,X19067,c_Orderings_Otop__class_Otop(tc_fun(X19068,tc_HOL_Obool)),X19066),esk39_3(X19066,X19067,X19068))) != esk39_3(X19066,X19067,X19068)
        | hAPP(c_Set_Oimage(X19068,X19067,X19066),c_Orderings_Otop__class_Otop(tc_fun(X19068,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X19067,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_7335,plain,
    ! [X34094,X34095,X34096,X34098,X34099,X34100,X34101,X34102] :
      ( ( hBOOL(hAPP(hAPP(c_member(X34096),esk521_3(X34094,X34095,X34096)),hAPP(c_List_Oset(X34096),X34094)))
        | ~ c_List_Olist__ex1(X34096,X34095,X34094) )
      & ( hBOOL(hAPP(X34095,esk521_3(X34094,X34095,X34096)))
        | ~ c_List_Olist__ex1(X34096,X34095,X34094) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X34096),X34098),hAPP(c_List_Oset(X34096),X34094)))
        | ~ hBOOL(hAPP(X34095,X34098))
        | X34098 = esk521_3(X34094,X34095,X34096)
        | ~ c_List_Olist__ex1(X34096,X34095,X34094) )
      & ( hBOOL(hAPP(hAPP(c_member(X34101),esk522_4(X34099,X34100,X34101,X34102)),hAPP(c_List_Oset(X34101),X34099)))
        | ~ hBOOL(hAPP(hAPP(c_member(X34101),X34102),hAPP(c_List_Oset(X34101),X34099)))
        | ~ hBOOL(hAPP(X34100,X34102))
        | c_List_Olist__ex1(X34101,X34100,X34099) )
      & ( hBOOL(hAPP(X34100,esk522_4(X34099,X34100,X34101,X34102)))
        | ~ hBOOL(hAPP(hAPP(c_member(X34101),X34102),hAPP(c_List_Oset(X34101),X34099)))
        | ~ hBOOL(hAPP(X34100,X34102))
        | c_List_Olist__ex1(X34101,X34100,X34099) )
      & ( esk522_4(X34099,X34100,X34101,X34102) != X34102
        | ~ hBOOL(hAPP(hAPP(c_member(X34101),X34102),hAPP(c_List_Oset(X34101),X34099)))
        | ~ hBOOL(hAPP(X34100,X34102))
        | c_List_Olist__ex1(X34101,X34100,X34099) ) ),
    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_7336,plain,
    ! [X33643,X33644,X33645,X33647,X33648,X33649,X33650,X33651] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33645),esk508_3(X33643,X33644,X33645)),hAPP(c_List_Oset(X33645),X33643)))
        | ~ c_List_Olist__ex1(X33645,X33644,X33643) )
      & ( hBOOL(hAPP(X33644,esk508_3(X33643,X33644,X33645)))
        | ~ c_List_Olist__ex1(X33645,X33644,X33643) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X33645),X33647),hAPP(c_List_Oset(X33645),X33643)))
        | ~ hBOOL(hAPP(X33644,X33647))
        | X33647 = esk508_3(X33643,X33644,X33645)
        | ~ c_List_Olist__ex1(X33645,X33644,X33643) )
      & ( hBOOL(hAPP(hAPP(c_member(X33650),esk509_4(X33648,X33649,X33650,X33651)),hAPP(c_List_Oset(X33650),X33648)))
        | ~ hBOOL(hAPP(hAPP(c_member(X33650),X33651),hAPP(c_List_Oset(X33650),X33648)))
        | ~ hBOOL(hAPP(X33649,X33651))
        | c_List_Olist__ex1(X33650,X33649,X33648) )
      & ( hBOOL(hAPP(X33649,esk509_4(X33648,X33649,X33650,X33651)))
        | ~ hBOOL(hAPP(hAPP(c_member(X33650),X33651),hAPP(c_List_Oset(X33650),X33648)))
        | ~ hBOOL(hAPP(X33649,X33651))
        | c_List_Olist__ex1(X33650,X33649,X33648) )
      & ( esk509_4(X33648,X33649,X33650,X33651) != X33651
        | ~ hBOOL(hAPP(hAPP(c_member(X33650),X33651),hAPP(c_List_Oset(X33650),X33648)))
        | ~ hBOOL(hAPP(X33649,X33651))
        | c_List_Olist__ex1(X33650,X33649,X33648) ) ),
    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_7337,plain,
    ! [X20585,X20586,X20587] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20587),X20586))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20587,tc_HOL_Obool)),hAPP(c_Set_Oimage(X20587,X20587,X20585),X20586)),X20586))
      | ~ c_Fun_Oinj__on(X20587,X20587,X20585,X20586)
      | hAPP(c_Set_Oimage(X20587,X20587,X20585),X20586) = X20586 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_endo__inj__surj])]) ).

fof(i_0_7338,plain,
    ! [X18816,X18817,X18818,X18819,X18820,X18821] :
      ( hBOOL(hAPP(hAPP(c_member(X18821),X18820),X18819))
      | hAPP(c_Fun_Ooverride__on(X18821,X18818,X18817,X18816,X18819),X18820) = hAPP(X18817,X18820) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5593])]) ).

fof(i_0_7339,plain,
    ! [X33030,X33031,X33032,X33033,X33034] : c_Map_Omap__upds(X33034,X33033,X33032,X33031,X33030) = c_Map_Omap__add(X33034,X33033,X33032,hAPP(c_Map_Omap__of(X33034,X33033),hAPP(c_List_Orev(tc_prod(X33034,X33033)),hAPP(hAPP(c_List_Ozip(X33034,X33033),X33031),X33030)))),
    inference(variable_rename,[status(thm)],[fact_map__upds__def]) ).

fof(i_0_7340,plain,
    ! [X32849,X32850,X32851,X32852,X32853] :
      ( ~ class_Orderings_Olinorder(X32853)
      | ~ hBOOL(hAPP(hAPP(c_member(X32853),hAPP(X32852,X32851)),hAPP(c_Set_Oimage(X32850,X32853,X32852),hAPP(c_List_Oset(X32850),X32849))))
      | c_List_Olinorder__class_Oinsort__insert__key(X32850,X32853,X32852,X32851,X32849) = X32849 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__insert__key__triv])]) ).

fof(i_0_7341,plain,
    ! [X32826,X32827,X32828] :
      ( ~ class_Orderings_Olinorder(X32828)
      | hAPP(c_List_Oset(X32828),c_List_Olinorder__class_Oinsort__insert__key(X32828,X32828,c_COMBI(X32828),X32827,X32826)) = hAPP(hAPP(c_Set_Oinsert(X32828),X32827),hAPP(c_List_Oset(X32828),X32826)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__insort__insert])]) ).

fof(i_0_7342,plain,
    ! [X30695,X30696,X30697] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30697,X30697),tc_HOL_Obool)),X30696),X30695))
      | ~ c_Relation_Orefl__on(X30697,c_Orderings_Otop__class_Otop(tc_fun(X30697,tc_HOL_Obool)),X30695)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X30697),tc_List_Olist(X30697)),tc_HOL_Obool)),c_List_Olistrel1(X30697,X30696)),c_List_Olistrel(X30697,X30695))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__subset__listrel])]) ).

cnf(i_0_7343,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_5594]) ).

cnf(i_0_7344,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_5573]) ).

fof(i_0_7345,plain,
    ! [X21325,X21326,X21327,X21328,X21329,X21330,X21331] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21330),X21326))
        | hAPP(hAPP(X21327,X21325),X21326) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21331,X21330,X21329),X21325),X21328),X21326)
        | ~ c_Big__Operators_Ocomm__monoid__big(X21331,X21330,X21329,X21328,X21327) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X21330),X21326))
        | hAPP(hAPP(X21327,X21325),X21326) = X21328
        | ~ c_Big__Operators_Ocomm__monoid__big(X21331,X21330,X21329,X21328,X21327) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5595])])]) ).

fof(i_0_7346,plain,
    ! [X21213,X21214,X21215,X21216,X21217,X21218,X21219] :
      ( ~ c_Finite__Set_Ofolding__image(X21219,X21218,X21217,X21216,X21215)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21218),X21214))
      | hAPP(hAPP(X21215,X21213),X21214) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21219,X21218,X21217),X21213),X21216),X21214) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image_Oeq__fold])]) ).

fof(i_0_7347,plain,
    ! [X29148,X29149,X29150,X29151,X29152,X29153] :
      ( ~ c_Finite__Set_Ofun__left__comm(X29153,X29152,X29151)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29153),X29150))
      | ~ hBOOL(hAPP(hAPP(c_member(X29153),X29149),X29150))
      | hAPP(hAPP(c_Finite__Set_Ofold(X29153,X29152,X29151),X29148),X29150) = hAPP(hAPP(X29151,X29149),hAPP(hAPP(c_Finite__Set_Ofold(X29153,X29152,X29151),X29148),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29153,tc_HOL_Obool)),X29150),hAPP(hAPP(c_Set_Oinsert(X29153),X29149),c_Orderings_Obot__class_Obot(tc_fun(X29153,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__rec])]) ).

fof(i_0_7348,plain,
    ! [X33666,X33667,X33668,X33669,X33670] :
      ( ( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X33668,X33669)),X33667),X33666))
        | ~ hBOOL(hAPP(hAPP(c_member(X33668),X33670),hAPP(c_List_Oset(X33668),c_Enum_Oenum__class_Oenum(X33668))))
        | hAPP(X33667,X33670) = hAPP(X33666,X33670)
        | ~ class_HOL_Oequal(X33669)
        | ~ class_Enum_Oenum(X33668) )
      & ( hBOOL(hAPP(hAPP(c_member(X33668),esk514_4(X33666,X33667,X33668,X33669)),hAPP(c_List_Oset(X33668),c_Enum_Oenum__class_Oenum(X33668))))
        | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X33668,X33669)),X33667),X33666))
        | ~ class_HOL_Oequal(X33669)
        | ~ class_Enum_Oenum(X33668) )
      & ( hAPP(X33667,esk514_4(X33666,X33667,X33668,X33669)) != hAPP(X33666,esk514_4(X33666,X33667,X33668,X33669))
        | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X33668,X33669)),X33667),X33666))
        | ~ class_HOL_Oequal(X33669)
        | ~ class_Enum_Oenum(X33668) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__fun__def])])])])]) ).

fof(i_0_7349,plain,
    ! [X19455,X19456,X19457,X19458,X19459,X19460] : hAPP(c_Set_Ovimage(X19460,X19459,hAPP(c_Fun_Ocomp(X19458,X19459,X19460,X19457),X19456)),X19455) = hAPP(c_Set_Ovimage(X19460,X19458,X19456),hAPP(c_Set_Ovimage(X19458,X19459,X19457),X19455)),
    inference(variable_rename,[status(thm)],[fact_vimage__compose]) ).

fof(i_0_7350,plain,
    ! [X18950,X18951,X18952,X18953,X18954,X18955] : hAPP(c_Set_Oimage(X18955,X18954,hAPP(c_Fun_Ocomp(X18953,X18954,X18955,X18952),X18951)),X18950) = hAPP(c_Set_Oimage(X18953,X18954,X18952),hAPP(c_Set_Oimage(X18955,X18953,X18951),X18950)),
    inference(variable_rename,[status(thm)],[fact_image__compose]) ).

fof(i_0_7351,plain,
    ! [X28872,X28873,X28874,X28876,X28877,X28878,X28879] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28874,X28874)),X28873),c_Transitive__Closure_Ortrancl(X28874,X28872)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28874,X28874)),X28873),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28874,X28874),tc_HOL_Obool),esk331_3(X28872,X28873,X28874)),X28872))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28878,X28878)),X28877),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28878,X28878),tc_HOL_Obool),X28879),X28876)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28878,X28878)),X28877),c_Transitive__Closure_Ortrancl(X28878,X28876))) ) ),
    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_7352,plain,
    ! [X28407,X28408,X28409,X28410,X28411,X28412,X28413] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X28413,X28412,X28411,X28410),X28409),X28408),X28407) = hAPP(hAPP(X28408,hAPP(c_Product__Type_Ofst(X28412,X28411),hAPP(X28409,X28407))),hAPP(c_Product__Type_Osnd(X28412,X28411),hAPP(X28409,X28407))),
    inference(variable_rename,[status(thm)],[fact_scomp__unfold]) ).

fof(i_0_7353,plain,
    ! [X20053,X20054,X20055,X20056,X20057] :
      ( ( hAPP(c_Relation_OImage(X20057,X20057,X20055),hAPP(hAPP(c_Set_Oinsert(X20057),X20054),c_Orderings_Obot__class_Obot(tc_fun(X20057,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X20057,X20057,X20055),hAPP(hAPP(c_Set_Oinsert(X20057),X20053),c_Orderings_Obot__class_Obot(tc_fun(X20057,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20057,X20057)),hAPP(hAPP(c_Product__Type_OPair(X20057,X20057),X20054),X20053)),X20055))
        | ~ c_Equiv__Relations_Oequiv(X20057,X20056,X20055) )
      & ( hBOOL(hAPP(hAPP(c_member(X20057),X20054),X20056))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20057,X20057)),hAPP(hAPP(c_Product__Type_OPair(X20057,X20057),X20054),X20053)),X20055))
        | ~ c_Equiv__Relations_Oequiv(X20057,X20056,X20055) )
      & ( hBOOL(hAPP(hAPP(c_member(X20057),X20053),X20056))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20057,X20057)),hAPP(hAPP(c_Product__Type_OPair(X20057,X20057),X20054),X20053)),X20055))
        | ~ c_Equiv__Relations_Oequiv(X20057,X20056,X20055) )
      & ( hAPP(c_Relation_OImage(X20057,X20057,X20055),hAPP(hAPP(c_Set_Oinsert(X20057),X20054),c_Orderings_Obot__class_Obot(tc_fun(X20057,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X20057,X20057,X20055),hAPP(hAPP(c_Set_Oinsert(X20057),X20053),c_Orderings_Obot__class_Obot(tc_fun(X20057,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(X20057),X20054),X20056))
        | ~ hBOOL(hAPP(hAPP(c_member(X20057),X20053),X20056))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X20057,X20057)),hAPP(hAPP(c_Product__Type_OPair(X20057,X20057),X20054),X20053)),X20055))
        | ~ c_Equiv__Relations_Oequiv(X20057,X20056,X20055) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__eq__iff])])]) ).

fof(i_0_7354,plain,
    ! [X22113,X22114,X22115] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22115),c_Groups_Ozero__class_Ozero(X22115)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22115),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22115),X22114),X22114)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22115),X22113),X22113))))
        | X22114 != c_Groups_Ozero__class_Ozero(X22115)
        | X22113 != c_Groups_Ozero__class_Ozero(X22115)
        | ~ class_Rings_Olinordered__ring__strict(X22115) )
      & ( X22114 = c_Groups_Ozero__class_Ozero(X22115)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22115),c_Groups_Ozero__class_Ozero(X22115)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22115),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22115),X22114),X22114)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22115),X22113),X22113))))
        | ~ class_Rings_Olinordered__ring__strict(X22115) )
      & ( X22113 = c_Groups_Ozero__class_Ozero(X22115)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22115),c_Groups_Ozero__class_Ozero(X22115)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22115),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22115),X22114),X22114)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22115),X22113),X22113))))
        | ~ class_Rings_Olinordered__ring__strict(X22115) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff])])]) ).

fof(i_0_7355,plain,
    ! [X28945,X28946] : c_Transitive__Closure_Ortrancl(X28946,X28945) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X28946,X28946),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(X28946,X28946),tc_HOL_Obool),tc_fun(tc_prod(X28946,X28946),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X28946,X28946),tc_HOL_Obool)),X28945)),
    inference(variable_rename,[status(thm)],[fact_rtrancl__is__UN__rel__pow]) ).

fof(i_0_7356,plain,
    ! [X33440,X33441,X33442,X33443] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33443),esk483_4(X33440,X33441,X33442,X33443)),hAPP(c_List_Oset(X33443),X33442)))
        | c_List_OtakeWhile(X33443,X33441,hAPP(hAPP(c_List_Oappend(X33443),X33442),X33440)) = hAPP(hAPP(c_List_Oappend(X33443),X33442),c_List_OtakeWhile(X33443,X33441,X33440)) )
      & ( ~ hBOOL(hAPP(X33441,esk483_4(X33440,X33441,X33442,X33443)))
        | c_List_OtakeWhile(X33443,X33441,hAPP(hAPP(c_List_Oappend(X33443),X33442),X33440)) = hAPP(hAPP(c_List_Oappend(X33443),X33442),c_List_OtakeWhile(X33443,X33441,X33440)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__append2])])])]) ).

fof(i_0_7357,plain,
    ! [X18989,X18990,X18991,X18992,X18993,X18994] :
      ( ~ c_Fun_Oinj__on(X18994,X18993,hAPP(c_Fun_Ocomp(X18992,X18993,X18994,X18991),X18990),X18989)
      | c_Fun_Oinj__on(X18992,X18993,X18991,hAPP(c_Set_Oimage(X18994,X18992,X18990),X18989)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__imageI])]) ).

fof(i_0_7358,plain,
    ! [X26722,X26723,X26724,X26726,X26727] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26724),esk233_3(X26722,X26723,X26724)),X26723))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26724,tc_Nat_Onat),X26722),X26723) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26724),X26723)) )
      & ( hAPP(X26722,esk233_3(X26722,X26723,X26724)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26724,tc_Nat_Onat),X26722),X26723) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26724),X26723)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26724),X26726),X26723))
        | esk233_3(X26722,X26723,X26724) = X26726
        | hAPP(X26722,X26726) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26724,tc_Nat_Onat),X26722),X26723) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26724),X26723)) )
      & ( hBOOL(hAPP(hAPP(c_member(X26724),esk234_4(X26722,X26723,X26724,X26727)),X26723))
        | ~ hBOOL(hAPP(hAPP(c_member(X26724),X26727),X26723))
        | hAPP(X26722,X26727) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26724,tc_Nat_Onat),X26722),X26723) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26724),X26723)) )
      & ( X26727 != esk234_4(X26722,X26723,X26724,X26727)
        | ~ hBOOL(hAPP(hAPP(c_member(X26724),X26727),X26723))
        | hAPP(X26722,X26727) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26724,tc_Nat_Onat),X26722),X26723) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26724),X26723)) )
      & ( hAPP(X26722,esk234_4(X26722,X26723,X26724,X26727)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X26724),X26727),X26723))
        | hAPP(X26722,X26727) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26724,tc_Nat_Onat),X26722),X26723) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26724),X26723)) ) ),
    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_7359,plain,
    ! [X32770,X32771,X32772] :
      ( ~ class_Orderings_Olinorder(X32772)
      | ~ c_List_Olinorder__class_Osorted(X32772,X32771)
      | c_List_Olinorder__class_Osorted(X32772,c_List_Olinorder__class_Oinsort__insert__key(X32772,X32772,c_COMBI(X32772),X32770,X32771)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort__insert])]) ).

fof(i_0_7360,plain,
    ! [X27071,X27072,X27073,X27074,X27075] :
      ( ~ class_Rings_Olinordered__idom(X27075)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27075),hAPP(c_Groups_Oabs__class_Oabs(X27075),X27074)),X27073))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27075),hAPP(c_Groups_Oabs__class_Oabs(X27075),X27072)),X27071))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27075),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27075),hAPP(c_Groups_Oabs__class_Oabs(X27075),X27074)),hAPP(c_Groups_Oabs__class_Oabs(X27075),X27072))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27075),X27073),X27071))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__less])]) ).

fof(i_0_7361,plain,
    ! [X29154,X29155,X29156,X29157,X29158,X29159] :
      ( ~ c_Finite__Set_Ofun__left__comm(X29159,X29158,X29157)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29159),X29156))
      | hAPP(hAPP(c_Finite__Set_Ofold(X29159,X29158,X29157),X29155),hAPP(hAPP(c_Set_Oinsert(X29159),X29154),X29156)) = hAPP(hAPP(X29157,X29154),hAPP(hAPP(c_Finite__Set_Ofold(X29159,X29158,X29157),X29155),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29159,tc_HOL_Obool)),X29156),hAPP(hAPP(c_Set_Oinsert(X29159),X29154),c_Orderings_Obot__class_Obot(tc_fun(X29159,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert__remove])]) ).

fof(i_0_7362,plain,
    ! [X32981,X32982,X32983,X32984,X32985] : c_List_OtakeWhile(X32985,X32984,hAPP(hAPP(c_List_Omap(X32983,X32985),X32982),X32981)) = hAPP(hAPP(c_List_Omap(X32983,X32985),X32982),c_List_OtakeWhile(X32983,hAPP(c_Fun_Ocomp(X32985,tc_HOL_Obool,X32983,X32984),X32982),X32981)),
    inference(variable_rename,[status(thm)],[fact_takeWhile__map]) ).

fof(i_0_7363,plain,
    ! [X26729,X26730,X26731,X26733,X26734] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26731),esk235_3(X26729,X26730,X26731)),X26730))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26731,tc_Nat_Onat),X26729),X26730) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26731),X26730)) )
      & ( hAPP(X26729,esk235_3(X26729,X26730,X26731)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26731,tc_Nat_Onat),X26729),X26730) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26731),X26730)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26731),X26733),X26730))
        | esk235_3(X26729,X26730,X26731) = X26733
        | hAPP(X26729,X26733) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26731,tc_Nat_Onat),X26729),X26730) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26731),X26730)) )
      & ( hBOOL(hAPP(hAPP(c_member(X26731),esk236_4(X26729,X26730,X26731,X26734)),X26730))
        | ~ hBOOL(hAPP(hAPP(c_member(X26731),X26734),X26730))
        | hAPP(X26729,X26734) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26731,tc_Nat_Onat),X26729),X26730) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26731),X26730)) )
      & ( X26734 != esk236_4(X26729,X26730,X26731,X26734)
        | ~ hBOOL(hAPP(hAPP(c_member(X26731),X26734),X26730))
        | hAPP(X26729,X26734) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26731,tc_Nat_Onat),X26729),X26730) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26731),X26730)) )
      & ( hAPP(X26729,esk236_4(X26729,X26730,X26731,X26734)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X26731),X26734),X26730))
        | hAPP(X26729,X26734) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26731,tc_Nat_Onat),X26729),X26730) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26731),X26730)) ) ),
    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_7364,plain,
    ! [X18275,X18276,X18277,X18278] :
      ( ~ c_Orderings_Oorder__class_Omono(tc_fun(X18278,tc_HOL_Obool),tc_fun(X18278,tc_HOL_Obool),X18277)
      | ~ hBOOL(hAPP(hAPP(c_member(X18278),X18276),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X18278,tc_HOL_Obool),X18277)))
      | hBOOL(hAPP(hAPP(c_member(X18278),X18276),hAPP(X18277,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18278,tc_HOL_Obool)),X18275),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X18278,tc_HOL_Obool),X18277))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gfp__fun__UnI2])]) ).

fof(i_0_7365,plain,
    ! [X28803,X28804,X28805] :
      ( ~ c_Relation_Orefl__on(X28805,X28804,X28803)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28805,X28805),tc_HOL_Obool)),X28803),hAPP(hAPP(c_Relation_Orel__comp(X28805,X28805,X28805),hAPP(c_Relation_Oconverse(X28805,X28805),X28803)),X28803))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__comp__subset])]) ).

fof(i_0_7366,plain,
    ! [X18983,X18984,X18985,X18986,X18987,X18988] :
      ( ~ c_Fun_Oinj__on(X18988,X18987,X18986,X18985)
      | ~ c_Fun_Oinj__on(X18987,X18984,X18983,hAPP(c_Set_Oimage(X18988,X18987,X18986),X18985))
      | c_Fun_Oinj__on(X18988,X18984,hAPP(c_Fun_Ocomp(X18987,X18984,X18988,X18983),X18986),X18985) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__inj__on])]) ).

fof(i_0_7367,plain,
    ! [X31698,X31699,X31700,X31701,X31702] : c_Enum_Oproduct(X31702,X31701,hAPP(hAPP(c_List_Olist_OCons(X31702),X31700),X31699),X31698) = hAPP(hAPP(c_List_Oappend(tc_prod(X31702,X31701)),hAPP(hAPP(c_List_Omap(X31701,tc_prod(X31702,X31701)),hAPP(c_Product__Type_OPair(X31702,X31701),X31700)),X31698)),c_Enum_Oproduct(X31702,X31701,X31699,X31698)),
    inference(variable_rename,[status(thm)],[fact_product_Osimps_I2_J]) ).

cnf(i_0_7368,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_5596]) ).

cnf(i_0_7369,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_5597]) ).

fof(i_0_7370,plain,
    ! [X32087,X32088] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X32088),hAPP(c_List_Oset(tc_Nat_Onat),X32087)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32088),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)),X32087))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_elem__le__sum])]) ).

fof(i_0_7371,plain,
    ! [X19995,X19996,X19997,X19998,X19999,X20000] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20000),X19999),X19998))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20000,X19997)),hAPP(hAPP(c_Product__Type_OPair(X20000,X19997),X19999),X19996)),X19995))
      | hBOOL(hAPP(hAPP(c_member(X19997),X19996),hAPP(c_Relation_OImage(X20000,X19997,X19995),X19998))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__ImageI])]) ).

fof(i_0_7372,plain,
    ! [X30183,X30184,X30185,X30186,X30187,X30188] : hAPP(hAPP(c_Option_Omap(X30188,X30187),X30186),hAPP(hAPP(c_Option_Omap(X30185,X30188),X30184),X30183)) = hAPP(hAPP(c_Option_Omap(X30185,X30187),hAPP(c_Fun_Ocomp(X30188,X30187,X30185,X30186),X30184)),X30183),
    inference(variable_rename,[status(thm)],[fact_Option_Omap_Ocompositionality]) ).

fof(i_0_7373,plain,
    ! [X30177,X30178,X30179,X30180,X30181,X30182] : hAPP(hAPP(c_Option_Omap(X30182,X30181),X30180),hAPP(hAPP(c_Option_Omap(X30179,X30182),X30178),X30177)) = hAPP(hAPP(c_Option_Omap(X30179,X30181),hAPP(c_Fun_Ocomp(X30182,X30181,X30179,X30180),X30178)),X30177),
    inference(variable_rename,[status(thm)],[fact_option__map__comp]) ).

fof(i_0_7374,plain,
    ! [X30094,X30095,X30096,X30097,X30098,X30099] : hAPP(hAPP(c_List_Omap(X30099,X30098),X30097),hAPP(hAPP(c_List_Omap(X30096,X30099),X30095),X30094)) = hAPP(hAPP(c_List_Omap(X30096,X30098),hAPP(c_Fun_Ocomp(X30099,X30098,X30096,X30097),X30095)),X30094),
    inference(variable_rename,[status(thm)],[fact_List_Omap_Ocompositionality]) ).

fof(i_0_7375,plain,
    ! [X30088,X30089,X30090,X30091,X30092,X30093] : hAPP(hAPP(c_List_Omap(X30093,X30092),X30091),hAPP(hAPP(c_List_Omap(X30090,X30093),X30089),X30088)) = hAPP(hAPP(c_List_Omap(X30090,X30092),hAPP(c_Fun_Ocomp(X30093,X30092,X30090,X30091),X30089)),X30088),
    inference(variable_rename,[status(thm)],[fact_map__map]) ).

fof(i_0_7376,plain,
    ! [X31439,X31440,X31441,X31442] : hAPP(hAPP(c_List_Otake(X31442),X31441),hAPP(hAPP(c_List_Olist_OCons(X31442),X31440),X31439)) = c_Nat_Onat_Onat__case(tc_List_Olist(X31442),c_List_Olist_ONil(X31442),hAPP(hAPP(c_COMBB(tc_List_Olist(X31442),tc_List_Olist(X31442),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X31442),X31440)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X31442),tc_List_Olist(X31442)),c_List_Otake(X31442)),X31439)),X31441),
    inference(variable_rename,[status(thm)],[fact_take__Cons]) ).

fof(i_0_7377,plain,
    ! [X19349,X19350,X19351,X19352,X19353] : hAPP(c_Relation_OImage(X19353,X19352,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X19353,X19352),tc_HOL_Obool)),X19351),X19350)),X19349) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19352,tc_HOL_Obool)),hAPP(c_Relation_OImage(X19353,X19352,X19351),X19349)),hAPP(c_Relation_OImage(X19353,X19352,X19350),X19349)),
    inference(variable_rename,[status(thm)],[fact_Un__Image]) ).

cnf(i_0_7378,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_5598]) ).

fof(i_0_7379,plain,
    ! [X28446,X28447,X28448,X28449,X28450] :
      ( ( X28450 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_Random_Oiterate(X28449,X28448,X28450,X28447),X28446) = hAPP(c_Product__Type_OPair(X28449,X28448),X28446) )
      & ( X28450 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_Random_Oiterate(X28449,X28448,X28450,X28447),X28446) = hAPP(hAPP(c_Product__Type_Oscomp(X28448,X28449,X28448,tc_prod(X28449,X28448)),hAPP(X28447,X28446)),c_Random_Oiterate(X28449,X28448,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X28450),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X28447)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iterate_Osimps])]) ).

fof(i_0_7380,plain,
    ! [X20030,X20031,X20032,X20033,X20034] :
      ( ~ c_Equiv__Relations_Oequiv(X20034,X20033,X20032)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20034,X20034)),hAPP(hAPP(c_Product__Type_OPair(X20034,X20034),X20031),X20030)),X20032))
      | hAPP(c_Relation_OImage(X20034,X20034,X20032),hAPP(hAPP(c_Set_Oinsert(X20034),X20031),c_Orderings_Obot__class_Obot(tc_fun(X20034,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X20034,X20034,X20032),hAPP(hAPP(c_Set_Oinsert(X20034),X20030),c_Orderings_Obot__class_Obot(tc_fun(X20034,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__eq])]) ).

fof(i_0_7381,plain,
    ! [X27804,X27805,X27806,X27807,X27808,X27809] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27809),X27807),X27805))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27809,X27808)),hAPP(hAPP(c_Product__Type_OPair(X27809,X27808),X27807),X27806)),hAPP(hAPP(c_Product__Type_OSigma(X27809,X27808),X27805),X27804))) )
      & ( hBOOL(hAPP(hAPP(c_member(X27808),X27806),hAPP(X27804,X27807)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27809,X27808)),hAPP(hAPP(c_Product__Type_OPair(X27809,X27808),X27807),X27806)),hAPP(hAPP(c_Product__Type_OSigma(X27809,X27808),X27805),X27804))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27809),X27807),X27805))
        | ~ hBOOL(hAPP(hAPP(c_member(X27808),X27806),hAPP(X27804,X27807)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X27809,X27808)),hAPP(hAPP(c_Product__Type_OPair(X27809,X27808),X27807),X27806)),hAPP(hAPP(c_Product__Type_OSigma(X27809,X27808),X27805),X27804))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__Sigma__iff])])]) ).

fof(i_0_7382,plain,
    ! [X27786,X27787,X27788,X27789,X27790,X27791] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27791),X27789),X27787))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27791,X27790)),hAPP(hAPP(c_Product__Type_OPair(X27791,X27790),X27789),X27788)),hAPP(hAPP(c_Product__Type_OSigma(X27791,X27790),X27787),X27786))) )
      & ( hBOOL(hAPP(hAPP(c_member(X27790),X27788),hAPP(X27786,X27789)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27791,X27790)),hAPP(hAPP(c_Product__Type_OPair(X27791,X27790),X27789),X27788)),hAPP(hAPP(c_Product__Type_OSigma(X27791,X27790),X27787),X27786))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5599])])]) ).

fof(i_0_7383,plain,
    ! [X27792,X27793,X27794,X27795,X27796,X27797] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27797,X27796)),hAPP(hAPP(c_Product__Type_OPair(X27797,X27796),X27795),X27794)),hAPP(hAPP(c_Product__Type_OSigma(X27797,X27796),X27793),X27792)))
      | hBOOL(hAPP(hAPP(c_member(X27796),X27794),hAPP(X27792,X27795))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaD2])]) ).

fof(i_0_7384,plain,
    ! [X30659,X30660,X30661] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30661,X30661),tc_HOL_Obool)),X30660),X30659))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X30661),tc_List_Olist(X30661)),tc_HOL_Obool)),c_List_Olistrel(X30661,X30660)),c_List_Olistrel(X30661,X30659))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__mono])]) ).

fof(i_0_7385,plain,
    ! [X30597,X30598,X30599] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30599,X30599),tc_HOL_Obool)),X30598),X30597))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X30599),tc_List_Olist(X30599)),tc_HOL_Obool)),c_List_Olistrel1(X30599,X30598)),c_List_Olistrel1(X30599,X30597))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__mono])]) ).

fof(i_0_7386,plain,
    ! [X33748,X33749,X33750,X33751,X33752] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X33752,X33751,X33750,X33749,X33748) = hAPP(c_Option_Ooption_Ooption__case(X33752,tc_prod(X33751,tc_Lazy__Sequence_Olazy__sequence(X33751)),X33750,hAPP(c_Product__Type_Oprod_Oprod__case(X33751,tc_Lazy__Sequence_Olazy__sequence(X33751),X33752),X33749)),hAPP(c_Lazy__Sequence_Oyield(X33751),X33748)),
    inference(variable_rename,[status(thm)],[fact_seq__case]) ).

cnf(i_0_7387,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_5600]) ).

fof(i_0_7388,plain,
    ! [X28439,X28440,X28441,X28442,X28443,X28444,X28445] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X28445,X28444,X28443,X28442),X28441),X28440),X28439) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28444,X28443,X28442),X28440),hAPP(X28441,X28439)),
    inference(variable_rename,[status(thm)],[fact_scomp__def]) ).

fof(i_0_7389,plain,
    ! [X28432,X28433,X28434,X28435,X28436,X28437,X28438] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X28438,X28437,X28436,X28435),X28434),X28433),X28432) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28437,X28436,X28435),X28433),hAPP(X28434,X28432)),
    inference(variable_rename,[status(thm)],[fact_scomp__apply]) ).

fof(i_0_7390,plain,
    ! [X17504,X17505,X17506,X17507] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17507,tc_HOL_Obool)),X17506),X17505))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17507,tc_HOL_Obool)),X17504),X17505))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17507,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17507,tc_HOL_Obool)),X17506),X17504)),X17505)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__least])]) ).

fof(i_0_7391,plain,
    ! [X20794,X20795,X20796,X20797,X20798] :
      ( ~ c_Finite__Set_Ofolding__one(X20798,X20797,X20796)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20798),X20795))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20798),X20794))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20798,tc_HOL_Obool)),X20795),X20794) = c_Orderings_Obot__class_Obot(tc_fun(X20798,tc_HOL_Obool))
      | hAPP(hAPP(X20797,hAPP(X20796,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20798,tc_HOL_Obool)),X20795),X20794))),hAPP(X20796,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20798,tc_HOL_Obool)),X20795),X20794))) = hAPP(hAPP(X20797,hAPP(X20796,X20795)),hAPP(X20796,X20794)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__inter])]) ).

fof(i_0_7392,plain,
    ! [X18773,X18774,X18775,X18776,X18777] :
      ( ~ c_Fun_Oinj__on(X18777,X18776,X18775,X18774)
      | ~ hBOOL(hAPP(hAPP(c_member(X18776),X18773),hAPP(c_Set_Oimage(X18777,X18776,X18775),X18774)))
      | hAPP(X18775,hAPP(c_Fun_Othe__inv__into(X18777,X18776,X18774,X18775),X18773)) = X18773 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__the__inv__into__f])]) ).

cnf(i_0_7393,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_5601]) ).

cnf(i_0_7394,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_5602]) ).

fof(i_0_7395,plain,
    ! [X29602,X29603,X29604,X29605] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X29605,tc_HOL_Obool),tc_fun(X29604,tc_HOL_Obool)),X29603),hAPP(hAPP(c_COMBC(tc_fun(X29605,tc_HOL_Obool),tc_fun(X29605,tc_fun(X29604,tc_HOL_Obool)),tc_fun(X29604,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29605,tc_fun(X29604,tc_HOL_Obool))),X29602)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29605,tc_fun(X29604,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29605,tc_HOL_Obool),X29603)),X29602),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I8_J]) ).

fof(i_0_7396,plain,
    ! [X29675,X29676,X29677,X29678] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X29678,tc_HOL_Obool),tc_fun(X29677,tc_HOL_Obool)),X29676),hAPP(hAPP(c_COMBC(tc_fun(X29678,tc_HOL_Obool),tc_fun(X29678,tc_fun(X29677,tc_HOL_Obool)),tc_fun(X29677,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29678,tc_fun(X29677,tc_HOL_Obool))),X29675)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29678,tc_fun(X29677,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29678,tc_HOL_Obool),X29676)),X29675),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I8_J]) ).

fof(i_0_7397,plain,
    ! [X29606,X29607,X29608,X29609] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29609,tc_fun(X29608,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29609,tc_HOL_Obool),X29607)),X29606) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X29609,tc_HOL_Obool),tc_fun(X29608,tc_HOL_Obool)),X29607),hAPP(hAPP(c_COMBC(tc_fun(X29609,tc_HOL_Obool),tc_fun(X29609,tc_fun(X29608,tc_HOL_Obool)),tc_fun(X29608,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29609,tc_fun(X29608,tc_HOL_Obool))),X29606)),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I8_J]) ).

fof(i_0_7398,plain,
    ! [X29671,X29672,X29673,X29674] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29674,tc_fun(X29673,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29674,tc_HOL_Obool),X29672)),X29671) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X29674,tc_HOL_Obool),tc_fun(X29673,tc_HOL_Obool)),X29672),hAPP(hAPP(c_COMBC(tc_fun(X29674,tc_HOL_Obool),tc_fun(X29674,tc_fun(X29673,tc_HOL_Obool)),tc_fun(X29673,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29674,tc_fun(X29673,tc_HOL_Obool))),X29671)),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I8_J]) ).

fof(i_0_7399,plain,
    ! [X18701,X18702,X18703,X18704,X18705,X18706,X18707,X18708,X18709,X18710] :
      ( ( ~ c_Fun_Oinj__on(X18704,X18703,X18702,X18701)
        | ~ hBOOL(hAPP(hAPP(c_member(X18704),X18705),X18701))
        | ~ hBOOL(hAPP(hAPP(c_member(X18704),X18706),X18701))
        | hAPP(X18702,X18705) != hAPP(X18702,X18706)
        | X18705 = X18706 )
      & ( hBOOL(hAPP(hAPP(c_member(X18710),esk32_4(X18707,X18708,X18709,X18710)),X18707))
        | c_Fun_Oinj__on(X18710,X18709,X18708,X18707) )
      & ( hBOOL(hAPP(hAPP(c_member(X18710),esk33_4(X18707,X18708,X18709,X18710)),X18707))
        | c_Fun_Oinj__on(X18710,X18709,X18708,X18707) )
      & ( hAPP(X18708,esk32_4(X18707,X18708,X18709,X18710)) = hAPP(X18708,esk33_4(X18707,X18708,X18709,X18710))
        | c_Fun_Oinj__on(X18710,X18709,X18708,X18707) )
      & ( esk32_4(X18707,X18708,X18709,X18710) != esk33_4(X18707,X18708,X18709,X18710)
        | c_Fun_Oinj__on(X18710,X18709,X18708,X18707) ) ),
    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_7400,plain,
    ! [X28550,X28551,X28552] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28552,X28552),tc_HOL_Obool)),X28551),X28550))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28552,X28552),tc_HOL_Obool)),X28550),c_Transitive__Closure_Ortrancl(X28552,X28551)))
      | c_Transitive__Closure_Ortrancl(X28552,X28550) = c_Transitive__Closure_Ortrancl(X28552,X28551) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset])]) ).

fof(i_0_7401,plain,
    ! [X20063,X20064,X20065,X20066,X20067] :
      ( hAPP(c_Relation_OImage(X20067,X20067,X20066),hAPP(hAPP(c_Set_Oinsert(X20067),X20065),c_Orderings_Obot__class_Obot(tc_fun(X20067,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X20067,X20067,X20066),hAPP(hAPP(c_Set_Oinsert(X20067),X20064),c_Orderings_Obot__class_Obot(tc_fun(X20067,tc_HOL_Obool))))
      | ~ c_Equiv__Relations_Oequiv(X20067,X20063,X20066)
      | ~ hBOOL(hAPP(hAPP(c_member(X20067),X20064),X20063))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X20067,X20067)),hAPP(hAPP(c_Product__Type_OPair(X20067,X20067),X20065),X20064)),X20066)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class])]) ).

fof(i_0_7402,plain,
    ! [X27798,X27799,X27800,X27801,X27802,X27803] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27803,X27802)),hAPP(hAPP(c_Product__Type_OPair(X27803,X27802),X27801),X27800)),hAPP(hAPP(c_Product__Type_OSigma(X27803,X27802),X27799),X27798)))
      | hBOOL(hAPP(hAPP(c_member(X27803),X27801),X27799)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaD1])]) ).

fof(i_0_7403,plain,
    ! [X23026,X23027,X23028,X23029,X23031] :
      ( ( hBOOL(hAPP(hAPP(c_member(X23028),esk118_4(X23026,X23027,X23028,X23029)),X23027))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23028,X23029),X23026),X23027) != c_Groups_Ozero__class_Ozero(X23029)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23028),X23027))
        | ~ class_Rings_Ocomm__semiring__1(X23029)
        | ~ class_Rings_Ono__zero__divisors(X23029) )
      & ( hAPP(X23026,esk118_4(X23026,X23027,X23028,X23029)) = c_Groups_Ozero__class_Ozero(X23029)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23028,X23029),X23026),X23027) != c_Groups_Ozero__class_Ozero(X23029)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23028),X23027))
        | ~ class_Rings_Ocomm__semiring__1(X23029)
        | ~ class_Rings_Ono__zero__divisors(X23029) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X23028),X23031),X23027))
        | hAPP(X23026,X23031) != c_Groups_Ozero__class_Ozero(X23029)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23028,X23029),X23026),X23027) = c_Groups_Ozero__class_Ozero(X23029)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23028),X23027))
        | ~ class_Rings_Ocomm__semiring__1(X23029)
        | ~ class_Rings_Ono__zero__divisors(X23029) ) ),
    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_7404,plain,
    ! [X21233,X21234,X21235,X21236] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21236),X21235))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21234),hAPP(c_Set_Oimage(X21236,X21234,X21233),X21235))),hAPP(c_Finite__Set_Ocard(X21236),X21235))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image__le])]) ).

fof(i_0_7405,plain,
    ! [X32716,X32717,X32718,X32719,X32720] :
      ( ~ class_Orderings_Olinorder(X32720)
      | hBOOL(hAPP(hAPP(c_member(X32720),hAPP(X32719,X32718)),hAPP(c_Set_Oimage(X32717,X32720,X32719),hAPP(c_List_Oset(X32717),X32716))))
      | c_List_Olinorder__class_Oinsort__insert__key(X32717,X32720,X32719,X32718,X32716) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32717,X32720,X32719),X32718),X32716) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5603])]) ).

cnf(i_0_7406,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_5604]) ).

fof(i_0_7407,plain,
    ! [X29336,X29337,X29338,X29339,X29340,X29341,X29342,X29343,X29344] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29339,tc_fun(X29338,tc_HOL_Obool)),X29337),X29336) != c_Orderings_Otop__class_Otop(tc_fun(X29338,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(X29339),X29340),X29337))
        | hAPP(X29336,X29340) = c_Orderings_Otop__class_Otop(tc_fun(X29338,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X29344),esk355_4(X29341,X29342,X29343,X29344)),X29342))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29344,tc_fun(X29343,tc_HOL_Obool)),X29342),X29341) = c_Orderings_Otop__class_Otop(tc_fun(X29343,tc_HOL_Obool)) )
      & ( hAPP(X29341,esk355_4(X29341,X29342,X29343,X29344)) != c_Orderings_Otop__class_Otop(tc_fun(X29343,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29344,tc_fun(X29343,tc_HOL_Obool)),X29342),X29341) = c_Orderings_Otop__class_Otop(tc_fun(X29343,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_7408,plain,
    ! [X19658,X19659,X19660,X19661,X19662,X19663,X19664,X19665,X19666] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19661,tc_fun(X19660,tc_HOL_Obool)),X19659),X19658) != c_Orderings_Obot__class_Obot(tc_fun(X19660,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(X19661),X19662),X19659))
        | hAPP(X19658,X19662) = c_Orderings_Obot__class_Obot(tc_fun(X19660,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X19666),esk51_4(X19663,X19664,X19665,X19666)),X19664))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19666,tc_fun(X19665,tc_HOL_Obool)),X19664),X19663) = c_Orderings_Obot__class_Obot(tc_fun(X19665,tc_HOL_Obool)) )
      & ( hAPP(X19663,esk51_4(X19663,X19664,X19665,X19666)) != c_Orderings_Obot__class_Obot(tc_fun(X19665,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19666,tc_fun(X19665,tc_HOL_Obool)),X19664),X19663) = c_Orderings_Obot__class_Obot(tc_fun(X19665,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_7409,plain,
    ! [X29326,X29327,X29328,X29329,X29330,X29331,X29332,X29333,X29334] :
      ( ( c_Orderings_Otop__class_Otop(tc_fun(X29329,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29328,tc_fun(X29329,tc_HOL_Obool)),X29327),X29326)
        | ~ hBOOL(hAPP(hAPP(c_member(X29328),X29330),X29327))
        | hAPP(X29326,X29330) = c_Orderings_Otop__class_Otop(tc_fun(X29329,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X29333),esk354_4(X29331,X29332,X29333,X29334)),X29332))
        | c_Orderings_Otop__class_Otop(tc_fun(X29334,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29333,tc_fun(X29334,tc_HOL_Obool)),X29332),X29331) )
      & ( hAPP(X29331,esk354_4(X29331,X29332,X29333,X29334)) != c_Orderings_Otop__class_Otop(tc_fun(X29334,tc_HOL_Obool))
        | c_Orderings_Otop__class_Otop(tc_fun(X29334,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29333,tc_fun(X29334,tc_HOL_Obool)),X29332),X29331) ) ),
    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_7410,plain,
    ! [X19675,X19676,X19677,X19678,X19679,X19680,X19681,X19682,X19683] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X19678,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19677,tc_fun(X19678,tc_HOL_Obool)),X19676),X19675)
        | ~ hBOOL(hAPP(hAPP(c_member(X19677),X19679),X19676))
        | hAPP(X19675,X19679) = c_Orderings_Obot__class_Obot(tc_fun(X19678,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X19682),esk52_4(X19680,X19681,X19682,X19683)),X19681))
        | c_Orderings_Obot__class_Obot(tc_fun(X19683,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19682,tc_fun(X19683,tc_HOL_Obool)),X19681),X19680) )
      & ( hAPP(X19680,esk52_4(X19680,X19681,X19682,X19683)) != c_Orderings_Obot__class_Obot(tc_fun(X19683,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(X19683,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19682,tc_fun(X19683,tc_HOL_Obool)),X19681),X19680) ) ),
    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_7411,plain,
    ! [X28286,X28287,X28288,X28289] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28289),esk308_4(X28286,X28287,X28288,X28289)),X28287))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28289,tc_Nat_Onat),X28288),X28287) != hAPP(c_Nat_OSuc,X28286) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X28288,esk308_4(X28286,X28287,X28288,X28289))))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28289,tc_Nat_Onat),X28288),X28287) != hAPP(c_Nat_OSuc,X28286) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__SucD])])])]) ).

fof(i_0_7412,plain,
    ! [X25915,X25916,X25917] :
      ( ~ class_Orderings_Olinorder(X25917)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25917),X25916))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25917),X25915))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25917,tc_HOL_Obool)),X25916),X25915) = c_Orderings_Obot__class_Obot(tc_fun(X25917,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25917),c_Big__Operators_Olinorder__class_OMax(X25917,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25917,tc_HOL_Obool)),X25916),X25915))),c_Big__Operators_Olinorder__class_OMax(X25917,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25917,tc_HOL_Obool)),X25916),X25915))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25917),c_Big__Operators_Olinorder__class_OMax(X25917,X25916)),c_Big__Operators_Olinorder__class_OMax(X25917,X25915)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Ounion__inter])]) ).

fof(i_0_7413,plain,
    ! [X25488,X25489,X25490] :
      ( ~ class_Orderings_Olinorder(X25490)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25490),X25489))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25490),X25488))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25490,tc_HOL_Obool)),X25489),X25488) = c_Orderings_Obot__class_Obot(tc_fun(X25490,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25490),c_Big__Operators_Olinorder__class_OMin(X25490,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25490,tc_HOL_Obool)),X25489),X25488))),c_Big__Operators_Olinorder__class_OMin(X25490,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25490,tc_HOL_Obool)),X25489),X25488))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25490),c_Big__Operators_Olinorder__class_OMin(X25490,X25489)),c_Big__Operators_Olinorder__class_OMin(X25490,X25488)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Ounion__inter])]) ).

fof(i_0_7414,plain,
    ! [X20894,X20895,X20896] :
      ( ~ class_Lattices_Olattice(X20896)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20896),X20895))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20896),X20894))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20896,tc_HOL_Obool)),X20895),X20894) = c_Orderings_Obot__class_Obot(tc_fun(X20896,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20896),c_Big__Operators_Olattice__class_OInf__fin(X20896,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20896,tc_HOL_Obool)),X20895),X20894))),c_Big__Operators_Olattice__class_OInf__fin(X20896,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20896,tc_HOL_Obool)),X20895),X20894))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20896),c_Big__Operators_Olattice__class_OInf__fin(X20896,X20895)),c_Big__Operators_Olattice__class_OInf__fin(X20896,X20894)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__inter])]) ).

fof(i_0_7415,plain,
    ! [X20888,X20889,X20890] :
      ( ~ class_Lattices_Olattice(X20890)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20890),X20889))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20890),X20888))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20890,tc_HOL_Obool)),X20889),X20888) = c_Orderings_Obot__class_Obot(tc_fun(X20890,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20890),c_Big__Operators_Olattice__class_OSup__fin(X20890,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20890,tc_HOL_Obool)),X20889),X20888))),c_Big__Operators_Olattice__class_OSup__fin(X20890,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20890,tc_HOL_Obool)),X20889),X20888))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20890),c_Big__Operators_Olattice__class_OSup__fin(X20890,X20889)),c_Big__Operators_Olattice__class_OSup__fin(X20890,X20888)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__inter])]) ).

fof(i_0_7416,plain,
    ! [X33169,X33170,X33173,X33174,X33175] :
      ( ( X33169 = hAPP(hAPP(c_List_Olist_OCons(X33170),esk470_2(X33169,X33170)),esk469_2(X33169,X33170))
        | X33169 = c_List_Olist_ONil(X33170)
        | ~ c_List_Olinorder__class_Osorted(X33170,X33169)
        | ~ class_Orderings_Olinorder(X33170) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X33170),X33173),hAPP(c_List_Oset(X33170),esk469_2(X33169,X33170))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33170),esk470_2(X33169,X33170)),X33173))
        | X33169 = c_List_Olist_ONil(X33170)
        | ~ c_List_Olinorder__class_Osorted(X33170,X33169)
        | ~ class_Orderings_Olinorder(X33170) )
      & ( c_List_Olinorder__class_Osorted(X33170,esk469_2(X33169,X33170))
        | X33169 = c_List_Olist_ONil(X33170)
        | ~ c_List_Olinorder__class_Osorted(X33170,X33169)
        | ~ class_Orderings_Olinorder(X33170) )
      & ( X33169 != c_List_Olist_ONil(X33170)
        | c_List_Olinorder__class_Osorted(X33170,X33169)
        | ~ class_Orderings_Olinorder(X33170) )
      & ( hBOOL(hAPP(hAPP(c_member(X33170),esk471_4(X33169,X33170,X33174,X33175)),hAPP(c_List_Oset(X33170),X33174)))
        | X33169 != hAPP(hAPP(c_List_Olist_OCons(X33170),X33175),X33174)
        | ~ c_List_Olinorder__class_Osorted(X33170,X33174)
        | c_List_Olinorder__class_Osorted(X33170,X33169)
        | ~ class_Orderings_Olinorder(X33170) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33170),X33175),esk471_4(X33169,X33170,X33174,X33175)))
        | X33169 != hAPP(hAPP(c_List_Olist_OCons(X33170),X33175),X33174)
        | ~ c_List_Olinorder__class_Osorted(X33170,X33174)
        | c_List_Olinorder__class_Osorted(X33170,X33169)
        | ~ class_Orderings_Olinorder(X33170) ) ),
    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_7417,plain,
    ! [X25987,X25988,X25989,X25990,X25991,X25992,X25993] :
      ( ( hAPP(X25990,X25988) != hAPP(X25990,X25987)
        | X25988 = X25987
        | ~ hBOOL(hAPP(hAPP(c_member(X25992),X25987),X25989))
        | ~ hBOOL(hAPP(hAPP(c_member(X25992),X25988),X25989))
        | ~ c_Typedef_Otype__definition(X25993,X25992,X25991,X25990,X25989) )
      & ( X25988 != X25987
        | hAPP(X25990,X25988) = hAPP(X25990,X25987)
        | ~ hBOOL(hAPP(hAPP(c_member(X25992),X25987),X25989))
        | ~ hBOOL(hAPP(hAPP(c_member(X25992),X25988),X25989))
        | ~ c_Typedef_Otype__definition(X25993,X25992,X25991,X25990,X25989) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inject])])]) ).

fof(i_0_7418,plain,
    ! [X33886,X33887] :
      ( ( ~ c_Wellfounded_Oacyclic(X33887,hAPP(c_Set_OCollect(tc_prod(X33887,X33887)),hAPP(c_Product__Type_Oprod_Oprod__case(X33887,X33887,tc_HOL_Obool),c_Predicate_Oconversep(X33887,X33887,X33886))))
        | c_Wellfounded_Oacyclic(X33887,hAPP(c_Set_OCollect(tc_prod(X33887,X33887)),hAPP(c_Product__Type_Oprod_Oprod__case(X33887,X33887,tc_HOL_Obool),X33886))) )
      & ( ~ c_Wellfounded_Oacyclic(X33887,hAPP(c_Set_OCollect(tc_prod(X33887,X33887)),hAPP(c_Product__Type_Oprod_Oprod__case(X33887,X33887,tc_HOL_Obool),X33886)))
        | c_Wellfounded_Oacyclic(X33887,hAPP(c_Set_OCollect(tc_prod(X33887,X33887)),hAPP(c_Product__Type_Oprod_Oprod__case(X33887,X33887,tc_HOL_Obool),c_Predicate_Oconversep(X33887,X33887,X33886)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclicP__converse])]) ).

cnf(i_0_7419,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_5529]) ).

fof(i_0_7420,plain,
    ! [X20216,X20217,X20218,X20219] : hAPP(c_Relation_OField(X20219),hAPP(hAPP(c_Set_Oinsert(tc_prod(X20219,X20219)),hAPP(hAPP(c_Product__Type_OPair(X20219,X20219),X20218),X20217)),X20216)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20219,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X20219),X20218),hAPP(hAPP(c_Set_Oinsert(X20219),X20217),c_Orderings_Obot__class_Obot(tc_fun(X20219,tc_HOL_Obool))))),hAPP(c_Relation_OField(X20219),X20216)),
    inference(variable_rename,[status(thm)],[fact_Field__insert]) ).

fof(i_0_7421,plain,
    ! [X32015,X32016,X32017] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32017),X32016))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32017),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32016),X32015))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_start__le__sum])]) ).

cnf(i_0_7422,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_5605]) ).

fof(i_0_7423,plain,
    ! [X34088,X34089,X34090,X34091,X34092,X34093] : c_Nitpick_Opair__box_Opair__box__size(X34093,X34092,X34091,X34090,c_Nitpick_Opair__box_OPairBox(X34093,X34092,X34089,X34088)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X34091,X34089)),hAPP(X34090,X34088))),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_7424,plain,
    ! [X29813,X29814,X29815] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X29815,tc_HOL_Obool)),esk368_3(X29813,X29814,X29815)),X29814))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29813),hAPP(c_Finite__Set_Ocard(tc_fun(X29815,tc_HOL_Obool)),X29814)) = hAPP(c_Finite__Set_Ocard(X29815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29815,tc_HOL_Obool),X29814))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X29815,tc_HOL_Obool)),esk367_3(X29813,X29814,X29815)),X29814))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29815,tc_HOL_Obool),X29814)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X29815,tc_HOL_Obool)),X29814)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X29815,tc_HOL_Obool)),esk369_3(X29813,X29814,X29815)),X29814))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29813),hAPP(c_Finite__Set_Ocard(tc_fun(X29815,tc_HOL_Obool)),X29814)) = hAPP(c_Finite__Set_Ocard(X29815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29815,tc_HOL_Obool),X29814))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X29815,tc_HOL_Obool)),esk367_3(X29813,X29814,X29815)),X29814))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29815,tc_HOL_Obool),X29814)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X29815,tc_HOL_Obool)),X29814)) )
      & ( esk368_3(X29813,X29814,X29815) != esk369_3(X29813,X29814,X29815)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29813),hAPP(c_Finite__Set_Ocard(tc_fun(X29815,tc_HOL_Obool)),X29814)) = hAPP(c_Finite__Set_Ocard(X29815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29815,tc_HOL_Obool),X29814))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X29815,tc_HOL_Obool)),esk367_3(X29813,X29814,X29815)),X29814))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29815,tc_HOL_Obool),X29814)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X29815,tc_HOL_Obool)),X29814)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29815,tc_HOL_Obool)),esk368_3(X29813,X29814,X29815)),esk369_3(X29813,X29814,X29815)) != c_Orderings_Obot__class_Obot(tc_fun(X29815,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29813),hAPP(c_Finite__Set_Ocard(tc_fun(X29815,tc_HOL_Obool)),X29814)) = hAPP(c_Finite__Set_Ocard(X29815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29815,tc_HOL_Obool),X29814))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X29815,tc_HOL_Obool)),esk367_3(X29813,X29814,X29815)),X29814))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29815,tc_HOL_Obool),X29814)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X29815,tc_HOL_Obool)),X29814)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X29815,tc_HOL_Obool)),esk368_3(X29813,X29814,X29815)),X29814))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29813),hAPP(c_Finite__Set_Ocard(tc_fun(X29815,tc_HOL_Obool)),X29814)) = hAPP(c_Finite__Set_Ocard(X29815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29815,tc_HOL_Obool),X29814))
        | hAPP(c_Finite__Set_Ocard(X29815),esk367_3(X29813,X29814,X29815)) != X29813
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29815,tc_HOL_Obool),X29814)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X29815,tc_HOL_Obool)),X29814)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X29815,tc_HOL_Obool)),esk369_3(X29813,X29814,X29815)),X29814))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29813),hAPP(c_Finite__Set_Ocard(tc_fun(X29815,tc_HOL_Obool)),X29814)) = hAPP(c_Finite__Set_Ocard(X29815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29815,tc_HOL_Obool),X29814))
        | hAPP(c_Finite__Set_Ocard(X29815),esk367_3(X29813,X29814,X29815)) != X29813
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29815,tc_HOL_Obool),X29814)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X29815,tc_HOL_Obool)),X29814)) )
      & ( esk368_3(X29813,X29814,X29815) != esk369_3(X29813,X29814,X29815)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29813),hAPP(c_Finite__Set_Ocard(tc_fun(X29815,tc_HOL_Obool)),X29814)) = hAPP(c_Finite__Set_Ocard(X29815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29815,tc_HOL_Obool),X29814))
        | hAPP(c_Finite__Set_Ocard(X29815),esk367_3(X29813,X29814,X29815)) != X29813
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29815,tc_HOL_Obool),X29814)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X29815,tc_HOL_Obool)),X29814)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29815,tc_HOL_Obool)),esk368_3(X29813,X29814,X29815)),esk369_3(X29813,X29814,X29815)) != c_Orderings_Obot__class_Obot(tc_fun(X29815,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29813),hAPP(c_Finite__Set_Ocard(tc_fun(X29815,tc_HOL_Obool)),X29814)) = hAPP(c_Finite__Set_Ocard(X29815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29815,tc_HOL_Obool),X29814))
        | hAPP(c_Finite__Set_Ocard(X29815),esk367_3(X29813,X29814,X29815)) != X29813
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29815,tc_HOL_Obool),X29814)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X29815,tc_HOL_Obool)),X29814)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__partition])])])]) ).

fof(i_0_7425,plain,
    ! [X30331,X30332,X30333,X30334,X30335,X30336] :
      ( ( X30336 != X30335
        | hAPP(hAPP(c_Map_Omap__of(X30334,X30333),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X30334,X30333)),hAPP(hAPP(c_Product__Type_OPair(X30334,X30333),X30336),X30332)),X30331)),X30335) = hAPP(c_Option_Ooption_OSome(X30333),X30332) )
      & ( X30336 = X30335
        | hAPP(hAPP(c_Map_Omap__of(X30334,X30333),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X30334,X30333)),hAPP(hAPP(c_Product__Type_OPair(X30334,X30333),X30336),X30332)),X30331)),X30335) = hAPP(hAPP(c_Map_Omap__of(X30334,X30333),X30331),X30335) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__Cons__code_I2_J])]) ).

fof(i_0_7426,plain,
    ! [X32761,X32762,X32763] :
      ( ~ class_Orderings_Olinorder(X32763)
      | c_List_Olinorder__class_Osorted(X32763,hAPP(c_List_Ofilter(X32763,hAPP(hAPP(c_COMBC(X32763,X32763,tc_HOL_Obool),c_fequal),hAPP(X32762,X32761))),X32761)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__same])]) ).

fof(i_0_7427,plain,
    ! [X19230,X19231,X19232,X19233,X19234] :
      ( ~ c_Fun_Oinj__on(X19234,X19233,X19232,c_Orderings_Otop__class_Otop(tc_fun(X19234,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(X19231,X19234,X19230,c_Orderings_Otop__class_Otop(tc_fun(X19231,tc_HOL_Obool)))
      | c_Fun_Oinj__on(X19231,X19233,hAPP(c_Fun_Ocomp(X19234,X19233,X19231,X19232),X19230),c_Orderings_Otop__class_Otop(tc_fun(X19231,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__comp])]) ).

fof(i_0_7428,plain,
    ! [X31194,X31195,X31196,X31197] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31197,tc_HOL_Obool)),hAPP(c_List_Oset(X31197),hAPP(hAPP(c_List_Olist__update(X31197,X31196),X31195),X31194))),hAPP(hAPP(c_Set_Oinsert(X31197),X31194),hAPP(c_List_Oset(X31197),X31196)))),
    inference(variable_rename,[status(thm)],[fact_set__update__subset__insert]) ).

cnf(i_0_7429,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_5606]) ).

fof(i_0_7430,plain,
    ! [X25982,X25983,X25984] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25984,tc_HOL_Obool)),X25983),hAPP(hAPP(c_Set_Oinsert(X25984),X25982),c_Orderings_Obot__class_Obot(tc_fun(X25984,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25984,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OSup__fin(X25984,c_Orderings_Oord__class_Omax(X25984),X25983) = X25982
        | ~ hBOOL(hAPP(hAPP(c_member(X25984),X25982),X25983))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25984),X25983))
        | ~ class_Orderings_Olinorder(X25984) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25984,tc_HOL_Obool)),X25983),hAPP(hAPP(c_Set_Oinsert(X25984),X25982),c_Orderings_Obot__class_Obot(tc_fun(X25984,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25984,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OSup__fin(X25984,c_Orderings_Oord__class_Omax(X25984),X25983) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25984),X25982),c_Big__Operators_Olattice_OSup__fin(X25984,c_Orderings_Oord__class_Omax(X25984),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25984,tc_HOL_Obool)),X25983),hAPP(hAPP(c_Set_Oinsert(X25984),X25982),c_Orderings_Obot__class_Obot(tc_fun(X25984,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X25984),X25982),X25983))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25984),X25983))
        | ~ class_Orderings_Olinorder(X25984) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oremove])])]) ).

fof(i_0_7431,plain,
    ! [X25624,X25625,X25626] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25626,tc_HOL_Obool)),X25625),hAPP(hAPP(c_Set_Oinsert(X25626),X25624),c_Orderings_Obot__class_Obot(tc_fun(X25626,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25626,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OInf__fin(X25626,c_Orderings_Oord__class_Omin(X25626),X25625) = X25624
        | ~ hBOOL(hAPP(hAPP(c_member(X25626),X25624),X25625))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25626),X25625))
        | ~ class_Orderings_Olinorder(X25626) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25626,tc_HOL_Obool)),X25625),hAPP(hAPP(c_Set_Oinsert(X25626),X25624),c_Orderings_Obot__class_Obot(tc_fun(X25626,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25626,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OInf__fin(X25626,c_Orderings_Oord__class_Omin(X25626),X25625) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25626),X25624),c_Big__Operators_Olattice_OInf__fin(X25626,c_Orderings_Oord__class_Omin(X25626),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25626,tc_HOL_Obool)),X25625),hAPP(hAPP(c_Set_Oinsert(X25626),X25624),c_Orderings_Obot__class_Obot(tc_fun(X25626,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X25626),X25624),X25625))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25626),X25625))
        | ~ class_Orderings_Olinorder(X25626) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oremove])])]) ).

fof(i_0_7432,plain,
    ! [X26738,X26739,X26740] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26740,tc_Nat_Onat),X26739),X26738) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26740,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X26740),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X26739)),X26738)),
    inference(variable_rename,[status(thm)],[fact_transfer__nat__int__sum__prod2_I1_J]) ).

fof(i_0_7433,plain,
    ! [X25216,X25217,X25218] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25218,tc_Nat_Onat),X25217),X25216) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25218,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X25218),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25217)),X25216)),
    inference(variable_rename,[status(thm)],[fact_transfer__nat__int__sum__prod2_I2_J]) ).

fof(i_0_7434,plain,
    ! [X19490,X19491,X19492,X19493,X19494] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X19494),X19493),hAPP(c_Set_Ovimage(X19494,X19492,X19491),hAPP(hAPP(c_Set_Oinsert(X19492),X19490),c_Orderings_Obot__class_Obot(tc_fun(X19492,tc_HOL_Obool))))))
        | hAPP(X19491,X19493) = X19490 )
      & ( hAPP(X19491,X19493) != X19490
        | hBOOL(hAPP(hAPP(c_member(X19494),X19493),hAPP(c_Set_Ovimage(X19494,X19492,X19491),hAPP(hAPP(c_Set_Oinsert(X19492),X19490),c_Orderings_Obot__class_Obot(tc_fun(X19492,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__singleton__eq])]) ).

cnf(i_0_7435,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_5607]) ).

fof(i_0_7436,plain,
    ! [X18956,X18957,X18958,X18959,X18960,X18961] :
      ( ~ c_Fun_Oinj__on(X18961,X18960,hAPP(c_Fun_Ocomp(X18959,X18960,X18961,X18958),X18957),X18956)
      | c_Fun_Oinj__on(X18961,X18959,X18957,X18956) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__imageI2])]) ).

cnf(i_0_7437,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_5608]) ).

fof(i_0_7438,plain,
    ! [X20550,X20551,X20552,X20553] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20553),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20553,tc_HOL_Obool)),X20552),hAPP(hAPP(c_Set_Oinsert(X20553),X20551),X20550))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20553),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20553,tc_HOL_Obool)),X20552),X20550))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20553),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20553,tc_HOL_Obool)),X20552),X20550)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20553),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20553,tc_HOL_Obool)),X20552),hAPP(hAPP(c_Set_Oinsert(X20553),X20551),X20550)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff__insert])]) ).

fof(i_0_7439,plain,
    ! [X17251,X17252,X17253] : hAPP(hAPP(c_Set_Oinsert(X17253),X17252),X17251) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17253,tc_HOL_Obool)),hAPP(c_Set_OCollect(X17253),hAPP(hAPP(c_COMBC(X17253,X17253,tc_HOL_Obool),c_fequal),X17252))),X17251),
    inference(variable_rename,[status(thm)],[fact_insert__def]) ).

cnf(i_0_7440,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_5609]) ).

cnf(i_0_7441,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_5610]) ).

cnf(i_0_7442,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_5611]) ).

cnf(i_0_7443,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_5612]) ).

cnf(i_0_7444,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_5535]) ).

cnf(i_0_7445,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_5536]) ).

cnf(i_0_7446,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_5537]) ).

cnf(i_0_7447,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_5538]) ).

fof(i_0_7448,plain,
    ! [X21792,X21793,X21794,X21795,X21796,X21797] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21797),X21796),X21795)),X21794) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21797),X21793),X21795)),X21792)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21797),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21797),X21796),X21793)),X21795)),X21794) = X21792
        | ~ class_Rings_Oring(X21797) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21797),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21797),X21796),X21793)),X21795)),X21794) != X21792
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21797),X21796),X21795)),X21794) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21797),X21793),X21795)),X21792)
        | ~ class_Rings_Oring(X21797) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff1])])]) ).

fof(i_0_7449,plain,
    ! [X21786,X21787,X21788,X21789,X21790,X21791] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21791),X21790),X21789)),X21788) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21791),X21787),X21789)),X21786)
        | X21788 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21791),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21791),X21787),X21790)),X21789)),X21786)
        | ~ class_Rings_Oring(X21791) )
      & ( X21788 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21791),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21791),X21787),X21790)),X21789)),X21786)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21791),X21790),X21789)),X21788) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21791),X21787),X21789)),X21786)
        | ~ class_Rings_Oring(X21791) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff2])])]) ).

fof(i_0_7450,plain,
    ! [X29556,X29557,X29558,X29559,X29560,X29561] :
      ( ~ c_Relation_Osingle__valued(X29561,X29560,hAPP(c_Relation_Oconverse(X29560,X29561),X29559))
      | X29558 = c_Orderings_Obot__class_Obot(tc_fun(X29557,tc_HOL_Obool))
      | hAPP(c_Relation_OImage(X29560,X29561,X29559),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29557,tc_fun(X29560,tc_HOL_Obool)),X29558),X29556)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29557,tc_fun(X29561,tc_HOL_Obool)),X29558),hAPP(hAPP(c_COMBB(tc_fun(X29560,tc_HOL_Obool),tc_fun(X29561,tc_HOL_Obool),X29557),c_Relation_OImage(X29560,X29561,X29559)),X29556)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__INT__eq])]) ).

fof(i_0_7451,plain,
    ! [X32604,X32605,X32606] : hAPP(c_Product__Type_Osnd(tc_List_Olist(X32606),tc_List_Olist(X32606)),c_List_Opartition(X32606,X32605,X32604)) = hAPP(c_List_Ofilter(X32606,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X32606,c_fNot),X32605)),X32604),
    inference(variable_rename,[status(thm)],[fact_partition__filter2]) ).

fof(i_0_7452,plain,
    ! [X19317,X19318,X19319,X19320,X19321] :
      ( ~ c_Fun_Oinj__on(X19321,X19320,X19319,X19318)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19321,tc_HOL_Obool)),X19317),X19318))
      | hAPP(c_Set_Oimage(X19320,X19321,c_Hilbert__Choice_Oinv__into(X19321,X19320,X19318,X19319)),hAPP(c_Set_Oimage(X19321,X19320,X19319),X19317)) = X19317 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__image__cancel])]) ).

fof(i_0_7453,plain,
    ! [X19437,X19438,X19439,X19440,X19441] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19441,tc_HOL_Obool)),X19440),X19439))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19438,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X19438,X19441,X19437),X19440)),hAPP(c_Set_Ovimage(X19438,X19441,X19437),X19439))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__mono])]) ).

fof(i_0_7454,plain,
    ! [X17462,X17463,X17464,X17465,X17466] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17466,tc_HOL_Obool)),X17465),X17464))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17463,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17466,X17463,X17462),X17465)),hAPP(c_Set_Oimage(X17466,X17463,X17462),X17464))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__mono])]) ).

fof(i_0_7455,plain,
    ! [X19540,X19541,X19542,X19543,X19544,X19545] :
      ( ~ c_Equiv__Relations_Oequiv(X19545,X19544,X19543)
      | ~ c_Equiv__Relations_Ocongruent(X19545,tc_fun(X19542,tc_HOL_Obool),X19543,X19541)
      | ~ hBOOL(hAPP(hAPP(c_member(X19545),X19540),X19544))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19545,tc_fun(X19542,tc_HOL_Obool)),hAPP(c_Relation_OImage(X19545,X19545,X19543),hAPP(hAPP(c_Set_Oinsert(X19545),X19540),c_Orderings_Obot__class_Obot(tc_fun(X19545,tc_HOL_Obool))))),X19541) = hAPP(X19541,X19540) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class])]) ).

fof(i_0_7456,plain,
    ! [X25973,X25974,X25975] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25975,tc_HOL_Obool)),X25974),hAPP(hAPP(c_Set_Oinsert(X25975),X25973),c_Orderings_Obot__class_Obot(tc_fun(X25975,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25975,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OSup__fin(X25975,c_Orderings_Oord__class_Omax(X25975),hAPP(hAPP(c_Set_Oinsert(X25975),X25973),X25974)) = X25973
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25975),X25974))
        | ~ class_Orderings_Olinorder(X25975) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25975,tc_HOL_Obool)),X25974),hAPP(hAPP(c_Set_Oinsert(X25975),X25973),c_Orderings_Obot__class_Obot(tc_fun(X25975,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25975,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OSup__fin(X25975,c_Orderings_Oord__class_Omax(X25975),hAPP(hAPP(c_Set_Oinsert(X25975),X25973),X25974)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25975),X25973),c_Big__Operators_Olattice_OSup__fin(X25975,c_Orderings_Oord__class_Omax(X25975),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25975,tc_HOL_Obool)),X25974),hAPP(hAPP(c_Set_Oinsert(X25975),X25973),c_Orderings_Obot__class_Obot(tc_fun(X25975,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25975),X25974))
        | ~ class_Orderings_Olinorder(X25975) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__remove])])]) ).

fof(i_0_7457,plain,
    ! [X25690,X25691,X25692] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25692,tc_HOL_Obool)),X25691),hAPP(hAPP(c_Set_Oinsert(X25692),X25690),c_Orderings_Obot__class_Obot(tc_fun(X25692,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25692,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OInf__fin(X25692,c_Orderings_Oord__class_Omin(X25692),hAPP(hAPP(c_Set_Oinsert(X25692),X25690),X25691)) = X25690
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25692),X25691))
        | ~ class_Orderings_Olinorder(X25692) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25692,tc_HOL_Obool)),X25691),hAPP(hAPP(c_Set_Oinsert(X25692),X25690),c_Orderings_Obot__class_Obot(tc_fun(X25692,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25692,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OInf__fin(X25692,c_Orderings_Oord__class_Omin(X25692),hAPP(hAPP(c_Set_Oinsert(X25692),X25690),X25691)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25692),X25690),c_Big__Operators_Olattice_OInf__fin(X25692,c_Orderings_Oord__class_Omin(X25692),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25692,tc_HOL_Obool)),X25691),hAPP(hAPP(c_Set_Oinsert(X25692),X25690),c_Orderings_Obot__class_Obot(tc_fun(X25692,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25692),X25691))
        | ~ class_Orderings_Olinorder(X25692) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__remove])])]) ).

fof(i_0_7458,plain,
    ! [X20262,X20263,X20264,X20265,X20266,X20267,X20268,X20269,X20270,X20271,X20272] :
      ( hAPP(X20272,hAPP(X20271,X20270)) != hAPP(X20269,hAPP(X20268,X20267))
      | hAPP(hAPP(c_Fun_Ocomp(X20266,X20265,X20264,X20272),X20271),X20270) = hAPP(hAPP(c_Fun_Ocomp(X20263,X20265,X20262,X20269),X20268),X20267) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__cong])]) ).

cnf(i_0_7459,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_5613]) ).

fof(i_0_7460,plain,
    ! [X27946,X27947,X27948] :
      ( ~ c_Fun_Oinj__on(X27948,X27947,X27946,c_Orderings_Otop__class_Otop(tc_fun(X27948,tc_HOL_Obool)))
      | hAPP(c_Fun_Ocomp(X27947,X27948,X27948,c_Hilbert__Choice_Oinv__into(X27948,X27947,c_Orderings_Otop__class_Otop(tc_fun(X27948,tc_HOL_Obool)),X27946)),X27946) = c_Fun_Oid(X27948) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__o__cancel])]) ).

fof(i_0_7461,plain,
    ! [X20635,X20636,X20637,X20638,X20639] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20639,tc_HOL_Obool)),X20636),hAPP(hAPP(c_Set_Oinsert(X20639),X20635),c_Orderings_Obot__class_Obot(tc_fun(X20639,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X20639,tc_HOL_Obool))
        | hAPP(X20637,X20636) = X20635
        | ~ hBOOL(hAPP(hAPP(c_member(X20639),X20635),X20636))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20639),X20636))
        | ~ c_Finite__Set_Ofolding__one(X20639,X20638,X20637) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20639,tc_HOL_Obool)),X20636),hAPP(hAPP(c_Set_Oinsert(X20639),X20635),c_Orderings_Obot__class_Obot(tc_fun(X20639,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X20639,tc_HOL_Obool))
        | hAPP(X20637,X20636) = hAPP(hAPP(X20638,X20635),hAPP(X20637,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20639,tc_HOL_Obool)),X20636),hAPP(hAPP(c_Set_Oinsert(X20639),X20635),c_Orderings_Obot__class_Obot(tc_fun(X20639,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X20639),X20635),X20636))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20639),X20636))
        | ~ c_Finite__Set_Ofolding__one(X20639,X20638,X20637) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oremove])])]) ).

fof(i_0_7462,plain,
    ! [X21933,X21934,X21935] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21935),X21934))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21935),X21933))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21935),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21935,tc_HOL_Obool)),X21934),X21933))),hAPP(c_Finite__Set_Ocard(X21935),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21935,tc_HOL_Obool)),X21934),X21933))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21935),X21934)),hAPP(c_Finite__Set_Ocard(X21935),X21933)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Ounion__inter])]) ).

fof(i_0_7463,plain,
    ! [X21936,X21937,X21938] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21938),X21937))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21938),X21936))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21938),X21937)),hAPP(c_Finite__Set_Ocard(X21938),X21936)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21938),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21938,tc_HOL_Obool)),X21937),X21936))),hAPP(c_Finite__Set_Ocard(X21938),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21938,tc_HOL_Obool)),X21937),X21936))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Un__Int])]) ).

fof(i_0_7464,plain,
    ! [X27503,X27504,X27505,X27506] :
      ( ( hBOOL(hAPP(X27506,esk264_4(X27503,X27504,X27505,X27506)))
        | c_Wellfounded_Owf(tc_prod(X27503,X27505),c_Recdef_Osame__fst(X27503,X27505,X27506,X27504)) )
      & ( ~ c_Wellfounded_Owf(X27505,hAPP(X27504,esk264_4(X27503,X27504,X27505,X27506)))
        | c_Wellfounded_Owf(tc_prod(X27503,X27505),c_Recdef_Osame__fst(X27503,X27505,X27506,X27504)) ) ),
    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_7465,plain,
    ! [X20287,X20288,X20289,X20290,X20291] :
      ( ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X20291,X20290,X20289),X20288),X20287))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X20291,X20290)),hAPP(hAPP(c_Product__Type_OPair(X20291,X20290),X20288),X20287)),X20289)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20291,X20290)),hAPP(hAPP(c_Product__Type_OPair(X20291,X20290),X20288),X20287)),X20289))
        | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X20291,X20290,X20289),X20288),X20287)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).

fof(i_0_7466,plain,
    ! [X20296,X20297,X20298,X20299,X20300] : c_Map_Orestrict__map(X20300,X20299,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X20300,tc_Option_Ooption(X20299)),X20298),X20297),hAPP(c_Option_Ooption_OSome(X20299),X20296)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20300,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X20300),X20297),c_Orderings_Obot__class_Obot(tc_fun(X20300,tc_HOL_Obool))))) = c_Map_Orestrict__map(X20300,X20299,X20298,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20300,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X20300),X20297),c_Orderings_Obot__class_Obot(tc_fun(X20300,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_restrict__upd__same]) ).

cnf(i_0_7467,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_5614]) ).

fof(i_0_7468,plain,
    ! [X28556,X28557,X28558] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28558,tc_HOL_Obool)),hAPP(c_Relation_OImage(X28558,X28558,X28557),X28556)),X28556))
      | hAPP(c_Relation_OImage(X28558,X28558,c_Transitive__Closure_Ortrancl(X28558,X28557)),X28556) = X28556 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__closed__trancl])]) ).

cnf(i_0_7469,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_5615]) ).

fof(i_0_7470,plain,
    ! [X28666,X28667,X28668,X28669] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28669,X28669)),hAPP(hAPP(c_Product__Type_OPair(X28669,X28669),X28668),X28667)),c_Transitive__Closure_Ortrancl(X28669,X28666)))
      | ~ hBOOL(hAPP(hAPP(c_member(X28669),X28667),c_Wellfounded_Oacc(X28669,X28666)))
      | hBOOL(hAPP(hAPP(c_member(X28669),X28668),c_Wellfounded_Oacc(X28669,X28666))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards__aux])]) ).

fof(i_0_7471,plain,
    ! [X28670,X28671,X28672,X28673] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X28673),X28672),c_Wellfounded_Oacc(X28673,X28671)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28673,X28673)),hAPP(hAPP(c_Product__Type_OPair(X28673,X28673),X28670),X28672)),c_Transitive__Closure_Ortrancl(X28673,X28671)))
      | hBOOL(hAPP(hAPP(c_member(X28673),X28670),c_Wellfounded_Oacc(X28673,X28671))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards])]) ).

cnf(i_0_7472,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2))),
    inference(split_conjunct,[status(thm)],[i_0_5616]) ).

fof(i_0_7473,plain,
    ! [X21347,X21348,X21349,X21350] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21350),X21349))
      | ~ hBOOL(hAPP(hAPP(c_member(X21350),X21348),X21349))
      | hBOOL(hAPP(hAPP(c_member(X21350),X21348),X21347))
      | hAPP(c_Finite__Set_Ocard(X21350),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21350,tc_HOL_Obool)),X21349),hAPP(hAPP(c_Set_Oinsert(X21350),X21348),X21347))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21350),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21350,tc_HOL_Obool)),X21349),X21347))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5617])]) ).

fof(i_0_7474,plain,
    ! [X30424,X30425,X30426] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30426),hAPP(hAPP(c_List_Omap(tc_prod(X30426,X30425),X30426),c_Product__Type_Ofst(X30426,X30425)),X30424)))
      | c_Map_Oran(X30426,X30425,hAPP(c_Map_Omap__of(X30426,X30425),X30424)) = hAPP(c_Set_Oimage(tc_prod(X30426,X30425),X30425,c_Product__Type_Osnd(X30426,X30425)),hAPP(c_List_Oset(tc_prod(X30426,X30425)),X30424)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ran__distinct])]) ).

cnf(i_0_7475,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_5618]) ).

fof(i_0_7476,plain,
    ! [X29526,X29527,X29528,X29529,X29530] :
      ( ( X29530 != c_Orderings_Obot__class_Obot(tc_fun(X29529,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29529,tc_fun(X29528,tc_HOL_Obool)),X29530),hAPP(hAPP(c_COMBB(tc_fun(X29528,tc_HOL_Obool),tc_fun(X29528,tc_HOL_Obool),X29529),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29528,tc_HOL_Obool)),X29527)),X29526)) = c_Orderings_Otop__class_Otop(tc_fun(X29528,tc_HOL_Obool)) )
      & ( X29530 = c_Orderings_Obot__class_Obot(tc_fun(X29529,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29529,tc_fun(X29528,tc_HOL_Obool)),X29530),hAPP(hAPP(c_COMBB(tc_fun(X29528,tc_HOL_Obool),tc_fun(X29528,tc_HOL_Obool),X29529),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29528,tc_HOL_Obool)),X29527)),X29526)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29528,tc_HOL_Obool)),X29527),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29529,tc_fun(X29528,tc_HOL_Obool)),X29530),X29526)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I2_J])]) ).

fof(i_0_7477,plain,
    ! [X29551,X29552,X29553,X29554,X29555] :
      ( ( X29555 != c_Orderings_Obot__class_Obot(tc_fun(X29554,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29554,tc_fun(X29553,tc_HOL_Obool)),X29555),hAPP(hAPP(c_COMBB(tc_fun(X29553,tc_HOL_Obool),tc_fun(X29553,tc_HOL_Obool),X29554),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29553,tc_HOL_Obool)),X29552)),X29551)) = c_Orderings_Otop__class_Otop(tc_fun(X29553,tc_HOL_Obool)) )
      & ( X29555 = c_Orderings_Obot__class_Obot(tc_fun(X29554,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29554,tc_fun(X29553,tc_HOL_Obool)),X29555),hAPP(hAPP(c_COMBB(tc_fun(X29553,tc_HOL_Obool),tc_fun(X29553,tc_HOL_Obool),X29554),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29553,tc_HOL_Obool)),X29552)),X29551)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29553,tc_HOL_Obool)),X29552),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29554,tc_fun(X29553,tc_HOL_Obool)),X29555),X29551)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I4_J])]) ).

fof(i_0_7478,plain,
    ! [X19817,X19818,X19819,X19820,X19821] :
      ( ( X19821 != c_Orderings_Obot__class_Obot(tc_fun(X19820,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19820,tc_fun(X19819,tc_HOL_Obool)),X19821),hAPP(hAPP(c_COMBB(tc_fun(X19819,tc_HOL_Obool),tc_fun(X19819,tc_HOL_Obool),X19820),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19819,tc_HOL_Obool)),X19818)),X19817)) = c_Orderings_Obot__class_Obot(tc_fun(X19819,tc_HOL_Obool)) )
      & ( X19821 = c_Orderings_Obot__class_Obot(tc_fun(X19820,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19820,tc_fun(X19819,tc_HOL_Obool)),X19821),hAPP(hAPP(c_COMBB(tc_fun(X19819,tc_HOL_Obool),tc_fun(X19819,tc_HOL_Obool),X19820),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19819,tc_HOL_Obool)),X19818)),X19817)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19819,tc_HOL_Obool)),X19818),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19820,tc_fun(X19819,tc_HOL_Obool)),X19821),X19817)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__simps_I3_J])]) ).

fof(i_0_7479,plain,
    ! [X29407,X29408,X29409,X29410,X29411] :
      ( ( X29411 != c_Orderings_Obot__class_Obot(tc_fun(X29410,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29409,tc_HOL_Obool)),X29408),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29410,tc_fun(X29409,tc_HOL_Obool)),X29411),X29407)) = X29408 )
      & ( X29411 = c_Orderings_Obot__class_Obot(tc_fun(X29410,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29409,tc_HOL_Obool)),X29408),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29410,tc_fun(X29409,tc_HOL_Obool)),X29411),X29407)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29410,tc_fun(X29409,tc_HOL_Obool)),X29411),hAPP(hAPP(c_COMBB(tc_fun(X29409,tc_HOL_Obool),tc_fun(X29409,tc_HOL_Obool),X29410),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29409,tc_HOL_Obool)),X29408)),X29407)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I2_J])]) ).

fof(i_0_7480,plain,
    ! [X29541,X29542,X29543,X29544,X29545] :
      ( ( X29545 != c_Orderings_Obot__class_Obot(tc_fun(X29544,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29543,tc_HOL_Obool)),X29542),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29544,tc_fun(X29543,tc_HOL_Obool)),X29545),X29541)) = X29542 )
      & ( X29545 = c_Orderings_Obot__class_Obot(tc_fun(X29544,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29543,tc_HOL_Obool)),X29542),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29544,tc_fun(X29543,tc_HOL_Obool)),X29545),X29541)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29544,tc_fun(X29543,tc_HOL_Obool)),X29545),hAPP(hAPP(c_COMBB(tc_fun(X29543,tc_HOL_Obool),tc_fun(X29543,tc_HOL_Obool),X29544),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29543,tc_HOL_Obool)),X29542)),X29541)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I4_J])]) ).

fof(i_0_7481,plain,
    ! [X19566,X19567,X19568,X19569,X19570] :
      ( ( X19570 != c_Orderings_Obot__class_Obot(tc_fun(X19569,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19568,tc_HOL_Obool)),X19567),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19569,tc_fun(X19568,tc_HOL_Obool)),X19570),X19566)) = X19567 )
      & ( X19570 = c_Orderings_Obot__class_Obot(tc_fun(X19569,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19568,tc_HOL_Obool)),X19567),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19569,tc_fun(X19568,tc_HOL_Obool)),X19570),X19566)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19569,tc_fun(X19568,tc_HOL_Obool)),X19570),hAPP(hAPP(c_COMBB(tc_fun(X19568,tc_HOL_Obool),tc_fun(X19568,tc_HOL_Obool),X19569),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19568,tc_HOL_Obool)),X19567)),X19566)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I3_J])]) ).

fof(i_0_7482,plain,
    ! [X20781,X20782,X20783,X20784,X20785] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20785,tc_HOL_Obool)),X20782),hAPP(hAPP(c_Set_Oinsert(X20785),X20781),c_Orderings_Obot__class_Obot(tc_fun(X20785,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X20785,tc_HOL_Obool))
        | hAPP(X20783,hAPP(hAPP(c_Set_Oinsert(X20785),X20781),X20782)) = X20781
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20785),X20782))
        | ~ c_Finite__Set_Ofolding__one(X20785,X20784,X20783) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20785,tc_HOL_Obool)),X20782),hAPP(hAPP(c_Set_Oinsert(X20785),X20781),c_Orderings_Obot__class_Obot(tc_fun(X20785,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X20785,tc_HOL_Obool))
        | hAPP(X20783,hAPP(hAPP(c_Set_Oinsert(X20785),X20781),X20782)) = hAPP(hAPP(X20784,X20781),hAPP(X20783,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20785,tc_HOL_Obool)),X20782),hAPP(hAPP(c_Set_Oinsert(X20785),X20781),c_Orderings_Obot__class_Obot(tc_fun(X20785,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20785),X20782))
        | ~ c_Finite__Set_Ofolding__one(X20785,X20784,X20783) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oinsert__remove])])]) ).

fof(i_0_7483,plain,
    ! [X25494,X25495,X25496] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25496,tc_HOL_Obool)),X25495),hAPP(hAPP(c_Set_Oinsert(X25496),X25494),c_Orderings_Obot__class_Obot(tc_fun(X25496,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25496,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMin(X25496,X25495) = X25494
        | ~ hBOOL(hAPP(hAPP(c_member(X25496),X25494),X25495))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25496),X25495))
        | ~ class_Orderings_Olinorder(X25496) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25496,tc_HOL_Obool)),X25495),hAPP(hAPP(c_Set_Oinsert(X25496),X25494),c_Orderings_Obot__class_Obot(tc_fun(X25496,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25496,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMin(X25496,X25495) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25496),X25494),c_Big__Operators_Olinorder__class_OMin(X25496,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25496,tc_HOL_Obool)),X25495),hAPP(hAPP(c_Set_Oinsert(X25496),X25494),c_Orderings_Obot__class_Obot(tc_fun(X25496,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X25496),X25494),X25495))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25496),X25495))
        | ~ class_Orderings_Olinorder(X25496) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oremove])])]) ).

fof(i_0_7484,plain,
    ! [X25918,X25919,X25920] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25920,tc_HOL_Obool)),X25919),hAPP(hAPP(c_Set_Oinsert(X25920),X25918),c_Orderings_Obot__class_Obot(tc_fun(X25920,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25920,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMax(X25920,X25919) = X25918
        | ~ hBOOL(hAPP(hAPP(c_member(X25920),X25918),X25919))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25920),X25919))
        | ~ class_Orderings_Olinorder(X25920) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25920,tc_HOL_Obool)),X25919),hAPP(hAPP(c_Set_Oinsert(X25920),X25918),c_Orderings_Obot__class_Obot(tc_fun(X25920,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25920,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMax(X25920,X25919) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25920),X25918),c_Big__Operators_Olinorder__class_OMax(X25920,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25920,tc_HOL_Obool)),X25919),hAPP(hAPP(c_Set_Oinsert(X25920),X25918),c_Orderings_Obot__class_Obot(tc_fun(X25920,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X25920),X25918),X25919))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25920),X25919))
        | ~ class_Orderings_Olinorder(X25920) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oremove])])]) ).

fof(i_0_7485,plain,
    ! [X20819,X20820,X20821] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20821,tc_HOL_Obool)),X20820),hAPP(hAPP(c_Set_Oinsert(X20821),X20819),c_Orderings_Obot__class_Obot(tc_fun(X20821,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X20821,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OSup__fin(X20821,X20820) = X20819
        | ~ hBOOL(hAPP(hAPP(c_member(X20821),X20819),X20820))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20821),X20820))
        | ~ class_Lattices_Olattice(X20821) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20821,tc_HOL_Obool)),X20820),hAPP(hAPP(c_Set_Oinsert(X20821),X20819),c_Orderings_Obot__class_Obot(tc_fun(X20821,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X20821,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OSup__fin(X20821,X20820) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20821),X20819),c_Big__Operators_Olattice__class_OSup__fin(X20821,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20821,tc_HOL_Obool)),X20820),hAPP(hAPP(c_Set_Oinsert(X20821),X20819),c_Orderings_Obot__class_Obot(tc_fun(X20821,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X20821),X20819),X20820))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20821),X20820))
        | ~ class_Lattices_Olattice(X20821) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oremove])])]) ).

fof(i_0_7486,plain,
    ! [X20816,X20817,X20818] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20818,tc_HOL_Obool)),X20817),hAPP(hAPP(c_Set_Oinsert(X20818),X20816),c_Orderings_Obot__class_Obot(tc_fun(X20818,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X20818,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OInf__fin(X20818,X20817) = X20816
        | ~ hBOOL(hAPP(hAPP(c_member(X20818),X20816),X20817))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20818),X20817))
        | ~ class_Lattices_Olattice(X20818) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20818,tc_HOL_Obool)),X20817),hAPP(hAPP(c_Set_Oinsert(X20818),X20816),c_Orderings_Obot__class_Obot(tc_fun(X20818,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X20818,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OInf__fin(X20818,X20817) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20818),X20816),c_Big__Operators_Olattice__class_OInf__fin(X20818,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20818,tc_HOL_Obool)),X20817),hAPP(hAPP(c_Set_Oinsert(X20818),X20816),c_Orderings_Obot__class_Obot(tc_fun(X20818,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X20818),X20816),X20817))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20818),X20817))
        | ~ class_Lattices_Olattice(X20818) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oremove])])]) ).

fof(i_0_7487,plain,
    ! [X26000,X26001,X26002,X26003,X26004,X26005] :
      ( ~ c_Typedef_Otype__definition(X26005,X26004,X26003,X26002,X26001)
      | hBOOL(hAPP(hAPP(c_member(X26004),hAPP(X26003,X26000)),X26001)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep])]) ).

fof(i_0_7488,plain,
    ! [X25994,X25995,X25996,X25997,X25998,X25999] :
      ( ~ c_Typedef_Otype__definition(X25999,X25998,X25997,X25996,X25995)
      | ~ hBOOL(hAPP(hAPP(c_member(X25998),X25994),X25995))
      | hAPP(X25997,hAPP(X25996,X25994)) = X25994 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inverse])]) ).

fof(i_0_7489,plain,
    ! [X32733,X32734,X32735,X32736,X32737] :
      ( ( ~ c_List_Olinorder__class_Osorted(X32737,hAPP(hAPP(c_List_Omap(X32736,X32737),X32735),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32736,X32737,X32735),X32734),X32733)))
        | c_List_Olinorder__class_Osorted(X32737,hAPP(hAPP(c_List_Omap(X32736,X32737),X32735),X32733))
        | ~ class_Orderings_Olinorder(X32737) )
      & ( ~ c_List_Olinorder__class_Osorted(X32737,hAPP(hAPP(c_List_Omap(X32736,X32737),X32735),X32733))
        | c_List_Olinorder__class_Osorted(X32737,hAPP(hAPP(c_List_Omap(X32736,X32737),X32735),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32736,X32737,X32735),X32734),X32733)))
        | ~ class_Orderings_Olinorder(X32737) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort__key])])]) ).

fof(i_0_7490,plain,
    ! [X28375,X28376,X28377] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk319_3(X28375,X28376,X28377)),X28377))
        | ~ hBOOL(hAPP(X28376,X28375))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28375),X28377))
        | hBOOL(hAPP(X28376,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
      & ( hBOOL(hAPP(X28376,esk319_3(X28375,X28376,X28377)))
        | ~ hBOOL(hAPP(X28376,X28375))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28375),X28377))
        | hBOOL(hAPP(X28376,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
      & ( ~ hBOOL(hAPP(X28376,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,esk319_3(X28375,X28376,X28377)),X28377)))
        | ~ hBOOL(hAPP(X28376,X28375))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28375),X28377))
        | hBOOL(hAPP(X28376,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_7491,plain,
    ! [X23491,X23492,X23493] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23493),X23492)),X23491) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23493),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23492),X23491))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23493),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23492,X23491))),X23491)),
    inference(variable_rename,[status(thm)],[fact_zdiv__zmult1__eq]) ).

fof(i_0_7492,plain,
    ! [X23661,X23662,X23663] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23663),X23662)),X23661) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23663),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23662),X23661))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23663),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23662,X23661))),X23661)),
    inference(variable_rename,[status(thm)],[fact_div__mult1__eq]) ).

fof(i_0_7493,plain,
    ! [X21968,X21969,X21970,X21971,X21972] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21971),X21970)),X21969) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21972),X21970)),X21968)
        | 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),X21971),X21972)),X21970)),X21969) = X21968
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21972),X21971)) )
      & ( 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),X21971),X21972)),X21970)),X21969) != X21968
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21971),X21970)),X21969) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21972),X21970)),X21968)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21972),X21971)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff1])])]) ).

fof(i_0_7494,plain,
    ! [X21987,X21988,X21989,X21990,X21991] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21991),X21989)),X21988) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21990),X21989)),X21987)
        | X21988 = 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),X21990),X21991)),X21989)),X21987)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21991),X21990)) )
      & ( X21988 != 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),X21990),X21991)),X21989)),X21987)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21991),X21989)),X21988) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21990),X21989)),X21987)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21991),X21990)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff2])])]) ).

fof(i_0_7495,plain,
    ! [X21280,X21281,X21282,X21283,X21284,X21285] :
      ( ~ class_Groups_Oab__semigroup__mult(X21285)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21284),X21283))
      | hBOOL(hAPP(hAPP(c_member(X21284),X21282),X21283))
      | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21285,X21284,c_Groups_Otimes__class_Otimes(X21285)),X21281),X21280),hAPP(hAPP(c_Set_Oinsert(X21284),X21282),X21283)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21285),hAPP(X21281,X21282)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21285,X21284,c_Groups_Otimes__class_Otimes(X21285)),X21281),X21280),X21283)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5619])]) ).

cnf(i_0_7496,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_5620]) ).

fof(i_0_7497,plain,
    ! [X18250,X18251,X18252,X18253] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18253,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18253,tc_HOL_Obool)),X18252),X18251)),X18250) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18253,tc_HOL_Obool)),X18252),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18253,tc_HOL_Obool)),X18251),X18250))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18253,tc_HOL_Obool)),X18250),X18252)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18253,tc_HOL_Obool)),X18250),X18252))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18253,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18253,tc_HOL_Obool)),X18252),X18251)),X18250) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18253,tc_HOL_Obool)),X18252),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18253,tc_HOL_Obool)),X18251),X18250)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__Int__assoc__eq])]) ).

fof(i_0_7498,plain,
    ! [X29501,X29502,X29503,X29504,X29505] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29505,tc_fun(X29504,tc_HOL_Obool)),X29503),hAPP(hAPP(c_COMBB(tc_fun(X29504,tc_HOL_Obool),tc_fun(X29504,tc_HOL_Obool),X29505),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29504,tc_HOL_Obool)),X29502)),X29501)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29504,tc_HOL_Obool)),X29502),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29505,tc_fun(X29504,tc_HOL_Obool)),X29503),X29501)),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I7_J]) ).

fof(i_0_7499,plain,
    ! [X19725,X19726,X19727,X19728,X19729] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19729,tc_fun(X19728,tc_HOL_Obool)),X19727),hAPP(hAPP(c_COMBB(tc_fun(X19728,tc_HOL_Obool),tc_fun(X19728,tc_HOL_Obool),X19729),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19728,tc_HOL_Obool)),X19726)),X19725)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19728,tc_HOL_Obool)),X19726),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19729,tc_fun(X19728,tc_HOL_Obool)),X19727),X19725)),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I5_J]) ).

fof(i_0_7500,plain,
    ! [X29290,X29291,X29292,X29293,X29294] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29294,tc_fun(X29293,tc_HOL_Obool)),X29292),hAPP(hAPP(c_COMBB(tc_fun(X29293,tc_HOL_Obool),tc_fun(X29293,tc_HOL_Obool),X29294),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29293,tc_HOL_Obool)),X29291)),X29290)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29293,tc_HOL_Obool)),X29291),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29294,tc_fun(X29293,tc_HOL_Obool)),X29292),X29290)),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I7_J]) ).

fof(i_0_7501,plain,
    ! [X19740,X19741,X19742,X19743,X19744] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19744,tc_HOL_Obool)),X19743),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19742,tc_fun(X19744,tc_HOL_Obool)),X19741),X19740)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19742,tc_fun(X19744,tc_HOL_Obool)),X19741),hAPP(hAPP(c_COMBB(tc_fun(X19744,tc_HOL_Obool),tc_fun(X19744,tc_HOL_Obool),X19742),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19744,tc_HOL_Obool)),X19743)),X19740)),
    inference(variable_rename,[status(thm)],[fact_Int__UN__distrib]) ).

fof(i_0_7502,plain,
    ! [X19735,X19736,X19737,X19738,X19739] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19739,tc_HOL_Obool)),X19738),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19737,tc_fun(X19739,tc_HOL_Obool)),X19736),X19735)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19737,tc_fun(X19739,tc_HOL_Obool)),X19736),hAPP(hAPP(c_COMBB(tc_fun(X19739,tc_HOL_Obool),tc_fun(X19739,tc_HOL_Obool),X19737),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19739,tc_HOL_Obool)),X19738)),X19735)),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I5_J]) ).

fof(i_0_7503,plain,
    ! [X29295,X29296,X29297,X29298,X29299] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29299,tc_HOL_Obool)),X29298),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29297,tc_fun(X29299,tc_HOL_Obool)),X29296),X29295)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29297,tc_fun(X29299,tc_HOL_Obool)),X29296),hAPP(hAPP(c_COMBB(tc_fun(X29299,tc_HOL_Obool),tc_fun(X29299,tc_HOL_Obool),X29297),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29299,tc_HOL_Obool)),X29298)),X29295)),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I7_J]) ).

fof(i_0_7504,plain,
    ! [X29491,X29492,X29493,X29494,X29495] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29495,tc_HOL_Obool)),X29494),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29493,tc_fun(X29495,tc_HOL_Obool)),X29492),X29491)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29493,tc_fun(X29495,tc_HOL_Obool)),X29492),hAPP(hAPP(c_COMBB(tc_fun(X29495,tc_HOL_Obool),tc_fun(X29495,tc_HOL_Obool),X29493),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29495,tc_HOL_Obool)),X29494)),X29491)),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I7_J]) ).

fof(i_0_7505,plain,
    ! [X29486,X29487,X29488,X29489,X29490] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29490,tc_HOL_Obool)),X29489),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29488,tc_fun(X29490,tc_HOL_Obool)),X29487),X29486)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29488,tc_fun(X29490,tc_HOL_Obool)),X29487),hAPP(hAPP(c_COMBB(tc_fun(X29490,tc_HOL_Obool),tc_fun(X29490,tc_HOL_Obool),X29488),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29490,tc_HOL_Obool)),X29489)),X29486)),
    inference(variable_rename,[status(thm)],[fact_Un__INT__distrib]) ).

fof(i_0_7506,plain,
    ! [X27325,X27326,X27327,X27328] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X27328,X27328,X27328),X27327),X27326) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27328,X27328),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(X27328,X27328,X27328),X27327),X27325) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27328,X27328),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(X27328,X27328,X27328),X27327),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27328,X27328),tc_HOL_Obool)),X27326),X27325)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27328,X27328),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_union__comp__emptyR])]) ).

cnf(i_0_7507,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_5566]) ).

cnf(i_0_7508,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_5567]) ).

fof(i_0_7509,plain,
    ! [X25930,X25931,X25932,X25933,X25934] :
      ( ~ c_Typedef_Otype__definition(X25934,X25933,X25932,X25931,X25930)
      | hAPP(c_Set_Oimage(X25934,X25933,X25932),c_Orderings_Otop__class_Otop(tc_fun(X25934,tc_HOL_Obool))) = X25930 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__range])]) ).

fof(i_0_7510,plain,
    ! [X19011,X19012,X19013] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X19013),hAPP(hAPP(c_Set_Oinsert(X19013),X19012),c_Orderings_Obot__class_Obot(tc_fun(X19013,tc_HOL_Obool)))),X19011) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X19013,tc_HOL_Obool)),hAPP(c_Relation_OImage(X19013,X19013,X19011),hAPP(hAPP(c_Set_Oinsert(X19013),X19012),c_Orderings_Obot__class_Obot(tc_fun(X19013,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X19013,tc_HOL_Obool),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_singleton__quotient]) ).

fof(i_0_7511,plain,
    ! [X19947,X19948,X19949,X19950,X19951,X19952] :
      ( ~ c_Equiv__Relations_Ocongruent(X19952,X19951,X19950,X19949)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X19952,X19952)),hAPP(hAPP(c_Product__Type_OPair(X19952,X19952),X19948),X19947)),X19950))
      | hAPP(X19949,X19948) = hAPP(X19949,X19947) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruentD])]) ).

fof(i_0_7512,plain,
    ! [X28553,X28554,X28555] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28555,X28555),tc_HOL_Obool)),X28554),c_Transitive__Closure_Ortrancl(X28555,X28553)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28555,X28555),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X28555,X28554)),c_Transitive__Closure_Ortrancl(X28555,X28553))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset__rtrancl])]) ).

cnf(i_0_7513,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_5555]) ).

cnf(i_0_7514,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_5551]) ).

fof(i_0_7515,plain,
    ! [X28868,X28869,X28870,X28871] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28871,X28871)),X28870),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28871,X28871),tc_HOL_Obool),X28869),X28868)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28871,X28871)),X28870),c_Transitive__Closure_Ortrancl(X28871,X28868))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__imp__rtrancl])]) ).

fof(i_0_7516,plain,
    ! [X27344,X27345,X27346,X27347] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X27347),X27346),c_Wellfounded_Oacc(X27347,X27345)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27347,X27347)),hAPP(hAPP(c_Product__Type_OPair(X27347,X27347),X27344),X27346)),X27345))
      | hBOOL(hAPP(hAPP(c_member(X27347),X27344),c_Wellfounded_Oacc(X27347,X27345))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downward])]) ).

fof(i_0_7517,plain,
    ! [X33387,X33388,X33389] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33389,X33389)),hAPP(hAPP(c_Product__Type_OPair(X33389,X33389),X33388),X33387)),c_List_Omeasures(X33389,c_List_Olist_ONil(tc_fun(X33389,tc_Nat_Onat))))),
    inference(variable_rename,[status(thm)],[i_0_5621]) ).

fof(i_0_7518,plain,
    ! [X25485,X25486,X25487] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25487,tc_HOL_Obool)),X25486),hAPP(hAPP(c_Set_Oinsert(X25487),X25485),c_Orderings_Obot__class_Obot(tc_fun(X25487,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25487,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMin(X25487,hAPP(hAPP(c_Set_Oinsert(X25487),X25485),X25486)) = X25485
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25487),X25486))
        | ~ class_Orderings_Olinorder(X25487) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25487,tc_HOL_Obool)),X25486),hAPP(hAPP(c_Set_Oinsert(X25487),X25485),c_Orderings_Obot__class_Obot(tc_fun(X25487,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25487,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMin(X25487,hAPP(hAPP(c_Set_Oinsert(X25487),X25485),X25486)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25487),X25485),c_Big__Operators_Olinorder__class_OMin(X25487,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25487,tc_HOL_Obool)),X25486),hAPP(hAPP(c_Set_Oinsert(X25487),X25485),c_Orderings_Obot__class_Obot(tc_fun(X25487,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25487),X25486))
        | ~ class_Orderings_Olinorder(X25487) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oinsert__remove])])]) ).

fof(i_0_7519,plain,
    ! [X25909,X25910,X25911] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25911,tc_HOL_Obool)),X25910),hAPP(hAPP(c_Set_Oinsert(X25911),X25909),c_Orderings_Obot__class_Obot(tc_fun(X25911,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25911,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMax(X25911,hAPP(hAPP(c_Set_Oinsert(X25911),X25909),X25910)) = X25909
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25911),X25910))
        | ~ class_Orderings_Olinorder(X25911) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25911,tc_HOL_Obool)),X25910),hAPP(hAPP(c_Set_Oinsert(X25911),X25909),c_Orderings_Obot__class_Obot(tc_fun(X25911,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25911,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMax(X25911,hAPP(hAPP(c_Set_Oinsert(X25911),X25909),X25910)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25911),X25909),c_Big__Operators_Olinorder__class_OMax(X25911,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25911,tc_HOL_Obool)),X25910),hAPP(hAPP(c_Set_Oinsert(X25911),X25909),c_Orderings_Obot__class_Obot(tc_fun(X25911,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25911),X25910))
        | ~ class_Orderings_Olinorder(X25911) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oinsert__remove])])]) ).

fof(i_0_7520,plain,
    ! [X20879,X20880,X20881] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20881,tc_HOL_Obool)),X20880),hAPP(hAPP(c_Set_Oinsert(X20881),X20879),c_Orderings_Obot__class_Obot(tc_fun(X20881,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X20881,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OSup__fin(X20881,hAPP(hAPP(c_Set_Oinsert(X20881),X20879),X20880)) = X20879
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20881),X20880))
        | ~ class_Lattices_Olattice(X20881) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20881,tc_HOL_Obool)),X20880),hAPP(hAPP(c_Set_Oinsert(X20881),X20879),c_Orderings_Obot__class_Obot(tc_fun(X20881,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X20881,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OSup__fin(X20881,hAPP(hAPP(c_Set_Oinsert(X20881),X20879),X20880)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20881),X20879),c_Big__Operators_Olattice__class_OSup__fin(X20881,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20881,tc_HOL_Obool)),X20880),hAPP(hAPP(c_Set_Oinsert(X20881),X20879),c_Orderings_Obot__class_Obot(tc_fun(X20881,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20881),X20880))
        | ~ class_Lattices_Olattice(X20881) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__remove])])]) ).

fof(i_0_7521,plain,
    ! [X20882,X20883,X20884] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20884,tc_HOL_Obool)),X20883),hAPP(hAPP(c_Set_Oinsert(X20884),X20882),c_Orderings_Obot__class_Obot(tc_fun(X20884,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X20884,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OInf__fin(X20884,hAPP(hAPP(c_Set_Oinsert(X20884),X20882),X20883)) = X20882
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20884),X20883))
        | ~ class_Lattices_Olattice(X20884) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20884,tc_HOL_Obool)),X20883),hAPP(hAPP(c_Set_Oinsert(X20884),X20882),c_Orderings_Obot__class_Obot(tc_fun(X20884,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X20884,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OInf__fin(X20884,hAPP(hAPP(c_Set_Oinsert(X20884),X20882),X20883)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20884),X20882),c_Big__Operators_Olattice__class_OInf__fin(X20884,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20884,tc_HOL_Obool)),X20883),hAPP(hAPP(c_Set_Oinsert(X20884),X20882),c_Orderings_Obot__class_Obot(tc_fun(X20884,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20884),X20883))
        | ~ class_Lattices_Olattice(X20884) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__remove])])]) ).

fof(i_0_7522,plain,
    ! [X25925,X25926,X25927,X25928,X25929] :
      ( ~ c_Typedef_Otype__definition(X25929,X25928,X25927,X25926,X25925)
      | hAPP(c_Set_Oimage(X25928,X25929,X25926),X25925) = c_Orderings_Otop__class_Otop(tc_fun(X25929,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__image])]) ).

fof(i_0_7523,plain,
    ! [X30354,X30355,X30356,X30357] :
      ( ~ c_Fun_Oinj__on(X30357,X30356,X30355,c_Complete__Lattice_OSup__class_OSup(tc_fun(X30357,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(X30357),tc_fun(X30357,tc_HOL_Obool),c_List_Oset(X30357)),X30354)))
      | c_Fun_Oinj__on(tc_List_Olist(X30357),tc_List_Olist(X30356),hAPP(c_List_Omap(X30357,X30356),X30355),X30354) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__mapI])]) ).

fof(i_0_7524,plain,
    ! [X24380,X24381,X24382,X24383] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),c_Groups_Ozero__class_Ozero(X24383)),X24381))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),X24382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24383),X24380),X24381)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24383),X24382),X24381)),X24380))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24383) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),X24381),c_Groups_Ozero__class_Ozero(X24383)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24383),X24380),X24381)),X24382))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),c_Groups_Ozero__class_Ozero(X24383)),X24381))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24383),X24382),X24381)),X24380))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24383) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),X24381),c_Groups_Ozero__class_Ozero(X24383)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),c_Groups_Ozero__class_Ozero(X24383)),X24380))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),c_Groups_Ozero__class_Ozero(X24383)),X24381))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24383),X24382),X24381)),X24380))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24383) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),c_Groups_Ozero__class_Ozero(X24383)),X24381))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),c_Groups_Ozero__class_Ozero(X24383)),X24381))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24383),X24382),X24381)),X24380))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24383) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),X24381),c_Groups_Ozero__class_Ozero(X24383)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),X24381),c_Groups_Ozero__class_Ozero(X24383)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),c_Groups_Ozero__class_Ozero(X24383)),X24381))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24383),X24382),X24381)),X24380))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24383) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),c_Groups_Ozero__class_Ozero(X24383)),X24380))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),X24381),c_Groups_Ozero__class_Ozero(X24383)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),c_Groups_Ozero__class_Ozero(X24383)),X24381))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24383),X24382),X24381)),X24380))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24383) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),X24381),c_Groups_Ozero__class_Ozero(X24383)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24383),X24380),X24381)),X24382))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),c_Groups_Ozero__class_Ozero(X24383)),X24381))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24383),X24382),X24381)),X24380))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24383) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),c_Groups_Ozero__class_Ozero(X24383)),X24380))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24383),X24380),X24381)),X24382))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),c_Groups_Ozero__class_Ozero(X24383)),X24381))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24383),X24382),X24381)),X24380))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24383) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),c_Groups_Ozero__class_Ozero(X24383)),X24381))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),X24382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24383),X24380),X24381)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24383),X24382),X24381)),X24380))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24383) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),X24381),c_Groups_Ozero__class_Ozero(X24383)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),X24381),c_Groups_Ozero__class_Ozero(X24383)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),X24382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24383),X24380),X24381)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24383),X24382),X24381)),X24380))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24383) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),c_Groups_Ozero__class_Ozero(X24383)),X24380))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),X24381),c_Groups_Ozero__class_Ozero(X24383)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),X24382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24383),X24380),X24381)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24383),X24382),X24381)),X24380))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24383) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),X24381),c_Groups_Ozero__class_Ozero(X24383)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24383),X24380),X24381)),X24382))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),X24382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24383),X24380),X24381)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24383),X24382),X24381)),X24380))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24383) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),c_Groups_Ozero__class_Ozero(X24383)),X24380))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24383),X24380),X24381)),X24382))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),X24382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24383),X24380),X24381)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24383),X24382),X24381)),X24380))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24383) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5622])])]) ).

fof(i_0_7525,plain,
    ! [X24460,X24461,X24462,X24463] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24463),c_Groups_Ozero__class_Ozero(X24463)),X24461))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),X24462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24463),X24460),X24461)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24463),X24462),X24461)),X24460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24463),X24461),c_Groups_Ozero__class_Ozero(X24463)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24463),X24460),X24461)),X24462))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24463),c_Groups_Ozero__class_Ozero(X24463)),X24461))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24463),X24462),X24461)),X24460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24463) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24463),X24461),c_Groups_Ozero__class_Ozero(X24463)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),c_Groups_Ozero__class_Ozero(X24463)),X24460))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24463),c_Groups_Ozero__class_Ozero(X24463)),X24461))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24463),X24462),X24461)),X24460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24463),c_Groups_Ozero__class_Ozero(X24463)),X24461))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24463),c_Groups_Ozero__class_Ozero(X24463)),X24461))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24463),X24462),X24461)),X24460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24463),X24461),c_Groups_Ozero__class_Ozero(X24463)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24463),X24461),c_Groups_Ozero__class_Ozero(X24463)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24463),c_Groups_Ozero__class_Ozero(X24463)),X24461))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24463),X24462),X24461)),X24460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),c_Groups_Ozero__class_Ozero(X24463)),X24460))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24463),X24461),c_Groups_Ozero__class_Ozero(X24463)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24463),c_Groups_Ozero__class_Ozero(X24463)),X24461))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24463),X24462),X24461)),X24460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24463),X24461),c_Groups_Ozero__class_Ozero(X24463)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24463),X24460),X24461)),X24462))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24463),c_Groups_Ozero__class_Ozero(X24463)),X24461))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24463),X24462),X24461)),X24460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),c_Groups_Ozero__class_Ozero(X24463)),X24460))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24463),X24460),X24461)),X24462))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24463),c_Groups_Ozero__class_Ozero(X24463)),X24461))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24463),X24462),X24461)),X24460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24463),c_Groups_Ozero__class_Ozero(X24463)),X24461))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),X24462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24463),X24460),X24461)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24463),X24462),X24461)),X24460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24463),X24461),c_Groups_Ozero__class_Ozero(X24463)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24463),X24461),c_Groups_Ozero__class_Ozero(X24463)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),X24462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24463),X24460),X24461)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24463),X24462),X24461)),X24460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),c_Groups_Ozero__class_Ozero(X24463)),X24460))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24463),X24461),c_Groups_Ozero__class_Ozero(X24463)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),X24462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24463),X24460),X24461)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24463),X24462),X24461)),X24460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24463),X24461),c_Groups_Ozero__class_Ozero(X24463)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24463),X24460),X24461)),X24462))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),X24462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24463),X24460),X24461)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24463),X24462),X24461)),X24460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),c_Groups_Ozero__class_Ozero(X24463)),X24460))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24463),X24460),X24461)),X24462))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),X24462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24463),X24460),X24461)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24463),X24462),X24461)),X24460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24463) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5623])])]) ).

fof(i_0_7526,plain,
    ! [X19100,X19101,X19102,X19103] :
      ( ~ c_Fun_Oinj__on(X19103,X19102,X19101,c_Orderings_Otop__class_Otop(tc_fun(X19103,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X19102,X19103,c_Hilbert__Choice_Oinv__into(X19103,X19102,c_Orderings_Otop__class_Otop(tc_fun(X19103,tc_HOL_Obool)),X19101)),hAPP(c_Set_Oimage(X19103,X19102,X19101),X19100)) = X19100 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__f__f])]) ).

fof(i_0_7527,plain,
    ! [X19096,X19097,X19098,X19099] :
      ( ~ c_Fun_Oinj__on(X19099,X19098,X19097,c_Orderings_Otop__class_Otop(tc_fun(X19099,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X19098,X19099,c_Hilbert__Choice_Oinv__into(X19099,X19098,c_Orderings_Otop__class_Otop(tc_fun(X19099,tc_HOL_Obool)),X19097)),hAPP(c_Set_Oimage(X19099,X19098,X19097),X19096)) = X19096 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__image__comp])]) ).

fof(i_0_7528,plain,
    ! [X31162,X31163,X31164,X31165,X31166,X31167] : hAPP(hAPP(c_List_Olist__update(tc_prod(X31167,X31166),hAPP(hAPP(c_List_Ozip(X31167,X31166),X31165),X31164)),X31163),X31162) = hAPP(hAPP(c_List_Ozip(X31167,X31166),hAPP(hAPP(c_List_Olist__update(X31167,X31165),X31163),hAPP(c_Product__Type_Ofst(X31167,X31166),X31162))),hAPP(hAPP(c_List_Olist__update(X31166,X31164),X31163),hAPP(c_Product__Type_Osnd(X31167,X31166),X31162))),
    inference(variable_rename,[status(thm)],[fact_update__zip]) ).

cnf(i_0_7529,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OMin)) ),
    inference(split_conjunct,[status(thm)],[i_0_5557]) ).

cnf(i_0_7530,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_5558]) ).

cnf(i_0_7531,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_5559]) ).

cnf(i_0_7532,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_5561]) ).

cnf(i_0_7533,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_5560]) ).

cnf(i_0_7534,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_5562]) ).

cnf(i_0_7535,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_5624]) ).

fof(i_0_7536,plain,
    ! [X20674] : 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)),X20674)))),
    inference(variable_rename,[status(thm)],[fact_finite__Collect__less__nat]) ).

fof(i_0_7537,plain,
    ! [X20673] : 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)),X20673)))),
    inference(variable_rename,[status(thm)],[fact_finite__Collect__le__nat]) ).

fof(i_0_7538,plain,
    ! [X27285,X27286,X27287,X27288,X27289,X27290,X27291] : hAPP(hAPP(c_Relation_Orel__comp(X27291,X27290,X27289),hAPP(hAPP(c_Relation_Orel__comp(X27291,X27288,X27290),X27287),X27286)),X27285) = hAPP(hAPP(c_Relation_Orel__comp(X27291,X27288,X27289),X27287),hAPP(hAPP(c_Relation_Orel__comp(X27288,X27290,X27289),X27286),X27285)),
    inference(variable_rename,[status(thm)],[fact_O__assoc]) ).

fof(i_0_7539,plain,
    ! [X26666,X26667,X26668,X26669,X26670] :
      ( ~ class_Groups_Ocomm__monoid__add(X26670)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26669),X26668))
      | ~ hBOOL(hAPP(hAPP(c_member(X26669),X26667),X26668))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26669,X26670),X26666),X26668) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26670),hAPP(X26666,X26667)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26669,X26670),X26666),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26669,tc_HOL_Obool)),X26668),hAPP(hAPP(c_Set_Oinsert(X26669),X26667),c_Orderings_Obot__class_Obot(tc_fun(X26669,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oremove])]) ).

fof(i_0_7540,plain,
    ! [X26661,X26662,X26663,X26664,X26665] :
      ( ~ class_Groups_Ocomm__monoid__add(X26665)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26664),X26663))
      | ~ hBOOL(hAPP(hAPP(c_member(X26664),X26662),X26663))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26664,X26665),X26661),X26663) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26665),hAPP(X26661,X26662)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26664,X26665),X26661),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26664,tc_HOL_Obool)),X26663),hAPP(hAPP(c_Set_Oinsert(X26664),X26662),c_Orderings_Obot__class_Obot(tc_fun(X26664,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff1_H])]) ).

fof(i_0_7541,plain,
    ! [X23234,X23235,X23236,X23237,X23238] :
      ( ~ class_Groups_Ocomm__monoid__mult(X23238)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23237),X23236))
      | ~ hBOOL(hAPP(hAPP(c_member(X23237),X23235),X23236))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23237,X23238),X23234),X23236) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23238),hAPP(X23234,X23235)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23237,X23238),X23234),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23237,tc_HOL_Obool)),X23236),hAPP(hAPP(c_Set_Oinsert(X23237),X23235),c_Orderings_Obot__class_Obot(tc_fun(X23237,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oremove])]) ).

fof(i_0_7542,plain,
    ! [X29352,X29353,X29354,X29355] : hAPP(c_Set_OPow(X29355),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29354,tc_fun(X29355,tc_HOL_Obool)),X29353),X29352)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29354,tc_fun(tc_fun(X29355,tc_HOL_Obool),tc_HOL_Obool)),X29353),hAPP(hAPP(c_COMBB(tc_fun(X29355,tc_HOL_Obool),tc_fun(tc_fun(X29355,tc_HOL_Obool),tc_HOL_Obool),X29354),c_Set_OPow(X29355)),X29352)),
    inference(variable_rename,[status(thm)],[fact_Pow__INT__eq]) ).

fof(i_0_7543,plain,
    ! [X22914,X22915,X22916] :
      ( ~ 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),X22916),X22915)),X22914)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22914),X22916))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22916))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22915)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__pos__lemma])]) ).

fof(i_0_7544,plain,
    ! [X26793,X26794,X26795] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26795,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X26794)),X26793) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26795,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26795,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X26794)),X26793)),hAPP(X26793,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_UN__le__eq__Un0]) ).

fof(i_0_7545,plain,
    ! [X21271,X21272,X21273] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21273),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21273,tc_HOL_Obool)),X21272),X21271)))
      | hAPP(c_Finite__Set_Ocard(X21273),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21273,tc_HOL_Obool)),X21272),X21271)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21273),X21272)),hAPP(c_Finite__Set_Ocard(X21273),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21273,tc_HOL_Obool)),X21272),X21271))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff__subset__Int])]) ).

cnf(i_0_7546,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_7547,plain,
    ! [X29455,X29456,X29457,X29458,X29459] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29459,tc_fun(X29458,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29459,tc_HOL_Obool)),X29457),X29456)),X29455) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29458,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29459,tc_fun(X29458,tc_HOL_Obool)),X29457),X29455)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29459,tc_fun(X29458,tc_HOL_Obool)),X29456),X29455)),
    inference(variable_rename,[status(thm)],[fact_INT__Un]) ).

fof(i_0_7548,plain,
    ! [X19720,X19721,X19722,X19723,X19724] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19724,tc_fun(X19723,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19724,tc_HOL_Obool)),X19722),X19721)),X19720) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19723,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19724,tc_fun(X19723,tc_HOL_Obool)),X19722),X19720)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19724,tc_fun(X19723,tc_HOL_Obool)),X19721),X19720)),
    inference(variable_rename,[status(thm)],[fact_UN__Un]) ).

fof(i_0_7549,plain,
    ! [X28662,X28663,X28664,X28665] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28665,X28665)),hAPP(hAPP(c_Product__Type_OPair(X28665,X28665),X28664),X28662)),c_Transitive__Closure_Ortrancl(X28665,X28663)))
        | X28664 = X28662
        | hBOOL(hAPP(hAPP(c_member(X28665),X28664),hAPP(c_Relation_ODomain(X28665,X28665),X28663))) )
      & ( X28664 != X28662
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28665,X28665)),hAPP(hAPP(c_Product__Type_OPair(X28665,X28665),X28664),X28662)),c_Transitive__Closure_Ortrancl(X28665,X28663)))
        | hBOOL(hAPP(hAPP(c_member(X28665),X28664),hAPP(c_Relation_ODomain(X28665,X28665),X28663))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5625])])]) ).

cnf(i_0_7550,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_5626]) ).

fof(i_0_7551,plain,
    ! [X19890,X19891,X19892,X19893,X19895,X19896,X19897,X19898,X19899] :
      ( ( c_Map_Odom(X19893,X19892,X19891) != hAPP(hAPP(c_Set_Oinsert(X19893),X19890),c_Orderings_Obot__class_Obot(tc_fun(X19893,tc_HOL_Obool)))
        | X19891 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X19893,tc_Option_Ooption(X19892)),hAPP(c_COMBK(tc_Option_Ooption(X19892),X19893),c_Option_Ooption_ONone(X19892))),X19890),hAPP(c_Option_Ooption_OSome(X19892),esk61_4(X19890,X19891,X19892,X19893))) )
      & ( X19896 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X19898,tc_Option_Ooption(X19897)),hAPP(c_COMBK(tc_Option_Ooption(X19897),X19898),c_Option_Ooption_ONone(X19897))),X19895),hAPP(c_Option_Ooption_OSome(X19897),X19899))
        | c_Map_Odom(X19898,X19897,X19896) = hAPP(hAPP(c_Set_Oinsert(X19898),X19895),c_Orderings_Obot__class_Obot(tc_fun(X19898,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_dom__eq__singleton__conv])])])])]) ).

fof(i_0_7552,plain,
    ! [X21377,X21378,X21379,X21380,X21381,X21382,X21383] :
      ( ~ c_Big__Operators_Ocomm__monoid__big(X21383,X21382,X21381,X21380,X21379)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X21382),X21378))
      | hAPP(hAPP(X21379,X21377),X21378) = X21380 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5627])]) ).

fof(i_0_7553,plain,
    ! [X20449,X20450,X20451] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20451,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20451,tc_HOL_Obool)),X20450)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20451,tc_HOL_Obool)),X20449)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20451,tc_HOL_Obool)),X20449),X20450)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20451,tc_HOL_Obool)),X20449),X20450))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20451,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20451,tc_HOL_Obool)),X20450)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20451,tc_HOL_Obool)),X20449))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__subset__Compl__iff])]) ).

fof(i_0_7554,plain,
    ! [X29450,X29451,X29452,X29453,X29454] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29454),X29453),X29452))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29451,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29454,tc_fun(X29451,tc_HOL_Obool)),X29452),X29450)),hAPP(X29450,X29453))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__lower])]) ).

fof(i_0_7555,plain,
    ! [X28547,X28548,X28549] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28549,X28549),tc_HOL_Obool)),X28548),X28547))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28549,X28549),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X28549,X28548)),c_Transitive__Closure_Ortrancl(X28549,X28547))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__mono])]) ).

fof(i_0_7556,plain,
    ! [X29373,X29374,X29375,X29376,X29377,X29378] : hAPP(c_Set_Ovimage(X29378,X29377,X29376),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29375,tc_fun(X29377,tc_HOL_Obool)),X29374),X29373)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29375,tc_fun(X29378,tc_HOL_Obool)),X29374),hAPP(hAPP(c_COMBB(tc_fun(X29377,tc_HOL_Obool),tc_fun(X29378,tc_HOL_Obool),X29375),c_Set_Ovimage(X29378,X29377,X29376)),X29373)),
    inference(variable_rename,[status(thm)],[fact_vimage__INT]) ).

fof(i_0_7557,plain,
    ! [X19773,X19774,X19775,X19776,X19777,X19778] : hAPP(c_Set_Ovimage(X19778,X19777,X19776),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19775,tc_fun(X19777,tc_HOL_Obool)),X19774),X19773)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19775,tc_fun(X19778,tc_HOL_Obool)),X19774),hAPP(hAPP(c_COMBB(tc_fun(X19777,tc_HOL_Obool),tc_fun(X19778,tc_HOL_Obool),X19775),c_Set_Ovimage(X19778,X19777,X19776)),X19773)),
    inference(variable_rename,[status(thm)],[fact_vimage__UN]) ).

fof(i_0_7558,plain,
    ! [X19407,X19408,X19409,X19410,X19411,X19412] : hAPP(c_Relation_OImage(X19412,X19411,X19410),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19409,tc_fun(X19412,tc_HOL_Obool)),X19408),X19407)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19409,tc_fun(X19411,tc_HOL_Obool)),X19408),hAPP(hAPP(c_COMBB(tc_fun(X19412,tc_HOL_Obool),tc_fun(X19411,tc_HOL_Obool),X19409),c_Relation_OImage(X19412,X19411,X19410)),X19407)),
    inference(variable_rename,[status(thm)],[fact_Image__UN]) ).

fof(i_0_7559,plain,
    ! [X19703,X19704,X19705,X19706,X19707,X19708] : hAPP(c_Set_Oimage(X19708,X19707,X19706),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19705,tc_fun(X19708,tc_HOL_Obool)),X19704),X19703)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19705,tc_fun(X19707,tc_HOL_Obool)),X19704),hAPP(hAPP(c_COMBB(tc_fun(X19708,tc_HOL_Obool),tc_fun(X19707,tc_HOL_Obool),X19705),c_Set_Oimage(X19708,X19707,X19706)),X19703)),
    inference(variable_rename,[status(thm)],[fact_image__UN]) ).

fof(i_0_7560,plain,
    ! [X24416,X24417,X24418,X24419,X24420] :
      ( ~ class_Fields_Ofield(X24420)
      | X24419 = c_Groups_Ozero__class_Ozero(X24420)
      | X24418 = c_Groups_Ozero__class_Ozero(X24420)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24420),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24420),X24417),X24419)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24420),X24416),X24418)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24420),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24420),X24417),X24418)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24420),X24416),X24419))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24420),X24419),X24418)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__eq])]) ).

fof(i_0_7561,plain,
    ! [X24437,X24438,X24439,X24440,X24441] :
      ( ~ class_Fields_Ofield(X24441)
      | X24440 = c_Groups_Ozero__class_Ozero(X24441)
      | X24439 = c_Groups_Ozero__class_Ozero(X24441)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24441),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24441),X24438),X24440)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24441),X24437),X24439)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24441),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24441),X24438),X24439)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24441),X24437),X24440))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24441),X24440),X24439)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__frac__eq])]) ).

fof(i_0_7562,plain,
    ! [X20558,X20559] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20559,tc_HOL_Obool)),X20558) = hAPP(c_Set_OCollect(X20559),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X20559),c_fNot),hAPP(hAPP(c_COMBC(X20559,tc_fun(X20559,tc_HOL_Obool),tc_HOL_Obool),c_member(X20559)),X20558))),
    inference(variable_rename,[status(thm)],[fact_Compl__eq]) ).

cnf(i_0_7563,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_5628]) ).

fof(i_0_7564,plain,
    ! [X33234,X33235,X33236,X33237,X33238] :
      ( ~ c_List_Olist__all2(X33238,X33237,X33236,X33235,X33234)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33238)),X33235) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33237)),X33234) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__lengthD])]) ).

fof(i_0_7565,plain,
    ! [X21823,X21824,X21825] :
      ( ( ~ 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,X21825)),X21824)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21825)),X21823)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21824),X21823)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21824),X21823))
        | 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,X21825)),X21824)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21825)),X21823))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1])]) ).

fof(i_0_7566,plain,
    ! [X21828,X21829,X21830] :
      ( ( ~ 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,X21830)),X21829)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21830)),X21828)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21829),X21828)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21829),X21828))
        | 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,X21830)),X21829)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21830)),X21828))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1])]) ).

fof(i_0_7567,plain,
    ! [X23583,X23584,X23585,X23586,X23587] :
      ( ( ~ hBOOL(hAPP(hAPP(X23584,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23583),X23585)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23583,X23585)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23587))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23587),X23585))
        | X23583 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23585),X23586)),X23587)
        | hBOOL(hAPP(hAPP(X23584,X23586),X23587))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23585)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk130_3(X23583,X23584,X23585)))
        | hBOOL(hAPP(hAPP(X23584,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23583),X23585)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23583,X23585)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23585)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk130_3(X23583,X23584,X23585)),X23585))
        | hBOOL(hAPP(hAPP(X23584,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23583),X23585)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23583,X23585)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23585)) )
      & ( X23583 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23585),esk129_3(X23583,X23584,X23585))),esk130_3(X23583,X23584,X23585))
        | hBOOL(hAPP(hAPP(X23584,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23583),X23585)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23583,X23585)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23585)) )
      & ( ~ hBOOL(hAPP(hAPP(X23584,esk129_3(X23583,X23584,X23585)),esk130_3(X23583,X23584,X23585)))
        | hBOOL(hAPP(hAPP(X23584,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23583),X23585)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23583,X23585)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23585)) ) ),
    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_7568,plain,
    ! [X32706,X32707,X32708,X32709,X32710] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X32709),X32707),hAPP(c_List_Oset(X32709),X32706)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X32709),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32709,X32710,X32708),X32707),X32706)))
        | ~ class_Orderings_Olinorder(X32710) )
      & ( hBOOL(hAPP(c_List_Odistinct(X32709),X32706))
        | ~ hBOOL(hAPP(c_List_Odistinct(X32709),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32709,X32710,X32708),X32707),X32706)))
        | ~ class_Orderings_Olinorder(X32710) )
      & ( hBOOL(hAPP(hAPP(c_member(X32709),X32707),hAPP(c_List_Oset(X32709),X32706)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X32709),X32706))
        | hBOOL(hAPP(c_List_Odistinct(X32709),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32709,X32710,X32708),X32707),X32706)))
        | ~ class_Orderings_Olinorder(X32710) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5629])])]) ).

fof(i_0_7569,plain,
    ! [X20021,X20022] :
      ( ( hBOOL(hAPP(X20021,c_Option_Ooption_ONone(X20022)))
        | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X20022)),X20021))
        | ~ class_Enum_Oenum(X20022) )
      & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X20022),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X20022),tc_HOL_Obool,X20022),X20021),c_Option_Ooption_OSome(X20022))))
        | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X20022)),X20021))
        | ~ class_Enum_Oenum(X20022) )
      & ( ~ hBOOL(hAPP(X20021,c_Option_Ooption_ONone(X20022)))
        | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X20022),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X20022),tc_HOL_Obool,X20022),X20021),c_Option_Ooption_OSome(X20022))))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X20022)),X20021))
        | ~ class_Enum_Oenum(X20022) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__all__option__def])])]) ).

fof(i_0_7570,plain,
    ! [X19322,X19323,X19324,X19325,X19326] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19326,tc_HOL_Obool)),X19325),hAPP(c_Set_Oimage(X19324,X19326,X19323),X19322)))
      | c_Fun_Oinj__on(X19326,X19324,c_Hilbert__Choice_Oinv__into(X19324,X19326,X19322,X19323),X19325) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__inv__into])]) ).

fof(i_0_7571,plain,
    ! [X19413,X19414,X19415,X19416,X19417,X19418] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19418,tc_fun(X19417,tc_HOL_Obool)),X19416),hAPP(c_Fun_Ocomp(X19415,tc_fun(X19417,tc_HOL_Obool),X19418,X19414),X19413)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19415,tc_fun(X19417,tc_HOL_Obool)),hAPP(c_Set_Oimage(X19418,X19415,X19413),X19416)),X19414),
    inference(variable_rename,[status(thm)],[fact_UN__o]) ).

fof(i_0_7572,plain,
    ! [X26623,X26624,X26625,X26626,X26627] :
      ( ~ class_Groups_Ocomm__monoid__add(X26627)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26626),X26625))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26626,X26627),X26624),hAPP(hAPP(c_Set_Oinsert(X26626),X26623),X26625)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26627),hAPP(X26624,X26623)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26626,X26627),X26624),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26626,tc_HOL_Obool)),X26625),hAPP(hAPP(c_Set_Oinsert(X26626),X26623),c_Orderings_Obot__class_Obot(tc_fun(X26626,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oinsert__remove])]) ).

fof(i_0_7573,plain,
    ! [X23208,X23209,X23210,X23211,X23212] :
      ( ~ class_Groups_Ocomm__monoid__mult(X23212)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23211),X23210))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23211,X23212),X23209),hAPP(hAPP(c_Set_Oinsert(X23211),X23208),X23210)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23212),hAPP(X23209,X23208)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23211,X23212),X23209),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23211,tc_HOL_Obool)),X23210),hAPP(hAPP(c_Set_Oinsert(X23211),X23208),c_Orderings_Obot__class_Obot(tc_fun(X23211,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oinsert__remove])]) ).

fof(i_0_7574,plain,
    ! [X18362,X18363,X18364,X18365,X18366,X18367] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18367,X18366),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18367,X18366),X18365),X18364),X18363)),X18364),X18362) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18367,X18366),X18365),X18364),X18362),
    inference(variable_rename,[status(thm)],[fact_fun__upd__upd]) ).

fof(i_0_7575,plain,
    ! [X19209,X19210,X19211,X19212,X19213] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X19213),X19212),hAPP(c_Set_Oimage(X19211,X19213,X19210),X19209)))
      | hAPP(X19210,hAPP(c_Hilbert__Choice_Oinv__into(X19211,X19213,X19209,X19210),X19212)) = X19212 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__inv__into__f])]) ).

fof(i_0_7576,plain,
    ! [X23576,X23577,X23578,X23579,X23580] :
      ( ( ~ hBOOL(hAPP(hAPP(X23577,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23576),X23578)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23576,X23578)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23578),X23580))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23580),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X23576 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23578),X23579)),X23580)
        | hBOOL(hAPP(hAPP(X23577,X23579),X23580))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23578),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23578),esk128_3(X23576,X23577,X23578)))
        | hBOOL(hAPP(hAPP(X23577,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23576),X23578)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23576,X23578)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23578),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk128_3(X23576,X23577,X23578)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(X23577,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23576),X23578)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23576,X23578)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23578),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( X23576 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23578),esk127_3(X23576,X23577,X23578))),esk128_3(X23576,X23577,X23578))
        | hBOOL(hAPP(hAPP(X23577,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23576),X23578)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23576,X23578)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23578),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(X23577,esk127_3(X23576,X23577,X23578)),esk128_3(X23576,X23577,X23578)))
        | hBOOL(hAPP(hAPP(X23577,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23576),X23578)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23576,X23578)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23578),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_7577,plain,
    ! [X30748,X30749] : hAPP(hAPP(c_List_Ozip(X30749,X30749),X30748),X30748) = hAPP(hAPP(c_List_Omap(X30749,tc_prod(X30749,X30749)),hAPP(hAPP(c_COMBS(X30749,X30749,tc_prod(X30749,X30749)),c_Product__Type_OPair(X30749,X30749)),c_COMBI(X30749))),X30748),
    inference(variable_rename,[status(thm)],[fact_zip__same__conv__map]) ).

fof(i_0_7578,plain,
    ! [X25198,X25199] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X25199),X25198) = 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)),X25199)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25198))),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J]) ).

fof(i_0_7579,plain,
    ! [X25200,X25201] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X25201),X25200) = 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)),X25201)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25200))),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J]) ).

fof(i_0_7580,plain,
    ! [X27943,X27944,X27945] :
      ( ( hAPP(c_Set_Oimage(X27945,X27944,X27943),c_Orderings_Otop__class_Otop(tc_fun(X27945,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X27944,tc_HOL_Obool))
        | hAPP(c_Fun_Ocomp(X27945,X27944,X27944,X27943),c_Hilbert__Choice_Oinv__into(X27945,X27944,c_Orderings_Otop__class_Otop(tc_fun(X27945,tc_HOL_Obool)),X27943)) = c_Fun_Oid(X27944) )
      & ( hAPP(c_Fun_Ocomp(X27945,X27944,X27944,X27943),c_Hilbert__Choice_Oinv__into(X27945,X27944,c_Orderings_Otop__class_Otop(tc_fun(X27945,tc_HOL_Obool)),X27943)) != c_Fun_Oid(X27944)
        | hAPP(c_Set_Oimage(X27945,X27944,X27943),c_Orderings_Otop__class_Otop(tc_fun(X27945,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X27944,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__iff])]) ).

fof(i_0_7581,plain,
    ! [X22755,X22756,X22757] :
      ( ~ class_Rings_Olinordered__semidom(X22757)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22757),c_Groups_Ozero__class_Ozero(X22757)),X22756))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22757),X22756),c_Groups_Oone__class_Oone(X22757)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22757),X22756),hAPP(hAPP(c_Power_Opower__class_Opower(X22757),X22756),X22755))),hAPP(hAPP(c_Power_Opower__class_Opower(X22757),X22756),X22755))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less])]) ).

fof(i_0_7582,plain,
    ! [X25945,X25946,X25947,X25948,X25949,X25950,X25951] :
      ( ( hAPP(X25949,X25946) != hAPP(X25949,X25945)
        | X25946 = X25945
        | ~ c_Typedef_Otype__definition(X25951,X25950,X25949,X25948,X25947) )
      & ( X25946 != X25945
        | hAPP(X25949,X25946) = hAPP(X25949,X25945)
        | ~ c_Typedef_Otype__definition(X25951,X25950,X25949,X25948,X25947) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inject])])]) ).

fof(i_0_7583,plain,
    ! [X27830,X27831,X27832,X27833] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27833,X27832)),hAPP(hAPP(c_Product__Type_OSigma(X27833,X27832),X27831),hAPP(c_COMBK(tc_fun(X27832,tc_HOL_Obool),X27833),X27830))))
      | X27831 = c_Orderings_Obot__class_Obot(tc_fun(X27833,tc_HOL_Obool))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27832),X27830)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__cartesian__productD2])]) ).

fof(i_0_7584,plain,
    ! [X27826,X27827,X27828,X27829] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27829,X27828)),hAPP(hAPP(c_Product__Type_OSigma(X27829,X27828),X27827),hAPP(c_COMBK(tc_fun(X27828,tc_HOL_Obool),X27829),X27826))))
      | X27826 = c_Orderings_Obot__class_Obot(tc_fun(X27828,tc_HOL_Obool))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27829),X27827)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__cartesian__productD1])]) ).

fof(i_0_7585,plain,
    ! [X25952,X25953,X25954,X25955,X25956,X25957] :
      ( ~ c_Typedef_Otype__definition(X25957,X25956,X25955,X25954,X25953)
      | hAPP(X25954,hAPP(X25955,X25952)) = X25952 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inverse])]) ).

cnf(i_0_7586,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_5630]) ).

fof(i_0_7587,plain,
    ! [X27065,X27066,X27067] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27067)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27067),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27067),hAPP(c_Groups_Oabs__class_Oabs(X27067),X27066)),hAPP(c_Groups_Oabs__class_Oabs(X27067),X27065))),hAPP(c_Groups_Oabs__class_Oabs(X27067),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27067),X27066),X27065)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2])]) ).

fof(i_0_7588,plain,
    ! [X27068,X27069,X27070] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27070)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27070),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27070),hAPP(c_Groups_Oabs__class_Oabs(X27070),X27069)),hAPP(c_Groups_Oabs__class_Oabs(X27070),X27068))),hAPP(c_Groups_Oabs__class_Oabs(X27070),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27070),X27068),X27069)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2__sym])]) ).

cnf(i_0_7589,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_5631]) ).

fof(i_0_7590,plain,
    ! [X19495,X19496,X19497,X19498,X19499] : hAPP(c_Set_Ovimage(X19499,X19498,X19497),hAPP(hAPP(c_Set_Oinsert(X19498),X19496),X19495)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19499,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X19499,X19498,X19497),hAPP(hAPP(c_Set_Oinsert(X19498),X19496),c_Orderings_Obot__class_Obot(tc_fun(X19498,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(X19499,X19498,X19497),X19495)),
    inference(variable_rename,[status(thm)],[fact_vimage__insert]) ).

fof(i_0_7591,plain,
    ! [X33249,X33250,X33251,X33252] :
      ( ( ~ c_List_Olist__all2(X33252,X33251,X33250,c_List_Olist_ONil(X33252),X33249)
        | X33249 = c_List_Olist_ONil(X33251) )
      & ( X33249 != c_List_Olist_ONil(X33251)
        | c_List_Olist__all2(X33252,X33251,X33250,c_List_Olist_ONil(X33252),X33249) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__Nil])]) ).

fof(i_0_7592,plain,
    ! [X33245,X33246,X33247,X33248] :
      ( ( ~ c_List_Olist__all2(X33248,X33247,X33246,X33245,c_List_Olist_ONil(X33247))
        | X33245 = c_List_Olist_ONil(X33248) )
      & ( X33245 != c_List_Olist_ONil(X33248)
        | c_List_Olist__all2(X33248,X33247,X33246,X33245,c_List_Olist_ONil(X33247)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__Nil2])]) ).

fof(i_0_7593,plain,
    ! [X27590,X27591,X27592,X27593,X27594] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27594,X27593)),hAPP(hAPP(c_Product__Type_OPair(X27594,X27593),X27592),X27591)),X27590))
      | hBOOL(hAPP(hAPP(c_member(X27594),X27592),hAPP(c_Relation_ODomain(X27594,X27593),X27590))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainI])]) ).

fof(i_0_7594,plain,
    ! [X27512,X27513,X27514,X27515,X27516] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27516,X27515)),hAPP(hAPP(c_Product__Type_OPair(X27516,X27515),X27514),X27513)),X27512))
      | hBOOL(hAPP(hAPP(c_member(X27515),X27513),hAPP(c_Relation_ORange(X27516,X27515),X27512))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeI])]) ).

fof(i_0_7595,plain,
    ! [X31817,X31818,X31819,X31820] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31820),X31819))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31818,tc_HOL_Obool)),hAPP(c_List_Oset(X31818),hAPP(hAPP(c_List_Odrop(X31818),X31819),X31817))),hAPP(c_List_Oset(X31818),hAPP(hAPP(c_List_Odrop(X31818),X31820),X31817)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__drop__subset__set__drop])]) ).

fof(i_0_7596,plain,
    ! [X31113,X31114,X31115,X31116] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31116),X31115))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31114,tc_HOL_Obool)),hAPP(c_List_Oset(X31114),hAPP(hAPP(c_List_Otake(X31114),X31116),X31113))),hAPP(c_List_Oset(X31114),hAPP(hAPP(c_List_Otake(X31114),X31115),X31113)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__take__subset__set__take])]) ).

fof(i_0_7597,plain,
    ! [X33231,X33232,X33233] :
      ( ( X33233 != X33232
        | c_List_Olist__all2(X33231,X33231,c_fequal,X33233,X33232) )
      & ( ~ c_List_Olist__all2(X33231,X33231,c_fequal,X33233,X33232)
        | X33233 = X33232 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__eq])]) ).

fof(i_0_7598,plain,
    ! [X32629,X32630,X32631] :
      ( ~ class_Orderings_Olinorder(X32631)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32631),X32630))
      | c_List_Olinorder__class_Osorted__list__of__set(X32631,hAPP(hAPP(c_Set_Oinsert(X32631),X32629),X32630)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32631,X32631,c_COMBI(X32631)),X32629),c_List_Olinorder__class_Osorted__list__of__set(X32631,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X32631,tc_HOL_Obool)),X32630),hAPP(hAPP(c_Set_Oinsert(X32631),X32629),c_Orderings_Obot__class_Obot(tc_fun(X32631,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__insert])]) ).

fof(i_0_7599,plain,
    ! [X22715,X22716,X22717,X22718] :
      ( ~ class_Rings_Olinordered__semidom(X22718)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22718),hAPP(hAPP(c_Power_Opower__class_Opower(X22718),X22717),hAPP(c_Nat_OSuc,X22716))),hAPP(hAPP(c_Power_Opower__class_Opower(X22718),X22715),hAPP(c_Nat_OSuc,X22716))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22718),c_Groups_Ozero__class_Ozero(X22718)),X22715))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22718),X22717),X22715)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__base])]) ).

fof(i_0_7600,plain,
    ! [X20023,X20024] :
      ( ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X20024)),X20023))
        | hBOOL(hAPP(X20023,c_Option_Ooption_ONone(X20024)))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X20024),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X20024),tc_HOL_Obool,X20024),X20023),c_Option_Ooption_OSome(X20024))))
        | ~ class_Enum_Oenum(X20024) )
      & ( ~ hBOOL(hAPP(X20023,c_Option_Ooption_ONone(X20024)))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X20024)),X20023))
        | ~ class_Enum_Oenum(X20024) )
      & ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X20024),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X20024),tc_HOL_Obool,X20024),X20023),c_Option_Ooption_OSome(X20024))))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X20024)),X20023))
        | ~ class_Enum_Oenum(X20024) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__ex__option__def])])]) ).

cnf(i_0_7601,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_5632]) ).

fof(i_0_7602,plain,
    ! [X29096,X29097,X29098,X29099] :
      ( ~ class_Orderings_Olinorder(X29099)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29099),X29098))
      | ~ hBOOL(hAPP(hAPP(c_member(X29099),X29097),X29098))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29099),hAPP(hAPP(c_Orderings_Oord__class_Omax(X29099),X29097),X29096)),hAPP(hAPP(c_Finite__Set_Ofold(X29099,X29099,c_Orderings_Oord__class_Omax(X29099)),X29096),X29098))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__le__fold__sup])]) ).

fof(i_0_7603,plain,
    ! [X29084,X29085,X29086,X29087] :
      ( ~ class_Lattices_Osemilattice__sup(X29087)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29087),X29086))
      | ~ hBOOL(hAPP(hAPP(c_member(X29087),X29085),X29086))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29087),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X29087),X29085),X29084)),hAPP(hAPP(c_Finite__Set_Ofold(X29087,X29087,c_Lattices_Osemilattice__sup__class_Osup(X29087)),X29084),X29086))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__le__fold__sup])]) ).

fof(i_0_7604,plain,
    ! [X27602,X27603,X27604,X27605] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27605,X27604),tc_HOL_Obool)),X27603),X27602))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27605,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X27605,X27604),X27603)),hAPP(c_Relation_ODomain(X27605,X27604),X27602))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__mono])]) ).

fof(i_0_7605,plain,
    ! [X19104,X19105,X19106] :
      ( ~ c_Fun_Oinj__on(X19106,X19105,X19104,c_Orderings_Otop__class_Otop(tc_fun(X19106,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X19105,X19106,c_Hilbert__Choice_Oinv__into(X19106,X19105,c_Orderings_Otop__class_Otop(tc_fun(X19106,tc_HOL_Obool)),X19104)),c_Orderings_Otop__class_Otop(tc_fun(X19105,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X19106,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__imp__surj__inv])]) ).

cnf(i_0_7606,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_5633]) ).

fof(i_0_7607,plain,
    ! [X24453,X24454,X24455] :
      ( ~ class_Fields_Olinordered__field(X24455)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24455),X24454),X24453))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24455),X24454),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24455),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24455),X24454),X24453)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24455),c_Groups_Oone__class_Oone(X24455)),c_Groups_Oone__class_Oone(X24455))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__half__sum])]) ).

fof(i_0_7608,plain,
    ! [X25501,X25502] :
      ( ~ c_Nat__Transfer_Onat__set(X25502)
      | ~ c_Nat__Transfer_Onat__set(X25501)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X25502),X25501) = 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),X25502)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25501))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J])]) ).

fof(i_0_7609,plain,
    ! [X25503,X25504] :
      ( ~ c_Nat__Transfer_Onat__set(X25504)
      | ~ c_Nat__Transfer_Onat__set(X25503)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X25504),X25503) = 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),X25504)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25503))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J])]) ).

fof(i_0_7610,plain,
    ! [X26213,X26214,X26215,X26216,X26217] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26217),X26214),X26216))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26217),X26216),X26215))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X26217,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26217,X26216,X26215)),c_SetInterval_Oord__class_OatLeastAtMost(X26217,X26214,X26213)))
        | ~ class_Orderings_Oorder(X26217) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26217),X26215),X26213))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26217),X26216),X26215))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X26217,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26217,X26216,X26215)),c_SetInterval_Oord__class_OatLeastAtMost(X26217,X26214,X26213)))
        | ~ class_Orderings_Oorder(X26217) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26217),X26214),X26216))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26217),X26215),X26213))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26217),X26216),X26215))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X26217,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26217,X26216,X26215)),c_SetInterval_Oord__class_OatLeastAtMost(X26217,X26214,X26213)))
        | ~ class_Orderings_Oorder(X26217) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26217),X26214),X26213))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X26217,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26217,X26216,X26215)),c_SetInterval_Oord__class_OatLeastAtMost(X26217,X26214,X26213)))
        | ~ class_Orderings_Oorder(X26217) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26217),X26216),X26215))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26217),X26214),X26213))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X26217,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26217,X26216,X26215)),c_SetInterval_Oord__class_OatLeastAtMost(X26217,X26214,X26213)))
        | ~ class_Orderings_Oorder(X26217) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26217),X26214),X26216))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26217),X26214),X26216))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26217),X26215),X26213))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26217),X26214),X26213))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X26217,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26217,X26216,X26215)),c_SetInterval_Oord__class_OatLeastAtMost(X26217,X26214,X26213)))
        | ~ class_Orderings_Oorder(X26217) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26217),X26215),X26213))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26217),X26214),X26216))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26217),X26215),X26213))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26217),X26214),X26213))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X26217,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26217,X26216,X26215)),c_SetInterval_Oord__class_OatLeastAtMost(X26217,X26214,X26213)))
        | ~ class_Orderings_Oorder(X26217) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5634])])]) ).

fof(i_0_7611,plain,
    ! [X21603,X21604,X21605,X21606,X21607] :
      ( ~ class_Rings_Osemiring(X21607)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21607),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21607),X21606),X21605)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21607),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21607),X21604),X21605)),X21603)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21607),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21607),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21607),X21606),X21604)),X21605)),X21603) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_combine__common__factor])]) ).

fof(i_0_7612,plain,
    ! [X27757,X27758] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27758,X27758),tc_HOL_Obool)),c_Relation_OId__on(X27758,X27757)),hAPP(hAPP(c_Product__Type_OSigma(X27758,X27758),X27757),hAPP(c_COMBK(tc_fun(X27758,tc_HOL_Obool),X27758),X27757)))),
    inference(variable_rename,[status(thm)],[fact_Id__on__subset__Times]) ).

fof(i_0_7613,plain,
    ! [X32634,X32635] :
      ( ~ class_Orderings_Olinorder(X32635)
      | c_List_Olinorder__class_Osort__key(X32635,X32635,c_COMBI(X32635),X32634) = hAPP(c_List_Ofoldl(tc_List_Olist(X32635),X32635,hAPP(c_COMBC(X32635,tc_List_Olist(X32635),tc_List_Olist(X32635)),c_List_Olinorder__class_Oinsort__key(X32635,X32635,c_COMBI(X32635))),c_List_Olist_ONil(X32635)),X32634) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sort__foldl__insort])]) ).

fof(i_0_7614,plain,
    ! [X18630,X18631,X18632,X18633] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X18633)
      | X18632 != c_Inductive_Ocomplete__lattice__class_Olfp(X18633,X18631)
      | ~ c_Orderings_Oorder__class_Omono(X18633,X18633,X18631)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18633),hAPP(X18631,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18633),X18632),X18630))),X18630))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18633),X18632),X18630)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_def__lfp__induct])]) ).

fof(i_0_7615,plain,
    ! [X27509,X27510,X27511] : hAPP(c_Relation_ORange(X27511,X27510),hAPP(c_Set_OCollect(tc_prod(X27511,X27510)),hAPP(c_Product__Type_Oprod_Oprod__case(X27511,X27510,tc_HOL_Obool),X27509))) = hAPP(c_Set_OCollect(X27510),hAPP(hAPP(c_COMBB(tc_fun(X27511,tc_HOL_Obool),tc_HOL_Obool,X27510),c_HOL_OEx(X27511)),hAPP(c_COMBC(X27511,X27510,tc_HOL_Obool),X27509))),
    inference(variable_rename,[status(thm)],[fact_Range__Collect__split]) ).

fof(i_0_7616,plain,
    ! [X27739,X27740,X27741] :
      ( ~ c_Equiv__Relations_Oequiv(X27741,X27740,X27739)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27741,X27741),tc_HOL_Obool)),X27739),hAPP(hAPP(c_Product__Type_OSigma(X27741,X27741),X27740),hAPP(c_COMBK(tc_fun(X27741,tc_HOL_Obool),X27741),X27740)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__type])]) ).

fof(i_0_7617,plain,
    ! [X30105,X30106,X30107,X30108,X30109] : hAPP(c_Fun_Ocomp(tc_List_Olist(X30109),tc_List_Olist(X30108),tc_List_Olist(X30107),hAPP(c_List_Omap(X30109,X30108),X30106)),hAPP(c_List_Omap(X30107,X30109),X30105)) = hAPP(c_List_Omap(X30107,X30108),hAPP(c_Fun_Ocomp(X30109,X30108,X30107,X30106),X30105)),
    inference(variable_rename,[status(thm)],[fact_List_Omap_Ocomp]) ).

fof(i_0_7618,plain,
    ! [X30100,X30101,X30102,X30103,X30104] : hAPP(c_Fun_Ocomp(tc_List_Olist(X30104),tc_List_Olist(X30103),tc_List_Olist(X30102),hAPP(c_List_Omap(X30104,X30103),X30101)),hAPP(c_List_Omap(X30102,X30104),X30100)) = hAPP(c_List_Omap(X30102,X30103),hAPP(c_Fun_Ocomp(X30104,X30103,X30102,X30101),X30100)),
    inference(variable_rename,[status(thm)],[fact_map__comp__map]) ).

fof(i_0_7619,plain,
    ! [X30189,X30190,X30191,X30192,X30193] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(X30193),tc_Option_Ooption(X30192),tc_Option_Ooption(X30191),hAPP(c_Option_Omap(X30193,X30192),X30190)),hAPP(c_Option_Omap(X30191,X30193),X30189)) = hAPP(c_Option_Omap(X30191,X30192),hAPP(c_Fun_Ocomp(X30193,X30192,X30191,X30190),X30189)),
    inference(variable_rename,[status(thm)],[fact_Option_Omap_Ocomp]) ).

fof(i_0_7620,plain,
    ! [X28146,X28147,X28148,X28149,X28150] :
      ( ~ c_Relation_Orefl__on(X28150,X28149,X28148)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28150,X28150)),hAPP(hAPP(c_Product__Type_OPair(X28150,X28150),X28147),X28146)),X28148))
      | hBOOL(hAPP(hAPP(c_member(X28150),X28147),X28149)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD1])]) ).

fof(i_0_7621,plain,
    ! [X28151,X28152,X28153,X28154,X28155] :
      ( ~ c_Relation_Orefl__on(X28155,X28154,X28153)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28155,X28155)),hAPP(hAPP(c_Product__Type_OPair(X28155,X28155),X28152),X28151)),X28153))
      | hBOOL(hAPP(hAPP(c_member(X28155),X28151),X28154)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD2])]) ).

cnf(i_0_7622,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_5635]) ).

fof(i_0_7623,plain,
    ! [X31428,X31429] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31429),tc_List_Olist(X31429))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31429),tc_List_Olist(X31429)),c_List_Olist_ONil(X31429)),c_List_Olist_ONil(X31429))),c_List_Olistrel(X31429,X31428))),
    inference(variable_rename,[status(thm)],[fact_listrel_ONil]) ).

fof(i_0_7624,plain,
    ! [X29682,X29683,X29684] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29684,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29684,tc_HOL_Obool),X29683)),X29682) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X29684,tc_HOL_Obool),tc_fun(X29684,tc_HOL_Obool)),X29683),hAPP(hAPP(c_COMBC(tc_fun(X29684,tc_HOL_Obool),tc_fun(X29684,tc_HOL_Obool),tc_fun(X29684,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29684,tc_HOL_Obool))),X29682)),
    inference(variable_rename,[status(thm)],[fact_Int__Union2]) ).

fof(i_0_7625,plain,
    ! [X20276,X20277,X20278,X20279] :
      ( ( X20278 = X20277
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20279,X20279)),hAPP(hAPP(c_Product__Type_OPair(X20279,X20279),X20278),X20277)),c_Relation_OId__on(X20279,X20276))) )
      & ( hBOOL(hAPP(hAPP(c_member(X20279),X20278),X20276))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20279,X20279)),hAPP(hAPP(c_Product__Type_OPair(X20279,X20279),X20278),X20277)),c_Relation_OId__on(X20279,X20276))) )
      & ( X20278 != X20277
        | ~ hBOOL(hAPP(hAPP(c_member(X20279),X20278),X20276))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X20279,X20279)),hAPP(hAPP(c_Product__Type_OPair(X20279,X20279),X20278),X20277)),c_Relation_OId__on(X20279,X20276))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__iff])])]) ).

fof(i_0_7626,plain,
    ! [X22614,X22615,X22616,X22617] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X22617),X22615))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X22617,X22616)),c_Sum__Type_OPlus(X22617,X22616,X22615,X22614))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X22616),X22614))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X22617,X22616)),c_Sum__Type_OPlus(X22617,X22616,X22615,X22614))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22617),X22615))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22616),X22614))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X22617,X22616)),c_Sum__Type_OPlus(X22617,X22616,X22615,X22614))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff])])]) ).

fof(i_0_7627,plain,
    ! [X22606,X22607,X22608,X22609] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X22609,X22608)),c_Sum__Type_OPlus(X22609,X22608,X22607,X22606)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X22609),X22607)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J])]) ).

fof(i_0_7628,plain,
    ! [X22602,X22603,X22604,X22605] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X22605,X22604)),c_Sum__Type_OPlus(X22605,X22604,X22603,X22602)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X22604),X22602)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J])]) ).

fof(i_0_7629,plain,
    ! [X27664,X27665,X27666,X27667,X27668,X27669] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X27669),X27668),X27667))
      | ~ hBOOL(hAPP(hAPP(c_member(X27666),X27665),hAPP(X27664,X27668)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X27669,X27666)),hAPP(hAPP(c_Product__Type_OPair(X27669,X27666),X27668),X27665)),hAPP(hAPP(c_Product__Type_OSigma(X27669,X27666),X27667),X27664))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaI])]) ).

fof(i_0_7630,plain,
    ! [X29826,X29827,X29828] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X29828,tc_HOL_Obool)),esk371_3(X29826,X29827,X29828)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X29828,tc_HOL_Obool)),X29827),X29826)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29828,tc_HOL_Obool)),X29827),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29828,tc_HOL_Obool),X29826)) = c_Orderings_Obot__class_Obot(tc_fun(X29828,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X29828,tc_HOL_Obool)),X29827),X29826)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X29828,tc_HOL_Obool)),esk372_3(X29826,X29827,X29828)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X29828,tc_HOL_Obool)),X29827),X29826)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29828,tc_HOL_Obool)),X29827),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29828,tc_HOL_Obool),X29826)) = c_Orderings_Obot__class_Obot(tc_fun(X29828,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X29828,tc_HOL_Obool)),X29827),X29826)) )
      & ( esk371_3(X29826,X29827,X29828) != esk372_3(X29826,X29827,X29828)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29828,tc_HOL_Obool)),X29827),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29828,tc_HOL_Obool),X29826)) = c_Orderings_Obot__class_Obot(tc_fun(X29828,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X29828,tc_HOL_Obool)),X29827),X29826)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29828,tc_HOL_Obool)),esk371_3(X29826,X29827,X29828)),esk372_3(X29826,X29827,X29828)) != c_Orderings_Obot__class_Obot(tc_fun(X29828,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29828,tc_HOL_Obool)),X29827),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29828,tc_HOL_Obool),X29826)) = c_Orderings_Obot__class_Obot(tc_fun(X29828,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X29828,tc_HOL_Obool)),X29827),X29826)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5636])])])]) ).

fof(i_0_7631,plain,
    ! [X32005,X32006,X32007,X32008] :
      ( ~ class_Groups_Osemigroup__add(X32008)
      | hAPP(c_List_Ofoldl(X32008,X32008,c_Groups_Oplus__class_Oplus(X32008),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X32008),X32007),X32006)),X32005) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X32008),X32007),hAPP(c_List_Ofoldl(X32008,X32008,c_Groups_Oplus__class_Oplus(X32008),X32006),X32005)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__assoc])]) ).

fof(i_0_7632,plain,
    ! [X28891,X28892,X28893] : hBOOL(hAPP(hAPP(c_member(tc_prod(X28893,X28893)),hAPP(hAPP(c_Product__Type_OPair(X28893,X28893),X28892),X28892)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28893,X28893),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28891))),
    inference(variable_rename,[status(thm)],[fact_rel__pow__0__I]) ).

cnf(i_0_7633,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_5637]) ).

fof(i_0_7634,plain,
    ! [X31693,X31694,X31695,X31696,X31697] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31697),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31696)),X31695)))
        | hAPP(hAPP(c_List_Olist__update(X31696,hAPP(hAPP(c_List_Oappend(X31696),X31695),X31694)),X31697),X31693) = hAPP(hAPP(c_List_Oappend(X31696),hAPP(hAPP(c_List_Olist__update(X31696,X31695),X31697),X31693)),X31694) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31697),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31696)),X31695)))
        | hAPP(hAPP(c_List_Olist__update(X31696,hAPP(hAPP(c_List_Oappend(X31696),X31695),X31694)),X31697),X31693) = hAPP(hAPP(c_List_Oappend(X31696),X31695),hAPP(hAPP(c_List_Olist__update(X31696,X31694),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31697),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31696)),X31695))),X31693)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5638])]) ).

fof(i_0_7635,plain,
    ! [X19023,X19024,X19025,X19026,X19027] :
      ( ~ c_Equiv__Relations_Oequiv(X19027,X19026,X19025)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X19027,tc_HOL_Obool)),X19024),hAPP(hAPP(c_Equiv__Relations_Oquotient(X19027),X19026),X19025)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X19027,tc_HOL_Obool)),X19023),hAPP(hAPP(c_Equiv__Relations_Oquotient(X19027),X19026),X19025)))
      | X19024 = X19023
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19027,tc_HOL_Obool)),X19024),X19023) = c_Orderings_Obot__class_Obot(tc_fun(X19027,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__disj])]) ).

fof(i_0_7636,plain,
    ! [X31061,X31062,X31063] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31063),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31062)),X31061)))
      | hAPP(c_Random_Opick(X31062,hAPP(hAPP(c_List_Omap(X31062,tc_prod(tc_Code__Numeral_Ocode__numeral,X31062)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X31062),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X31061)),hAPP(c_Code__Numeral_Oof__nat,X31063)) = hAPP(hAPP(c_List_Onth(X31062),X31061),X31063) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pick__same])]) ).

fof(i_0_7637,plain,
    ! [X24376,X24377,X24378,X24379] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),c_Groups_Ozero__class_Ozero(X24379)),X24376))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24379),X24378),X24376)),X24377))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24378),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24379),X24377),X24376)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24379) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24376),c_Groups_Ozero__class_Ozero(X24379)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24379),X24378),X24376)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),c_Groups_Ozero__class_Ozero(X24379)),X24376))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24378),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24379),X24377),X24376)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24379) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24376),c_Groups_Ozero__class_Ozero(X24379)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24378),c_Groups_Ozero__class_Ozero(X24379)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),c_Groups_Ozero__class_Ozero(X24379)),X24376))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24378),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24379),X24377),X24376)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24379) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),c_Groups_Ozero__class_Ozero(X24379)),X24376))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),c_Groups_Ozero__class_Ozero(X24379)),X24376))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24378),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24379),X24377),X24376)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24379) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24376),c_Groups_Ozero__class_Ozero(X24379)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24376),c_Groups_Ozero__class_Ozero(X24379)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),c_Groups_Ozero__class_Ozero(X24379)),X24376))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24378),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24379),X24377),X24376)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24379) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24378),c_Groups_Ozero__class_Ozero(X24379)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24376),c_Groups_Ozero__class_Ozero(X24379)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),c_Groups_Ozero__class_Ozero(X24379)),X24376))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24378),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24379),X24377),X24376)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24379) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24376),c_Groups_Ozero__class_Ozero(X24379)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24379),X24378),X24376)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),c_Groups_Ozero__class_Ozero(X24379)),X24376))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24378),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24379),X24377),X24376)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24379) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24378),c_Groups_Ozero__class_Ozero(X24379)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24379),X24378),X24376)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),c_Groups_Ozero__class_Ozero(X24379)),X24376))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24378),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24379),X24377),X24376)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24379) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),c_Groups_Ozero__class_Ozero(X24379)),X24376))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24379),X24378),X24376)),X24377))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24378),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24379),X24377),X24376)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24379) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24376),c_Groups_Ozero__class_Ozero(X24379)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24376),c_Groups_Ozero__class_Ozero(X24379)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24379),X24378),X24376)),X24377))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24378),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24379),X24377),X24376)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24379) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24378),c_Groups_Ozero__class_Ozero(X24379)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24376),c_Groups_Ozero__class_Ozero(X24379)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24379),X24378),X24376)),X24377))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24378),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24379),X24377),X24376)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24379) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24376),c_Groups_Ozero__class_Ozero(X24379)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24379),X24378),X24376)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24379),X24378),X24376)),X24377))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24378),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24379),X24377),X24376)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24379) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24378),c_Groups_Ozero__class_Ozero(X24379)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24379),X24378),X24376)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24379),X24378),X24376)),X24377))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24379),X24378),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24379),X24377),X24376)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24379) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5639])])]) ).

fof(i_0_7638,plain,
    ! [X24456,X24457,X24458,X24459] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24459),c_Groups_Ozero__class_Ozero(X24459)),X24456))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24459),X24458),X24456)),X24457))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24458),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24459),X24457),X24456)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24459) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24459),X24456),c_Groups_Ozero__class_Ozero(X24459)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24457),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24459),X24458),X24456)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24459),c_Groups_Ozero__class_Ozero(X24459)),X24456))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24458),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24459),X24457),X24456)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24459) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24459),X24456),c_Groups_Ozero__class_Ozero(X24459)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24458),c_Groups_Ozero__class_Ozero(X24459)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24459),c_Groups_Ozero__class_Ozero(X24459)),X24456))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24458),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24459),X24457),X24456)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24459) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24459),c_Groups_Ozero__class_Ozero(X24459)),X24456))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24459),c_Groups_Ozero__class_Ozero(X24459)),X24456))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24458),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24459),X24457),X24456)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24459) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24459),X24456),c_Groups_Ozero__class_Ozero(X24459)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24459),X24456),c_Groups_Ozero__class_Ozero(X24459)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24459),c_Groups_Ozero__class_Ozero(X24459)),X24456))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24458),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24459),X24457),X24456)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24459) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24458),c_Groups_Ozero__class_Ozero(X24459)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24459),X24456),c_Groups_Ozero__class_Ozero(X24459)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24459),c_Groups_Ozero__class_Ozero(X24459)),X24456))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24458),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24459),X24457),X24456)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24459) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24459),X24456),c_Groups_Ozero__class_Ozero(X24459)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24457),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24459),X24458),X24456)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24459),c_Groups_Ozero__class_Ozero(X24459)),X24456))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24458),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24459),X24457),X24456)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24459) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24458),c_Groups_Ozero__class_Ozero(X24459)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24457),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24459),X24458),X24456)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24459),c_Groups_Ozero__class_Ozero(X24459)),X24456))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24458),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24459),X24457),X24456)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24459) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24459),c_Groups_Ozero__class_Ozero(X24459)),X24456))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24459),X24458),X24456)),X24457))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24458),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24459),X24457),X24456)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24459) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24459),X24456),c_Groups_Ozero__class_Ozero(X24459)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24459),X24456),c_Groups_Ozero__class_Ozero(X24459)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24459),X24458),X24456)),X24457))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24458),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24459),X24457),X24456)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24459) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24458),c_Groups_Ozero__class_Ozero(X24459)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24459),X24456),c_Groups_Ozero__class_Ozero(X24459)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24459),X24458),X24456)),X24457))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24458),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24459),X24457),X24456)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24459) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24459),X24456),c_Groups_Ozero__class_Ozero(X24459)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24457),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24459),X24458),X24456)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24459),X24458),X24456)),X24457))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24458),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24459),X24457),X24456)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24459) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24458),c_Groups_Ozero__class_Ozero(X24459)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24457),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24459),X24458),X24456)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24459),X24458),X24456)),X24457))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24459),X24458),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24459),X24457),X24456)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24459) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5640])])]) ).

fof(i_0_7639,plain,
    ! [X26242,X26243] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X26243),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26242),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26242),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X26243)))))
      | X26243 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26242),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26242),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X26243))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__card__intvl__is__intvl])]) ).

fof(i_0_7640,plain,
    ! [X20926,X20927,X20928,X20929,X20930] :
      ( ( hBOOL(hAPP(hAPP(X20928,X20927),X20929))
        | ~ hBOOL(hAPP(hAPP(c_member(X20930),X20929),c_SetInterval_Oord_OgreaterThanLessThan(X20930,X20928,X20927,X20926))) )
      & ( hBOOL(hAPP(hAPP(X20928,X20929),X20926))
        | ~ hBOOL(hAPP(hAPP(c_member(X20930),X20929),c_SetInterval_Oord_OgreaterThanLessThan(X20930,X20928,X20927,X20926))) )
      & ( ~ hBOOL(hAPP(hAPP(X20928,X20927),X20929))
        | ~ hBOOL(hAPP(hAPP(X20928,X20929),X20926))
        | hBOOL(hAPP(hAPP(c_member(X20930),X20929),c_SetInterval_Oord_OgreaterThanLessThan(X20930,X20928,X20927,X20926))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanLessThan__iff])])]) ).

fof(i_0_7641,plain,
    ! [X20921,X20922,X20923,X20924,X20925] :
      ( ( hBOOL(hAPP(hAPP(X20923,X20922),X20924))
        | ~ hBOOL(hAPP(hAPP(c_member(X20925),X20924),c_SetInterval_Oord_OatLeastAtMost(X20925,X20923,X20922,X20921))) )
      & ( hBOOL(hAPP(hAPP(X20923,X20924),X20921))
        | ~ hBOOL(hAPP(hAPP(c_member(X20925),X20924),c_SetInterval_Oord_OatLeastAtMost(X20925,X20923,X20922,X20921))) )
      & ( ~ hBOOL(hAPP(hAPP(X20923,X20922),X20924))
        | ~ hBOOL(hAPP(hAPP(X20923,X20924),X20921))
        | hBOOL(hAPP(hAPP(c_member(X20925),X20924),c_SetInterval_Oord_OatLeastAtMost(X20925,X20923,X20922,X20921))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastAtMost__iff])])]) ).

fof(i_0_7642,plain,
    ! [X31460,X31461] : c_List_Oset__Cons(X31461,X31460,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X31461)),c_List_Olist_ONil(X31461)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X31461),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(X31461,tc_List_Olist(X31461),hAPP(hAPP(c_COMBC(X31461,tc_List_Olist(X31461),tc_List_Olist(X31461)),c_List_Olist_OCons(X31461)),c_List_Olist_ONil(X31461))),X31460),
    inference(variable_rename,[status(thm)],[fact_set__Cons__sing__Nil]) ).

fof(i_0_7643,plain,
    ! [X29392,X29393,X29394,X29395,X29396,X29397] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29397),X29396),X29395))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29397,tc_fun(X29394,tc_HOL_Obool)),X29395),hAPP(hAPP(c_COMBB(tc_fun(X29394,tc_HOL_Obool),tc_fun(X29394,tc_HOL_Obool),X29397),hAPP(c_Set_Oinsert(X29394),X29393)),X29392)) = hAPP(hAPP(c_Set_Oinsert(X29394),X29393),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29397,tc_fun(X29394,tc_HOL_Obool)),X29395),X29392)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__insert__distrib])]) ).

fof(i_0_7644,plain,
    ! [X19789,X19790,X19791,X19792,X19793,X19794] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X19794),X19793),X19792))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19794,tc_fun(X19791,tc_HOL_Obool)),X19792),hAPP(hAPP(c_COMBB(tc_fun(X19791,tc_HOL_Obool),tc_fun(X19791,tc_HOL_Obool),X19794),hAPP(c_Set_Oinsert(X19791),X19790)),X19789)) = hAPP(hAPP(c_Set_Oinsert(X19791),X19790),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19794,tc_fun(X19791,tc_HOL_Obool)),X19792),X19789)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__insert__distrib])]) ).

fof(i_0_7645,plain,
    ! [X21138,X21139,X21142,X21143,X21144,X21145] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21139),X21138))
        | X21138 = hAPP(c_Set_Oimage(tc_Nat_Onat,X21139,esk96_2(X21138,X21139)),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)),esk95_2(X21138,X21139)))) )
      & ( X21142 != hAPP(c_Set_Oimage(tc_Nat_Onat,X21143,X21145),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)),X21144)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X21143),X21142)) ) ),
    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_7646,plain,
    ! [X20395,X20396,X20397,X20398] :
      ( X20398 != hAPP(c_Set_Oimage(tc_Nat_Onat,X20397,X20396),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)),X20395)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20397),X20398)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__seg__image__imp__finite])]) ).

fof(i_0_7647,plain,
    ! [X31882,X31883,X31884] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31884),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31883)),X31882)))
      | hAPP(hAPP(c_List_Oappend(X31883),hAPP(hAPP(c_List_Otake(X31883),X31884),X31882)),hAPP(hAPP(c_List_Olist_OCons(X31883),hAPP(c_List_Ohd(X31883),hAPP(hAPP(c_List_Odrop(X31883),X31884),X31882))),c_List_Olist_ONil(X31883))) = hAPP(hAPP(c_List_Otake(X31883),hAPP(c_Nat_OSuc,X31884)),X31882) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__hd__drop])]) ).

fof(i_0_7648,plain,
    ! [X18196,X18197,X18198,X18199] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18199,tc_HOL_Obool)),X18198),hAPP(hAPP(c_Set_Oinsert(X18199),X18197),X18196)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18199,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18199,tc_HOL_Obool)),X18198),hAPP(hAPP(c_Set_Oinsert(X18199),X18197),c_Orderings_Obot__class_Obot(tc_fun(X18199,tc_HOL_Obool))))),X18196),
    inference(variable_rename,[status(thm)],[fact_Diff__insert2]) ).

fof(i_0_7649,plain,
    ! [X30656,X30657,X30658] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30658),tc_List_Olist(X30658))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30658),tc_List_Olist(X30658)),X30657),X30657)),c_List_Olistrel(X30658,c_Transitive__Closure_Ortrancl(X30658,X30656)))),
    inference(variable_rename,[status(thm)],[fact_listrel__rtrancl__refl]) ).

cnf(i_0_7650,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_5641]) ).

fof(i_0_7651,plain,
    ! [X29836,X29837,X29838] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X29838,tc_HOL_Obool)),esk374_3(X29836,X29837,X29838)),X29837))
        | X29837 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X29838,tc_HOL_Obool),tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29838,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X29838,tc_HOL_Obool),X29837)),X29836)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29838,tc_HOL_Obool)),esk374_3(X29836,X29837,X29838)),X29836))
        | X29837 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X29838,tc_HOL_Obool),tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29838,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X29838,tc_HOL_Obool),X29837)),X29836)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inter__subset])])])]) ).

fof(i_0_7652,plain,
    ! [X23562,X23563,X23564] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23564))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23563,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23562),X23564)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23562),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23563),X23562),X23564))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23563,X23562)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zmult2__eq])]) ).

fof(i_0_7653,plain,
    ! [X18107,X18108,X18109,X18110] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18110,tc_HOL_Obool)),X18109),X18108))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18110,tc_HOL_Obool)),X18109),X18107))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18110,tc_HOL_Obool)),X18109),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18110,tc_HOL_Obool)),X18108),X18107))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greatest])]) ).

fof(i_0_7654,plain,
    ! [X34187,X34188,X34189] :
      ( ( ~ c_List_Olist__ex(tc_Int_Oint,X34189,c_List_Oupto(X34188,X34187))
        | ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X34189),X34188,X34187) )
      & ( c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X34189),X34188,X34187)
        | c_List_Olist__ex(tc_Int_Oint,X34189,c_List_Oupto(X34188,X34187)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5642])]) ).

fof(i_0_7655,plain,
    ! [X25870,X25871] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X25871),hAPP(c_Nat_OSuc,X25870)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X25870),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)),X25870)),X25871),
    inference(variable_rename,[status(thm)],[fact_max__Suc2]) ).

cnf(i_0_7656,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_5596]) ).

fof(i_0_7657,plain,
    ! [X28885,X28886,X28887,X28888] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28888,X28888),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28887),X28886)),X28885) = hAPP(hAPP(c_Relation_Orel__comp(X28888,X28888,X28888),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28888,X28888),tc_HOL_Obool),X28887),X28885)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28888,X28888),tc_HOL_Obool),X28886),X28885)),
    inference(variable_rename,[status(thm)],[fact_rel__pow__add]) ).

fof(i_0_7658,plain,
    ! [X29708,X29709,X29710] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X29710,tc_HOL_Obool),tc_HOL_Obool)),X29709),X29708))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29710,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29710,tc_HOL_Obool),X29709)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29710,tc_HOL_Obool),X29708))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__mono])]) ).

fof(i_0_7659,plain,
    ! [X29721,X29722,X29723] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X29723,tc_HOL_Obool),tc_HOL_Obool)),X29722),X29721))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29723,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X29723,tc_HOL_Obool),X29721)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X29723,tc_HOL_Obool),X29722))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inter__anti__mono])]) ).

fof(i_0_7660,plain,
    ! [X27076,X27077,X27078] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27078)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27078),hAPP(c_Groups_Oabs__class_Oabs(X27078),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27078),X27077),X27076))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27078),hAPP(c_Groups_Oabs__class_Oabs(X27078),X27077)),hAPP(c_Groups_Oabs__class_Oabs(X27078),X27076)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq])]) ).

fof(i_0_7661,plain,
    ! [X27116,X27117,X27118] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27118)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27118),hAPP(c_Groups_Oabs__class_Oabs(X27118),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27118),X27117),X27116))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27118),hAPP(c_Groups_Oabs__class_Oabs(X27118),X27117)),hAPP(c_Groups_Oabs__class_Oabs(X27118),X27116)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq4])]) ).

cnf(i_0_7662,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_5643]) ).

fof(i_0_7663,plain,
    ! [X26149,X26150,X26151,X26152,X26153] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26153),X26150),X26152))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26153),X26152),X26151))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26153,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26153,X26152,X26151)),c_SetInterval_Oord__class_OatLeastAtMost(X26153,X26150,X26149)))
        | ~ class_Orderings_Oorder(X26153) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26153),X26151),X26149))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26153),X26152),X26151))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26153,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26153,X26152,X26151)),c_SetInterval_Oord__class_OatLeastAtMost(X26153,X26150,X26149)))
        | ~ class_Orderings_Oorder(X26153) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26153),X26152),X26151))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26153,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26153,X26152,X26151)),c_SetInterval_Oord__class_OatLeastAtMost(X26153,X26150,X26149)))
        | ~ class_Orderings_Oorder(X26153) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26153),X26150),X26152))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26153),X26151),X26149))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26153,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26153,X26152,X26151)),c_SetInterval_Oord__class_OatLeastAtMost(X26153,X26150,X26149)))
        | ~ class_Orderings_Oorder(X26153) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5644])])]) ).

fof(i_0_7664,plain,
    ! [X25445,X25446] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X25446),hAPP(c_Nat_OSuc,X25445)) = 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)),X25445)),X25446),
    inference(variable_rename,[status(thm)],[fact_min__Suc2]) ).

fof(i_0_7665,plain,
    ! [X21402,X21403,X21404] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21404),X21403))
      | ~ hBOOL(hAPP(hAPP(c_member(X21404),X21402),X21403))
      | hAPP(c_Finite__Set_Ocard(X21404),X21403) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X21404),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21404,tc_HOL_Obool)),X21403),hAPP(hAPP(c_Set_Oinsert(X21404),X21402),c_Orderings_Obot__class_Obot(tc_fun(X21404,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oremove])]) ).

fof(i_0_7666,plain,
    ! [X31168,X31169,X31170,X31171,X31172,X31173,X31174] : hAPP(hAPP(c_List_Ozip(X31174,X31173),hAPP(hAPP(c_List_Olist__update(X31174,X31172),X31171),X31170)),hAPP(hAPP(c_List_Olist__update(X31173,X31169),X31171),X31168)) = hAPP(hAPP(c_List_Olist__update(tc_prod(X31174,X31173),hAPP(hAPP(c_List_Ozip(X31174,X31173),X31172),X31169)),X31171),hAPP(hAPP(c_Product__Type_OPair(X31174,X31173),X31170),X31168)),
    inference(variable_rename,[status(thm)],[fact_zip__update]) ).

fof(i_0_7667,plain,
    ! [X19307,X19308,X19309,X19310,X19311] :
      ( ~ c_Fun_Oinj__on(X19311,X19310,X19309,c_Orderings_Otop__class_Otop(tc_fun(X19311,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X19311,X19310,X19309),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19311,tc_HOL_Obool)),X19308),X19307)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19310,tc_HOL_Obool)),hAPP(c_Set_Oimage(X19311,X19310,X19309),X19308)),hAPP(c_Set_Oimage(X19311,X19310,X19309),X19307)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Int])]) ).

fof(i_0_7668,plain,
    ! [X19312,X19313,X19314,X19315,X19316] :
      ( ~ c_Fun_Oinj__on(X19316,X19315,X19314,c_Orderings_Otop__class_Otop(tc_fun(X19316,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X19316,X19315,X19314),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19316,tc_HOL_Obool)),X19313),X19312)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19315,tc_HOL_Obool)),hAPP(c_Set_Oimage(X19316,X19315,X19314),X19313)),hAPP(c_Set_Oimage(X19316,X19315,X19314),X19312)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__set__diff])]) ).

fof(i_0_7669,plain,
    ! [X18732,X18733,X18734,X18735] :
      ( ~ c_Fun_Oinj__on(X18735,X18734,X18733,X18732)
      | hAPP(c_Set_Oimage(X18734,X18735,c_Fun_Othe__inv__into(X18735,X18734,X18732,X18733)),hAPP(c_Set_Oimage(X18735,X18734,X18733),X18732)) = X18732 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__onto])]) ).

fof(i_0_7670,plain,
    ! [X34120,X34121,X34122,X34123,X34124,X34125] : c_Nitpick_Opair__box_Opair__box__rec(X34125,X34124,X34123,X34122,c_Nitpick_Opair__box_OPairBox(X34125,X34124,X34121,X34120)) = hAPP(hAPP(X34122,X34121),X34120),
    inference(variable_rename,[status(thm)],[fact_pair__box_Orecs]) ).

fof(i_0_7671,plain,
    ! [X34114,X34115,X34116,X34117,X34118,X34119] : c_Nitpick_Opair__box_Opair__box__case(X34119,X34118,X34117,X34116,c_Nitpick_Opair__box_OPairBox(X34119,X34118,X34115,X34114)) = hAPP(hAPP(X34116,X34115),X34114),
    inference(variable_rename,[status(thm)],[fact_pair__box_Osimps_I2_J]) ).

fof(i_0_7672,plain,
    ! [X32976,X32977,X32978,X32979,X32980] : hAPP(hAPP(c_List_Ozip(X32980,X32979),c_List_OtakeWhile(X32980,X32978,X32977)),X32976) = c_List_OtakeWhile(tc_prod(X32980,X32979),hAPP(c_Fun_Ocomp(X32980,tc_HOL_Obool,tc_prod(X32980,X32979),X32978),c_Product__Type_Ofst(X32980,X32979)),hAPP(hAPP(c_List_Ozip(X32980,X32979),X32977),X32976)),
    inference(variable_rename,[status(thm)],[fact_zip__takeWhile__fst]) ).

cnf(i_0_7673,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_5645]) ).

cnf(i_0_7674,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_5646]) ).

cnf(i_0_7675,plain,
    ( X2 = hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk349_2(X2,X1)),esk349_2(X2,X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Relation_OId(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5647]) ).

cnf(i_0_7676,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_5648]) ).

fof(i_0_7677,plain,
    ! [X25260,X25261,X25262] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25262),X25261))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25260))
      | 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),X25260)),X25262)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25260)),X25261))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2__lemma])]) ).

cnf(i_0_7678,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_5584]) ).

cnf(i_0_7679,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_5649]) ).

fof(i_0_7680,plain,
    ! [X17886,X17887,X17888,X17889] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17889,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17889,tc_HOL_Obool)),X17888),X17887)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17889,tc_HOL_Obool)),X17886),X17887)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17889,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17889,tc_HOL_Obool)),X17888),X17887)),X17886),
    inference(variable_rename,[status(thm)],[fact_Diff__Int2]) ).

fof(i_0_7681,plain,
    ! [X17890,X17891,X17892,X17893] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17893,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17893,tc_HOL_Obool)),X17892),X17891)),X17890) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17893,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17893,tc_HOL_Obool)),X17892),X17890)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17893,tc_HOL_Obool)),X17891),X17890)),
    inference(variable_rename,[status(thm)],[fact_Diff__Int__distrib2]) ).

fof(i_0_7682,plain,
    ! [X18131,X18132,X18133,X18134] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18134,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18134,tc_HOL_Obool)),X18133),X18132)),X18131) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18134,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18134,tc_HOL_Obool)),X18133),X18131)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18134,tc_HOL_Obool)),X18132),X18131)),
    inference(variable_rename,[status(thm)],[fact_Int__Un__distrib2]) ).

fof(i_0_7683,plain,
    ! [X18092,X18093,X18094,X18095] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18095,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18095,tc_HOL_Obool)),X18094),X18093)),X18092) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18095,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18095,tc_HOL_Obool)),X18094),X18092)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18095,tc_HOL_Obool)),X18093),X18092)),
    inference(variable_rename,[status(thm)],[fact_Un__Diff]) ).

fof(i_0_7684,plain,
    ! [X18127,X18128,X18129,X18130] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18130,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18130,tc_HOL_Obool)),X18129),X18128)),X18127) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18130,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18130,tc_HOL_Obool)),X18129),X18127)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18130,tc_HOL_Obool)),X18128),X18127)),
    inference(variable_rename,[status(thm)],[fact_Un__Int__distrib2]) ).

fof(i_0_7685,plain,
    ! [X26326,X26327,X26328] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk204_3(X26326,X26327,X26328)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26328)))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26327),X26328) = X26327
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26327),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26326))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26328)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk205_3(X26326,X26327,X26328)),X26326))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26327),X26328) = X26327
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26327),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26326))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26328)) )
      & ( X26327 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk205_3(X26326,X26327,X26328)),esk204_3(X26326,X26327,X26328))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26327),X26328) = X26327
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26327),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26326))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26328)) ) ),
    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_7686,plain,
    ! [X26289,X26290,X26291] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk194_3(X26289,X26290,X26291)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26291)))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26290),X26291) = X26290
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26290),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26289))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26291)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk195_3(X26289,X26290,X26291)),X26289))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26290),X26291) = X26290
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26290),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26289))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26291)) )
      & ( X26290 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk195_3(X26289,X26290,X26291)),esk194_3(X26289,X26290,X26291))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26290),X26291) = X26290
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26290),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26289))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26291)) ) ),
    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_7687,plain,
    ! [X31863,X31864,X31865,X31866] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31866),X31865)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31864)),X31863)))
      | hAPP(hAPP(c_List_Otake(X31864),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31866),X31865)),X31863) = hAPP(hAPP(c_List_Oappend(X31864),hAPP(hAPP(c_List_Otake(X31864),X31866),X31863)),hAPP(hAPP(c_List_Otake(X31864),X31865),hAPP(hAPP(c_List_Odrop(X31864),X31866),X31863))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__add])]) ).

fof(i_0_7688,plain,
    ! [X22548,X22549,X22550] :
      ( ( hBOOL(hAPP(hAPP(c_member(X22550),esk114_3(X22548,X22549,X22550)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X22550,tc_HOL_Obool)),X22549),X22548)))
        | hAPP(c_Finite__Set_Ocard(X22550),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22550,tc_HOL_Obool)),X22549),X22548)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X22550),X22549)),hAPP(c_Finite__Set_Ocard(X22550),X22548))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22550),X22548))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22550),X22549)) )
      & ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Finite__Set_Ocard(X22550),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22550,tc_HOL_Obool)),X22549),X22548)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X22550),X22549)),hAPP(c_Finite__Set_Ocard(X22550),X22548))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22550),X22548))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22550),X22549)) ) ),
    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_7689,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_5650]) ).

cnf(i_0_7690,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_5651]) ).

fof(i_0_7691,plain,
    ! [X30016,X30017,X30018,X30019] :
      ( ( ~ c_Fun_Oinj__on(X30019,tc_Option_Ooption(X30018),c_Map_Omap__add(X30019,X30018,X30017,X30016),c_Map_Odom(X30019,X30018,X30016))
        | c_Fun_Oinj__on(X30019,tc_Option_Ooption(X30018),X30016,c_Map_Odom(X30019,X30018,X30016)) )
      & ( ~ c_Fun_Oinj__on(X30019,tc_Option_Ooption(X30018),X30016,c_Map_Odom(X30019,X30018,X30016))
        | c_Fun_Oinj__on(X30019,tc_Option_Ooption(X30018),c_Map_Omap__add(X30019,X30018,X30017,X30016),c_Map_Odom(X30019,X30018,X30016)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__map__add__dom])]) ).

fof(i_0_7692,plain,
    ! [X21412,X21413,X21414] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21414),X21413))
      | ~ hBOOL(hAPP(hAPP(c_member(X21414),X21412),X21413))
      | hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X21414),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21414,tc_HOL_Obool)),X21413),hAPP(hAPP(c_Set_Oinsert(X21414),X21412),c_Orderings_Obot__class_Obot(tc_fun(X21414,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(X21414),X21413) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Suc__Diff1])]) ).

fof(i_0_7693,plain,
    ! [X25876,X25877,X25878,X25879,X25880] :
      ( ~ class_Lattices_Osemilattice__sup(X25880)
      | ~ class_Orderings_Olinorder(X25879)
      | ~ c_Orderings_Oorder__class_Omono(X25879,X25880,X25878)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25880),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25880),hAPP(X25878,X25877)),hAPP(X25878,X25876))),hAPP(X25878,hAPP(hAPP(c_Orderings_Oord__class_Omax(X25879),X25877),X25876)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Omono__sup])]) ).

fof(i_0_7694,plain,
    ! [X17617,X17618,X17619,X17620,X17621] :
      ( ~ class_Lattices_Osemilattice__sup(X17621)
      | ~ class_Lattices_Osemilattice__sup(X17620)
      | ~ c_Orderings_Oorder__class_Omono(X17620,X17621,X17619)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17621),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17621),hAPP(X17619,X17618)),hAPP(X17619,X17617))),hAPP(X17619,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17620),X17618),X17617)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mono__sup])]) ).

fof(i_0_7695,plain,
    ! [X20724,X20725,X20726,X20727,X20728,X20729] :
      ( ~ c_Finite__Set_Ofolding(X20729,X20728,X20727,X20726)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20729),X20725))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20729),X20724))
      | hAPP(c_Fun_Ocomp(X20728,X20728,X20728,hAPP(X20726,X20724)),hAPP(X20726,X20725)) = hAPP(c_Fun_Ocomp(X20728,X20728,X20728,hAPP(X20726,X20725)),hAPP(X20726,X20724)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H_H])]) ).

fof(i_0_7696,plain,
    ! [X33035,X33036] :
      ( X33036 = c_List_Olist_ONil(X33035)
      | ~ hBOOL(hAPP(c_List_Odistinct(X33035),X33036))
      | c_List_OtakeWhile(X33035,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33035),c_fNot),hAPP(hAPP(c_COMBC(X33035,X33035,tc_HOL_Obool),c_fequal),c_List_Olast(X33035,X33036))),X33036) = c_List_Obutlast(X33035,X33036) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__not__last])]) ).

fof(i_0_7697,plain,
    ! [X29274,X29275,X29276,X29277] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X29277,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29276,tc_fun(X29277,tc_HOL_Obool)),X29275),X29274)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29276,tc_fun(X29277,tc_HOL_Obool)),X29275),hAPP(hAPP(c_COMBB(tc_fun(X29277,tc_HOL_Obool),tc_fun(X29277,tc_HOL_Obool),X29276),c_Groups_Ouminus__class_Ouminus(tc_fun(X29277,tc_HOL_Obool))),X29274)),
    inference(variable_rename,[status(thm)],[fact_Compl__INT]) ).

fof(i_0_7698,plain,
    ! [X29270,X29271,X29272,X29273] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X29273,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29272,tc_fun(X29273,tc_HOL_Obool)),X29271),X29270)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29272,tc_fun(X29273,tc_HOL_Obool)),X29271),hAPP(hAPP(c_COMBB(tc_fun(X29273,tc_HOL_Obool),tc_fun(X29273,tc_HOL_Obool),X29272),c_Groups_Ouminus__class_Ouminus(tc_fun(X29273,tc_HOL_Obool))),X29270)),
    inference(variable_rename,[status(thm)],[fact_Compl__UN]) ).

fof(i_0_7699,plain,
    ! [X19049,X19050,X19051,X19052] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X19052,X19051,hAPP(hAPP(c_Set_Oinsert(X19052),X19050),c_Orderings_Obot__class_Obot(tc_fun(X19052,tc_HOL_Obool)))),X19049))
        | X19050 = X19049 )
      & ( X19050 != X19049
        | hBOOL(hAPP(c_Finite__Set_Ofold1Set(X19052,X19051,hAPP(hAPP(c_Set_Oinsert(X19052),X19050),c_Orderings_Obot__class_Obot(tc_fun(X19052,tc_HOL_Obool)))),X19049)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1Set__sing])]) ).

fof(i_0_7700,plain,
    ! [X32854,X32855,X32856] :
      ( ~ class_Orderings_Olinorder(X32856)
      | hBOOL(hAPP(hAPP(c_member(X32856),X32855),hAPP(c_List_Oset(X32856),X32854)))
      | c_List_Olinorder__class_Oinsort__insert__key(X32856,X32856,c_COMBI(X32856),X32855,X32854) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32856,X32856,c_COMBI(X32856)),X32855),X32854) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5652])]) ).

fof(i_0_7701,plain,
    ! [X20084,X20085,X20086,X20087,X20088] :
      ( ( ~ c_Relation_Oirrefl(X20085,X20084)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20085,X20085)),hAPP(hAPP(c_Product__Type_OPair(X20085,X20085),X20086),X20086)),X20084)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X20088,X20088)),hAPP(hAPP(c_Product__Type_OPair(X20088,X20088),esk66_2(X20087,X20088)),esk66_2(X20087,X20088))),X20087))
        | c_Relation_Oirrefl(X20088,X20087) ) ),
    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_5653])])])])]) ).

fof(i_0_7702,plain,
    ! [X20648,X20649,X20650,X20651,X20652,X20653] :
      ( ~ c_Finite__Set_Ofolding(X20653,X20652,X20651,X20650)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20653),X20649))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20653),X20648))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20653,tc_HOL_Obool)),X20649),X20648) != c_Orderings_Obot__class_Obot(tc_fun(X20653,tc_HOL_Obool))
      | hAPP(X20650,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20653,tc_HOL_Obool)),X20649),X20648)) = hAPP(c_Fun_Ocomp(X20652,X20652,X20652,hAPP(X20650,X20649)),hAPP(X20650,X20648)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ounion])]) ).

fof(i_0_7703,plain,
    ! [X23528,X23529,X23530,X23532,X23533,X23534,X23535] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23528),esk126_3(X23528,X23529,X23530))),X23529))
        | X23528 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X23530,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23529),X23528))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23529),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23528),hAPP(c_Nat_OSuc,esk126_3(X23528,X23529,X23530)))))
        | X23528 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X23530,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23529),X23528))) )
      & ( hBOOL(hAPP(X23530,esk126_3(X23528,X23529,X23530)))
        | X23528 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X23530,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23529),X23528))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23528),esk126_3(X23528,X23529,X23530))),X23529))
        | hBOOL(hAPP(X23530,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X23530,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23529),X23528))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23529),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23528),hAPP(c_Nat_OSuc,esk126_3(X23528,X23529,X23530)))))
        | hBOOL(hAPP(X23530,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X23530,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23529),X23528))) )
      & ( hBOOL(hAPP(X23530,esk126_3(X23528,X23529,X23530)))
        | hBOOL(hAPP(X23530,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X23530,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23529),X23528))) )
      & ( X23532 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X23534,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X23534,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23533),X23532))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23532),X23535)),X23533))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23533),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23532),hAPP(c_Nat_OSuc,X23535))))
        | ~ hBOOL(hAPP(X23534,X23535))
        | hBOOL(hAPP(X23534,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23533),X23532))) ) ),
    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_7704,plain,
    ! [X21409,X21410,X21411] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21411),X21410))
      | hAPP(c_Finite__Set_Ocard(X21411),hAPP(hAPP(c_Set_Oinsert(X21411),X21409),X21410)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X21411),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21411,tc_HOL_Obool)),X21410),hAPP(hAPP(c_Set_Oinsert(X21411),X21409),c_Orderings_Obot__class_Obot(tc_fun(X21411,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oinsert__remove])]) ).

fof(i_0_7705,plain,
    ! [X18899,X18900,X18901,X18902,X18903,X18904,X18905,X18906,X18907] :
      ( hAPP(c_Fun_Ocomp(X18906,X18905,X18904,X18903),X18902) != hAPP(c_Fun_Ocomp(X18901,X18905,X18904,X18900),X18899)
      | hAPP(X18903,hAPP(X18902,X18907)) = hAPP(X18900,hAPP(X18899,X18907)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__elim])])]) ).

fof(i_0_7706,plain,
    ! [X18890,X18891,X18892,X18893,X18894,X18895,X18896,X18897,X18898] :
      ( hAPP(c_Fun_Ocomp(X18898,X18897,X18896,X18895),X18894) != hAPP(c_Fun_Ocomp(X18893,X18897,X18896,X18892),X18891)
      | hAPP(X18895,hAPP(X18894,X18890)) = hAPP(X18892,hAPP(X18891,X18890)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__dest])]) ).

fof(i_0_7707,plain,
    ! [X32672,X32673,X32674,X32675] :
      ( ~ class_Orderings_Olinorder(X32675)
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32675,X32675,c_COMBI(X32675)),X32674),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32675,X32675,c_COMBI(X32675)),X32673),X32672)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32675,X32675,c_COMBI(X32675)),X32673),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32675,X32675,c_COMBI(X32675)),X32674),X32672)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__left__comm])]) ).

fof(i_0_7708,plain,
    ! [X27918,X27919,X27920,X27921,X27922,X27923,X27924] :
      ( hAPP(c_Fun_Ocomp(X27924,X27923,X27922,X27921),X27920) != hAPP(c_Fun_Ocomp(X27923,X27923,X27922,c_Fun_Oid(X27923)),X27919)
      | hAPP(X27921,hAPP(X27920,X27918)) = hAPP(X27919,X27918) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__id__dest])]) ).

fof(i_0_7709,plain,
    ! [X32651,X32652,X32653,X32654] :
      ( ( ~ hBOOL(hAPP(c_List_Odistinct(X32653),c_List_Olinorder__class_Osort__key(X32653,X32654,X32652,X32651)))
        | hBOOL(hAPP(c_List_Odistinct(X32653),X32651))
        | ~ class_Orderings_Olinorder(X32654) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X32653),X32651))
        | hBOOL(hAPP(c_List_Odistinct(X32653),c_List_Olinorder__class_Osort__key(X32653,X32654,X32652,X32651)))
        | ~ class_Orderings_Olinorder(X32654) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__sort])])]) ).

fof(i_0_7710,plain,
    ! [X19152,X19153,X19154,X19155] :
      ( ~ c_Equiv__Relations_Oequiv(X19155,X19154,X19153)
      | ~ hBOOL(hAPP(hAPP(c_member(X19155),X19152),X19154))
      | hBOOL(hAPP(hAPP(c_member(X19155),X19152),hAPP(c_Relation_OImage(X19155,X19155,X19153),hAPP(hAPP(c_Set_Oinsert(X19155),X19152),c_Orderings_Obot__class_Obot(tc_fun(X19155,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__self])]) ).

fof(i_0_7711,plain,
    ! [X19297,X19298,X19299,X19300,X19301] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X19300),hAPP(X19299,X19298)),hAPP(c_Set_Oimage(X19301,X19300,X19299),X19297)))
        | hBOOL(hAPP(hAPP(c_member(X19301),X19298),X19297))
        | ~ c_Fun_Oinj__on(X19301,X19300,X19299,c_Orderings_Otop__class_Otop(tc_fun(X19301,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X19301),X19298),X19297))
        | hBOOL(hAPP(hAPP(c_member(X19300),hAPP(X19299,X19298)),hAPP(c_Set_Oimage(X19301,X19300,X19299),X19297)))
        | ~ c_Fun_Oinj__on(X19301,X19300,X19299,c_Orderings_Otop__class_Otop(tc_fun(X19301,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_7712,plain,
    ! [X29512,X29513,X29514,X29515,X29516] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29516)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29515,tc_HOL_Obool)),X29514),X29513))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29516),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29515,X29516),X29513),X29512)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29515,X29516),X29514),X29512))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__subset])]) ).

fof(i_0_7713,plain,
    ! [X19779,X19780,X19781,X19782,X19783] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X19783)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19782,tc_HOL_Obool)),X19781),X19780))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19783),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19782,X19783),X19781),X19779)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19782,X19783),X19780),X19779))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__subset])]) ).

fof(i_0_7714,plain,
    ! [X27441,X27442,X27443] :
      ( ~ c_Wellfounded_Owf(X27443,X27442)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27443,X27443)),hAPP(hAPP(c_Product__Type_OPair(X27443,X27443),X27441),X27441)),X27442)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5654])]) ).

fof(i_0_7715,plain,
    ! [X27430,X27431,X27432] :
      ( ~ c_Wellfounded_Owf(X27432,X27431)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27432,X27432)),hAPP(hAPP(c_Product__Type_OPair(X27432,X27432),X27430),X27430)),X27431)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5655])]) ).

fof(i_0_7716,plain,
    ! [X19812,X19813,X19814,X19815,X19816] :
      ( ( X19816 != c_Orderings_Obot__class_Obot(tc_fun(X19815,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19815,tc_fun(X19814,tc_HOL_Obool)),X19816),hAPP(hAPP(c_COMBB(tc_fun(X19814,tc_HOL_Obool),tc_fun(X19814,tc_HOL_Obool),X19815),hAPP(c_Set_Oinsert(X19814),X19813)),X19812)) = c_Orderings_Obot__class_Obot(tc_fun(X19814,tc_HOL_Obool)) )
      & ( X19816 = c_Orderings_Obot__class_Obot(tc_fun(X19815,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19815,tc_fun(X19814,tc_HOL_Obool)),X19816),hAPP(hAPP(c_COMBB(tc_fun(X19814,tc_HOL_Obool),tc_fun(X19814,tc_HOL_Obool),X19815),hAPP(c_Set_Oinsert(X19814),X19813)),X19812)) = hAPP(hAPP(c_Set_Oinsert(X19814),X19813),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19815,tc_fun(X19814,tc_HOL_Obool)),X19816),X19812)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__simps_I1_J])]) ).

fof(i_0_7717,plain,
    ! [X19805,X19806,X19807,X19808,X19809] :
      ( ( X19809 != c_Orderings_Obot__class_Obot(tc_fun(X19808,tc_HOL_Obool))
        | hAPP(hAPP(c_Set_Oinsert(X19807),X19806),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19808,tc_fun(X19807,tc_HOL_Obool)),X19809),X19805)) = hAPP(hAPP(c_Set_Oinsert(X19807),X19806),c_Orderings_Obot__class_Obot(tc_fun(X19807,tc_HOL_Obool))) )
      & ( X19809 = c_Orderings_Obot__class_Obot(tc_fun(X19808,tc_HOL_Obool))
        | hAPP(hAPP(c_Set_Oinsert(X19807),X19806),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19808,tc_fun(X19807,tc_HOL_Obool)),X19809),X19805)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19808,tc_fun(X19807,tc_HOL_Obool)),X19809),hAPP(hAPP(c_COMBB(tc_fun(X19807,tc_HOL_Obool),tc_fun(X19807,tc_HOL_Obool),X19808),hAPP(c_Set_Oinsert(X19807),X19806)),X19805)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I1_J])]) ).

cnf(i_0_7718,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_5656]) ).

fof(i_0_7719,plain,
    ! [X26466,X26467,X26468,X26469,X26470] :
      ( ~ class_Rings_Osemiring__0(X26470)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26470),X26469),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26468,X26470),X26467),X26466)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26468,X26470),hAPP(hAPP(c_COMBB(X26470,X26470,X26468),hAPP(c_Groups_Otimes__class_Otimes(X26470),X26469)),X26467)),X26466) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__right__distrib])]) ).

fof(i_0_7720,plain,
    ! [X22817,X22818,X22819,X22820,X22821] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X22821,X22820)),hAPP(X22821,X22819)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X22818,X22818)),hAPP(hAPP(c_Product__Type_OPair(X22818,X22818),X22820),X22819)),c_Wellfounded_Omlex__prod(X22818,X22821,X22817))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__less])]) ).

fof(i_0_7721,plain,
    ! [X19147,X19148,X19149,X19150,X19151] : hAPP(c_Set_Oimage(X19151,X19150,hAPP(hAPP(c_COMBB(X19149,X19150,X19151),X19148),X19147)),c_Orderings_Otop__class_Otop(tc_fun(X19151,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X19149,X19150,X19148),hAPP(c_Set_Oimage(X19151,X19149,X19147),c_Orderings_Otop__class_Otop(tc_fun(X19151,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_range__composition]) ).

fof(i_0_7722,plain,
    ! [X33856,X33857,X33858] : c_Lazy__Sequence_Ohb__flat(X33858,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X33858))),X33857,X33856)) = c_Lazy__Sequence_Oappend(tc_Option_Ooption(X33858),hAPP(c_Option_Ooption_Ooption__case(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X33858)),tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X33858)),c_Lazy__Sequence_Ohit__bound(X33858),c_COMBI(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X33858)))),X33857),c_Lazy__Sequence_Ohb__flat(X33858,X33856)),
    inference(variable_rename,[status(thm)],[fact_hb__flat_Osimps_I2_J]) ).

fof(i_0_7723,plain,
    ! [X25429,X25430,X25431,X25432,X25433] :
      ( ~ class_Lattices_Osemilattice__inf(X25433)
      | ~ class_Orderings_Olinorder(X25432)
      | ~ c_Orderings_Oorder__class_Omono(X25432,X25433,X25431)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25433),hAPP(X25431,hAPP(hAPP(c_Orderings_Oord__class_Omin(X25432),X25430),X25429))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25433),hAPP(X25431,X25430)),hAPP(X25431,X25429)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Omono__inf])]) ).

fof(i_0_7724,plain,
    ! [X18233,X18234,X18235,X18236,X18237] :
      ( ~ class_Lattices_Osemilattice__inf(X18237)
      | ~ class_Lattices_Osemilattice__inf(X18236)
      | ~ c_Orderings_Oorder__class_Omono(X18236,X18237,X18235)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18237),hAPP(X18235,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18236),X18234),X18233))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18237),hAPP(X18235,X18234)),hAPP(X18235,X18233)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mono__inf])]) ).

fof(i_0_7725,plain,
    ! [X32964,X32965] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk460_2(X32964,X32965)),esk461_2(X32964,X32965)))
        | c_List_Olinorder__class_Osorted(X32965,X32964)
        | ~ class_Orderings_Olinorder(X32965) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk461_2(X32964,X32965)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32965)),X32964)))
        | c_List_Olinorder__class_Osorted(X32965,X32964)
        | ~ class_Orderings_Olinorder(X32965) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32965),hAPP(hAPP(c_List_Onth(X32965),X32964),esk460_2(X32964,X32965))),hAPP(hAPP(c_List_Onth(X32965),X32964),esk461_2(X32964,X32965))))
        | c_List_Olinorder__class_Osorted(X32965,X32964)
        | ~ class_Orderings_Olinorder(X32965) ) ),
    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_7726,plain,
    ! [X32834,X32835,X32836,X32837] :
      ( ( ~ c_List_Olinorder__class_Osorted(X32835,X32834)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32836),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32835)),X32834)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32837),X32836))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32835),hAPP(hAPP(c_List_Onth(X32835),X32834),X32837)),hAPP(hAPP(c_List_Onth(X32835),X32834),X32836)))
        | ~ class_Orderings_Olinorder(X32835) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk458_2(X32834,X32835)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32835)),X32834)))
        | c_List_Olinorder__class_Osorted(X32835,X32834)
        | ~ class_Orderings_Olinorder(X32835) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk459_2(X32834,X32835)),esk458_2(X32834,X32835)))
        | c_List_Olinorder__class_Osorted(X32835,X32834)
        | ~ class_Orderings_Olinorder(X32835) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32835),hAPP(hAPP(c_List_Onth(X32835),X32834),esk459_2(X32834,X32835))),hAPP(hAPP(c_List_Onth(X32835),X32834),esk458_2(X32834,X32835))))
        | c_List_Olinorder__class_Osorted(X32835,X32834)
        | ~ class_Orderings_Olinorder(X32835) ) ),
    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_7727,plain,
    ! [X29231,X29232,X29233,X29234,X29235,X29236] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29236),X29235),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29234,tc_fun(X29236,tc_HOL_Obool)),X29233),X29232)))
      | hBOOL(hAPP(hAPP(c_member(X29236),X29235),hAPP(X29232,X29231)))
      | ~ hBOOL(hAPP(hAPP(c_member(X29234),X29231),X29233)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5657])]) ).

fof(i_0_7728,plain,
    ! [X29225,X29226,X29227,X29228,X29229,X29230] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29230),X29229),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29228,tc_fun(X29230,tc_HOL_Obool)),X29227),X29226)))
      | ~ hBOOL(hAPP(hAPP(c_member(X29228),X29225),X29227))
      | hBOOL(hAPP(hAPP(c_member(X29230),X29229),hAPP(X29226,X29225))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__D])]) ).

fof(i_0_7729,plain,
    ! [X32009,X32010,X32011] :
      ( ~ class_Groups_Omonoid__add(X32011)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X32011),X32010),hAPP(c_List_Ofoldl(X32011,X32011,c_Groups_Oplus__class_Oplus(X32011),c_Groups_Ozero__class_Ozero(X32011)),X32009)) = hAPP(c_List_Ofoldl(X32011,X32011,c_Groups_Oplus__class_Oplus(X32011),X32010),X32009) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__absorb0])]) ).

fof(i_0_7730,plain,
    ! [X31156,X31157,X31158,X31159,X31160,X31161] :
      ( X31161 = X31160
      | hAPP(hAPP(c_List_Olist__update(X31159,hAPP(hAPP(c_List_Olist__update(X31159,X31158),X31161),X31157)),X31160),X31156) = hAPP(hAPP(c_List_Olist__update(X31159,hAPP(hAPP(c_List_Olist__update(X31159,X31158),X31160),X31156)),X31161),X31157) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__swap])]) ).

fof(i_0_7731,plain,
    ! [X28859,X28860,X28861] : hAPP(hAPP(c_Relation_Orel__comp(X28861,X28861,X28861),X28860),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28861,X28861),tc_HOL_Obool),X28859),X28860)) = hAPP(hAPP(c_Relation_Orel__comp(X28861,X28861,X28861),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28861,X28861),tc_HOL_Obool),X28859),X28860)),X28860),
    inference(variable_rename,[status(thm)],[fact_rel__pow__commute]) ).

fof(i_0_7732,plain,
    ! [X34360,X34361,X34362,X34363,X34364,X34365,X34366,X34367,X34368,X34369] :
      ( ( X34361 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(X34362,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ epred1_3(X34362,X34361,X34360) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34361))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34364))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34364),X34361))
        | X34360 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34361),X34363)),X34364)
        | hBOOL(hAPP(X34362,X34363))
        | ~ epred1_3(X34362,X34361,X34360) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34361),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34361),X34366))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X34366),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34360 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34361),X34365)),X34366)
        | hBOOL(hAPP(X34362,X34365))
        | ~ epred1_3(X34362,X34361,X34360) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34368),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)),X34368))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34368),esk536_3(X34367,X34368,X34369)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34368))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk536_3(X34367,X34368,X34369)),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)),X34368))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( X34367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34368),esk535_3(X34367,X34368,X34369))),esk536_3(X34367,X34368,X34369))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34368))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( ~ hBOOL(hAPP(X34369,esk535_3(X34367,X34368,X34369)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34368))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34368),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)),esk534_3(X34367,X34368,X34369)))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34368),esk536_3(X34367,X34368,X34369)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X34367,X34368,X34369)))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk536_3(X34367,X34368,X34369)),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)),esk534_3(X34367,X34368,X34369)))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( X34367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34368),esk535_3(X34367,X34368,X34369))),esk536_3(X34367,X34368,X34369))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X34367,X34368,X34369)))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( ~ hBOOL(hAPP(X34369,esk535_3(X34367,X34368,X34369)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X34367,X34368,X34369)))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34368),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X34367,X34368,X34369)),X34368))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34368),esk536_3(X34367,X34368,X34369)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X34367,X34368,X34369)),X34368))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk536_3(X34367,X34368,X34369)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X34367,X34368,X34369)),X34368))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( X34367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34368),esk535_3(X34367,X34368,X34369))),esk536_3(X34367,X34368,X34369))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X34367,X34368,X34369)),X34368))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( ~ hBOOL(hAPP(X34369,esk535_3(X34367,X34368,X34369)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X34367,X34368,X34369)),X34368))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34368),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34368),esk533_3(X34367,X34368,X34369))),esk534_3(X34367,X34368,X34369))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34368),esk536_3(X34367,X34368,X34369)))
        | X34367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34368),esk533_3(X34367,X34368,X34369))),esk534_3(X34367,X34368,X34369))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk536_3(X34367,X34368,X34369)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34368),esk533_3(X34367,X34368,X34369))),esk534_3(X34367,X34368,X34369))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( X34367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34368),esk535_3(X34367,X34368,X34369))),esk536_3(X34367,X34368,X34369))
        | X34367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34368),esk533_3(X34367,X34368,X34369))),esk534_3(X34367,X34368,X34369))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( ~ hBOOL(hAPP(X34369,esk535_3(X34367,X34368,X34369)))
        | X34367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34368),esk533_3(X34367,X34368,X34369))),esk534_3(X34367,X34368,X34369))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34368),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34369,esk533_3(X34367,X34368,X34369)))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34368),esk536_3(X34367,X34368,X34369)))
        | ~ hBOOL(hAPP(X34369,esk533_3(X34367,X34368,X34369)))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk536_3(X34367,X34368,X34369)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34369,esk533_3(X34367,X34368,X34369)))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( X34367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34368),esk535_3(X34367,X34368,X34369))),esk536_3(X34367,X34368,X34369))
        | ~ hBOOL(hAPP(X34369,esk533_3(X34367,X34368,X34369)))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( ~ hBOOL(hAPP(X34369,esk535_3(X34367,X34368,X34369)))
        | ~ hBOOL(hAPP(X34369,esk533_3(X34367,X34368,X34369)))
        | X34368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34368),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)),X34368))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34368),esk536_3(X34367,X34368,X34369)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34368))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk536_3(X34367,X34368,X34369)),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)),X34368))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( X34367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34368),esk535_3(X34367,X34368,X34369))),esk536_3(X34367,X34368,X34369))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34368))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( ~ hBOOL(hAPP(X34369,esk535_3(X34367,X34368,X34369)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34368))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34368),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)),esk534_3(X34367,X34368,X34369)))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34368),esk536_3(X34367,X34368,X34369)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X34367,X34368,X34369)))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk536_3(X34367,X34368,X34369)),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)),esk534_3(X34367,X34368,X34369)))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( X34367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34368),esk535_3(X34367,X34368,X34369))),esk536_3(X34367,X34368,X34369))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X34367,X34368,X34369)))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( ~ hBOOL(hAPP(X34369,esk535_3(X34367,X34368,X34369)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X34367,X34368,X34369)))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34368),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X34367,X34368,X34369)),X34368))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34368),esk536_3(X34367,X34368,X34369)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X34367,X34368,X34369)),X34368))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk536_3(X34367,X34368,X34369)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X34367,X34368,X34369)),X34368))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( X34367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34368),esk535_3(X34367,X34368,X34369))),esk536_3(X34367,X34368,X34369))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X34367,X34368,X34369)),X34368))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( ~ hBOOL(hAPP(X34369,esk535_3(X34367,X34368,X34369)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X34367,X34368,X34369)),X34368))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34368),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34368),esk533_3(X34367,X34368,X34369))),esk534_3(X34367,X34368,X34369))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34368),esk536_3(X34367,X34368,X34369)))
        | X34367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34368),esk533_3(X34367,X34368,X34369))),esk534_3(X34367,X34368,X34369))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk536_3(X34367,X34368,X34369)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34368),esk533_3(X34367,X34368,X34369))),esk534_3(X34367,X34368,X34369))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( X34367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34368),esk535_3(X34367,X34368,X34369))),esk536_3(X34367,X34368,X34369))
        | X34367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34368),esk533_3(X34367,X34368,X34369))),esk534_3(X34367,X34368,X34369))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( ~ hBOOL(hAPP(X34369,esk535_3(X34367,X34368,X34369)))
        | X34367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34368),esk533_3(X34367,X34368,X34369))),esk534_3(X34367,X34368,X34369))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34368),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34369,esk533_3(X34367,X34368,X34369)))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34368),esk536_3(X34367,X34368,X34369)))
        | ~ hBOOL(hAPP(X34369,esk533_3(X34367,X34368,X34369)))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk536_3(X34367,X34368,X34369)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34369,esk533_3(X34367,X34368,X34369)))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( X34367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34368),esk535_3(X34367,X34368,X34369))),esk536_3(X34367,X34368,X34369))
        | ~ hBOOL(hAPP(X34369,esk533_3(X34367,X34368,X34369)))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) )
      & ( ~ hBOOL(hAPP(X34369,esk535_3(X34367,X34368,X34369)))
        | ~ hBOOL(hAPP(X34369,esk533_3(X34367,X34368,X34369)))
        | ~ hBOOL(hAPP(X34369,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34369,X34368,X34367) ) ),
    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_5243])])])])])]) ).

fof(i_0_7733,plain,
    ! [X21939,X21940,X21941] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21941),X21940))
      | hAPP(c_Finite__Set_Ocard(X21941),hAPP(hAPP(c_Set_Oinsert(X21941),X21939),X21940)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X21941),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21941,tc_HOL_Obool)),X21940),hAPP(hAPP(c_Set_Oinsert(X21941),X21939),c_Orderings_Obot__class_Obot(tc_fun(X21941,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert])]) ).

cnf(i_0_7734,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X1))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5658]) ).

cnf(i_0_7735,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_5659]) ).

cnf(i_0_7736,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_5660]) ).

cnf(i_0_7737,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_5661]) ).

cnf(i_0_7738,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_5662]) ).

fof(i_0_7739,plain,
    ! [X24408,X24409,X24410,X24411] :
      ( ~ class_Fields_Olinordered__field(X24411)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24411),X24410),X24409))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24411),c_Groups_Ozero__class_Ozero(X24411)),X24408))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24411),c_Groups_Ozero__class_Ozero(X24411)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24411),X24409),X24410)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24411),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24411),X24408),X24409)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24411),X24408),X24410))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono])]) ).

fof(i_0_7740,plain,
    ! [X24261,X24262,X24263,X24264] :
      ( ~ class_Fields_Olinordered__field(X24264)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24264),X24263),X24262))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24264),c_Groups_Ozero__class_Ozero(X24264)),X24261))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24264),c_Groups_Ozero__class_Ozero(X24264)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24264),X24262),X24263)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24264),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24264),X24261),X24262)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24264),X24261),X24263))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__left__mono])]) ).

fof(i_0_7741,plain,
    ! [X20259,X20260,X20261] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X20261,X20261),tc_HOL_Obool)),X20260),X20259))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20261,tc_HOL_Obool)),hAPP(c_Relation_OField(X20261),X20260)),hAPP(c_Relation_OField(X20261),X20259))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mono__Field])]) ).

fof(i_0_7742,plain,
    ! [X20738,X20739,X20740,X20741,X20742,X20743] :
      ( ~ c_Finite__Set_Ofolding(X20743,X20742,X20741,X20740)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20743),X20739))
      | hAPP(c_Fun_Ocomp(X20742,X20742,X20742,hAPP(X20741,X20738)),hAPP(X20740,X20739)) = hAPP(c_Fun_Ocomp(X20742,X20742,X20742,hAPP(X20740,X20739)),hAPP(X20741,X20738)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H])]) ).

fof(i_0_7743,plain,
    ! [X34374,X34375,X34376,X34377,X34378,X34379,X34380,X34381,X34382,X34383] :
      ( ( X34375 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(X34376,X34374))
        | ~ epred2_3(X34376,X34375,X34374) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34375))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34378))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34378),X34375))
        | X34374 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34375),X34377)),X34378)
        | hBOOL(hAPP(X34376,X34378))
        | ~ epred2_3(X34376,X34375,X34374) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34375),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34375),X34380))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X34380),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34374 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34375),X34379)),X34380)
        | hBOOL(hAPP(X34376,X34380))
        | ~ epred2_3(X34376,X34375,X34374) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34382),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)),X34382))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34382),esk540_3(X34381,X34382,X34383)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34382))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk540_3(X34381,X34382,X34383)),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)),X34382))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( X34381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34382),esk539_3(X34381,X34382,X34383))),esk540_3(X34381,X34382,X34383))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34382))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( ~ hBOOL(hAPP(X34383,esk540_3(X34381,X34382,X34383)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34382))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34382),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)),esk538_3(X34381,X34382,X34383)))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34382),esk540_3(X34381,X34382,X34383)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk538_3(X34381,X34382,X34383)))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk540_3(X34381,X34382,X34383)),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)),esk538_3(X34381,X34382,X34383)))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( X34381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34382),esk539_3(X34381,X34382,X34383))),esk540_3(X34381,X34382,X34383))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk538_3(X34381,X34382,X34383)))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( ~ hBOOL(hAPP(X34383,esk540_3(X34381,X34382,X34383)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk538_3(X34381,X34382,X34383)))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34382),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk538_3(X34381,X34382,X34383)),X34382))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34382),esk540_3(X34381,X34382,X34383)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk538_3(X34381,X34382,X34383)),X34382))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk540_3(X34381,X34382,X34383)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk538_3(X34381,X34382,X34383)),X34382))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( X34381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34382),esk539_3(X34381,X34382,X34383))),esk540_3(X34381,X34382,X34383))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk538_3(X34381,X34382,X34383)),X34382))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( ~ hBOOL(hAPP(X34383,esk540_3(X34381,X34382,X34383)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk538_3(X34381,X34382,X34383)),X34382))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34382),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34382),esk537_3(X34381,X34382,X34383))),esk538_3(X34381,X34382,X34383))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34382),esk540_3(X34381,X34382,X34383)))
        | X34381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34382),esk537_3(X34381,X34382,X34383))),esk538_3(X34381,X34382,X34383))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk540_3(X34381,X34382,X34383)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34382),esk537_3(X34381,X34382,X34383))),esk538_3(X34381,X34382,X34383))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( X34381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34382),esk539_3(X34381,X34382,X34383))),esk540_3(X34381,X34382,X34383))
        | X34381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34382),esk537_3(X34381,X34382,X34383))),esk538_3(X34381,X34382,X34383))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( ~ hBOOL(hAPP(X34383,esk540_3(X34381,X34382,X34383)))
        | X34381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34382),esk537_3(X34381,X34382,X34383))),esk538_3(X34381,X34382,X34383))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34382),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34383,esk538_3(X34381,X34382,X34383)))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34382),esk540_3(X34381,X34382,X34383)))
        | ~ hBOOL(hAPP(X34383,esk538_3(X34381,X34382,X34383)))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk540_3(X34381,X34382,X34383)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34383,esk538_3(X34381,X34382,X34383)))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( X34381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34382),esk539_3(X34381,X34382,X34383))),esk540_3(X34381,X34382,X34383))
        | ~ hBOOL(hAPP(X34383,esk538_3(X34381,X34382,X34383)))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( ~ hBOOL(hAPP(X34383,esk540_3(X34381,X34382,X34383)))
        | ~ hBOOL(hAPP(X34383,esk538_3(X34381,X34382,X34383)))
        | X34382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34382),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)),X34382))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34382),esk540_3(X34381,X34382,X34383)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34382))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk540_3(X34381,X34382,X34383)),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)),X34382))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( X34381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34382),esk539_3(X34381,X34382,X34383))),esk540_3(X34381,X34382,X34383))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34382))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( ~ hBOOL(hAPP(X34383,esk540_3(X34381,X34382,X34383)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34382))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34382),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)),esk538_3(X34381,X34382,X34383)))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34382),esk540_3(X34381,X34382,X34383)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk538_3(X34381,X34382,X34383)))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk540_3(X34381,X34382,X34383)),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)),esk538_3(X34381,X34382,X34383)))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( X34381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34382),esk539_3(X34381,X34382,X34383))),esk540_3(X34381,X34382,X34383))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk538_3(X34381,X34382,X34383)))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( ~ hBOOL(hAPP(X34383,esk540_3(X34381,X34382,X34383)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk538_3(X34381,X34382,X34383)))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34382),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk538_3(X34381,X34382,X34383)),X34382))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34382),esk540_3(X34381,X34382,X34383)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk538_3(X34381,X34382,X34383)),X34382))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk540_3(X34381,X34382,X34383)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk538_3(X34381,X34382,X34383)),X34382))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( X34381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34382),esk539_3(X34381,X34382,X34383))),esk540_3(X34381,X34382,X34383))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk538_3(X34381,X34382,X34383)),X34382))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( ~ hBOOL(hAPP(X34383,esk540_3(X34381,X34382,X34383)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk538_3(X34381,X34382,X34383)),X34382))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34382),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34382),esk537_3(X34381,X34382,X34383))),esk538_3(X34381,X34382,X34383))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34382),esk540_3(X34381,X34382,X34383)))
        | X34381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34382),esk537_3(X34381,X34382,X34383))),esk538_3(X34381,X34382,X34383))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk540_3(X34381,X34382,X34383)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34382),esk537_3(X34381,X34382,X34383))),esk538_3(X34381,X34382,X34383))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( X34381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34382),esk539_3(X34381,X34382,X34383))),esk540_3(X34381,X34382,X34383))
        | X34381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34382),esk537_3(X34381,X34382,X34383))),esk538_3(X34381,X34382,X34383))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( ~ hBOOL(hAPP(X34383,esk540_3(X34381,X34382,X34383)))
        | X34381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34382),esk537_3(X34381,X34382,X34383))),esk538_3(X34381,X34382,X34383))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34382),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34383,esk538_3(X34381,X34382,X34383)))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34382),esk540_3(X34381,X34382,X34383)))
        | ~ hBOOL(hAPP(X34383,esk538_3(X34381,X34382,X34383)))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk540_3(X34381,X34382,X34383)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34383,esk538_3(X34381,X34382,X34383)))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( X34381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34382),esk539_3(X34381,X34382,X34383))),esk540_3(X34381,X34382,X34383))
        | ~ hBOOL(hAPP(X34383,esk538_3(X34381,X34382,X34383)))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) )
      & ( ~ hBOOL(hAPP(X34383,esk540_3(X34381,X34382,X34383)))
        | ~ hBOOL(hAPP(X34383,esk538_3(X34381,X34382,X34383)))
        | ~ hBOOL(hAPP(X34383,X34381))
        | epred2_3(X34383,X34382,X34381) ) ),
    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_5241])])])])])]) ).

fof(i_0_7744,plain,
    ! [X29309,X29310,X29311,X29312,X29313] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29313,tc_fun(X29312,tc_HOL_Obool)),X29311),hAPP(hAPP(c_COMBB(tc_fun(X29312,tc_HOL_Obool),tc_fun(X29312,tc_HOL_Obool),X29313),hAPP(c_Set_Oinsert(X29312),X29310)),X29309)) = hAPP(hAPP(c_Set_Oinsert(X29312),X29310),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29313,tc_fun(X29312,tc_HOL_Obool)),X29311),X29309)),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I5_J]) ).

fof(i_0_7745,plain,
    ! [X29304,X29305,X29306,X29307,X29308] : hAPP(hAPP(c_Set_Oinsert(X29308),X29307),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29306,tc_fun(X29308,tc_HOL_Obool)),X29305),X29304)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29306,tc_fun(X29308,tc_HOL_Obool)),X29305),hAPP(hAPP(c_COMBB(tc_fun(X29308,tc_HOL_Obool),tc_fun(X29308,tc_HOL_Obool),X29306),hAPP(c_Set_Oinsert(X29308),X29307)),X29304)),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I5_J]) ).

fof(i_0_7746,plain,
    ! [X21983,X21984,X21985,X21986] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21986),X21985)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21984),X21985)),X21983)) = 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),X21986),X21984)),X21985)),X21983),
    inference(variable_rename,[status(thm)],[fact_left__add__mult__distrib]) ).

fof(i_0_7747,plain,
    ! [X32971,X32972,X32973,X32974,X32975] : hAPP(hAPP(c_List_Ozip(X32975,X32974),X32973),c_List_OtakeWhile(X32974,X32972,X32971)) = c_List_OtakeWhile(tc_prod(X32975,X32974),hAPP(c_Fun_Ocomp(X32974,tc_HOL_Obool,tc_prod(X32975,X32974),X32972),c_Product__Type_Osnd(X32975,X32974)),hAPP(hAPP(c_List_Ozip(X32975,X32974),X32973),X32971)),
    inference(variable_rename,[status(thm)],[fact_zip__takeWhile__snd]) ).

cnf(i_0_7748,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_5663]) ).

fof(i_0_7749,plain,
    ! [X30141,X30142,X30143,X30144,X30145] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(X30145),tc_Option_Ooption(X30144),X30143,hAPP(c_Option_Omap(X30145,X30144),X30142)),hAPP(c_COMBK(tc_Option_Ooption(X30145),X30143),c_Option_Ooption_ONone(X30145))),X30141) = c_Option_Ooption_ONone(X30144),
    inference(variable_rename,[status(thm)],[fact_option__map__o__empty]) ).

fof(i_0_7750,plain,
    ! [X19280,X19281,X19282,X19283] :
      ( ~ c_Fun_Oinj__on(X19283,X19282,X19281,c_Orderings_Otop__class_Otop(tc_fun(X19283,tc_HOL_Obool)))
      | c_Fun_Oinj__on(X19283,tc_fun(X19280,X19282),hAPP(hAPP(c_COMBB(X19282,tc_fun(X19280,X19282),X19283),c_COMBK(X19282,X19280)),X19281),c_Orderings_Otop__class_Otop(tc_fun(X19283,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__fun])]) ).

fof(i_0_7751,plain,
    ! [X18810,X18811,X18812,X18813,X18814,X18815] :
      ( ~ c_Fun_Oinj__on(X18815,X18814,X18813,X18812)
      | hBOOL(hAPP(hAPP(c_member(X18814),X18811),hAPP(c_Set_Oimage(X18815,X18814,X18813),X18812)))
      | c_Fun_Oinj__on(X18815,X18814,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18815,X18814),X18813),X18810),X18811),X18812) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5664])]) ).

fof(i_0_7752,plain,
    ! [X29782,X29783,X29784] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29784,tc_HOL_Obool)),X29783),X29782) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X29784,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X29784,tc_HOL_Obool)),X29783),hAPP(hAPP(c_Set_Oinsert(tc_fun(X29784,tc_HOL_Obool)),X29782),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X29784,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_Int__eq__Inter]) ).

fof(i_0_7753,plain,
    ! [X29771,X29772,X29773] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29773,tc_HOL_Obool)),X29772),X29771) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X29773,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X29773,tc_HOL_Obool)),X29772),hAPP(hAPP(c_Set_Oinsert(tc_fun(X29773,tc_HOL_Obool)),X29771),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X29773,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_Un__eq__Union]) ).

fof(i_0_7754,plain,
    ! [X24412,X24413,X24414,X24415] :
      ( ~ class_Fields_Olinordered__field(X24415)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24415),X24414),X24413))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24415),X24412),c_Groups_Ozero__class_Ozero(X24415)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24415),c_Groups_Ozero__class_Ozero(X24415)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24415),X24414),X24413)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24415),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24415),X24412),X24414)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24415),X24412),X24413))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono__neg])]) ).

fof(i_0_7755,plain,
    ! [X24257,X24258,X24259,X24260] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X24260)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24260),X24259),X24258))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24260),X24257),c_Groups_Ozero__class_Ozero(X24260)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24260),c_Groups_Ozero__class_Ozero(X24260)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24260),X24259),X24258)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24260),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24260),X24257),X24259)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24260),X24257),X24258))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__left__mono__neg])]) ).

fof(i_0_7756,plain,
    ! [X33692,X33693,X33694,X33695,X33696] :
      ( ( X33696 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_New__DSequence_Opos__decr__bind(X33695,X33694,X33693,X33692),X33696) = c_Lazy__Sequence_Oempty(X33694) )
      & ( X33696 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_New__DSequence_Opos__decr__bind(X33695,X33694,X33693,X33692),X33696) = hAPP(c_Lazy__Sequence_Obind(X33695,X33694,hAPP(X33693,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X33696),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(X33695,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X33694)),X33692),X33696)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__decr__bind__def])]) ).

fof(i_0_7757,plain,
    ! [X30932,X30933,X30934,X30935,X30936] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30936),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30935)),X30934)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30936),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30933)),X30932)))
      | hAPP(hAPP(c_List_Onth(tc_prod(X30935,X30933)),hAPP(hAPP(c_List_Ozip(X30935,X30933),X30934),X30932)),X30936) = hAPP(hAPP(c_Product__Type_OPair(X30935,X30933),hAPP(hAPP(c_List_Onth(X30935),X30934),X30936)),hAPP(hAPP(c_List_Onth(X30933),X30932),X30936)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__zip])]) ).

fof(i_0_7758,plain,
    ! [X23658,X23659,X23660] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23660,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23659),X23658)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23659),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23660),X23659),X23658))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23660,X23659)),
    inference(variable_rename,[status(thm)],[fact_mod__mult2__eq]) ).

cnf(i_0_7759,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_5613]) ).

fof(i_0_7760,plain,
    ! [X26271,X26272,X26273] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26273),X26272))
        | 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)),X26273)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26271),X26272)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26271),X26273)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26272),X26273)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26271),X26272))
        | 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)),X26273)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26271),X26272)) = 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),X26273),X26272)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26271),X26272))
        | 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)),X26273)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26271),X26272)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26273),X26272)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5665])])]) ).

cnf(i_0_7761,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_5666]) ).

fof(i_0_7762,plain,
    ! [X31670,X31671,X31672,X31673,X31674] : hAPP(hAPP(c_List_Olist__update(X31674,hAPP(hAPP(c_List_Oappend(X31674),X31673),hAPP(hAPP(c_List_Olist_OCons(X31674),X31672),X31671))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31674)),X31673)),X31670) = hAPP(hAPP(c_List_Oappend(X31674),X31673),hAPP(hAPP(c_List_Olist_OCons(X31674),X31670),X31671)),
    inference(variable_rename,[status(thm)],[fact_list__update__length]) ).

cnf(i_0_7763,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_5667]) ).

fof(i_0_7764,plain,
    ! [X30602,X30603] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X30603),tc_List_Olist(X30603)),tc_HOL_Obool)),c_List_Olistrel1(X30603,c_Transitive__Closure_Ortrancl(X30603,X30602))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X30603),c_List_Olistrel1(X30603,X30602)))),
    inference(variable_rename,[status(thm)],[fact_listrel1__rtrancl__subset__rtrancl__listrel1]) ).

fof(i_0_7765,plain,
    ! [X28591,X28592,X28593] : c_Transitive__Closure_Ortrancl(X28593,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28593,X28593),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X28593,X28592)),c_Transitive__Closure_Ortrancl(X28593,X28591))) = c_Transitive__Closure_Ortrancl(X28593,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28593,X28593),tc_HOL_Obool)),X28592),X28591)),
    inference(variable_rename,[status(thm)],[fact_rtrancl__Un__rtrancl]) ).

cnf(i_0_7766,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_5668]) ).

cnf(i_0_7767,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_5669]) ).

fof(i_0_7768,plain,
    ! [X30771,X30772,X30773] : hAPP(hAPP(c_List_Ozip(X30773,X30772),hAPP(hAPP(c_List_Omap(tc_prod(X30773,X30772),X30773),c_Product__Type_Ofst(X30773,X30772)),X30771)),hAPP(hAPP(c_List_Omap(tc_prod(X30773,X30772),X30772),c_Product__Type_Osnd(X30773,X30772)),X30771)) = X30771,
    inference(variable_rename,[status(thm)],[fact_zip__map__fst__snd]) ).

fof(i_0_7769,plain,
    ! [X23095,X23096,X23097,X23098,X23099,X23100,X23101,X23102] :
      ( ~ class_Groups_Ocomm__monoid__mult(X23102)
      | ~ c_Fun_Oinj__on(X23101,X23100,X23099,X23098)
      | X23097 != hAPP(c_Set_Oimage(X23101,X23100,X23099),X23098)
      | X23096 != hAPP(c_Fun_Ocomp(X23100,X23102,X23101,X23095),X23099)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23100,X23102),X23095),X23097) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23101,X23102),X23096),X23098) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__reindex__cong])]) ).

fof(i_0_7770,plain,
    ! [X22110,X22111,X22112] :
      ( ~ class_Rings_Olinordered__ring(X22112)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22112),c_Groups_Ozero__class_Ozero(X22112)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22112),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22112),X22111),X22111)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22112),X22110),X22110)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero])]) ).

fof(i_0_7771,plain,
    ! [X28687,X28688] :
      ( ( ~ 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),X28688),X28687)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28688),X28687)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28688),X28687))
        | 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),X28688),X28687)),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_7772,plain,
    ! [X18686,X18687,X18688] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18688,tc_HOL_Obool)),X18687),X18686))
      | hBOOL(hAPP(hAPP(c_member(X18688),esk31_3(X18686,X18687,X18688)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18688,tc_HOL_Obool)),X18686),X18687))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__imp__ex__mem])])]) ).

fof(i_0_7773,plain,
    ! [X20685,X20686,X20687,X20688,X20689,X20690] :
      ( ~ c_Finite__Set_Ofolding(X20690,X20689,X20688,X20687)
      | hAPP(c_Fun_Ocomp(X20689,X20689,X20689,hAPP(X20688,X20686)),hAPP(X20688,X20685)) = hAPP(c_Fun_Ocomp(X20689,X20689,X20689,hAPP(X20688,X20685)),hAPP(X20688,X20686)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp])]) ).

fof(i_0_7774,plain,
    ! [X27742,X27743,X27744,X27745,X27746] : hAPP(hAPP(c_Product__Type_OSigma(X27746,X27745),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27746,tc_HOL_Obool)),X27744),X27743)),X27742) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27746,X27745),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27746,X27745),X27744),X27742)),hAPP(hAPP(c_Product__Type_OSigma(X27746,X27745),X27743),X27742)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib1]) ).

fof(i_0_7775,plain,
    ! [X27769,X27770,X27771,X27772,X27773] : hAPP(hAPP(c_Product__Type_OSigma(X27773,X27772),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27773,tc_HOL_Obool)),X27771),X27770)),X27769) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X27773,X27772),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27773,X27772),X27771),X27769)),hAPP(hAPP(c_Product__Type_OSigma(X27773,X27772),X27770),X27769)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Diff__distrib1]) ).

fof(i_0_7776,plain,
    ! [X27708,X27709,X27710,X27711,X27712] : hAPP(hAPP(c_Product__Type_OSigma(X27712,X27711),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27712,tc_HOL_Obool)),X27710),X27709)),X27708) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27712,X27711),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27712,X27711),X27710),X27708)),hAPP(hAPP(c_Product__Type_OSigma(X27712,X27711),X27709),X27708)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Un__distrib1]) ).

fof(i_0_7777,plain,
    ! [X32198,X32199,X32200,X32201] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X32201),X32200),hAPP(c_List_Oset(X32201),c_List_Obutlast(X32201,X32199))))
        | hBOOL(hAPP(hAPP(c_member(X32201),X32200),hAPP(c_List_Oset(X32201),c_List_Obutlast(X32201,hAPP(hAPP(c_List_Oappend(X32201),X32199),X32198))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32201),X32200),hAPP(c_List_Oset(X32201),c_List_Obutlast(X32201,X32198))))
        | hBOOL(hAPP(hAPP(c_member(X32201),X32200),hAPP(c_List_Oset(X32201),c_List_Obutlast(X32201,hAPP(hAPP(c_List_Oappend(X32201),X32199),X32198))))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__butlast__appendI])])]) ).

fof(i_0_7778,plain,
    ! [X27333,X27334,X27335] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27335,X27335),tc_HOL_Obool)),X27334),X27333))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27335,tc_HOL_Obool)),c_Wellfounded_Oacc(X27335,X27333)),c_Wellfounded_Oacc(X27335,X27334))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__subset])]) ).

fof(i_0_7779,plain,
    ! [X32676,X32677,X32678,X32679,X32680,X32681] :
      ( ~ class_Orderings_Olinorder(X32681)
      | hAPP(X32680,X32679) = hAPP(X32680,X32678)
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32677,X32681,X32680),X32678),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32677,X32681,X32680),X32679),X32676)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32677,X32681,X32680),X32679),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32677,X32681,X32680),X32678),X32676)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__key__left__comm])]) ).

fof(i_0_7780,plain,
    ! [X19070,X19071,X19072,X19073] :
      ( hAPP(c_Set_Oimage(X19073,X19072,X19071),c_Orderings_Otop__class_Otop(tc_fun(X19073,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X19072,tc_HOL_Obool))
      | hAPP(X19071,hAPP(c_Hilbert__Choice_Oinv__into(X19073,X19072,c_Orderings_Otop__class_Otop(tc_fun(X19073,tc_HOL_Obool)),X19071),X19070)) = X19070 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__f__inv__f])]) ).

cnf(i_0_7781,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X1))),
    inference(split_conjunct,[status(thm)],[i_0_5670]) ).

fof(i_0_7782,plain,
    ! [X23524,X23525] :
      ( X23525 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X23524,X23525),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23524),X23525)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23524,X23525)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div__mod])]) ).

fof(i_0_7783,plain,
    ! [X29385,X29386,X29387,X29388,X29389,X29390] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29390,tc_fun(X29389,tc_HOL_Obool)),X29388),hAPP(hAPP(c_COMBB(X29387,tc_fun(X29389,tc_HOL_Obool),X29390),X29386),X29385)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29387,tc_fun(X29389,tc_HOL_Obool)),hAPP(c_Set_Oimage(X29390,X29387,X29385),X29388)),X29386),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I10_J]) ).

fof(i_0_7784,plain,
    ! [X19697,X19698,X19699,X19700,X19701,X19702] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19702,tc_fun(X19701,tc_HOL_Obool)),X19700),hAPP(hAPP(c_COMBB(X19699,tc_fun(X19701,tc_HOL_Obool),X19702),X19698),X19697)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19699,tc_fun(X19701,tc_HOL_Obool)),hAPP(c_Set_Oimage(X19702,X19699,X19697),X19700)),X19698),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I10_J]) ).

fof(i_0_7785,plain,
    ! [X29379,X29380,X29381,X29382,X29383,X29384] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29384,tc_fun(X29383,tc_HOL_Obool)),hAPP(c_Set_Oimage(X29382,X29384,X29381),X29380)),X29379) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29382,tc_fun(X29383,tc_HOL_Obool)),X29380),hAPP(hAPP(c_COMBB(X29384,tc_fun(X29383,tc_HOL_Obool),X29382),X29379),X29381)),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I10_J]) ).

fof(i_0_7786,plain,
    ! [X19709,X19710,X19711,X19712,X19713,X19714] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19714,tc_fun(X19713,tc_HOL_Obool)),hAPP(c_Set_Oimage(X19712,X19714,X19711),X19710)),X19709) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19712,tc_fun(X19713,tc_HOL_Obool)),X19710),hAPP(hAPP(c_COMBB(X19714,tc_fun(X19713,tc_HOL_Obool),X19712),X19709),X19711)),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I10_J]) ).

fof(i_0_7787,plain,
    ! [X23737,X23738] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23738,X23737),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23738),X23737)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23738,X23737)))),
    inference(variable_rename,[status(thm)],[fact_divmod__nat__rel]) ).

cnf(i_0_7788,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_5671]) ).

fof(i_0_7789,plain,
    ! [X20446,X20447,X20448] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20448,tc_HOL_Obool)),X20447),X20446))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20448,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20448,tc_HOL_Obool)),X20446)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20448,tc_HOL_Obool)),X20447))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__anti__mono])]) ).

fof(i_0_7790,plain,
    ! [X20582,X20583,X20584] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20584),X20583))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20584,tc_HOL_Obool)),X20583),hAPP(c_Set_Oimage(X20584,X20584,X20582),X20583)))
      | c_Fun_Oinj__on(X20584,X20584,X20582,X20583) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj__inj])]) ).

fof(i_0_7791,plain,
    ! [X27696,X27697,X27698] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X27698,X27697),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27698,X27697),c_Orderings_Otop__class_Otop(tc_fun(X27698,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X27697,tc_HOL_Obool),X27698),X27696))) = hAPP(hAPP(c_Product__Type_OSigma(X27698,X27697),c_Orderings_Otop__class_Otop(tc_fun(X27698,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X27697,tc_HOL_Obool),X27698),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27697,tc_HOL_Obool)),X27696))),
    inference(variable_rename,[status(thm)],[fact_Compl__Times__UNIV1]) ).

fof(i_0_7792,plain,
    ! [X27699,X27700,X27701] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X27701,X27700),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27701,X27700),X27699),hAPP(c_COMBK(tc_fun(X27700,tc_HOL_Obool),X27701),c_Orderings_Otop__class_Otop(tc_fun(X27700,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(X27701,X27700),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27701,tc_HOL_Obool)),X27699)),hAPP(c_COMBK(tc_fun(X27700,tc_HOL_Obool),X27701),c_Orderings_Otop__class_Otop(tc_fun(X27700,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_Compl__Times__UNIV2]) ).

fof(i_0_7793,plain,
    ! [X30588,X30589,X30590,X30591] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X30591),X30590),c_Wellfounded_Oacc(X30591,X30589)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30591)),X30588),c_Wellfounded_Oacc(tc_List_Olist(X30591),c_List_Olistrel1(X30591,X30589))))
      | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30591)),hAPP(hAPP(c_List_Olist_OCons(X30591),X30590),X30588)),c_Wellfounded_Oacc(tc_List_Olist(X30591),c_List_Olistrel1(X30591,X30589)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__acc__listrel1I])]) ).

fof(i_0_7794,plain,
    ! [X24404,X24405,X24406,X24407] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24407),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24407),X24405),X24406)),X24404))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24407),X24404),X24406)),X24405))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24407),X24406),c_Groups_Ozero__class_Ozero(X24407)))
        | ~ class_Fields_Olinordered__field(X24407) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24407),X24404),X24406)),X24405))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24407),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24407),X24405),X24406)),X24404))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24407),X24406),c_Groups_Ozero__class_Ozero(X24407)))
        | ~ class_Fields_Olinordered__field(X24407) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__divide__less__eq])])]) ).

fof(i_0_7795,plain,
    ! [X24265,X24266,X24267,X24268] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24268),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24268),X24266),X24267)),X24265))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24268),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24268),X24265),X24267)),X24266))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24268),X24267),c_Groups_Ozero__class_Ozero(X24268)))
        | ~ class_Fields_Olinordered__field(X24268) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24268),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24268),X24265),X24267)),X24266))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24268),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24268),X24266),X24267)),X24265))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24268),X24267),c_Groups_Ozero__class_Ozero(X24268)))
        | ~ class_Fields_Olinordered__field(X24268) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__divide__le__eq])])]) ).

cnf(i_0_7796,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_5604]) ).

fof(i_0_7797,plain,
    ! [X30875,X30876,X30877,X30878,X30879] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X30879),X30878),hAPP(c_List_Oset(X30879),X30877)))
        | hAPP(hAPP(c_Map_Omap__of(X30879,X30876),hAPP(hAPP(c_List_Ozip(X30879,X30876),X30877),hAPP(hAPP(c_List_Omap(X30879,X30876),X30875),X30877))),X30878) = hAPP(c_Option_Ooption_OSome(X30876),hAPP(X30875,X30878)) )
      & ( hBOOL(hAPP(hAPP(c_member(X30879),X30878),hAPP(c_List_Oset(X30879),X30877)))
        | hAPP(hAPP(c_Map_Omap__of(X30879,X30876),hAPP(hAPP(c_List_Ozip(X30879,X30876),X30877),hAPP(hAPP(c_List_Omap(X30879,X30876),X30875),X30877))),X30878) = c_Option_Ooption_ONone(X30876) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5672])]) ).

fof(i_0_7798,plain,
    ! [X23678,X23679,X23680] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23680,tc_fun(X23680,tc_HOL_Obool))),X23679),X23678))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23680,tc_HOL_Obool)),c_Wellfounded_Oaccp(X23680,X23678)),c_Wellfounded_Oaccp(X23680,X23679))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__subset])]) ).

fof(i_0_7799,plain,
    ! [X21034,X21035,X21036,X21037,X21038,X21039] :
      ( ~ c_Finite__Set_Ofolding__idem(X21039,X21038,X21037,X21036)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21039),X21035))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21039,tc_HOL_Obool)),X21034),X21035))
      | hAPP(c_Fun_Ocomp(X21038,X21038,X21038,hAPP(X21036,X21035)),hAPP(X21036,X21034)) = hAPP(X21036,X21035) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Osubset__comp__idem])]) ).

fof(i_0_7800,plain,
    ! [X32823,X32824,X32825] :
      ( ~ class_Orderings_Olinorder(X32825)
      | ~ hBOOL(hAPP(hAPP(c_member(X32825),X32824),hAPP(c_List_Oset(X32825),X32823)))
      | c_List_Olinorder__class_Oinsort__insert__key(X32825,X32825,c_COMBI(X32825),X32824,X32823) = X32823 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__insert__triv])]) ).

fof(i_0_7801,plain,
    ! [X23536,X23537,X23538] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23538),X23537)),X23536))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23536),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23538),hAPP(c_Nat_OSuc,X23537))))
        | X23537 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23536),X23538)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23538)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23538),X23537)),X23536))
        | X23537 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23536),X23538)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23538)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23536),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23538),hAPP(c_Nat_OSuc,X23537))))
        | X23537 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23536),X23538)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23538)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__div__lemma])])]) ).

fof(i_0_7802,plain,
    ! [X26578,X26579,X26580,X26581,X26582] :
      ( ~ class_Groups_Oab__group__add(X26582)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26581),X26580))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26581,tc_HOL_Obool)),X26579),X26580))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26581,X26582),X26578),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26581,tc_HOL_Obool)),X26580),X26579)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26582),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26581,X26582),X26578),X26580)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26581,X26582),X26578),X26579)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff])]) ).

cnf(i_0_7803,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_5673]) ).

fof(i_0_7804,plain,
    ! [X31879,X31880,X31881] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31881),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31880)),X31879)))
      | X31879 = hAPP(hAPP(c_List_Oappend(X31880),hAPP(hAPP(c_List_Otake(X31880),X31881),X31879)),hAPP(hAPP(c_List_Olist_OCons(X31880),hAPP(hAPP(c_List_Onth(X31880),X31879),X31881)),hAPP(hAPP(c_List_Odrop(X31880),hAPP(c_Nat_OSuc,X31881)),X31879))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_id__take__nth__drop])]) ).

fof(i_0_7805,plain,
    ! [X30346,X30347,X30348,X30349,X30350] :
      ( hAPP(hAPP(c_Map_Omap__of(X30350,X30349),X30348),X30347) != hAPP(c_Option_Ooption_OSome(X30349),X30346)
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X30350,X30349)),hAPP(hAPP(c_Product__Type_OPair(X30350,X30349),X30347),X30346)),hAPP(c_List_Oset(tc_prod(X30350,X30349)),X30348))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__is__SomeD])]) ).

fof(i_0_7806,plain,
    ! [X30341,X30342,X30343,X30344,X30345] :
      ( hAPP(hAPP(c_Map_Omap__of(X30345,X30344),X30343),X30342) != hAPP(c_Option_Ooption_OSome(X30344),X30341)
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X30345,X30344)),hAPP(hAPP(c_Product__Type_OPair(X30345,X30344),X30342),X30341)),hAPP(c_List_Oset(tc_prod(X30345,X30344)),X30343))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__SomeD])]) ).

fof(i_0_7807,plain,
    ! [X19984,X19985,X19986,X19987,X19988,X19989] :
      ( hBOOL(hAPP(hAPP(c_member(X19989),X19988),X19987))
      | hAPP(c_Set_Oimage(X19989,tc_Option_Ooption(X19986),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X19989,tc_Option_Ooption(X19986)),X19985),X19988),hAPP(c_Option_Ooption_OSome(X19986),X19984))),X19987) = hAPP(c_Set_Oimage(X19989,tc_Option_Ooption(X19986),X19985),X19987) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5674])]) ).

cnf(i_0_7808,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_5609]) ).

cnf(i_0_7809,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_5610]) ).

cnf(i_0_7810,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_5611]) ).

cnf(i_0_7811,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_5612]) ).

fof(i_0_7812,plain,
    ! [X25622,X25623] :
      ( ( ~ 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),X25623),X25622)),c_Wellfounded_Oless__than))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25623),X25622)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25623),X25622))
        | 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),X25623),X25622)),c_Wellfounded_Oless__than)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__than__iff])]) ).

cnf(i_0_7813,plain,
    c_Int_Opred(c_Int_OBit0(X1)) = c_Int_OBit1(c_Int_Opred(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5675]) ).

fof(i_0_7814,plain,
    ! [X17423,X17424,X17425,X17426,X17427,X17428] : hAPP(c_Set_Oimage(X17428,X17427,X17426),hAPP(c_Set_Oimage(X17425,X17428,X17424),X17423)) = hAPP(c_Set_Oimage(X17425,X17427,hAPP(hAPP(c_COMBB(X17428,X17427,X17425),X17426),X17424)),X17423),
    inference(variable_rename,[status(thm)],[fact_image__image]) ).

fof(i_0_7815,plain,
    ! [X24106,X24107,X24108,X24109,X24110] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24109),X24106),X24108))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24109,X24110),X24107),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24109,tc_HOL_Obool)),X24108),hAPP(hAPP(c_Set_Oinsert(X24109),X24106),c_Orderings_Obot__class_Obot(tc_fun(X24109,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24110),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24109,X24110),X24107),X24108)),hAPP(X24107,X24106))
        | hAPP(X24107,X24106) = c_Groups_Ozero__class_Ozero(X24110)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24109),X24108))
        | ~ class_Fields_Ofield(X24110) )
      & ( hBOOL(hAPP(hAPP(c_member(X24109),X24106),X24108))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24109,X24110),X24107),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24109,tc_HOL_Obool)),X24108),hAPP(hAPP(c_Set_Oinsert(X24109),X24106),c_Orderings_Obot__class_Obot(tc_fun(X24109,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24109,X24110),X24107),X24108)
        | hAPP(X24107,X24106) = c_Groups_Ozero__class_Ozero(X24110)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24109),X24108))
        | ~ class_Fields_Ofield(X24110) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5676])])]) ).

cnf(i_0_7816,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_5615]) ).

fof(i_0_7817,plain,
    ! [X30320,X30321,X30322,X30323,X30324] :
      ( ( hAPP(hAPP(c_List_Omap(X30324,X30323),X30322),X30321) != hAPP(hAPP(c_List_Omap(X30324,X30323),X30322),X30320)
        | X30321 = X30320
        | ~ c_Fun_Oinj__on(X30324,X30323,X30322,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30324,tc_HOL_Obool)),hAPP(c_List_Oset(X30324),X30321)),hAPP(c_List_Oset(X30324),X30320))) )
      & ( X30321 != X30320
        | hAPP(hAPP(c_List_Omap(X30324,X30323),X30322),X30321) = hAPP(hAPP(c_List_Omap(X30324,X30323),X30322),X30320)
        | ~ c_Fun_Oinj__on(X30324,X30323,X30322,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30324,tc_HOL_Obool)),hAPP(c_List_Oset(X30324),X30321)),hAPP(c_List_Oset(X30324),X30320))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__map__eq__map])])]) ).

fof(i_0_7818,plain,
    ! [X30315,X30316,X30317,X30318,X30319] :
      ( hAPP(hAPP(c_List_Omap(X30319,X30318),X30317),X30316) != hAPP(hAPP(c_List_Omap(X30319,X30318),X30317),X30315)
      | ~ c_Fun_Oinj__on(X30319,X30318,X30317,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30319,tc_HOL_Obool)),hAPP(c_List_Oset(X30319),X30316)),hAPP(c_List_Oset(X30319),X30315)))
      | X30316 = X30315 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__inj__on])]) ).

fof(i_0_7819,plain,
    ! [X25274,X25275,X25276] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25274),X25275))
        | hBOOL(hAPP(X25276,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25275)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25274))))
        | ~ hBOOL(hAPP(X25276,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25275),X25274)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25275),X25274))
        | hBOOL(hAPP(X25276,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X25276,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25275),X25274)))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25275),X25274))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25274),X25275))
        | hBOOL(hAPP(X25276,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25275),X25274)))) )
      & ( ~ hBOOL(hAPP(X25276,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25274),X25275))
        | hBOOL(hAPP(X25276,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25275),X25274)))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25275),X25274))
        | ~ hBOOL(hAPP(X25276,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25275)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25274))))
        | hBOOL(hAPP(X25276,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25275),X25274)))) )
      & ( ~ hBOOL(hAPP(X25276,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X25276,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25275)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25274))))
        | hBOOL(hAPP(X25276,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25275),X25274)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiff__int__split])])]) ).

fof(i_0_7820,plain,
    ! [X33132,X33133,X33134,X33135] :
      ( ~ hBOOL(hAPP(c_List_Olistsp(X33135,X33134),X33133))
      | ~ hBOOL(hAPP(c_List_Olistsp(X33135,X33132),X33133))
      | hBOOL(hAPP(c_List_Olistsp(X33135,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33135,tc_HOL_Obool)),X33134),X33132)),X33133)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__infI])]) ).

cnf(i_0_7821,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_5677]) ).

fof(i_0_7822,plain,
    ! [X29974,X29975,X29976,X29977,X29978] : c_Map_Omap__add(X29978,X29977,X29976,c_Map_Omap__add(X29978,X29977,X29975,X29974)) = c_Map_Omap__add(X29978,X29977,c_Map_Omap__add(X29978,X29977,X29976,X29975),X29974),
    inference(variable_rename,[status(thm)],[fact_map__add__assoc]) ).

fof(i_0_7823,plain,
    ! [X28830,X28831,X28832,X28833,X28834] :
      ( ~ c_Relation_Osingle__valued(X28834,X28833,hAPP(c_Relation_Oconverse(X28833,X28834),X28832))
      | hAPP(c_Relation_OImage(X28833,X28834,X28832),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28833,tc_HOL_Obool)),X28831),X28830)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28834,tc_HOL_Obool)),hAPP(c_Relation_OImage(X28833,X28834,X28832),X28831)),hAPP(c_Relation_OImage(X28833,X28834,X28832),X28830)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__Int__eq])]) ).

fof(i_0_7824,plain,
    ! [X24365,X24366,X24367,X24368,X24369] :
      ( ~ class_Fields_Olinordered__field(X24369)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24369),c_Groups_Ozero__class_Ozero(X24369)),X24368))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24369),X24368),X24367))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24369),c_Groups_Ozero__class_Ozero(X24369)),X24366))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24369),X24366),X24365))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24369),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24369),X24368),X24365)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24369),X24367),X24366))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__less2])]) ).

fof(i_0_7825,plain,
    ! [X24360,X24361,X24362,X24363,X24364] :
      ( ~ class_Fields_Olinordered__field(X24364)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24364),c_Groups_Ozero__class_Ozero(X24364)),X24363))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24364),X24363),X24362))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24364),c_Groups_Ozero__class_Ozero(X24364)),X24361))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24364),X24361),X24360))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24364),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24364),X24363),X24360)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24364),X24362),X24361))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__less])]) ).

fof(i_0_7826,plain,
    ! [X22411,X22412,X22413,X22414,X22415] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22415)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22415),X22414),X22413))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22415),X22412),X22411))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22415),c_Groups_Ozero__class_Ozero(X22415)),X22413))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22415),c_Groups_Ozero__class_Ozero(X22415)),X22412))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22415),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22415),X22414),X22412)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22415),X22413),X22411))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono])]) ).

fof(i_0_7827,plain,
    ! [X22416,X22417,X22418,X22419,X22420] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22420)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22420),X22419),X22418))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22420),X22417),X22416))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22420),c_Groups_Ozero__class_Ozero(X22420)),X22419))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22420),c_Groups_Ozero__class_Ozero(X22420)),X22417))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22420),X22419),X22417)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22420),X22418),X22416))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H])]) ).

fof(i_0_7828,plain,
    ! [X22426,X22427,X22428,X22429,X22430] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22430)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22430),X22429),X22428))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22430),X22427),X22426))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22430),c_Groups_Ozero__class_Ozero(X22430)),X22429))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22430),c_Groups_Ozero__class_Ozero(X22430)),X22427))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22430),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22430),X22429),X22427)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22430),X22428),X22426))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less])]) ).

fof(i_0_7829,plain,
    ! [X22421,X22422,X22423,X22424,X22425] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22425)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22425),X22424),X22423))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22425),X22422),X22421))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22425),c_Groups_Ozero__class_Ozero(X22425)),X22424))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22425),c_Groups_Ozero__class_Ozero(X22425)),X22422))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22425),X22424),X22422)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22425),X22423),X22421))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less])]) ).

fof(i_0_7830,plain,
    ! [X24355,X24356,X24357,X24358,X24359] :
      ( ~ class_Fields_Olinordered__field(X24359)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24359),c_Groups_Ozero__class_Ozero(X24359)),X24358))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24359),X24358),X24357))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24359),c_Groups_Ozero__class_Ozero(X24359)),X24356))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24359),X24356),X24355))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24359),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24359),X24358),X24355)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24359),X24357),X24356))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__le])]) ).

fof(i_0_7831,plain,
    ! [X22183,X22184,X22185,X22186,X22187] :
      ( ~ class_Rings_Oordered__semiring(X22187)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22187),X22186),X22185))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22187),X22184),X22183))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22187),c_Groups_Ozero__class_Ozero(X22187)),X22186))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22187),c_Groups_Ozero__class_Ozero(X22187)),X22184))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22187),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22187),X22186),X22184)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22187),X22185),X22183))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono_H])]) ).

fof(i_0_7832,plain,
    ! [X22188,X22189,X22190,X22191,X22192] :
      ( ~ class_Rings_Oordered__semiring(X22192)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22192),X22191),X22190))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22192),X22189),X22188))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22192),c_Groups_Ozero__class_Ozero(X22192)),X22190))
      | ~ 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__eq(X22192),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22192),X22191),X22189)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22192),X22190),X22188))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono])]) ).

cnf(i_0_7833,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_5678]) ).

fof(i_0_7834,plain,
    ! [X26671,X26672,X26673,X26674,X26675] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26674),X26672),X26673))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26674,X26675),X26671),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26674,tc_HOL_Obool)),X26673),hAPP(hAPP(c_Set_Oinsert(X26674),X26672),c_Orderings_Obot__class_Obot(tc_fun(X26674,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26675),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26674,X26675),X26671),X26673)),hAPP(X26671,X26672))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26674),X26673))
        | ~ class_Groups_Oab__group__add(X26675) )
      & ( hBOOL(hAPP(hAPP(c_member(X26674),X26672),X26673))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26674,X26675),X26671),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26674,tc_HOL_Obool)),X26673),hAPP(hAPP(c_Set_Oinsert(X26674),X26672),c_Orderings_Obot__class_Obot(tc_fun(X26674,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26674,X26675),X26671),X26673)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26674),X26673))
        | ~ class_Groups_Oab__group__add(X26675) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5679])])]) ).

fof(i_0_7835,plain,
    ! [X26676,X26677,X26678,X26679,X26680] :
      ( ~ class_Rings_Oring(X26680)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26679),X26678))
      | ~ hBOOL(hAPP(hAPP(c_member(X26679),X26677),X26678))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26679,X26680),X26676),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26679,tc_HOL_Obool)),X26678),hAPP(hAPP(c_Set_Oinsert(X26679),X26677),c_Orderings_Obot__class_Obot(tc_fun(X26679,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26680),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26679,X26680),X26676),X26678)),hAPP(X26676,X26677)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff1__ring])]) ).

fof(i_0_7836,plain,
    ! [X26681,X26682,X26683] :
      ( ~ class_Fields_Ofield(X26683)
      | X26682 = c_Groups_Oone__class_Oone(X26683)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26683),hAPP(c_Power_Opower__class_Opower(X26683),X26682)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26681)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X26683),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26683),hAPP(hAPP(c_Power_Opower__class_Opower(X26683),X26682),X26681)),c_Groups_Oone__class_Oone(X26683))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26683),X26682),c_Groups_Oone__class_Oone(X26683))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_geometric__sum])]) ).

fof(i_0_7837,plain,
    ! [X30409,X30410] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X30410)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30410),hAPP(c_Groups_Oabs__class_Oabs(X30410),hAPP(c_List_Omonoid__add__class_Olistsum(X30410),X30409))),hAPP(c_List_Omonoid__add__class_Olistsum(X30410),hAPP(hAPP(c_List_Omap(X30410,X30410),c_Groups_Oabs__class_Oabs(X30410)),X30409)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__abs])]) ).

fof(i_0_7838,plain,
    ! [X18282,X18283,X18284] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X18284)
      | ~ c_Orderings_Oorder__class_Omono(X18284,X18284,X18283)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18284),X18282),hAPP(X18283,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18284),X18282),c_Inductive_Ocomplete__lattice__class_Ogfp(X18284,X18283)))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18284),X18282),c_Inductive_Ocomplete__lattice__class_Ogfp(X18284,X18283))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coinduct])]) ).

cnf(i_0_7839,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_5680]) ).

fof(i_0_7840,plain,
    ! [X26089,X26090,X26091] : 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)),X26091)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26090),X26089)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26090),X26091)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26089),X26091)),
    inference(variable_rename,[status(thm)],[fact_image__add__atLeastLessThan]) ).

fof(i_0_7841,plain,
    ! [X26529,X26530,X26531,X26532,X26533] :
      ( ~ class_Groups_Ocomm__monoid__add(X26533)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26532),X26531))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26531),X26530))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26533),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26533),X26529),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26532),X26531))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26533),X26529),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26531),X26530))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26533),X26529),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26532),X26530)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__add__nat__ivl])]) ).

fof(i_0_7842,plain,
    ! [X26534,X26535,X26536,X26537,X26538] :
      ( ~ class_Groups_Oab__group__add(X26538)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26537),X26536))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26536),X26535))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26538),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26538),X26534),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26537),X26535))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26538),X26534),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26537),X26536))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26538),X26534),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26536),X26535)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat__ivl])]) ).

fof(i_0_7843,plain,
    ! [X22431,X22432,X22433,X22434] :
      ( ~ class_Rings_Olinordered__semiring(X22434)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22434),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22434),X22433),X22432)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22434),X22431),X22432)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22434),c_Groups_Ozero__class_Ozero(X22434)),X22432))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22434),X22433),X22431)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less])]) ).

fof(i_0_7844,plain,
    ! [X22435,X22436,X22437,X22438] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22438)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22438),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22438),X22437),X22436)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22438),X22435),X22436)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22438),c_Groups_Ozero__class_Ozero(X22438)),X22436))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22438),X22437),X22435)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right])]) ).

fof(i_0_7845,plain,
    ! [X22711,X22712,X22713,X22714] :
      ( ~ class_Rings_Olinordered__semidom(X22714)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22714),hAPP(hAPP(c_Power_Opower__class_Opower(X22714),X22713),X22712)),hAPP(hAPP(c_Power_Opower__class_Opower(X22714),X22711),X22712)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22714),c_Groups_Ozero__class_Ozero(X22714)),X22711))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22714),X22713),X22711)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base])]) ).

fof(i_0_7846,plain,
    ! [X22439,X22440,X22441,X22442] :
      ( ~ class_Rings_Olinordered__semiring(X22442)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22442),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22442),X22441),X22440)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22442),X22441),X22439)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22442),c_Groups_Ozero__class_Ozero(X22442)),X22441))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22442),X22440),X22439)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less])]) ).

fof(i_0_7847,plain,
    ! [X22443,X22444,X22445,X22446] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22446)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22446),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22446),X22445),X22444)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22446),X22445),X22443)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22446),c_Groups_Ozero__class_Ozero(X22446)),X22445))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22446),X22444),X22443)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left])]) ).

fof(i_0_7848,plain,
    ! [X22258,X22259,X22260,X22261] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22261),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22261),X22260),X22259)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22261),X22260),X22258)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22261),X22259),X22258))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22261),c_Groups_Ozero__class_Ozero(X22261)),X22260))
        | ~ class_Rings_Olinordered__ring__strict(X22261) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22261),X22259),X22258))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22261),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22261),X22260),X22259)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22261),X22260),X22258)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22261),c_Groups_Ozero__class_Ozero(X22261)),X22260))
        | ~ class_Rings_Olinordered__ring__strict(X22261) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos])])]) ).

fof(i_0_7849,plain,
    ! [X22447,X22448,X22449,X22450] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22450)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22450),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22450),X22449),X22448)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22450),X22447),X22448)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22450),c_Groups_Ozero__class_Ozero(X22450)),X22448))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22450),X22449),X22447)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le])]) ).

fof(i_0_7850,plain,
    ! [X22451,X22452,X22453,X22454] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22454)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22454),X22453),X22452)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22454),X22453),X22451)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22454),c_Groups_Ozero__class_Ozero(X22454)),X22453))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22454),X22452),X22451)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le])]) ).

fof(i_0_7851,plain,
    ! [X22403,X22404,X22405,X22406] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22406),X22405),X22404)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22406),X22405),X22403)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22406),X22404),X22403))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22406),c_Groups_Ozero__class_Ozero(X22406)),X22405))
        | ~ class_Rings_Olinordered__ring__strict(X22406) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22406),X22404),X22403))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22406),X22405),X22404)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22406),X22405),X22403)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22406),c_Groups_Ozero__class_Ozero(X22406)),X22405))
        | ~ class_Rings_Olinordered__ring__strict(X22406) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos])])]) ).

cnf(i_0_7852,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_5681]) ).

fof(i_0_7853,plain,
    ! [X26741,X26742,X26743,X26744] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26744),X26743))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26744,tc_HOL_Obool)),X26743),X26742))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26744,tc_Nat_Onat),X26741),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26744,tc_HOL_Obool)),X26742),X26743)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26744,tc_Nat_Onat),X26741),X26742)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26744,tc_Nat_Onat),X26741),X26743)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat])]) ).

fof(i_0_7854,plain,
    ! [X25465,X25466,X25467,X25469] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25467),esk162_3(X25465,X25466,X25467)),X25466))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25467),hAPP(c_Finite__Set_Ofold1(X25467,c_Orderings_Oord__class_Omin(X25467)),X25466)),X25465))
        | X25466 = c_Orderings_Obot__class_Obot(tc_fun(X25467,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25467),X25466))
        | ~ class_Orderings_Olinorder(X25467) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25467),esk162_3(X25465,X25466,X25467)),X25465))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25467),hAPP(c_Finite__Set_Ofold1(X25467,c_Orderings_Oord__class_Omin(X25467)),X25466)),X25465))
        | X25466 = c_Orderings_Obot__class_Obot(tc_fun(X25467,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25467),X25466))
        | ~ class_Orderings_Olinorder(X25467) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X25467),X25469),X25466))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25467),X25469),X25465))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25467),hAPP(c_Finite__Set_Ofold1(X25467,c_Orderings_Oord__class_Omin(X25467)),X25466)),X25465))
        | X25466 = c_Orderings_Obot__class_Obot(tc_fun(X25467,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25467),X25466))
        | ~ class_Orderings_Olinorder(X25467) ) ),
    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_7855,plain,
    ! [X25455,X25456,X25457,X25459] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25457),esk160_3(X25455,X25456,X25457)),X25456))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25457),hAPP(c_Finite__Set_Ofold1(X25457,c_Orderings_Oord__class_Omin(X25457)),X25456)),X25455))
        | X25456 = c_Orderings_Obot__class_Obot(tc_fun(X25457,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25457),X25456))
        | ~ class_Orderings_Olinorder(X25457) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25457),esk160_3(X25455,X25456,X25457)),X25455))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25457),hAPP(c_Finite__Set_Ofold1(X25457,c_Orderings_Oord__class_Omin(X25457)),X25456)),X25455))
        | X25456 = c_Orderings_Obot__class_Obot(tc_fun(X25457,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25457),X25456))
        | ~ class_Orderings_Olinorder(X25457) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X25457),X25459),X25456))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25457),X25459),X25455))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25457),hAPP(c_Finite__Set_Ofold1(X25457,c_Orderings_Oord__class_Omin(X25457)),X25456)),X25455))
        | X25456 = c_Orderings_Obot__class_Obot(tc_fun(X25457,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25457),X25456))
        | ~ class_Orderings_Olinorder(X25457) ) ),
    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_7856,plain,
    ! [X29243,X29244,X29245,X29246,X29247,X29248] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29248,tc_fun(X29247,tc_HOL_Obool)),X29246),X29245),X29244))
      | ~ hBOOL(hAPP(hAPP(c_member(X29248),X29243),X29246))
      | hBOOL(hAPP(hAPP(X29245,X29243),X29244)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF1__D])]) ).

fof(i_0_7857,plain,
    ! [X29237,X29238,X29239,X29240,X29241,X29242] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29242,tc_fun(X29241,tc_HOL_Obool)),X29240),X29239),X29238))
      | hBOOL(hAPP(hAPP(X29239,X29237),X29238))
      | ~ hBOOL(hAPP(hAPP(c_member(X29242),X29237),X29240)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5682])]) ).

fof(i_0_7858,plain,
    ! [X22738,X22739,X22740,X22741] :
      ( ~ class_Rings_Olinordered__semidom(X22741)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),c_Groups_Oone__class_Oone(X22741)),X22740))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),hAPP(hAPP(c_Power_Opower__class_Opower(X22741),X22740),X22739)),hAPP(hAPP(c_Power_Opower__class_Opower(X22741),X22740),X22738)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22739),X22738)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp])]) ).

fof(i_0_7859,plain,
    ! [X22734,X22735,X22736,X22737] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),hAPP(hAPP(c_Power_Opower__class_Opower(X22737),X22736),X22735)),hAPP(hAPP(c_Power_Opower__class_Opower(X22737),X22736),X22734)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22735),X22734))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),c_Groups_Oone__class_Oone(X22737)),X22736))
        | ~ class_Rings_Olinordered__semidom(X22737) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22735),X22734))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),hAPP(hAPP(c_Power_Opower__class_Opower(X22737),X22736),X22735)),hAPP(hAPP(c_Power_Opower__class_Opower(X22737),X22736),X22734)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),c_Groups_Oone__class_Oone(X22737)),X22736))
        | ~ class_Rings_Olinordered__semidom(X22737) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff])])]) ).

fof(i_0_7860,plain,
    ! [X22633,X22634,X22635,X22636] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22636),hAPP(hAPP(c_Power_Opower__class_Opower(X22636),X22635),X22634)),hAPP(hAPP(c_Power_Opower__class_Opower(X22636),X22635),X22633)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22634),X22633))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22636),c_Groups_Oone__class_Oone(X22636)),X22635))
        | ~ class_Rings_Olinordered__semidom(X22636) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22634),X22633))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22636),hAPP(hAPP(c_Power_Opower__class_Opower(X22636),X22635),X22634)),hAPP(hAPP(c_Power_Opower__class_Opower(X22636),X22635),X22633)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22636),c_Groups_Oone__class_Oone(X22636)),X22635))
        | ~ class_Rings_Olinordered__semidom(X22636) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing__iff])])]) ).

fof(i_0_7861,plain,
    ! [X22629,X22630,X22631,X22632] :
      ( ~ class_Rings_Olinordered__semidom(X22632)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22632),c_Groups_Oone__class_Oone(X22632)),X22631))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22632),hAPP(hAPP(c_Power_Opower__class_Opower(X22632),X22631),X22630)),hAPP(hAPP(c_Power_Opower__class_Opower(X22632),X22631),X22629)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22630),X22629)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp])]) ).

fof(i_0_7862,plain,
    ! [X31455,X31456,X31457] :
      ( X31457 = c_List_Olist_ONil(X31456)
      | hBOOL(hAPP(hAPP(c_member(X31456),hAPP(c_Product__Type_Ofst(X31456,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X31456,X31457),X31455))),hAPP(c_List_Oset(X31456),X31457))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_select])]) ).

fof(i_0_7863,plain,
    ! [X27810,X27811,X27812,X27813] : hAPP(c_Finite__Set_Ocard(tc_prod(X27813,X27812)),hAPP(hAPP(c_Product__Type_OSigma(X27813,X27812),hAPP(hAPP(c_Set_Oinsert(X27813),X27811),c_Orderings_Obot__class_Obot(tc_fun(X27813,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(X27812,tc_HOL_Obool),X27813),X27810))) = hAPP(c_Finite__Set_Ocard(X27812),X27810),
    inference(variable_rename,[status(thm)],[fact_card__cartesian__product__singleton]) ).

fof(i_0_7864,plain,
    ! [X23829,X23830,X23831,X23832,X23833] :
      ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X23833,X23832,tc_HOL_Obool),X23831),hAPP(hAPP(c_Product__Type_OPair(X23833,X23832),X23830),X23829)))
      | hBOOL(hAPP(hAPP(X23831,X23830),X23829)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitD])]) ).

fof(i_0_7865,plain,
    ! [X23943,X23944,X23945] : c_Fun_Oinj__on(tc_prod(X23945,X23944),tc_prod(X23944,X23945),hAPP(c_Product__Type_Oprod_Oprod__case(X23945,X23944,tc_prod(X23944,X23945)),hAPP(c_COMBC(X23944,X23945,tc_prod(X23944,X23945)),c_Product__Type_OPair(X23944,X23945))),X23943),
    inference(variable_rename,[status(thm)],[fact_swap__inj__on]) ).

fof(i_0_7866,plain,
    ! [X28172,X28173,X28174] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28174),esk287_3(X28172,X28173,X28174)),X28173))
        | 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(X28174,tc_Nat_Onat),X28172),X28173)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28174),X28173)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X28172,esk287_3(X28172,X28173,X28174))))
        | 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(X28174,tc_Nat_Onat),X28172),X28173)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28174),X28173)) ) ),
    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_7867,plain,
    ! [X23090,X23091,X23092,X23093] :
      ( ( ~ 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(X23092,tc_Nat_Onat),X23090),X23091)))
        | ~ hBOOL(hAPP(hAPP(c_member(X23092),X23093),X23091))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X23090,X23093)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23092),X23091)) )
      & ( hBOOL(hAPP(hAPP(c_member(X23092),esk120_3(X23090,X23091,X23092)),X23091))
        | 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(X23092,tc_Nat_Onat),X23090),X23091)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23092),X23091)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X23090,esk120_3(X23090,X23091,X23092))))
        | 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(X23092,tc_Nat_Onat),X23090),X23091)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23092),X23091)) ) ),
    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_7868,plain,
    ! [X26514,X26515,X26516,X26517] :
      ( ~ class_Groups_Ocomm__monoid__add(X26517)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26517),X26516),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X26515),hAPP(c_Nat_OSuc,X26514))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26517),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X26517,tc_Nat_Onat),X26516),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26515,X26514)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__Suc__ivl])]) ).

fof(i_0_7869,plain,
    ! [X22239,X22240,X22241,X22242] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22242),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22242),X22241),X22240)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22242),X22241),X22239)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22242),X22239),X22240))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22242),X22241),c_Groups_Ozero__class_Ozero(X22242)))
        | ~ class_Rings_Olinordered__ring__strict(X22242) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22242),X22239),X22240))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22242),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22242),X22241),X22240)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22242),X22241),X22239)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22242),X22241),c_Groups_Ozero__class_Ozero(X22242)))
        | ~ class_Rings_Olinordered__ring__strict(X22242) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg])])]) ).

fof(i_0_7870,plain,
    ! [X22407,X22408,X22409,X22410] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22410),X22409),X22408)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22410),X22409),X22407)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22410),X22407),X22408))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22410),X22409),c_Groups_Ozero__class_Ozero(X22410)))
        | ~ class_Rings_Olinordered__ring__strict(X22410) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22410),X22407),X22408))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22410),X22409),X22408)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22410),X22409),X22407)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22410),X22409),c_Groups_Ozero__class_Ozero(X22410)))
        | ~ class_Rings_Olinordered__ring__strict(X22410) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg])])]) ).

fof(i_0_7871,plain,
    ! [X19156,X19157,X19158,X19159] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X19159,tc_Option_Ooption(X19158)),hAPP(c_COMBK(tc_Option_Ooption(X19158),X19159),c_Option_Ooption_ONone(X19158))),X19157),c_Option_Ooption_ONone(X19158)),X19156) = c_Option_Ooption_ONone(X19158),
    inference(variable_rename,[status(thm)],[fact_empty__upd__none]) ).

fof(i_0_7872,plain,
    ! [X18120,X18121,X18122] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18122,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18122,tc_HOL_Obool)),X18121),X18120)),X18121)),
    inference(variable_rename,[status(thm)],[fact_Int__lower1]) ).

fof(i_0_7873,plain,
    ! [X18117,X18118,X18119] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18119,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18119,tc_HOL_Obool)),X18118),X18117)),X18117)),
    inference(variable_rename,[status(thm)],[fact_Int__lower2]) ).

fof(i_0_7874,plain,
    ! [X18085,X18086,X18087] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18087,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18087,tc_HOL_Obool)),X18086),X18085)),X18086)),
    inference(variable_rename,[status(thm)],[fact_Diff__subset]) ).

fof(i_0_7875,plain,
    ! [X32543,X32544,X32545,X32546,X32547] :
      ( ~ class_Groups_Ocomm__monoid__add(X32547)
      | ~ hBOOL(hAPP(hAPP(c_member(X32546),X32545),hAPP(c_List_Oset(X32546),X32544)))
      | hAPP(c_List_Omonoid__add__class_Olistsum(X32547),hAPP(hAPP(c_List_Omap(X32546,X32547),X32543),X32544)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X32547),hAPP(X32543,X32545)),hAPP(c_List_Omonoid__add__class_Olistsum(X32547),hAPP(hAPP(c_List_Omap(X32546,X32547),X32543),c_List_Oremove1(X32546,X32545,X32544)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__map__remove1])]) ).

fof(i_0_7876,plain,
    ! [X17905,X17906,X17907,X17908] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17908,tc_HOL_Obool)),X17907),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17908,tc_HOL_Obool)),X17906),X17905)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17908,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17908,tc_HOL_Obool)),X17907),X17906)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17908,tc_HOL_Obool)),X17907),X17905)),
    inference(variable_rename,[status(thm)],[fact_Diff__Int__distrib]) ).

fof(i_0_7877,plain,
    ! [X18139,X18140,X18141,X18142] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18142,tc_HOL_Obool)),X18141),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18142,tc_HOL_Obool)),X18140),X18139)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18142,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18142,tc_HOL_Obool)),X18141),X18140)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18142,tc_HOL_Obool)),X18141),X18139)),
    inference(variable_rename,[status(thm)],[fact_Int__Un__distrib]) ).

fof(i_0_7878,plain,
    ! [X17944,X17945,X17946,X17947] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17947,tc_HOL_Obool)),X17946),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17947,tc_HOL_Obool)),X17945),X17944)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17947,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17947,tc_HOL_Obool)),X17946),X17945)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17947,tc_HOL_Obool)),X17946),X17944)),
    inference(variable_rename,[status(thm)],[fact_Diff__Int]) ).

fof(i_0_7879,plain,
    ! [X17940,X17941,X17942,X17943] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17943,tc_HOL_Obool)),X17942),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17943,tc_HOL_Obool)),X17941),X17940)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17943,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17943,tc_HOL_Obool)),X17942),X17941)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17943,tc_HOL_Obool)),X17942),X17940)),
    inference(variable_rename,[status(thm)],[fact_Diff__Un]) ).

fof(i_0_7880,plain,
    ! [X18135,X18136,X18137,X18138] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18138,tc_HOL_Obool)),X18137),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18138,tc_HOL_Obool)),X18136),X18135)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18138,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18138,tc_HOL_Obool)),X18137),X18136)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18138,tc_HOL_Obool)),X18137),X18135)),
    inference(variable_rename,[status(thm)],[fact_Un__Int__distrib]) ).

fof(i_0_7881,plain,
    ! [X30040,X30041,X30042] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X30042)),hAPP(c_Set_Oimage(X30041,tc_Option_Ooption(X30042),hAPP(c_Map_Omap__of(X30041,X30042),X30040)),c_Orderings_Otop__class_Otop(tc_fun(X30041,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_finite__range__map__of]) ).

fof(i_0_7882,plain,
    ! [X23993,X23994,X23995,X23996,X23997,X23998] : c_Product__Type_Oprod_Oprod__rec(X23998,X23997,X23996,X23995,hAPP(hAPP(c_Product__Type_OPair(X23998,X23997),X23994),X23993)) = hAPP(hAPP(X23995,X23994),X23993),
    inference(variable_rename,[status(thm)],[fact_prod_Orecs]) ).

fof(i_0_7883,plain,
    ! [X26505,X26506,X26507,X26508] :
      ( ~ class_Groups_Ocomm__monoid__add(X26508)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26508),X26507),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X26506)),hAPP(c_Nat_OSuc,X26505))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26508),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X26508,tc_Nat_Onat),X26507),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26506),X26505)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__Suc__ivl])]) ).

fof(i_0_7884,plain,
    ! [X26098,X26099,X26100] : 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)),X26100)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26099,X26098)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26099),X26100),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26098),X26100)),
    inference(variable_rename,[status(thm)],[fact_image__add__atLeastAtMost]) ).

cnf(i_0_7885,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_5683]) ).

fof(i_0_7886,plain,
    ! [X18268,X18269,X18270,X18271] :
      ( ( hBOOL(hAPP(hAPP(c_member(X18271),X18270),X18269))
        | ~ hBOOL(hAPP(hAPP(c_member(X18271),X18270),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18271,tc_HOL_Obool)),X18269),hAPP(c_Set_OCollect(X18271),X18268)))) )
      & ( hBOOL(hAPP(X18268,X18270))
        | ~ hBOOL(hAPP(hAPP(c_member(X18271),X18270),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18271,tc_HOL_Obool)),X18269),hAPP(c_Set_OCollect(X18271),X18268)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18271),X18270),X18269))
        | ~ hBOOL(hAPP(X18268,X18270))
        | hBOOL(hAPP(hAPP(c_member(X18271),X18270),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18271,tc_HOL_Obool)),X18269),hAPP(c_Set_OCollect(X18271),X18268)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__Collect])])]) ).

fof(i_0_7887,plain,
    ! [X32301,X32302,X32303,X32304] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X32304),X32303),hAPP(c_List_Oset(X32304),X32302)))
      | hBOOL(hAPP(X32301,X32303))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32304)),hAPP(c_List_Ofilter(X32304,X32301),X32302))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32304)),X32302))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5684])]) ).

fof(i_0_7888,plain,
    ! [X26172,X26173,X26174,X26175,X26176] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26176),X26173),X26175))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26176),X26174),X26175))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26176,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26176,X26175),X26174)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26176,X26173),X26172)))
        | ~ class_Orderings_Olinorder(X26176) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26176),X26174),X26172))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26176),X26174),X26175))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26176,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26176,X26175),X26174)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26176,X26173),X26172)))
        | ~ class_Orderings_Olinorder(X26176) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__subset__iff])])]) ).

fof(i_0_7889,plain,
    ! [X21028,X21029,X21030,X21031,X21032,X21033] :
      ( ~ c_Finite__Set_Ofolding__idem(X21033,X21032,X21031,X21030)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21033),X21029))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21033),X21028))
      | hAPP(X21030,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21033,tc_HOL_Obool)),X21029),X21028)) = hAPP(c_Fun_Ocomp(X21032,X21032,X21032,hAPP(X21030,X21029)),hAPP(X21030,X21028)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Ounion__idem])]) ).

cnf(i_0_7890,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_5685]) ).

cnf(i_0_7891,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_5686]) ).

cnf(i_0_7892,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_5687]) ).

fof(i_0_7893,plain,
    ! [X27587,X27588,X27589] :
      ( ~ c_Wellfounded_Owf(X27589,X27588)
      | ~ c_Wellfounded_Owf(X27589,X27587)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27589,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X27589,X27589),X27588)),hAPP(c_Relation_ORange(X27589,X27589),X27587)) != c_Orderings_Obot__class_Obot(tc_fun(X27589,tc_HOL_Obool))
      | c_Wellfounded_Owf(X27589,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27589,X27589),tc_HOL_Obool)),X27588),X27587)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Un])]) ).

fof(i_0_7894,plain,
    ! [X32527,X32528,X32529,X32530,X32531] :
      ( ~ c_Finite__Set_Ofun__left__comm(X32531,X32530,X32529)
      | hAPP(hAPP(c_Finite__Set_Ofold(X32531,X32530,X32529),X32528),hAPP(c_List_Oset(X32531),X32527)) = hAPP(c_List_Ofoldl(X32530,X32531,hAPP(c_COMBC(X32531,X32530,X32530),X32529),X32528),c_List_Oremdups(X32531,X32527)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__set__remdups])]) ).

fof(i_0_7895,plain,
    ! [X33928,X33929,X33930,X33931] : c_Predicate_Oconversep(X33931,X33930,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33931,tc_fun(X33930,tc_HOL_Obool))),X33929),X33928)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33930,tc_fun(X33931,tc_HOL_Obool))),c_Predicate_Oconversep(X33931,X33930,X33929)),c_Predicate_Oconversep(X33931,X33930,X33928)),
    inference(variable_rename,[status(thm)],[fact_converse__meet]) ).

fof(i_0_7896,plain,
    ! [X33924,X33925,X33926,X33927] : c_Predicate_Oconversep(X33927,X33926,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X33927,tc_fun(X33926,tc_HOL_Obool))),X33925),X33924)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X33926,tc_fun(X33927,tc_HOL_Obool))),c_Predicate_Oconversep(X33927,X33926,X33925)),c_Predicate_Oconversep(X33927,X33926,X33924)),
    inference(variable_rename,[status(thm)],[fact_converse__join]) ).

fof(i_0_7897,plain,
    ! [X21025,X21026,X21027] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21026),X21027)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21025),X21027)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21026),X21025))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21027),X21025))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21027),X21026)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21026),X21025))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21026),X21027)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21025),X21027)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21027),X21025))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21027),X21026)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__iff])])]) ).

fof(i_0_7898,plain,
    ! [X21000,X21001,X21002] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21001),X21002)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21000),X21002)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21001),X21000))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21002),X21000))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21002),X21001)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21001),X21000))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21001),X21002)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21000),X21002)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21002),X21000))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21002),X21001)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__iff])])]) ).

cnf(i_0_7899,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_5688]) ).

fof(i_0_7900,plain,
    ! [X22262,X22263,X22264,X22265] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22265),X22264),c_Groups_Ozero__class_Ozero(X22265)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22265),c_Groups_Ozero__class_Ozero(X22265)),X22264))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22265),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22265),X22264),X22263)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22265),X22264),X22262)))
        | ~ class_Rings_Olinordered__ring__strict(X22265) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22265),X22262),X22263))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22265),c_Groups_Ozero__class_Ozero(X22265)),X22264))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22265),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22265),X22264),X22263)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22265),X22264),X22262)))
        | ~ class_Rings_Olinordered__ring__strict(X22265) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22265),X22264),c_Groups_Ozero__class_Ozero(X22265)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22265),X22263),X22262))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22265),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22265),X22264),X22263)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22265),X22264),X22262)))
        | ~ class_Rings_Olinordered__ring__strict(X22265) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22265),X22262),X22263))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22265),X22263),X22262))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22265),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22265),X22264),X22263)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22265),X22264),X22262)))
        | ~ class_Rings_Olinordered__ring__strict(X22265) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22265),c_Groups_Ozero__class_Ozero(X22265)),X22264))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22265),X22263),X22262))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22265),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22265),X22264),X22263)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22265),X22264),X22262)))
        | ~ class_Rings_Olinordered__ring__strict(X22265) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22265),X22264),c_Groups_Ozero__class_Ozero(X22265)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22265),X22262),X22263))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22265),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22265),X22264),X22263)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22265),X22264),X22262)))
        | ~ class_Rings_Olinordered__ring__strict(X22265) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj])])]) ).

fof(i_0_7901,plain,
    ! [X22266,X22267,X22268,X22269] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22269),X22267),c_Groups_Ozero__class_Ozero(X22269)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22269),c_Groups_Ozero__class_Ozero(X22269)),X22267))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22269),X22268),X22267)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22269),X22266),X22267)))
        | ~ class_Rings_Olinordered__ring__strict(X22269) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22269),X22266),X22268))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22269),c_Groups_Ozero__class_Ozero(X22269)),X22267))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22269),X22268),X22267)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22269),X22266),X22267)))
        | ~ class_Rings_Olinordered__ring__strict(X22269) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22269),X22267),c_Groups_Ozero__class_Ozero(X22269)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22269),X22268),X22266))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22269),X22268),X22267)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22269),X22266),X22267)))
        | ~ class_Rings_Olinordered__ring__strict(X22269) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22269),X22266),X22268))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22269),X22268),X22266))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22269),X22268),X22267)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22269),X22266),X22267)))
        | ~ class_Rings_Olinordered__ring__strict(X22269) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22269),c_Groups_Ozero__class_Ozero(X22269)),X22267))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22269),X22268),X22266))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22269),X22268),X22267)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22269),X22266),X22267)))
        | ~ class_Rings_Olinordered__ring__strict(X22269) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22269),X22267),c_Groups_Ozero__class_Ozero(X22269)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22269),X22266),X22268))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22269),X22268),X22267)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22269),X22266),X22267)))
        | ~ class_Rings_Olinordered__ring__strict(X22269) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj])])]) ).

fof(i_0_7902,plain,
    ! [X17613,X17614,X17615,X17616] :
      ( ( hBOOL(hAPP(hAPP(c_member(X17616),X17615),X17613))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17616,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17616),X17615),X17614)),X17613)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17616,tc_HOL_Obool)),X17614),X17613))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17616,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17616),X17615),X17614)),X17613)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17616),X17615),X17613))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17616,tc_HOL_Obool)),X17614),X17613))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17616,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17616),X17615),X17614)),X17613)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__subset])])]) ).

fof(i_0_7903,plain,
    ! [X26756,X26757,X26758] :
      ( ~ class_Groups_Ocomm__monoid__add(X26758)
      | ~ class_Groups_Ocomm__monoid__mult(X26758)
      | ~ c_Nat__Transfer_Onat__set(X26757)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X26758),X26756),X26757) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26758),hAPP(hAPP(c_COMBB(tc_Int_Oint,X26758,tc_Nat_Onat),X26756),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X26757)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I1_J])]) ).

fof(i_0_7904,plain,
    ! [X25527,X25528,X25529] :
      ( ~ class_Groups_Ocomm__monoid__add(X25529)
      | ~ class_Groups_Ocomm__monoid__mult(X25529)
      | ~ c_Nat__Transfer_Onat__set(X25528)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X25529),X25527),X25528) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X25529),hAPP(hAPP(c_COMBB(tc_Int_Oint,X25529,tc_Nat_Onat),X25527),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25528)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I2_J])]) ).

fof(i_0_7905,plain,
    ! [X26628,X26629,X26630,X26631,X26632] :
      ( ~ class_Groups_Ocomm__monoid__add(X26632)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26631),X26630))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26631),X26629))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26631,tc_HOL_Obool)),X26630),X26629) != c_Orderings_Obot__class_Obot(tc_fun(X26631,tc_HOL_Obool))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26631,X26632),X26628),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26631,tc_HOL_Obool)),X26630),X26629)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26632),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26631,X26632),X26628),X26630)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26631,X26632),X26628),X26629)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un__disjoint])]) ).

fof(i_0_7906,plain,
    ! [X23218,X23219,X23220,X23221,X23222] :
      ( ~ class_Groups_Ocomm__monoid__mult(X23222)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23221),X23220))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23221),X23219))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23221,tc_HOL_Obool)),X23220),X23219) != c_Orderings_Obot__class_Obot(tc_fun(X23221,tc_HOL_Obool))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23221,X23222),X23218),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23221,tc_HOL_Obool)),X23220),X23219)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23222),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23221,X23222),X23218),X23220)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23221,X23222),X23218),X23219)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Un__disjoint])]) ).

fof(i_0_7907,plain,
    ! [X23213,X23214,X23215,X23216,X23217] :
      ( ~ class_Groups_Ocomm__monoid__mult(X23217)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23216),X23215))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23216),X23214))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23216,tc_HOL_Obool)),X23215),X23214) != c_Orderings_Obot__class_Obot(tc_fun(X23216,tc_HOL_Obool))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23216,X23217),X23213),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23216,tc_HOL_Obool)),X23215),X23214)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23217),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23216,X23217),X23213),X23215)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23216,X23217),X23213),X23214)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__disjoint])]) ).

fof(i_0_7908,plain,
    ! [X26745,X26746,X26747] :
      ( ~ class_Groups_Ocomm__monoid__add(X26747)
      | ~ class_Groups_Ocomm__monoid__mult(X26747)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26747),X26746),X26745) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X26747),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X26747,tc_Int_Oint),X26746),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X26745)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I1_J])]) ).

fof(i_0_7909,plain,
    ! [X25109,X25110,X25111] :
      ( ~ class_Groups_Ocomm__monoid__add(X25111)
      | ~ class_Groups_Ocomm__monoid__mult(X25111)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X25111),X25110),X25109) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X25111),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X25111,tc_Int_Oint),X25110),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25109)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I2_J])]) ).

cnf(i_0_7910,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_5689]) ).

fof(i_0_7911,plain,
    ! [X30668,X30669] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X30669),tc_List_Olist(X30669)),tc_HOL_Obool)),c_List_Olistrel(X30669,X30668)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X30669),c_List_Olistrel1(X30669,X30668)))),
    inference(variable_rename,[status(thm)],[fact_listrel__subset__rtrancl__listrel1]) ).

fof(i_0_7912,plain,
    ! [X22967,X22968,X22969,X22970] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22969))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22969))
        | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22970,X22969),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22968),X22967)))
        | X22970 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22969),X22968)),X22967) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22969),X22967))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22967),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)),X22969))
        | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22970,X22969),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22968),X22967)))
        | X22970 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22969),X22968)),X22967) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22969))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22967))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22967),X22969))
        | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22970,X22969),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22968),X22967)))
        | X22970 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22969),X22968)),X22967) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22969),X22967))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22967),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)),X22967))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22967),X22969))
        | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22970,X22969),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22968),X22967)))
        | X22970 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22969),X22968)),X22967) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5690])])]) ).

fof(i_0_7913,plain,
    ! [X26254,X26255] : 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)),X26255)),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),X26254),X26255))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X26255),X26254),
    inference(variable_rename,[status(thm)],[fact_image__add__int__atLeastLessThan]) ).

fof(i_0_7914,plain,
    ! [X31827,X31828,X31829,X31830] : hAPP(hAPP(c_List_Odrop(X31830),X31829),hAPP(hAPP(c_List_Oappend(X31830),X31828),X31827)) = hAPP(hAPP(c_List_Oappend(X31830),hAPP(hAPP(c_List_Odrop(X31830),X31829),X31828)),hAPP(hAPP(c_List_Odrop(X31830),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31829),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31830)),X31828))),X31827)),
    inference(variable_rename,[status(thm)],[fact_drop__append]) ).

fof(i_0_7915,plain,
    ! [X31661,X31662,X31663,X31664] : hAPP(hAPP(c_List_Otake(X31664),X31663),hAPP(hAPP(c_List_Oappend(X31664),X31662),X31661)) = hAPP(hAPP(c_List_Oappend(X31664),hAPP(hAPP(c_List_Otake(X31664),X31663),X31662)),hAPP(hAPP(c_List_Otake(X31664),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31663),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31664)),X31662))),X31661)),
    inference(variable_rename,[status(thm)],[fact_take__append]) ).

fof(i_0_7916,plain,
    ! [X32578,X32579,X32580] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32580,tc_HOL_Obool)),hAPP(c_List_Oset(X32580),c_List_Oremove1(X32580,X32579,X32578))),hAPP(c_List_Oset(X32580),X32578))),
    inference(variable_rename,[status(thm)],[fact_set__remove1__subset]) ).

fof(i_0_7917,plain,
    ! [X30571,X30572,X30573] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30573,tc_HOL_Obool)),hAPP(c_List_Oset(X30573),c_List_Osublist(X30573,X30572,X30571))),hAPP(c_List_Oset(X30573),X30572))),
    inference(variable_rename,[status(thm)],[fact_set__sublist__subset]) ).

fof(i_0_7918,plain,
    ! [X18736,X18737,X18738,X18739] :
      ( ~ c_Fun_Oinj__on(X18739,X18738,X18737,X18736)
      | c_Fun_Oinj__on(X18738,X18739,c_Fun_Othe__inv__into(X18739,X18738,X18736,X18737),hAPP(c_Set_Oimage(X18739,X18738,X18737),X18736)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__the__inv__into])]) ).

fof(i_0_7919,plain,
    ! [X27641,X27642,X27643] : hAPP(c_Relation_ODomain(X27643,X27642),hAPP(c_Set_OCollect(tc_prod(X27643,X27642)),hAPP(c_Product__Type_Oprod_Oprod__case(X27643,X27642,tc_HOL_Obool),X27641))) = hAPP(c_Set_OCollect(X27643),hAPP(hAPP(c_COMBB(tc_fun(X27642,tc_HOL_Obool),tc_HOL_Obool,X27643),c_HOL_OEx(X27642)),X27641)),
    inference(variable_rename,[status(thm)],[fact_Domain__Collect__split]) ).

cnf(i_0_7920,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_5691]) ).

fof(i_0_7921,plain,
    ! [X32047,X32048,X32049,X32050,X32051] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X32051,X32050,X32049)
      | hAPP(hAPP(c_Finite__Set_Ofold(X32051,X32050,X32049),X32048),hAPP(c_List_Oset(X32051),X32047)) = hAPP(c_List_Ofoldl(X32050,X32051,hAPP(c_COMBC(X32051,X32050,X32050),X32049),X32048),X32047) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__set])]) ).

fof(i_0_7922,plain,
    ! [X26748,X26749,X26750,X26751] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26751),X26750),X26749))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26751,tc_Nat_Onat),X26748),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26751,tc_HOL_Obool)),X26749),hAPP(hAPP(c_Set_Oinsert(X26751),X26750),c_Orderings_Obot__class_Obot(tc_fun(X26751,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26751,tc_Nat_Onat),X26748),X26749)),hAPP(X26748,X26750)) )
      & ( hBOOL(hAPP(hAPP(c_member(X26751),X26750),X26749))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26751,tc_Nat_Onat),X26748),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26751,tc_HOL_Obool)),X26749),hAPP(hAPP(c_Set_Oinsert(X26751),X26750),c_Orderings_Obot__class_Obot(tc_fun(X26751,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26751,tc_Nat_Onat),X26748),X26749) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5692])]) ).

fof(i_0_7923,plain,
    ! [X26440,X26441,X26442,X26443] :
      ( ~ class_Groups_Oab__group__add(X26443)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26442,X26443),hAPP(hAPP(c_COMBB(X26443,X26443,X26442),c_Groups_Ouminus__class_Ouminus(X26443)),X26441)),X26440) = hAPP(c_Groups_Ouminus__class_Ouminus(X26443),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26442,X26443),X26441),X26440)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__negf])]) ).

fof(i_0_7924,plain,
    ! [X27031,X27032,X27033,X27034] :
      ( ~ class_Fields_Olinordered__field(X27034)
      | hAPP(c_Groups_Oabs__class_Oabs(X27034),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27033,X27034),X27032),X27031)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27033,X27034),hAPP(hAPP(c_COMBB(X27034,X27034,X27033),c_Groups_Oabs__class_Oabs(X27034)),X27032)),X27031) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__setprod])]) ).

fof(i_0_7925,plain,
    ! [X30959,X30960,X30961,X30963,X30964,X30965,X30966,X30968] :
      ( ( hBOOL(hAPP(hAPP(c_member(X30961),esk411_3(X30959,X30960,X30961)),hAPP(c_List_Oset(X30961),X30960)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30963),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30961)),X30960)))
        | hBOOL(hAPP(X30959,hAPP(hAPP(c_List_Onth(X30961),X30960),X30963))) )
      & ( ~ hBOOL(hAPP(X30959,esk411_3(X30959,X30960,X30961)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30963),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30961)),X30960)))
        | hBOOL(hAPP(X30959,hAPP(hAPP(c_List_Onth(X30961),X30960),X30963))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk412_3(X30964,X30965,X30966)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30966)),X30965)))
        | ~ hBOOL(hAPP(hAPP(c_member(X30966),X30968),hAPP(c_List_Oset(X30966),X30965)))
        | hBOOL(hAPP(X30964,X30968)) )
      & ( ~ hBOOL(hAPP(X30964,hAPP(hAPP(c_List_Onth(X30966),X30965),esk412_3(X30964,X30965,X30966))))
        | ~ hBOOL(hAPP(hAPP(c_member(X30966),X30968),hAPP(c_List_Oset(X30966),X30965)))
        | hBOOL(hAPP(X30964,X30968)) ) ),
    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_7926,plain,
    ! [X17031,X17032,X17033,X17034] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17034,tc_HOL_Obool)),X17033),X17032))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17034,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17034),X17031),X17033)),hAPP(hAPP(c_Set_Oinsert(X17034),X17031),X17032))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__mono])]) ).

cnf(i_0_7927,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_5645]) ).

cnf(i_0_7928,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_5646]) ).

cnf(i_0_7929,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_5693]) ).

fof(i_0_7930,plain,
    ! [X33758,X33759,X33760,X33761,X33762,X33763] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X33763,X33762,X33761,X33760,c_Lazy__Sequence_Olazy__sequence_OInsert(X33762,X33759,X33758)) = hAPP(hAPP(X33760,X33759),X33758),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I5_J]) ).

fof(i_0_7931,plain,
    ! [X32805,X32806,X32807,X32808,X32809] :
      ( ( c_List_Olinorder__class_Osorted(X32807,X32806)
        | ~ c_List_Olinorder__class_Osorted(X32807,hAPP(hAPP(c_List_Oappend(X32807),X32806),X32805))
        | ~ class_Orderings_Olinorder(X32807) )
      & ( c_List_Olinorder__class_Osorted(X32807,X32805)
        | ~ c_List_Olinorder__class_Osorted(X32807,hAPP(hAPP(c_List_Oappend(X32807),X32806),X32805))
        | ~ class_Orderings_Olinorder(X32807) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32807),X32808),hAPP(c_List_Oset(X32807),X32806)))
        | ~ hBOOL(hAPP(hAPP(c_member(X32807),X32809),hAPP(c_List_Oset(X32807),X32805)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32807),X32808),X32809))
        | ~ c_List_Olinorder__class_Osorted(X32807,hAPP(hAPP(c_List_Oappend(X32807),X32806),X32805))
        | ~ class_Orderings_Olinorder(X32807) )
      & ( hBOOL(hAPP(hAPP(c_member(X32807),esk455_3(X32805,X32806,X32807)),hAPP(c_List_Oset(X32807),X32806)))
        | ~ c_List_Olinorder__class_Osorted(X32807,X32806)
        | ~ c_List_Olinorder__class_Osorted(X32807,X32805)
        | c_List_Olinorder__class_Osorted(X32807,hAPP(hAPP(c_List_Oappend(X32807),X32806),X32805))
        | ~ class_Orderings_Olinorder(X32807) )
      & ( hBOOL(hAPP(hAPP(c_member(X32807),esk456_3(X32805,X32806,X32807)),hAPP(c_List_Oset(X32807),X32805)))
        | ~ c_List_Olinorder__class_Osorted(X32807,X32806)
        | ~ c_List_Olinorder__class_Osorted(X32807,X32805)
        | c_List_Olinorder__class_Osorted(X32807,hAPP(hAPP(c_List_Oappend(X32807),X32806),X32805))
        | ~ class_Orderings_Olinorder(X32807) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32807),esk455_3(X32805,X32806,X32807)),esk456_3(X32805,X32806,X32807)))
        | ~ c_List_Olinorder__class_Osorted(X32807,X32806)
        | ~ c_List_Olinorder__class_Osorted(X32807,X32805)
        | c_List_Olinorder__class_Osorted(X32807,hAPP(hAPP(c_List_Oappend(X32807),X32806),X32805))
        | ~ class_Orderings_Olinorder(X32807) ) ),
    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_7932,plain,
    ! [X22726,X22727,X22728] :
      ( ~ class_Rings_Olinordered__semidom(X22728)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22728),c_Groups_Oone__class_Oone(X22728)),X22727))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22728),hAPP(hAPP(c_Power_Opower__class_Opower(X22728),X22727),X22726)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22728),X22727),hAPP(hAPP(c_Power_Opower__class_Opower(X22728),X22727),X22726)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__power__Suc])]) ).

fof(i_0_7933,plain,
    ! [X18076,X18077,X18078,X18079] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18079,tc_HOL_Obool)),X18078),X18077))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18079,tc_HOL_Obool)),X18077),X18076))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18079,tc_HOL_Obool)),X18077),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18079,tc_HOL_Obool)),X18076),X18078)) = X18078 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__diff])]) ).

fof(i_0_7934,plain,
    ! [X18279,X18280,X18281] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18281,tc_HOL_Obool)),X18280),X18279))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X18281,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X18281),X18280)),hAPP(c_Set_OPow(X18281),X18279))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pow__mono])]) ).

fof(i_0_7935,plain,
    ! [X19028,X19029,X19030,X19031,X19032,X19033] : hAPP(hAPP(c_Fun_Ocomp(X19033,X19032,X19031,hAPP(c_COMBK(X19032,X19033),X19030)),X19029),X19028) = X19030,
    inference(variable_rename,[status(thm)],[fact_K__record__comp]) ).

fof(i_0_7936,plain,
    ! [X31767,X31768,X31769] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31769,tc_HOL_Obool)),hAPP(c_List_Oset(X31769),hAPP(hAPP(c_List_Odrop(X31769),X31768),X31767))),hAPP(c_List_Oset(X31769),X31767))),
    inference(variable_rename,[status(thm)],[fact_set__drop__subset]) ).

fof(i_0_7937,plain,
    ! [X31086,X31087,X31088] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31088,tc_HOL_Obool)),hAPP(c_List_Oset(X31088),hAPP(hAPP(c_List_Otake(X31088),X31087),X31086))),hAPP(c_List_Oset(X31088),X31086))),
    inference(variable_rename,[status(thm)],[fact_set__take__subset]) ).

fof(i_0_7938,plain,
    ! [X24384,X24385,X24386,X24387] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24387),X24385),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24387),X24384),X24386)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24387),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24387),X24385),X24386)),X24384))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24387),c_Groups_Ozero__class_Ozero(X24387)),X24386))
        | ~ class_Fields_Olinordered__field(X24387) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24387),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24387),X24385),X24386)),X24384))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24387),X24385),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24387),X24384),X24386)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24387),c_Groups_Ozero__class_Ozero(X24387)),X24386))
        | ~ class_Fields_Olinordered__field(X24387) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq])])]) ).

fof(i_0_7939,plain,
    ! [X24388,X24389,X24390,X24391] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24391),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24391),X24389),X24390)),X24388))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24391),X24389),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24391),X24388),X24390)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24391),c_Groups_Ozero__class_Ozero(X24391)),X24390))
        | ~ class_Fields_Olinordered__field(X24391) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24391),X24389),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24391),X24388),X24390)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24391),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24391),X24389),X24390)),X24388))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24391),c_Groups_Ozero__class_Ozero(X24391)),X24390))
        | ~ class_Fields_Olinordered__field(X24391) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__divide__less__eq])])]) ).

fof(i_0_7940,plain,
    ! [X24396,X24397,X24398,X24399] :
      ( ~ class_Fields_Olinordered__field(X24399)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24399),c_Groups_Ozero__class_Ozero(X24399)),X24398))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24399),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24399),X24397),X24398)),X24396))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24399),X24397),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24399),X24396),X24398))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__less__div__pos])]) ).

fof(i_0_7941,plain,
    ! [X24464,X24465,X24466,X24467] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24467),X24465),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24467),X24464),X24466)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24467),X24465),X24466)),X24464))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24467),c_Groups_Ozero__class_Ozero(X24467)),X24466))
        | ~ class_Fields_Olinordered__field(X24467) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24467),X24465),X24466)),X24464))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24467),X24465),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24467),X24464),X24466)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24467),c_Groups_Ozero__class_Ozero(X24467)),X24466))
        | ~ class_Fields_Olinordered__field(X24467) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__le__divide__eq])])]) ).

fof(i_0_7942,plain,
    ! [X24468,X24469,X24470,X24471] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24471),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24471),X24469),X24470)),X24468))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24471),X24469),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24471),X24468),X24470)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24471),c_Groups_Ozero__class_Ozero(X24471)),X24470))
        | ~ class_Fields_Olinordered__field(X24471) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24471),X24469),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24471),X24468),X24470)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24471),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24471),X24469),X24470)),X24468))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24471),c_Groups_Ozero__class_Ozero(X24471)),X24470))
        | ~ class_Fields_Olinordered__field(X24471) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__divide__le__eq])])]) ).

fof(i_0_7943,plain,
    ! [X24273,X24274,X24275,X24276] :
      ( ~ class_Fields_Olinordered__field(X24276)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24276),c_Groups_Ozero__class_Ozero(X24276)),X24275))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24276),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24276),X24274),X24275)),X24273))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24276),X24274),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24276),X24273),X24275))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__le__div__pos])]) ).

fof(i_0_7944,plain,
    ! [X30052,X30053,X30054] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30054),X30053))
        | c_Smallcheck_Osmall_H(X30052,X30054,X30053) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30054),X30053))
        | c_Smallcheck_Osmall_H(X30052,X30054,X30053) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X30052,X30054,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X30053),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X30052,X30053)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5694])]) ).

fof(i_0_7945,plain,
    ! [X33026,X33027,X33028,X33029] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33029),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33028)),c_List_OtakeWhile(X33028,X33027,X33026))))
      | hAPP(hAPP(c_List_Onth(X33028),c_List_OtakeWhile(X33028,X33027,X33026)),X33029) = hAPP(hAPP(c_List_Onth(X33028),X33026),X33029) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__nth])]) ).

fof(i_0_7946,plain,
    ! [X25237,X25238,X25239,X25240] :
      ( ~ class_Groups_Ocomm__monoid__mult(X25240)
      | ~ class_Rings_Osemiring__1(X25240)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25240),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25239,tc_Nat_Onat),X25238),X25237)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25239,X25240),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X25240,X25239),c_Nat_Osemiring__1__class_Oof__nat(X25240)),X25238)),X25237) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__setprod])]) ).

fof(i_0_7947,plain,
    ! [X24996,X24997,X24998,X24999] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24999)
      | ~ class_Rings_Oring__1(X24999)
      | hAPP(c_Int_Oring__1__class_Oof__int(X24999),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24998,tc_Int_Oint),X24997),X24996)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24998,X24999),hAPP(hAPP(c_COMBB(tc_Int_Oint,X24999,X24998),c_Int_Oring__1__class_Oof__int(X24999)),X24997)),X24996) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__setprod])]) ).

cnf(i_0_7948,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_5624]) ).

cnf(i_0_7949,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_5695]) ).

cnf(i_0_7950,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_5696]) ).

fof(i_0_7951,plain,
    ! [X28751,X28752,X28753,X28754] : hAPP(c_Relation_Oconverse(X28754,X28753),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28754,X28753),tc_HOL_Obool)),X28752),X28751)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28753,X28754),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X28754,X28753),X28752)),hAPP(c_Relation_Oconverse(X28754,X28753),X28751)),
    inference(variable_rename,[status(thm)],[fact_converse__Int]) ).

fof(i_0_7952,plain,
    ! [X28734,X28735,X28736,X28737] : hAPP(c_Relation_Oconverse(X28737,X28736),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28737,X28736),tc_HOL_Obool)),X28735),X28734)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28736,X28737),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X28737,X28736),X28735)),hAPP(c_Relation_Oconverse(X28737,X28736),X28734)),
    inference(variable_rename,[status(thm)],[fact_converse__Un]) ).

fof(i_0_7953,plain,
    ! [X32998,X32999,X33000] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33000)),c_List_OtakeWhile(X33000,X32999,X32998))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33000)),X32998))),
    inference(variable_rename,[status(thm)],[fact_length__takeWhile__le]) ).

fof(i_0_7954,plain,
    ! [X28913,X28914,X28915,X28916] : hAPP(hAPP(c_Nat_Ocompow(X28916,X28916),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28915),X28914)),X28913) = hAPP(c_Fun_Ocomp(X28916,X28916,X28916,hAPP(hAPP(c_Nat_Ocompow(X28916,X28916),X28915),X28913)),hAPP(hAPP(c_Nat_Ocompow(X28916,X28916),X28914),X28913)),
    inference(variable_rename,[status(thm)],[fact_funpow__add]) ).

fof(i_0_7955,plain,
    ! [X26482,X26483,X26484,X26485] :
      ( ~ class_Rings_Osemiring__1(X26485)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26485),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26484,tc_Nat_Onat),X26483),X26482)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26484,X26485),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X26485,X26484),c_Nat_Osemiring__1__class_Oof__nat(X26485)),X26483)),X26482) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__setsum])]) ).

fof(i_0_7956,plain,
    ! [X26433,X26434,X26435,X26436] :
      ( ~ class_Rings_Oring__1(X26436)
      | hAPP(c_Int_Oring__1__class_Oof__int(X26436),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26435,tc_Int_Oint),X26434),X26433)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26435,X26436),hAPP(hAPP(c_COMBB(tc_Int_Oint,X26436,X26435),c_Int_Oring__1__class_Oof__int(X26436)),X26434)),X26433) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__setsum])]) ).

fof(i_0_7957,plain,
    ! [X19048] : c_Fun_Oinj__on(X19048,tc_fun(X19048,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X19048,tc_fun(X19048,tc_HOL_Obool),tc_fun(X19048,tc_HOL_Obool)),c_Set_Oinsert(X19048)),c_Orderings_Obot__class_Obot(tc_fun(X19048,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X19048,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_inj__singleton]) ).

fof(i_0_7958,plain,
    ! [X27735,X27736,X27737,X27738] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27738),X27737))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27736),X27735))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27738,X27736)),hAPP(hAPP(c_Product__Type_OSigma(X27738,X27736),X27737),hAPP(c_COMBK(tc_fun(X27736,tc_HOL_Obool),X27738),X27735)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__cartesian__product])]) ).

fof(i_0_7959,plain,
    ! [X21277,X21278,X21279] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21279),X21278))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21279,tc_HOL_Obool)),X21277),X21278))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21279),X21277)),hAPP(c_Finite__Set_Ocard(X21279),X21278)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X21279,tc_HOL_Obool)),X21277),X21278)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__psubset])]) ).

fof(i_0_7960,plain,
    ! [X20545,X20546,X20547,X20548,X20549] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20549),X20548))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20547,tc_HOL_Obool)),X20546),hAPP(c_Set_Oimage(X20549,X20547,X20545),X20548)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20547),X20546)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj])]) ).

cnf(i_0_7961,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_5697]) ).

fof(i_0_7962,plain,
    ! [X30920,X30921,X30922,X30923] :
      ( ( ~ c_Enum_Oall__n__lists(X30922,X30921,X30920)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30922)),X30923),hAPP(c_List_Oset(tc_List_Olist(X30922)),c_Enum_On__lists(X30922,X30920,c_Enum_Oenum__class_Oenum(X30922)))))
        | hBOOL(hAPP(X30921,X30923))
        | ~ class_Enum_Oenum(X30922) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30922)),esk409_3(X30920,X30921,X30922)),hAPP(c_List_Oset(tc_List_Olist(X30922)),c_Enum_On__lists(X30922,X30920,c_Enum_Oenum__class_Oenum(X30922)))))
        | c_Enum_Oall__n__lists(X30922,X30921,X30920)
        | ~ class_Enum_Oenum(X30922) )
      & ( ~ hBOOL(hAPP(X30921,esk409_3(X30920,X30921,X30922)))
        | c_Enum_Oall__n__lists(X30922,X30921,X30920)
        | ~ class_Enum_Oenum(X30922) ) ),
    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__n__lists__def])])])])]) ).

fof(i_0_7963,plain,
    ! [X18763,X18764,X18765,X18766,X18767] :
      ( ~ c_Fun_Oinj__on(X18767,X18766,X18765,X18764)
      | ~ c_Fun_Oinj__on(X18767,X18766,X18765,X18763)
      | c_Fun_Oinj__on(X18767,X18766,X18765,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18767,tc_HOL_Obool)),X18764),X18763)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Int])]) ).

fof(i_0_7964,plain,
    ! [X31843,X31844,X31845,X31846] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31846),X31845)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31844)),X31843)))
      | hAPP(hAPP(c_List_Onth(X31844),hAPP(hAPP(c_List_Odrop(X31844),X31846),X31843)),X31845) = hAPP(hAPP(c_List_Onth(X31844),X31843),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31846),X31845)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__drop])]) ).

fof(i_0_7965,plain,
    ! [X26642,X26643,X26644,X26645] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26644)),X26643))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26645),X26642),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26643,hAPP(c_Nat_OSuc,X26644))) = c_Groups_Ozero__class_Ozero(X26645)
        | ~ class_Groups_Ocomm__monoid__add(X26645) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26644)),X26643))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26645),X26642),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26643,hAPP(c_Nat_OSuc,X26644))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26645),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26645),X26642),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26643,X26644))),hAPP(X26642,hAPP(c_Nat_OSuc,X26644)))
        | ~ class_Groups_Ocomm__monoid__add(X26645) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5698])])]) ).

fof(i_0_7966,plain,
    ! [X32950,X32951,X32952,X32953] :
      ( ~ class_Orderings_Olinorder(X32953)
      | ~ c_List_Olinorder__class_Osorted(X32953,hAPP(c_List_Orev(X32953),X32952))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32951),X32950))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32950),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32953)),X32952)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32953),hAPP(hAPP(c_List_Onth(X32953),X32952),X32950)),hAPP(hAPP(c_List_Onth(X32953),X32952),X32951))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__rev__nth__mono])]) ).

fof(i_0_7967,plain,
    ! [X31582,X31583,X31584,X31585,X31586,X31587] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31587)),X31586) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31585)),X31584)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31587)),X31583) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31585)),X31582)
      | hAPP(hAPP(c_List_Ozip(X31587,X31585),hAPP(hAPP(c_List_Oappend(X31587),X31586),X31583)),hAPP(hAPP(c_List_Oappend(X31585),X31584),X31582)) = hAPP(hAPP(c_List_Oappend(tc_prod(X31587,X31585)),hAPP(hAPP(c_List_Ozip(X31587,X31585),X31586),X31584)),hAPP(hAPP(c_List_Ozip(X31587,X31585),X31583),X31582)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__append])]) ).

fof(i_0_7968,plain,
    ! [X30909,X30910,X30911,X30913] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30911)),esk408_3(X30909,X30910,X30911)),hAPP(c_List_Oset(tc_List_Olist(X30911)),c_Enum_On__lists(X30911,X30909,c_Enum_Oenum__class_Oenum(X30911)))))
        | ~ c_Enum_Oex__n__lists(X30911,X30910,X30909)
        | ~ class_Enum_Oenum(X30911) )
      & ( hBOOL(hAPP(X30910,esk408_3(X30909,X30910,X30911)))
        | ~ c_Enum_Oex__n__lists(X30911,X30910,X30909)
        | ~ class_Enum_Oenum(X30911) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30911)),X30913),hAPP(c_List_Oset(tc_List_Olist(X30911)),c_Enum_On__lists(X30911,X30909,c_Enum_Oenum__class_Oenum(X30911)))))
        | ~ hBOOL(hAPP(X30910,X30913))
        | c_Enum_Oex__n__lists(X30911,X30910,X30909)
        | ~ class_Enum_Oenum(X30911) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__n__lists__def])])])])]) ).

fof(i_0_7969,plain,
    ! [X30592,X30593,X30594,X30595,X30596] : c_List_Olist_Olist__size(X30596,X30595,hAPP(hAPP(c_List_Omap(X30594,X30596),X30593),X30592)) = c_List_Olist_Olist__size(X30594,hAPP(c_Fun_Ocomp(X30596,tc_Nat_Onat,X30594,X30595),X30593),X30592),
    inference(variable_rename,[status(thm)],[fact_list__size__map]) ).

fof(i_0_7970,plain,
    ! [X28142,X28143,X28144,X28145] :
      ( ~ c_Relation_Orefl__on(X28145,X28144,X28143)
      | ~ hBOOL(hAPP(hAPP(c_member(X28145),X28142),X28144))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28145,X28145)),hAPP(hAPP(c_Product__Type_OPair(X28145,X28145),X28142),X28142)),X28143)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD])]) ).

fof(i_0_7971,plain,
    ! [X19795,X19796,X19797,X19798,X19799] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X19799),X19798),X19797))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19796,tc_HOL_Obool)),hAPP(X19795,X19798)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19799,tc_fun(X19796,tc_HOL_Obool)),X19797),X19795))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__upper])]) ).

fof(i_0_7972,plain,
    ! [X31462,X31463,X31464,X31465] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31465) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(X31464),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31465)),hAPP(hAPP(c_List_Olist_OCons(X31464),X31463),X31462)) = c_List_Olist_ONil(X31464) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31465) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(X31464),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31465)),hAPP(hAPP(c_List_Olist_OCons(X31464),X31463),X31462)) = hAPP(hAPP(c_List_Olist_OCons(X31464),X31463),hAPP(hAPP(c_List_Otake(X31464),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31465)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X31462)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Cons__number__of])]) ).

fof(i_0_7973,plain,
    ! [X20155,X20156,X20157,X20158,X20159,X20160] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20160,tc_fun(X20159,tc_HOL_Obool))),X20158),X20157))
      | ~ hBOOL(hAPP(hAPP(X20158,X20156),X20155))
      | hBOOL(hAPP(hAPP(X20157,X20156),X20155)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate2D])]) ).

fof(i_0_7974,plain,
    ! [X20161,X20162,X20163,X20164,X20165,X20166] :
      ( ~ hBOOL(hAPP(hAPP(X20166,X20165),X20164))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20163,tc_fun(X20162,tc_HOL_Obool))),X20166),X20161))
      | hBOOL(hAPP(hAPP(X20161,X20165),X20164)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate2D])]) ).

fof(i_0_7975,plain,
    ! [X25482,X25483,X25484] :
      ( ~ class_Orderings_Olinorder(X25484)
      | X25483 = c_Orderings_Obot__class_Obot(tc_fun(X25484,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25484,tc_HOL_Obool)),X25483),X25482))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25484),X25482))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25484),hAPP(c_Finite__Set_Ofold1(X25484,c_Orderings_Oord__class_Omin(X25484)),X25482)),hAPP(c_Finite__Set_Ofold1(X25484,c_Orderings_Oord__class_Omin(X25484)),X25483))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__antimono])]) ).

fof(i_0_7976,plain,
    ! [X17382,X17383,X17384,X17385] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17385),X17384),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17385,tc_HOL_Obool)),X17383),X17382)))
        | hBOOL(hAPP(hAPP(c_member(X17385),X17384),X17383))
        | hBOOL(hAPP(hAPP(c_member(X17385),X17384),X17382)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17385),X17384),X17383))
        | hBOOL(hAPP(hAPP(c_member(X17385),X17384),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17385,tc_HOL_Obool)),X17383),X17382))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17385),X17384),X17382))
        | hBOOL(hAPP(hAPP(c_member(X17385),X17384),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17385,tc_HOL_Obool)),X17383),X17382))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__iff])])]) ).

fof(i_0_7977,plain,
    ! [X17297,X17298,X17299,X17300] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17300),X17299),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17300,tc_HOL_Obool)),X17298),X17297)))
      | hBOOL(hAPP(hAPP(c_member(X17300),X17299),X17298))
      | hBOOL(hAPP(hAPP(c_member(X17300),X17299),X17297)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5699])]) ).

cnf(i_0_7978,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_5700]) ).

fof(i_0_7979,plain,
    ! [X34065,X34066,X34067] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X34067),c_Groups_Ozero__class_Ozero(X34067)),esk519_3(X34065,X34066,X34067)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34067),X34066),X34065))
        | ~ class_Fields_Olinordered__field(X34067) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34067),X34066),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X34067),X34065),esk519_3(X34065,X34066,X34067))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34067),X34066),X34065))
        | ~ class_Fields_Olinordered__field(X34067) ) ),
    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_7980,plain,
    ! [X18942,X18943,X18944,X18945,X18946] : c_Map_Orestrict__map(X18946,X18945,c_Map_Orestrict__map(X18946,X18945,X18944,X18943),X18942) = c_Map_Orestrict__map(X18946,X18945,X18944,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18946,tc_HOL_Obool)),X18943),X18942)),
    inference(variable_rename,[status(thm)],[fact_restrict__restrict]) ).

fof(i_0_7981,plain,
    ! [X31999,X32000,X32001,X32002,X32003,X32004] : hAPP(c_List_Ofoldl(X32004,X32003,X32002,X32001),hAPP(hAPP(c_List_Olist_OCons(X32003),X32000),X31999)) = hAPP(c_List_Ofoldl(X32004,X32003,X32002,hAPP(hAPP(X32002,X32001),X32000)),X31999),
    inference(variable_rename,[status(thm)],[fact_foldl__Cons]) ).

fof(i_0_7982,plain,
    ! [X32957,X32958] :
      ( ( X32957 != c_List_Olist_ONil(tc_List_Olist(X32958))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32958))),c_List_Otranspose(X32958,X32957)) = 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(X32958),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X32958))),X32957))) )
      & ( X32957 = c_List_Olist_ONil(tc_List_Olist(X32958))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X32958))),c_List_Otranspose(X32958,X32957)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32958)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X32958)),X32957),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(X32958),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X32958))),X32957))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__transpose__sorted])])]) ).

fof(i_0_7983,plain,
    ! [X22622,X22623,X22624,X22625] :
      ( ~ class_Rings_Olinordered__semidom(X22625)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22625),X22624),X22623))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22625),c_Groups_Ozero__class_Ozero(X22625)),X22624))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22622))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22625),hAPP(hAPP(c_Power_Opower__class_Opower(X22625),X22624),X22622)),hAPP(hAPP(c_Power_Opower__class_Opower(X22625),X22623),X22622))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__mono])]) ).

fof(i_0_7984,plain,
    ! [X22641,X22642,X22643,X22644] :
      ( ~ class_Rings_Olinordered__semidom(X22644)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22643),X22642))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22644),c_Groups_Ozero__class_Ozero(X22644)),X22641))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22644),X22641),c_Groups_Oone__class_Oone(X22644)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22644),hAPP(hAPP(c_Power_Opower__class_Opower(X22644),X22641),X22642)),hAPP(hAPP(c_Power_Opower__class_Opower(X22644),X22641),X22643))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing])]) ).

fof(i_0_7985,plain,
    ! [X22637,X22638,X22639,X22640] :
      ( ~ class_Rings_Olinordered__semidom(X22640)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22639),X22638))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22640),c_Groups_Ozero__class_Ozero(X22640)),X22637))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22640),X22637),c_Groups_Oone__class_Oone(X22640)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22640),hAPP(hAPP(c_Power_Opower__class_Opower(X22640),X22637),X22638)),hAPP(hAPP(c_Power_Opower__class_Opower(X22640),X22637),X22639))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__decreasing])]) ).

fof(i_0_7986,plain,
    ! [X21595,X21596,X21597] :
      ( ( ~ c_Orderings_Oorder__class_Omono(tc_Nat_Onat,X21596,X21595)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21596),hAPP(X21595,X21597)),hAPP(X21595,hAPP(c_Nat_OSuc,X21597))))
        | ~ class_Orderings_Oorder(X21596) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21596),hAPP(X21595,esk108_2(X21595,X21596))),hAPP(X21595,hAPP(c_Nat_OSuc,esk108_2(X21595,X21596)))))
        | c_Orderings_Oorder__class_Omono(tc_Nat_Onat,X21596,X21595)
        | ~ class_Orderings_Oorder(X21596) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mono__iff__le__Suc])])])])]) ).

fof(i_0_7987,plain,
    ! [X19450,X19451,X19452,X19453,X19454] : hAPP(c_Set_Ovimage(X19454,X19453,X19452),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19453,tc_HOL_Obool)),X19451),X19450)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19454,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X19454,X19453,X19452),X19451)),hAPP(c_Set_Ovimage(X19454,X19453,X19452),X19450)),
    inference(variable_rename,[status(thm)],[fact_vimage__Int]) ).

fof(i_0_7988,plain,
    ! [X19461,X19462,X19463,X19464,X19465] : hAPP(c_Set_Ovimage(X19465,X19464,X19463),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19464,tc_HOL_Obool)),X19462),X19461)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19465,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X19465,X19464,X19463),X19462)),hAPP(c_Set_Ovimage(X19465,X19464,X19463),X19461)),
    inference(variable_rename,[status(thm)],[fact_vimage__Diff]) ).

fof(i_0_7989,plain,
    ! [X19445,X19446,X19447,X19448,X19449] : hAPP(c_Set_Ovimage(X19449,X19448,X19447),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19448,tc_HOL_Obool)),X19446),X19445)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19449,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X19449,X19448,X19447),X19446)),hAPP(c_Set_Ovimage(X19449,X19448,X19447),X19445)),
    inference(variable_rename,[status(thm)],[fact_vimage__Un]) ).

fof(i_0_7990,plain,
    ! [X19344,X19345,X19346,X19347,X19348] : hAPP(c_Relation_OImage(X19348,X19347,X19346),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19348,tc_HOL_Obool)),X19345),X19344)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19347,tc_HOL_Obool)),hAPP(c_Relation_OImage(X19348,X19347,X19346),X19345)),hAPP(c_Relation_OImage(X19348,X19347,X19346),X19344)),
    inference(variable_rename,[status(thm)],[fact_Image__Un]) ).

fof(i_0_7991,plain,
    ! [X17386,X17387,X17388,X17389,X17390] : hAPP(c_Set_Oimage(X17390,X17389,X17388),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17390,tc_HOL_Obool)),X17387),X17386)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17389,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17390,X17389,X17388),X17387)),hAPP(c_Set_Oimage(X17390,X17389,X17388),X17386)),
    inference(variable_rename,[status(thm)],[fact_image__Un]) ).

fof(i_0_7992,plain,
    ! [X31636,X31637,X31638,X31639] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31639)),X31638),c_List_Olists(X31639,X31636)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31639)),hAPP(hAPP(c_List_Oappend(X31639),X31638),X31637)),c_List_Olists(X31639,X31636))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31639)),X31637),c_List_Olists(X31639,X31636)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31639)),hAPP(hAPP(c_List_Oappend(X31639),X31638),X31637)),c_List_Olists(X31639,X31636))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31639)),X31638),c_List_Olists(X31639,X31636)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31639)),X31637),c_List_Olists(X31639,X31636)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31639)),hAPP(hAPP(c_List_Oappend(X31639),X31638),X31637)),c_List_Olists(X31639,X31636))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__lists__conv])])]) ).

cnf(i_0_7993,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_5687]) ).

fof(i_0_7994,plain,
    ! [X17228,X17229,X17230] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17230,tc_HOL_Obool)),X17229),X17228))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X17230,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X17230,X17229)),c_Predicate_OPowp(X17230,X17228))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Powp__mono])]) ).

fof(i_0_7995,plain,
    ! [X30020,X30021,X30022,X30023] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30023,tc_HOL_Obool)),c_Map_Odom(X30023,X30022,X30021)),c_Map_Odom(X30023,X30022,X30020)) != c_Orderings_Obot__class_Obot(tc_fun(X30023,tc_HOL_Obool))
      | c_Map_Omap__add(X30023,X30022,X30021,X30020) = c_Map_Omap__add(X30023,X30022,X30020,X30021) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__comm])]) ).

fof(i_0_7996,plain,
    ! [X30433,X30434,X30435,X30436] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30436),X30435))
      | ~ hBOOL(hAPP(c_List_Odistinct(X30434),X30433))
      | hBOOL(hAPP(c_List_Odistinct(tc_prod(X30436,X30434)),c_Enum_Oproduct(X30436,X30434,X30435,X30433))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__product])]) ).

fof(i_0_7997,plain,
    ! [X22610,X22611,X22612,X22613] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22613),X22612))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22611),X22610))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X22613,X22611)),c_Sum__Type_OPlus(X22613,X22611,X22612,X22610))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus])]) ).

cnf(i_0_7998,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_5701]) ).

fof(i_0_7999,plain,
    ! [X20764,X20765,X20766,X20767,X20768,X20769] :
      ( ~ c_Finite__Set_Ofolding(X20769,X20768,X20767,X20766)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20769),X20765))
      | hBOOL(hAPP(hAPP(c_member(X20769),X20764),X20765))
      | hAPP(X20766,hAPP(hAPP(c_Set_Oinsert(X20769),X20764),X20765)) = hAPP(c_Fun_Ocomp(X20768,X20768,X20768,hAPP(X20766,X20765)),hAPP(X20767,X20764)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5702])]) ).

fof(i_0_8000,plain,
    ! [X20280,X20281,X20282,X20283] :
      ( X20283 != X20282
      | ~ hBOOL(hAPP(hAPP(c_member(X20281),X20283),X20280))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X20281,X20281)),hAPP(hAPP(c_Product__Type_OPair(X20281,X20281),X20283),X20282)),c_Relation_OId__on(X20281,X20280))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__eqI])]) ).

fof(i_0_8001,plain,
    ! [X28176,X28177] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X28177),c_Int_OInteg))
      | ~ hBOOL(hAPP(X28176,hAPP(c_Int_ORep__Integ,esk288_2(X28176,X28177))))
      | hBOOL(hAPP(X28176,X28177)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__induct])])]) ).

fof(i_0_8002,plain,
    ! [X31665,X31666,X31667,X31668,X31669] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31669),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31668)),X31667)))
      | hAPP(hAPP(c_List_Olist__update(X31668,hAPP(hAPP(c_List_Oappend(X31668),X31667),X31666)),X31669),X31665) = hAPP(hAPP(c_List_Oappend(X31668),hAPP(hAPP(c_List_Olist__update(X31668,X31667),X31669),X31665)),X31666) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__append1])]) ).

fof(i_0_8003,plain,
    ! [X22708,X22709,X22710] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22710))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22710),X22709)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22710),X22708)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22709),X22708)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less])]) ).

fof(i_0_8004,plain,
    ! [X22362,X22363,X22364] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22364),X22363)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22364),X22362)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22363),X22362))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22364)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22363),X22362))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22364),X22363)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22364),X22362)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22364)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1])])]) ).

fof(i_0_8005,plain,
    ! [X22498,X22499,X22500] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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),X22498),X22499)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22499))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22500),X22498)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22499))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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),X22498),X22499))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22500),X22498))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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),X22498),X22499))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2])])]) ).

fof(i_0_8006,plain,
    ! [X22501,X22502,X22503] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),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__eq(tc_Nat_Onat),X22502),X22501))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22503)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22502),X22501))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),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__le__cancel1])])]) ).

fof(i_0_8007,plain,
    ! [X22495,X22496,X22497] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22497),X22496)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22497),X22495)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22497))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22496),X22495)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22497))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22497),X22496)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22497),X22495))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22496),X22495))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22497),X22496)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22497),X22495))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1])])]) ).

fof(i_0_8008,plain,
    ! [X27468,X27469,X27470] :
      ( ~ c_Wellfounded_Owf(X27470,X27469)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27470,tc_HOL_Obool)),X27468),hAPP(c_Relation_OImage(X27470,X27470,X27469),X27468)))
      | X27468 = c_Orderings_Obot__class_Obot(tc_fun(X27470,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfE__pf])]) ).

fof(i_0_8009,plain,
    ! [X26719,X26720,X26721] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26721,tc_Nat_Onat),X26720),X26719)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26721,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X26721),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X26720)),X26719),
    inference(variable_rename,[status(thm)],[fact_int__setsum]) ).

fof(i_0_8010,plain,
    ! [X25112,X25113,X25114] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25114,tc_Nat_Onat),X25113),X25112)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25114,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X25114),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25113)),X25112),
    inference(variable_rename,[status(thm)],[fact_int__setprod]) ).

fof(i_0_8011,plain,
    ! [X18828,X18829,X18830,X18831] : c_Fun_Ooverride__on(X18831,X18830,X18829,X18828,c_Orderings_Obot__class_Obot(tc_fun(X18831,tc_HOL_Obool))) = X18829,
    inference(variable_rename,[status(thm)],[fact_override__on__emptyset]) ).

fof(i_0_8012,plain,
    ! [X29179,X29180,X29181,X29182,X29183] :
      ( ~ c_Finite__Set_Ofun__left__comm(X29183,X29182,X29181)
      | hAPP(c_Fun_Ocomp(X29182,X29182,X29182,hAPP(X29181,X29180)),hAPP(X29181,X29179)) = hAPP(c_Fun_Ocomp(X29182,X29182,X29182,hAPP(X29181,X29179)),hAPP(X29181,X29180)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__comp__comm])]) ).

fof(i_0_8013,plain,
    ! [X20320,X20321,X20322,X20323,X20324] : c_Option_Ooption_Ooption__rec(X20324,X20323,X20322,X20321,hAPP(c_Option_Ooption_OSome(X20323),X20320)) = hAPP(X20321,X20320),
    inference(variable_rename,[status(thm)],[fact_option_Orecs_I2_J]) ).

fof(i_0_8014,plain,
    ! [X30261,X30262,X30263,X30264] : hAPP(c_Map_Omap__of(X30264,X30263),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X30264,X30263)),X30262),X30261)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X30264,tc_Option_Ooption(X30263)),hAPP(c_Map_Omap__of(X30264,X30263),X30261)),hAPP(c_Product__Type_Ofst(X30264,X30263),X30262)),hAPP(c_Option_Ooption_OSome(X30263),hAPP(c_Product__Type_Osnd(X30264,X30263),X30262))),
    inference(variable_rename,[status(thm)],[fact_map__of_Osimps_I2_J]) ).

fof(i_0_8015,plain,
    ! [X31211,X31212,X31213,X31214] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31214),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31213)),X31212)))
      | hBOOL(hAPP(hAPP(c_member(X31213),X31211),hAPP(c_List_Oset(X31213),hAPP(hAPP(c_List_Olist__update(X31213,X31212),X31214),X31211)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__update__memI])]) ).

fof(i_0_8016,plain,
    ! [X19522,X19523,X19524,X19525,X19526,X19527] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X19527),X19526),X19525))
      | ~ hBOOL(hAPP(hAPP(c_member(X19524),X19523),hAPP(X19522,X19526)))
      | hBOOL(hAPP(hAPP(c_member(X19524),X19523),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19527,tc_fun(X19524,tc_HOL_Obool)),X19525),X19522))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__I])]) ).

fof(i_0_8017,plain,
    ! [X23014,X23015,X23016,X23017,X23018,X23019] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X23019,X23018),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X23017),X23016)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X23019,X23018),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X23015),X23014)))
      | X23018 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | X23017 = X23015 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient])]) ).

fof(i_0_8018,plain,
    ! [X23020,X23021,X23022,X23023,X23024,X23025] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X23025,X23024),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X23023),X23022)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X23025,X23024),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X23021),X23020)))
      | X23024 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | X23022 = X23020 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__remainder])]) ).

fof(i_0_8019,plain,
    ! [X20554,X20555,X20556,X20557] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20557),hAPP(c_Set_Oimage(X20556,X20557,X20555),X20554)))
      | ~ c_Fun_Oinj__on(X20556,X20557,X20555,X20554)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20556),X20554)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).

cnf(i_0_8020,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_5703]) ).

fof(i_0_8021,plain,
    ! [X28835,X28836,X28837,X28838] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28838,X28837),tc_HOL_Obool)),X28836),X28835))
      | ~ c_Relation_Osingle__valued(X28838,X28837,X28835)
      | c_Relation_Osingle__valued(X28838,X28837,X28836) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__subset])]) ).

fof(i_0_8022,plain,
    ! [X33531,X33532,X33533,X33536,X33537,X33538,X33539,X33540] :
      ( ( X33531 = hAPP(hAPP(c_List_Oappend(X33533),esk497_3(X33531,X33532,X33533)),hAPP(hAPP(c_List_Olist_OCons(X33533),X33532),esk498_3(X33531,X33532,X33533)))
        | ~ hBOOL(hAPP(hAPP(c_member(X33533),X33532),hAPP(c_List_Oset(X33533),X33531))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X33533),X33532),hAPP(c_List_Oset(X33533),esk498_3(X33531,X33532,X33533))))
        | ~ hBOOL(hAPP(hAPP(c_member(X33533),X33532),hAPP(c_List_Oset(X33533),X33531))) )
      & ( X33536 != hAPP(hAPP(c_List_Oappend(X33538),X33539),hAPP(hAPP(c_List_Olist_OCons(X33538),X33537),X33540))
        | hBOOL(hAPP(hAPP(c_member(X33538),X33537),hAPP(c_List_Oset(X33538),X33540)))
        | hBOOL(hAPP(hAPP(c_member(X33538),X33537),hAPP(c_List_Oset(X33538),X33536))) ) ),
    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_5704])])])])])]) ).

fof(i_0_8023,plain,
    ! [X33521,X33522,X33523,X33526,X33527,X33528,X33529,X33530] :
      ( ( X33521 = hAPP(hAPP(c_List_Oappend(X33523),esk495_3(X33521,X33522,X33523)),hAPP(hAPP(c_List_Olist_OCons(X33523),X33522),esk496_3(X33521,X33522,X33523)))
        | ~ hBOOL(hAPP(hAPP(c_member(X33523),X33522),hAPP(c_List_Oset(X33523),X33521))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X33523),X33522),hAPP(c_List_Oset(X33523),esk495_3(X33521,X33522,X33523))))
        | ~ hBOOL(hAPP(hAPP(c_member(X33523),X33522),hAPP(c_List_Oset(X33523),X33521))) )
      & ( X33526 != hAPP(hAPP(c_List_Oappend(X33528),X33529),hAPP(hAPP(c_List_Olist_OCons(X33528),X33527),X33530))
        | hBOOL(hAPP(hAPP(c_member(X33528),X33527),hAPP(c_List_Oset(X33528),X33529)))
        | hBOOL(hAPP(hAPP(c_member(X33528),X33527),hAPP(c_List_Oset(X33528),X33526))) ) ),
    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_5705])])])])])]) ).

cnf(i_0_8024,plain,
    c_Int_Osucc(c_Int_OBit1(X1)) = c_Int_OBit0(c_Int_Osucc(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5706]) ).

fof(i_0_8025,plain,
    ! [X21591,X21592,X21593,X21594] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21594),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21594),X21593),X21592)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21594),X21591),X21592)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21594),X21593),X21591))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X21594) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21594),X21593),X21591))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21594),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21594),X21593),X21592)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21594),X21591),X21592)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X21594) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).

fof(i_0_8026,plain,
    ! [X21570,X21571,X21572,X21573] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X21573)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21573),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21573),X21572),X21571)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21573),X21570),X21571)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21573),X21572),X21570)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).

fof(i_0_8027,plain,
    ! [X21587,X21588,X21589,X21590] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21590),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21590),X21589),X21588)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21590),X21589),X21587)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21590),X21588),X21587))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X21590) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21590),X21588),X21587))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21590),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21590),X21589),X21588)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21590),X21589),X21587)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X21590) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).

fof(i_0_8028,plain,
    ! [X21566,X21567,X21568,X21569] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X21569)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21569),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21569),X21568),X21567)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21569),X21568),X21566)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21569),X21567),X21566)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).

fof(i_0_8029,plain,
    ! [X21558,X21559,X21560,X21561] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X21561)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21561),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21561),X21560),X21559)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21561),X21558),X21559)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21561),X21560),X21558)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).

fof(i_0_8030,plain,
    ! [X21537,X21538,X21539,X21540] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21540),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21540),X21539),X21538)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21540),X21537),X21538)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21540),X21539),X21537))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X21540) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21540),X21539),X21537))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21540),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21540),X21539),X21538)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21540),X21537),X21538)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X21540) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).

fof(i_0_8031,plain,
    ! [X21562,X21563,X21564,X21565] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X21565)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21565),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21565),X21564),X21563)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21565),X21564),X21562)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21565),X21563),X21562)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).

fof(i_0_8032,plain,
    ! [X21541,X21542,X21543,X21544] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21544),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21544),X21543),X21542)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21544),X21543),X21541)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21544),X21542),X21541))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X21544) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21544),X21542),X21541))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21544),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21544),X21543),X21542)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21544),X21543),X21541)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X21544) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).

fof(i_0_8033,plain,
    ! [X32840,X32841,X32842,X32843] :
      ( ~ class_Orderings_Olinorder(X32843)
      | ~ c_List_Olinorder__class_Osorted(X32843,X32842)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32841),X32840))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32840),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32843)),X32842)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32843),hAPP(hAPP(c_List_Onth(X32843),X32842),X32841)),hAPP(hAPP(c_List_Onth(X32843),X32842),X32840))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__nth__mono])]) ).

fof(i_0_8034,plain,
    ! [X28882,X28883,X28884] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28884,X28884),tc_HOL_Obool),hAPP(c_Nat_OSuc,X28883)),X28882) = hAPP(hAPP(c_Relation_Orel__comp(X28884,X28884,X28884),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28884,X28884),tc_HOL_Obool),X28883),X28882)),X28882),
    inference(variable_rename,[status(thm)],[fact_relpow_Osimps_I2_J]) ).

fof(i_0_8035,plain,
    ! [X24429,X24430,X24431,X24432] :
      ( ~ class_Fields_Ofield(X24432)
      | X24431 = c_Groups_Ozero__class_Ozero(X24432)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24432),X24430),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24432),X24429),X24431)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24432),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24432),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24432),X24431),X24430)),X24429)),X24431) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__eq__iff])]) ).

fof(i_0_8036,plain,
    ! [X24446,X24447,X24448,X24449] :
      ( ~ class_Fields_Ofield(X24449)
      | X24448 = c_Groups_Ozero__class_Ozero(X24449)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24449),X24447),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24449),X24446),X24448)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24449),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24449),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24449),X24448),X24447)),X24446)),X24448) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__divide__eq__iff])]) ).

fof(i_0_8037,plain,
    ! [X32812,X32813,X32814,X32815,X32816,X32817] :
      ( ~ class_Orderings_Olinorder(X32817)
      | ~ c_List_Olinorder__class_Osorted(X32817,hAPP(hAPP(c_List_Omap(X32816,X32817),X32815),X32814))
      | ~ hBOOL(hAPP(X32813,X32812))
      | hAPP(c_List_Ofilter(X32816,X32813),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32816,X32817,X32815),X32812),X32814)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32816,X32817,X32815),X32812),hAPP(c_List_Ofilter(X32816,X32813),X32814)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__insort])]) ).

cnf(i_0_8038,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_5707]) ).

cnf(i_0_8039,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_5461]) ).

fof(i_0_8040,plain,
    ! [X17013,X17014,X17015] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17015,tc_HOL_Obool)),X17014),hAPP(hAPP(c_Set_Oinsert(X17015),X17013),c_Orderings_Obot__class_Obot(tc_fun(X17015,tc_HOL_Obool)))))
      | X17014 = c_Orderings_Obot__class_Obot(tc_fun(X17015,tc_HOL_Obool))
      | X17014 = hAPP(hAPP(c_Set_Oinsert(X17015),X17013),c_Orderings_Obot__class_Obot(tc_fun(X17015,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__singletonD])]) ).

fof(i_0_8041,plain,
    ! [X18040,X18041,X18042,X18043] :
      ( ( hBOOL(hAPP(hAPP(c_member(X18043),X18042),X18041))
        | ~ hBOOL(hAPP(hAPP(c_member(X18043),X18042),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18043,tc_HOL_Obool)),X18041),X18040))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18043),X18042),X18040))
        | ~ hBOOL(hAPP(hAPP(c_member(X18043),X18042),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18043,tc_HOL_Obool)),X18041),X18040))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18043),X18042),X18041))
        | hBOOL(hAPP(hAPP(c_member(X18043),X18042),X18040))
        | hBOOL(hAPP(hAPP(c_member(X18043),X18042),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18043,tc_HOL_Obool)),X18041),X18040))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5708])])]) ).

fof(i_0_8042,plain,
    ! [X17801,X17802,X17803,X17804] :
      ( ( hBOOL(hAPP(hAPP(c_member(X17804),X17803),X17802))
        | ~ hBOOL(hAPP(hAPP(c_member(X17804),X17803),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17804,tc_HOL_Obool)),X17802),X17801))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17804),X17803),X17801))
        | ~ hBOOL(hAPP(hAPP(c_member(X17804),X17803),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17804,tc_HOL_Obool)),X17802),X17801))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DiffE])])]) ).

fof(i_0_8043,plain,
    ! [X18032,X18033,X18034,X18035] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X18035),X18034),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18035,tc_HOL_Obool)),X18033),X18032)))
      | ~ hBOOL(hAPP(hAPP(c_member(X18035),X18034),X18032)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5709])]) ).

cnf(i_0_8044,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_5710]) ).

cnf(i_0_8045,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_5711]) ).

cnf(i_0_8046,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_5712]) ).

cnf(i_0_8047,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_5713]) ).

fof(i_0_8048,plain,
    ! [X22552,X22553,X22554,X22557,X22558,X22559,X22560,X22561] :
      ( ( X22553 = hAPP(hAPP(c_Set_Oinsert(X22554),esk115_3(X22552,X22553,X22554)),esk116_3(X22552,X22553,X22554))
        | hAPP(c_Finite__Set_Ocard(X22554),X22553) != hAPP(c_Nat_OSuc,X22552) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X22554),esk115_3(X22552,X22553,X22554)),esk116_3(X22552,X22553,X22554)))
        | hAPP(c_Finite__Set_Ocard(X22554),X22553) != hAPP(c_Nat_OSuc,X22552) )
      & ( hAPP(c_Finite__Set_Ocard(X22554),esk116_3(X22552,X22553,X22554)) = X22552
        | hAPP(c_Finite__Set_Ocard(X22554),X22553) != hAPP(c_Nat_OSuc,X22552) )
      & ( X22552 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | esk116_3(X22552,X22553,X22554) = c_Orderings_Obot__class_Obot(tc_fun(X22554,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(X22554),X22553) != hAPP(c_Nat_OSuc,X22552) )
      & ( X22557 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22558 != hAPP(hAPP(c_Set_Oinsert(X22559),X22560),X22561)
        | hBOOL(hAPP(hAPP(c_member(X22559),X22560),X22561))
        | hAPP(c_Finite__Set_Ocard(X22559),X22561) != X22557
        | hAPP(c_Finite__Set_Ocard(X22559),X22558) = hAPP(c_Nat_OSuc,X22557) )
      & ( X22561 != c_Orderings_Obot__class_Obot(tc_fun(X22559,tc_HOL_Obool))
        | X22558 != hAPP(hAPP(c_Set_Oinsert(X22559),X22560),X22561)
        | hBOOL(hAPP(hAPP(c_member(X22559),X22560),X22561))
        | hAPP(c_Finite__Set_Ocard(X22559),X22561) != X22557
        | hAPP(c_Finite__Set_Ocard(X22559),X22558) = hAPP(c_Nat_OSuc,X22557) ) ),
    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_5714])])])])])]) ).

fof(i_0_8049,plain,
    ! [X21096,X21097,X21098,X21099,X21100,X21101] :
      ( ~ c_Finite__Set_Ofolding__idem(X21101,X21100,X21099,X21098)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21101),X21097))
      | ~ hBOOL(hAPP(hAPP(c_member(X21101),X21096),X21097))
      | hAPP(c_Fun_Ocomp(X21100,X21100,X21100,hAPP(X21098,X21097)),hAPP(X21099,X21096)) = hAPP(X21098,X21097) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oin__comp__idem])]) ).

fof(i_0_8050,plain,
    ! [X31722,X31723,X31724] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31724),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31723)),X31722)))
      | hAPP(hAPP(c_List_Otake(X31723),hAPP(c_Nat_OSuc,X31724)),X31722) = hAPP(hAPP(c_List_Oappend(X31723),hAPP(hAPP(c_List_Otake(X31723),X31724),X31722)),hAPP(hAPP(c_List_Olist_OCons(X31723),hAPP(hAPP(c_List_Onth(X31723),X31722),X31724)),c_List_Olist_ONil(X31723))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Suc__conv__app__nth])]) ).

fof(i_0_8051,plain,
    ! [X25979,X25980,X25981] :
      ( ~ class_Orderings_Olinorder(X25981)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25981),X25980))
      | X25980 = c_Orderings_Obot__class_Obot(tc_fun(X25981,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25981),X25979))
      | X25979 = c_Orderings_Obot__class_Obot(tc_fun(X25981,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25981,tc_HOL_Obool)),X25980),X25979) != c_Orderings_Obot__class_Obot(tc_fun(X25981,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OSup__fin(X25981,c_Orderings_Oord__class_Omax(X25981),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25981,tc_HOL_Obool)),X25980),X25979)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25981),c_Big__Operators_Olattice_OSup__fin(X25981,c_Orderings_Oord__class_Omax(X25981),X25980)),c_Big__Operators_Olattice_OSup__fin(X25981,c_Orderings_Oord__class_Omax(X25981),X25979)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__disjoint])]) ).

fof(i_0_8052,plain,
    ! [X25696,X25697,X25698] :
      ( ~ class_Orderings_Olinorder(X25698)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25698),X25697))
      | X25697 = c_Orderings_Obot__class_Obot(tc_fun(X25698,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25698),X25696))
      | X25696 = c_Orderings_Obot__class_Obot(tc_fun(X25698,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25698,tc_HOL_Obool)),X25697),X25696) != c_Orderings_Obot__class_Obot(tc_fun(X25698,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OInf__fin(X25698,c_Orderings_Oord__class_Omin(X25698),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25698,tc_HOL_Obool)),X25697),X25696)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25698),c_Big__Operators_Olattice_OInf__fin(X25698,c_Orderings_Oord__class_Omin(X25698),X25697)),c_Big__Operators_Olattice_OInf__fin(X25698,c_Orderings_Oord__class_Omin(X25698),X25696)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__disjoint])]) ).

fof(i_0_8053,plain,
    ! [X28855,X28856,X28857,X28858] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(X28858,X28857),tc_fun(X28858,X28857)),X28856),c_Fun_Ocomp(X28857,X28857,X28858,X28855)) = c_Fun_Ocomp(X28857,X28857,X28858,hAPP(hAPP(c_Nat_Ocompow(X28857,X28857),X28856),X28855)),
    inference(variable_rename,[status(thm)],[fact_comp__funpow]) ).

fof(i_0_8054,plain,
    ! [X33731,X33732,X33733,X33734,X33735] : hAPP(c_New__DSequence_Opos__bind(X33735,X33734,X33733,X33732),X33731) = hAPP(c_Lazy__Sequence_Obind(X33735,X33734,hAPP(X33733,X33731)),hAPP(hAPP(c_COMBC(X33735,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X33734)),X33732),X33731)),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__bind__def]) ).

fof(i_0_8055,plain,
    ! [X18788,X18789,X18790,X18791,X18792] :
      ( ( hAPP(c_Set_Oimage(X18792,X18791,X18790),X18789) != hAPP(c_Set_Oimage(X18792,X18791,X18790),X18788)
        | X18789 = X18788
        | ~ c_Fun_Oinj__on(X18792,X18791,X18790,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18792,tc_HOL_Obool)),X18789),X18788)) )
      & ( X18789 != X18788
        | hAPP(c_Set_Oimage(X18792,X18791,X18790),X18789) = hAPP(c_Set_Oimage(X18792,X18791,X18790),X18788)
        | ~ c_Fun_Oinj__on(X18792,X18791,X18790,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18792,tc_HOL_Obool)),X18789),X18788)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Un__image__eq__iff])])]) ).

cnf(i_0_8056,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk463_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_5700]) ).

fof(i_0_8057,plain,
    ! [X24392,X24393,X24394,X24395] :
      ( ~ class_Fields_Olinordered__field(X24395)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24395),c_Groups_Ozero__class_Ozero(X24395)),X24394))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24395),X24393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24395),X24392),X24394)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24395),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24395),X24393),X24394)),X24392)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__less])]) ).

fof(i_0_8058,plain,
    ! [X24472,X24473,X24474,X24475] :
      ( ~ class_Fields_Olinordered__field(X24475)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24475),c_Groups_Ozero__class_Ozero(X24475)),X24474))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24475),X24473),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24475),X24472),X24474)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24475),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24475),X24473),X24474)),X24472)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__le])]) ).

fof(i_0_8059,plain,
    ! [X28137,X28138,X28139,X28140,X28141] :
      ( ~ c_Relation_Orefl__on(X28141,X28140,X28139)
      | ~ c_Relation_Orefl__on(X28141,X28138,X28137)
      | c_Relation_Orefl__on(X28141,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28141,tc_HOL_Obool)),X28140),X28138),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28141,X28141),tc_HOL_Obool)),X28139),X28137)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__Int])]) ).

fof(i_0_8060,plain,
    ! [X28132,X28133,X28134,X28135,X28136] :
      ( ~ c_Relation_Orefl__on(X28136,X28135,X28134)
      | ~ c_Relation_Orefl__on(X28136,X28133,X28132)
      | c_Relation_Orefl__on(X28136,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28136,tc_HOL_Obool)),X28135),X28133),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28136,X28136),tc_HOL_Obool)),X28134),X28132)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__Un])]) ).

fof(i_0_8061,plain,
    ! [X31399,X31400,X31401,X31402] : c_Map_Omap__upds(X31402,X31401,X31400,c_List_Olist_ONil(X31402),X31399) = X31400,
    inference(variable_rename,[status(thm)],[fact_map__upds__Nil1]) ).

fof(i_0_8062,plain,
    ! [X34178,X34179,X34180,X34181] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X34181,X34180,X34179,X34178,c_Lazy__Sequence_Olazy__sequence_OEmpty(X34180)) = X34179,
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I4_J]) ).

fof(i_0_8063,plain,
    ! [X31403,X31404,X31405,X31406] : c_Map_Omap__upds(X31406,X31405,X31404,X31403,c_List_Olist_ONil(X31405)) = X31404,
    inference(variable_rename,[status(thm)],[fact_map__upds__Nil2]) ).

fof(i_0_8064,plain,
    ! [X20613,X20614,X20615,X20616] : c_Option_Ooption_Ooption__rec(X20616,X20615,X20614,X20613,c_Option_Ooption_ONone(X20615)) = X20614,
    inference(variable_rename,[status(thm)],[fact_option_Orecs_I1_J]) ).

fof(i_0_8065,plain,
    ! [X19093,X19094,X19095] :
      ( hAPP(c_Set_Oimage(X19095,X19094,X19093),c_Orderings_Otop__class_Otop(tc_fun(X19095,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X19094,tc_HOL_Obool))
      | c_Fun_Oinj__on(X19094,X19095,c_Hilbert__Choice_Oinv__into(X19095,X19094,c_Orderings_Otop__class_Otop(tc_fun(X19095,tc_HOL_Obool)),X19093),c_Orderings_Otop__class_Otop(tc_fun(X19094,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__imp__inj__inv])]) ).

fof(i_0_8066,plain,
    ! [X27626,X27627,X27628,X27629,X27630] : hAPP(c_Relation_ODomain(X27630,X27629),hAPP(hAPP(c_Set_Oinsert(tc_prod(X27630,X27629)),hAPP(hAPP(c_Product__Type_OPair(X27630,X27629),X27628),X27627)),X27626)) = hAPP(hAPP(c_Set_Oinsert(X27630),X27628),hAPP(c_Relation_ODomain(X27630,X27629),X27626)),
    inference(variable_rename,[status(thm)],[fact_Domain__insert]) ).

fof(i_0_8067,plain,
    ! [X27548,X27549,X27550,X27551,X27552] : hAPP(c_Relation_ORange(X27552,X27551),hAPP(hAPP(c_Set_Oinsert(tc_prod(X27552,X27551)),hAPP(hAPP(c_Product__Type_OPair(X27552,X27551),X27550),X27549)),X27548)) = hAPP(hAPP(c_Set_Oinsert(X27551),X27549),hAPP(c_Relation_ORange(X27552,X27551),X27548)),
    inference(variable_rename,[status(thm)],[fact_Range__insert]) ).

cnf(i_0_8068,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_5715]) ).

fof(i_0_8069,plain,
    ! [X18443,X18444,X18445,X18446] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18446,tc_HOL_Obool)),X18445),X18444))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18446,tc_HOL_Obool)),X18444),X18443))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18446,tc_HOL_Obool)),X18445),X18443)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__trans])]) ).

fof(i_0_8070,plain,
    ! [X18596,X18597,X18598,X18599] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18599,tc_HOL_Obool)),X18598),X18597))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18599,tc_HOL_Obool)),X18597),X18596))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18599,tc_HOL_Obool)),X18598),X18596)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans])]) ).

fof(i_0_8071,plain,
    ! [X18592,X18593,X18594,X18595] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18595,tc_HOL_Obool)),X18594),X18593))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18595,tc_HOL_Obool)),X18593),X18592))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18595,tc_HOL_Obool)),X18594),X18592)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans])]) ).

fof(i_0_8072,plain,
    ! [X17107,X17108,X17109,X17110] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17110,tc_HOL_Obool)),X17109),X17108))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17110,tc_HOL_Obool)),X17108),X17107))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17110,tc_HOL_Obool)),X17109),X17107)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__trans])]) ).

fof(i_0_8073,plain,
    ! [X25100,X25101] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25101),X25100))
        | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25101)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25100))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25101)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25100)))
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25101),X25100)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I2_J])]) ).

fof(i_0_8074,plain,
    ! [X28427,X28428,X28429,X28430,X28431] : hAPP(hAPP(c_Product__Type_Oscomp(X28431,X28430,X28431,X28429),hAPP(c_Product__Type_OPair(X28430,X28431),X28428)),X28427) = hAPP(X28427,X28428),
    inference(variable_rename,[status(thm)],[fact_Pair__scomp]) ).

cnf(i_0_8075,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_5716]) ).

fof(i_0_8076,plain,
    ! [X23450,X23451,X23452] :
      ( ~ class_Divides_Osemiring__div(X23452)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23452),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23452),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23452),X23451),X23450)),X23450)),c_Divides_Odiv__class_Omod(X23452,X23451,X23450)) = X23451 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__equality])]) ).

fof(i_0_8077,plain,
    ! [X29879,X29880,X29881] :
      ( ~ class_Divides_Osemiring__div(X29881)
      | X29880 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X29881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29881),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X29881),X29880),X29879)),X29879)),c_Divides_Odiv__class_Omod(X29881,X29880,X29879)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__decomp])]) ).

fof(i_0_8078,plain,
    ! [X32729,X32730,X32731,X32732] :
      ( ~ class_Orderings_Olinorder(X32732)
      | c_List_Olinorder__class_Osorted(X32732,hAPP(hAPP(c_List_Omap(X32731,X32732),X32730),c_List_Olinorder__class_Osort__key(X32731,X32732,X32730,X32729))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__sort__key])]) ).

cnf(i_0_8079,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_5717]) ).

cnf(i_0_8080,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_5718]) ).

fof(i_0_8081,plain,
    ! [X19810,X19811] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19811,tc_fun(X19811,tc_HOL_Obool)),X19810),hAPP(hAPP(c_COMBC(X19811,tc_fun(X19811,tc_HOL_Obool),tc_fun(X19811,tc_HOL_Obool)),c_Set_Oinsert(X19811)),c_Orderings_Obot__class_Obot(tc_fun(X19811,tc_HOL_Obool)))) = X19810,
    inference(variable_rename,[status(thm)],[fact_UN__singleton]) ).

fof(i_0_8082,plain,
    ! [X31751,X31752,X31753,X31754] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31754),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31753)),X31752)))
      | hAPP(hAPP(c_List_Olist__update(X31753,X31752),X31754),X31751) = hAPP(hAPP(c_List_Oappend(X31753),hAPP(hAPP(c_List_Otake(X31753),X31754),X31752)),hAPP(hAPP(c_List_Olist_OCons(X31753),X31751),hAPP(hAPP(c_List_Odrop(X31753),hAPP(c_Nat_OSuc,X31754)),X31752))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upd__conv__take__nth__drop])]) ).

fof(i_0_8083,plain,
    ! [X32645,X32646,X32647,X32648,X32649,X32650] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32650),hAPP(X32649,X32648)),hAPP(X32649,X32647)))
        | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32646,X32650,X32649),X32648),hAPP(hAPP(c_List_Olist_OCons(X32646),X32647),X32645)) = hAPP(hAPP(c_List_Olist_OCons(X32646),X32648),hAPP(hAPP(c_List_Olist_OCons(X32646),X32647),X32645))
        | ~ class_Orderings_Olinorder(X32650) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32650),hAPP(X32649,X32648)),hAPP(X32649,X32647)))
        | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32646,X32650,X32649),X32648),hAPP(hAPP(c_List_Olist_OCons(X32646),X32647),X32645)) = hAPP(hAPP(c_List_Olist_OCons(X32646),X32647),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32646,X32650,X32649),X32648),X32645))
        | ~ class_Orderings_Olinorder(X32650) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5719])])]) ).

fof(i_0_8084,plain,
    ! [X30427,X30428] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30428),X30427))
      | hBOOL(hAPP(c_List_Odistinct(tc_fun(X30428,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X30428),tc_fun(X30428,tc_HOL_Obool)),c_List_Oset(X30428)),c_Enum_Osublists(X30428,X30427)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__set__sublists])]) ).

fof(i_0_8085,plain,
    ! [X31453,X31454] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X31454)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X31453)))
        | c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X31454),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X31453)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X31454)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X31454)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X31453))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X31454)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X31453)))
        | c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X31454),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X31453)) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5720])]) ).

fof(i_0_8086,plain,
    ! [X18146,X18147,X18148] : hAPP(c_Set_OPow(X18148),hAPP(hAPP(c_Set_Oinsert(X18148),X18147),X18146)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X18148,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X18148),X18146)),hAPP(c_Set_Oimage(tc_fun(X18148,tc_HOL_Obool),tc_fun(X18148,tc_HOL_Obool),hAPP(c_Set_Oinsert(X18148),X18147)),hAPP(c_Set_OPow(X18148),X18146))),
    inference(variable_rename,[status(thm)],[fact_Pow__insert]) ).

fof(i_0_8087,plain,
    ! [X20592,X20593,X20594,X20595] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20595),hAPP(c_Set_Ovimage(X20595,X20594,X20593),X20592)))
      | hAPP(c_Set_Oimage(X20595,X20594,X20593),c_Orderings_Otop__class_Otop(tc_fun(X20595,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X20594,tc_HOL_Obool))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20594),X20592)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__vimageD])]) ).

fof(i_0_8088,plain,
    ! [X31012,X31013,X31014,X31015] :
      ( ( hBOOL(hAPP(hAPP(c_member(X31015),X31014),X31012))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31015)),hAPP(hAPP(c_List_Olist_OCons(X31015),X31014),X31013)),c_List_Olists(X31015,X31012))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31015)),X31013),c_List_Olists(X31015,X31012)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31015)),hAPP(hAPP(c_List_Olist_OCons(X31015),X31014),X31013)),c_List_Olists(X31015,X31012))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X31015),X31014),X31012))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31015)),X31013),c_List_Olists(X31015,X31012)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31015)),hAPP(hAPP(c_List_Olist_OCons(X31015),X31014),X31013)),c_List_Olists(X31015,X31012))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lists__iff])])]) ).

fof(i_0_8089,plain,
    ! [X17609,X17610,X17611,X17612] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17612,tc_HOL_Obool)),X17610),hAPP(hAPP(c_Set_Oinsert(X17612),X17611),X17609)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17612,tc_HOL_Obool)),X17610),X17609))
        | hBOOL(hAPP(hAPP(c_member(X17612),X17611),X17610)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17612,tc_HOL_Obool)),X17610),X17609))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17612,tc_HOL_Obool)),X17610),hAPP(hAPP(c_Set_Oinsert(X17612),X17611),X17609)))
        | hBOOL(hAPP(hAPP(c_member(X17612),X17611),X17610)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5721])])]) ).

fof(i_0_8090,plain,
    ! [X28525,X28526] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X28526))
      | 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(X28526),X28525))),X28526)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range])]) ).

fof(i_0_8091,plain,
    ! [X18052,X18053,X18054,X18055] :
      ( ( hBOOL(hAPP(hAPP(c_member(X18055),X18054),X18053))
        | ~ hBOOL(hAPP(hAPP(c_member(X18055),X18054),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18055,tc_HOL_Obool)),X18053),X18052))) )
      & ( hBOOL(hAPP(hAPP(c_member(X18055),X18054),X18052))
        | ~ hBOOL(hAPP(hAPP(c_member(X18055),X18054),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18055,tc_HOL_Obool)),X18053),X18052))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18055),X18054),X18053))
        | ~ hBOOL(hAPP(hAPP(c_member(X18055),X18054),X18052))
        | hBOOL(hAPP(hAPP(c_member(X18055),X18054),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18055,tc_HOL_Obool)),X18053),X18052))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__iff])])]) ).

fof(i_0_8092,plain,
    ! [X18048,X18049,X18050,X18051] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X18051),X18050),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18051,tc_HOL_Obool)),X18049),X18048)))
      | hBOOL(hAPP(hAPP(c_member(X18051),X18050),X18049)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD1])]) ).

fof(i_0_8093,plain,
    ! [X17793,X17794,X17795,X17796] :
      ( ( hBOOL(hAPP(hAPP(c_member(X17796),X17795),X17794))
        | ~ hBOOL(hAPP(hAPP(c_member(X17796),X17795),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17796,tc_HOL_Obool)),X17794),X17793))) )
      & ( hBOOL(hAPP(hAPP(c_member(X17796),X17795),X17793))
        | ~ hBOOL(hAPP(hAPP(c_member(X17796),X17795),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17796,tc_HOL_Obool)),X17794),X17793))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5722])])]) ).

fof(i_0_8094,plain,
    ! [X18036,X18037,X18038,X18039] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X18039),X18038),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18039,tc_HOL_Obool)),X18037),X18036)))
      | hBOOL(hAPP(hAPP(c_member(X18039),X18038),X18037)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DiffD1])]) ).

fof(i_0_8095,plain,
    ! [X18044,X18045,X18046,X18047] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X18047),X18046),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18047,tc_HOL_Obool)),X18045),X18044)))
      | hBOOL(hAPP(hAPP(c_member(X18047),X18046),X18044)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD2])]) ).

fof(i_0_8096,plain,
    ! [X18200,X18201,X18202,X18203] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18203,tc_HOL_Obool)),X18202),hAPP(hAPP(c_Set_Oinsert(X18203),X18201),X18200)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18203,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18203,tc_HOL_Obool)),X18202),X18200)),hAPP(hAPP(c_Set_Oinsert(X18203),X18201),c_Orderings_Obot__class_Obot(tc_fun(X18203,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_Diff__insert]) ).

fof(i_0_8097,plain,
    ! [X31466,X31467] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X31467),X31466))
        | c_List_Oupto(X31467,X31466) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X31467),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X31467),c_Groups_Oone__class_Oone(tc_Int_Oint)),X31466))
        | ~ 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),X31467),X31466))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X31467),X31466))
        | c_List_Oupto(X31467,X31466) = 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),X31467),X31466))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5723])])]) ).

fof(i_0_8098,plain,
    ! [X21159,X21160,X21161] :
      ( ~ class_Groups_Oab__semigroup__mult(X21161)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21161),X21160))
      | X21160 = c_Orderings_Obot__class_Obot(tc_fun(X21161,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21161),X21159))
      | X21159 = c_Orderings_Obot__class_Obot(tc_fun(X21161,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21161,tc_HOL_Obool)),X21160),X21159) != c_Orderings_Obot__class_Obot(tc_fun(X21161,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ofold1(X21161,c_Groups_Otimes__class_Otimes(X21161)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21161,tc_HOL_Obool)),X21160),X21159)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21161),hAPP(c_Finite__Set_Ofold1(X21161,c_Groups_Otimes__class_Otimes(X21161)),X21160)),hAPP(c_Finite__Set_Ofold1(X21161,c_Groups_Otimes__class_Otimes(X21161)),X21159)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__Un])]) ).

fof(i_0_8099,plain,
    ! [X29201,X29202,X29203,X29204,X29205,X29206] :
      ( ~ c_Finite__Set_Ofun__left__comm(X29206,X29205,X29204)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29206),X29203))
      | hBOOL(hAPP(hAPP(c_member(X29206),X29202),X29203))
      | hAPP(hAPP(c_Finite__Set_Ofold(X29206,X29205,X29204),X29201),hAPP(hAPP(c_Set_Oinsert(X29206),X29202),X29203)) = hAPP(hAPP(X29204,X29202),hAPP(hAPP(c_Finite__Set_Ofold(X29206,X29205,X29204),X29201),X29203)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5724])]) ).

cnf(i_0_8100,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_5479]) ).

fof(i_0_8101,plain,
    ! [X21040,X21041,X21042,X21043,X21044,X21045] :
      ( ~ c_Finite__Set_Ofolding__idem(X21045,X21044,X21043,X21042)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21045),X21041))
      | hAPP(X21042,hAPP(hAPP(c_Set_Oinsert(X21045),X21040),X21041)) = hAPP(c_Fun_Ocomp(X21044,X21044,X21044,hAPP(X21042,X21041)),hAPP(X21043,X21040)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oinsert__idem])]) ).

fof(i_0_8102,plain,
    ! [X28423,X28424,X28425,X28426] : hAPP(hAPP(c_Product__Type_Oscomp(X28426,X28425,X28424,tc_prod(X28425,X28424)),X28423),c_Product__Type_OPair(X28425,X28424)) = X28423,
    inference(variable_rename,[status(thm)],[fact_scomp__Pair]) ).

fof(i_0_8103,plain,
    ! [X18171,X18172] : hAPP(c_Set_OPow(X18172),X18171) = hAPP(c_Set_OCollect(tc_fun(X18172,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X18172,tc_HOL_Obool),tc_fun(X18172,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X18172,tc_HOL_Obool))),X18171)),
    inference(variable_rename,[status(thm)],[fact_Pow__def]) ).

fof(i_0_8104,plain,
    ! [X32932,X32933] : hAPP(c_List_Orev(X32933),X32932) = hAPP(c_List_Ofoldl(tc_List_Olist(X32933),X32933,hAPP(c_COMBC(X32933,tc_List_Olist(X32933),tc_List_Olist(X32933)),c_List_Olist_OCons(X32933)),c_List_Olist_ONil(X32933)),X32932),
    inference(variable_rename,[status(thm)],[fact_rev__foldl__cons]) ).

fof(i_0_8105,plain,
    ! [X33848,X33849] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33849),X33848))
        | c_Lazy__Sequence_Osmall__lazy_H(X33849,X33848) = 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),X33849),X33848))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33849),X33848))
        | c_Lazy__Sequence_Osmall__lazy_H(X33849,X33848) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X33848),c_Lazy__Sequence_Osmall__lazy_H(X33849,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X33848),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),X33849),X33848))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5725])])]) ).

cnf(i_0_8106,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_5683]) ).

fof(i_0_8107,plain,
    ! [X26684,X26685] :
      ( ~ class_Rings_Ocomm__semiring__1(X26685)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26685),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26685),c_Groups_Oone__class_Oone(X26685)),c_Groups_Oone__class_Oone(X26685))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26685),c_Nat_Osemiring__1__class_Oof__nat(X26685)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X26684))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26685),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26685),X26684)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26685),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26685),X26684)),c_Groups_Oone__class_Oone(X26685))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gauss__sum])]) ).

fof(i_0_8108,plain,
    ! [X30547,X30548,X30549,X30550] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30550)),X30549),hAPP(c_List_Oset(tc_List_Olist(X30550)),c_Enum_On__lists(X30550,X30548,X30547))))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30550)),X30549) = X30548 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__n__lists__elem])]) ).

cnf(i_0_8109,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_5492]) ).

fof(i_0_8110,plain,
    ! [X30325,X30326,X30327,X30328,X30329,X30330] :
      ( hBOOL(hAPP(hAPP(c_member(X30330),X30329),hAPP(c_List_Oset(X30330),X30328)))
      | hAPP(hAPP(c_List_Omap(X30330,X30327),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X30330,X30327),X30326),X30329),X30325)),X30328) = hAPP(hAPP(c_List_Omap(X30330,X30327),X30326),X30328) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5726])]) ).

fof(i_0_8111,plain,
    ! [X28205,X28206,X28207] :
      ( ~ c_Wellfounded_Oacyclic(X28207,X28206)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28207,X28207),tc_HOL_Obool)),X28205),X28206))
      | c_Wellfounded_Oacyclic(X28207,X28205) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__subset])]) ).

fof(i_0_8112,plain,
    ! [X27407,X27408,X27409] :
      ( ~ c_Wellfounded_Owf(X27409,X27408)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27409,X27409),tc_HOL_Obool)),X27407),X27408))
      | c_Wellfounded_Owf(X27409,X27407) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__subset])]) ).

fof(i_0_8113,plain,
    ! [X32574,X32575,X32576,X32577] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X32575),X32577),hAPP(c_List_Oset(X32575),c_List_Oremove1(X32575,X32576,X32574))))
        | hBOOL(hAPP(hAPP(c_member(X32575),X32577),hAPP(c_List_Oset(X32575),X32574)))
        | X32577 = X32576 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32575),X32577),hAPP(c_List_Oset(X32575),X32574)))
        | hBOOL(hAPP(hAPP(c_member(X32575),X32577),hAPP(c_List_Oset(X32575),c_List_Oremove1(X32575,X32576,X32574))))
        | X32577 = X32576 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__remove1])])]) ).

fof(i_0_8114,plain,
    ! [X17894,X17895,X17896,X17897] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17897,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17897,tc_HOL_Obool)),X17896),X17895)),X17894) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17897,tc_HOL_Obool)),X17896),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17897,tc_HOL_Obool)),X17895),X17894)),
    inference(variable_rename,[status(thm)],[fact_Int__assoc]) ).

fof(i_0_8115,plain,
    ! [X17898,X17899,X17900,X17901] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17901,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17901,tc_HOL_Obool)),X17900),X17899)),X17898) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17901,tc_HOL_Obool)),X17900),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17901,tc_HOL_Obool)),X17899),X17898)),
    inference(variable_rename,[status(thm)],[fact_Int__Diff]) ).

fof(i_0_8116,plain,
    ! [X17378,X17379,X17380,X17381] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17381,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17381,tc_HOL_Obool)),X17380),X17379)),X17378) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17381,tc_HOL_Obool)),X17380),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17381,tc_HOL_Obool)),X17379),X17378)),
    inference(variable_rename,[status(thm)],[fact_Un__assoc]) ).

fof(i_0_8117,plain,
    ! [X21842,X21843,X21844] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21844),X21843))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21842),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21843),X21842)),X21844))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff])]) ).

fof(i_0_8118,plain,
    ! [X32994,X32995,X32996,X32997] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32997),X32996),hAPP(c_List_Oset(X32997),X32994)))
        | ~ hBOOL(hAPP(hAPP(c_member(X32997),X32996),hAPP(c_List_Oset(X32997),c_List_OtakeWhile(X32997,X32995,X32994)))) )
      & ( hBOOL(hAPP(X32995,X32996))
        | ~ hBOOL(hAPP(hAPP(c_member(X32997),X32996),hAPP(c_List_Oset(X32997),c_List_OtakeWhile(X32997,X32995,X32994)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__takeWhileD])])]) ).

fof(i_0_8119,plain,
    ! [X32570,X32571,X32572,X32573] :
      ( hBOOL(hAPP(hAPP(c_member(X32573),X32572),hAPP(c_List_Oset(X32573),X32571)))
      | ~ hBOOL(hAPP(hAPP(c_member(X32573),X32572),hAPP(c_List_Oset(X32573),c_List_Oremove1(X32573,X32570,X32571)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5727])]) ).

fof(i_0_8120,plain,
    ! [X30567,X30568,X30569,X30570] :
      ( hBOOL(hAPP(hAPP(c_member(X30570),X30569),hAPP(c_List_Oset(X30570),X30568)))
      | ~ hBOOL(hAPP(hAPP(c_member(X30570),X30569),hAPP(c_List_Oset(X30570),c_List_Osublist(X30570,X30568,X30567)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5728])]) ).

fof(i_0_8121,plain,
    ! [X30563,X30564,X30565,X30566] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X30566),X30565),hAPP(c_List_Oset(X30566),c_List_Osublist(X30566,X30564,X30563))))
      | hBOOL(hAPP(hAPP(c_member(X30566),X30565),hAPP(c_List_Oset(X30566),X30564))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__sublistD])]) ).

fof(i_0_8122,plain,
    ! [X32270,X32271,X32272] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32272,tc_HOL_Obool)),hAPP(c_List_Oset(X32272),hAPP(c_List_Ofilter(X32272,X32271),X32270))),hAPP(c_List_Oset(X32272),X32270))),
    inference(variable_rename,[status(thm)],[fact_filter__is__subset]) ).

fof(i_0_8123,plain,
    ! [X21518,X21519,X21520,X21521,X21522] :
      ( ( X21521 = X21520
        | X21519 = X21518
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21522),X21521),X21519)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21522),X21520),X21518)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21522),X21521),X21518)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21522),X21520),X21519))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X21522) )
      & ( X21521 != X21520
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21522),X21521),X21519)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21522),X21520),X21518)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21522),X21521),X21518)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21522),X21520),X21519))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X21522) )
      & ( X21519 != X21518
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21522),X21521),X21519)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21522),X21520),X21518)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21522),X21521),X21518)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21522),X21520),X21519))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X21522) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq])])]) ).

fof(i_0_8124,plain,
    ! [X21505,X21506,X21507,X21508,X21509] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21509),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21509),X21508),X21507)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21509),X21506),X21505)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21509),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21509),X21508),X21505)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21509),X21506),X21507))
        | X21508 = X21506
        | X21507 = X21505
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X21509) )
      & ( X21508 != X21506
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21509),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21509),X21508),X21507)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21509),X21506),X21505)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21509),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21509),X21508),X21505)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21509),X21506),X21507))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X21509) )
      & ( X21507 != X21505
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21509),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21509),X21508),X21507)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21509),X21506),X21505)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21509),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21509),X21508),X21505)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21509),X21506),X21507))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X21509) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__eq])])]) ).

cnf(i_0_8125,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_5729]) ).

fof(i_0_8126,plain,
    ! [X28156,X28157] :
      ( ( ~ c_Predicate_Oreflp(X28157,X28156)
        | c_Relation_Orefl__on(X28157,c_Orderings_Otop__class_Otop(tc_fun(X28157,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X28157,X28157)),hAPP(c_Product__Type_Oprod_Oprod__case(X28157,X28157,tc_HOL_Obool),X28156))) )
      & ( ~ c_Relation_Orefl__on(X28157,c_Orderings_Otop__class_Otop(tc_fun(X28157,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X28157,X28157)),hAPP(c_Product__Type_Oprod_Oprod__case(X28157,X28157,tc_HOL_Obool),X28156)))
        | c_Predicate_Oreflp(X28157,X28156) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflp__def])]) ).

fof(i_0_8127,plain,
    ! [X21850,X21851,X21852] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21850),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21851),X21852)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21850),X21852)),X21851))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21852),X21851)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21850),X21852)),X21851))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21850),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21851),X21852)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21852),X21851)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv2])])]) ).

fof(i_0_8128,plain,
    ! [X32135,X32136,X32137,X32138] :
      ( ~ class_Enum_Oenum(X32138)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32137)),X32136) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32138)),c_Enum_Oenum__class_Oenum(X32138))
      | hAPP(hAPP(c_Map_Omap__of(X32138,X32137),hAPP(hAPP(c_List_Ozip(X32138,X32137),c_Enum_Oenum__class_Oenum(X32138)),X32136)),X32135) = hAPP(c_Option_Ooption_OSome(X32137),esk436_4(X32135,X32136,X32137,X32138)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__zip__enum__is__Some])])]) ).

cnf(i_0_8129,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_5730]) ).

fof(i_0_8130,plain,
    ! [X34126,X34127,X34128,X34129,X34131,X34132,X34133,X34135] :
      ( ( hBOOL(hAPP(X34128,esk523_4(X34126,X34127,X34128,X34129)))
        | ~ hBOOL(hAPP(X34128,X34129))
        | c_FunDef_OTHE__default(X34127,X34126,X34128) = c_HOL_OThe(X34127,X34128) )
      & ( esk523_4(X34126,X34127,X34128,X34129) != X34129
        | ~ hBOOL(hAPP(X34128,X34129))
        | c_FunDef_OTHE__default(X34127,X34126,X34128) = c_HOL_OThe(X34127,X34128) )
      & ( hBOOL(hAPP(X34133,esk524_3(X34131,X34132,X34133)))
        | c_FunDef_OTHE__default(X34132,X34131,X34133) = X34131 )
      & ( ~ hBOOL(hAPP(X34133,X34135))
        | X34135 = esk524_3(X34131,X34132,X34133)
        | c_FunDef_OTHE__default(X34132,X34131,X34133) = X34131 ) ),
    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_8131,plain,
    ! [X19424,X19425,X19426,X19427,X19428] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X19428),X19427),hAPP(c_Set_Ovimage(X19428,X19426,X19425),X19424)))
      | hBOOL(hAPP(hAPP(c_member(X19426),hAPP(X19425,X19427)),X19424)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimageD])]) ).

fof(i_0_8132,plain,
    ! [X19419,X19420,X19421,X19422,X19423] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X19423),X19422),hAPP(c_Set_Ovimage(X19423,X19421,X19420),X19419)))
        | hBOOL(hAPP(hAPP(c_member(X19421),hAPP(X19420,X19422)),X19419)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X19421),hAPP(X19420,X19422)),X19419))
        | hBOOL(hAPP(hAPP(c_member(X19423),X19422),hAPP(c_Set_Ovimage(X19423,X19421,X19420),X19419))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__eq])]) ).

fof(i_0_8133,plain,
    ! [X18490,X18491,X18492,X18493] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18492,X18493)),X18491),X18490))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18492,X18493)),X18491),X18490))
        | ~ class_Orderings_Oord(X18493) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18492,X18493)),X18490),X18491))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18492,X18493)),X18491),X18490))
        | ~ class_Orderings_Oord(X18493) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18492,X18493)),X18491),X18490))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18492,X18493)),X18490),X18491))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18492,X18493)),X18491),X18490))
        | ~ class_Orderings_Oord(X18493) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5731])])]) ).

fof(i_0_8134,plain,
    ! [X18873,X18874,X18875] :
      ( ( hBOOL(hAPP(hAPP(c_member(X18875),esk38_3(X18873,X18874,X18875)),X18874))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18875,tc_HOL_Obool)),X18874),X18873)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18875),esk38_3(X18873,X18874,X18875)),X18873))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18875,tc_HOL_Obool)),X18874),X18873)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetI])])])]) ).

fof(i_0_8135,plain,
    ! [X31835,X31836,X31837,X31838] : hAPP(hAPP(c_List_Odrop(X31838),X31837),hAPP(hAPP(c_List_Olist_OCons(X31838),X31836),X31835)) = c_Nat_Onat_Onat__case(tc_List_Olist(X31838),hAPP(hAPP(c_List_Olist_OCons(X31838),X31836),X31835),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X31838),tc_List_Olist(X31838)),c_List_Odrop(X31838)),X31835),X31837),
    inference(variable_rename,[status(thm)],[fact_drop__Cons]) ).

fof(i_0_8136,plain,
    ! [X22460,X22461,X22462] :
      ( ~ class_Rings_Olinordered__idom(X22462)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22462),c_Groups_Ozero__class_Ozero(X22462)),X22461))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22462),c_Groups_Ozero__class_Ozero(X22462)),X22460))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22462),X22460),c_Groups_Oone__class_Oone(X22462)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22462),X22461),X22460)),X22461)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le])]) ).

fof(i_0_8137,plain,
    ! [X22457,X22458,X22459] :
      ( ~ class_Rings_Olinordered__idom(X22459)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22459),c_Groups_Ozero__class_Ozero(X22459)),X22458))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22459),c_Groups_Ozero__class_Ozero(X22459)),X22457))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22459),X22457),c_Groups_Oone__class_Oone(X22459)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22459),X22457),X22458)),X22458)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le])]) ).

fof(i_0_8138,plain,
    ! [X30373,X30374,X30375,X30376] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X30376),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X30375),X30374)))
        | hAPP(c_Random_Opick(X30375,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X30375)),X30374),X30373)),X30376) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X30375),X30374) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X30376),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X30375),X30374)))
        | hAPP(c_Random_Opick(X30375,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X30375)),X30374),X30373)),X30376) = hAPP(c_Random_Opick(X30375,X30373),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X30376),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X30375),X30374))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5732])]) ).

cnf(i_0_8139,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5658]) ).

cnf(i_0_8140,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_5659]) ).

cnf(i_0_8141,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_5661]) ).

cnf(i_0_8142,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_5660]) ).

cnf(i_0_8143,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_5662]) ).

fof(i_0_8144,plain,
    ! [X29660,X29661,X29662,X29663,X29664,X29665,X29666] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29662,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29662,tc_HOL_Obool),X29661)),X29660) != c_Orderings_Obot__class_Obot(tc_fun(X29662,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X29662,tc_HOL_Obool)),X29663),X29661))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29662,tc_HOL_Obool)),X29663),X29660) = c_Orderings_Obot__class_Obot(tc_fun(X29662,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X29666,tc_HOL_Obool)),esk365_3(X29664,X29665,X29666)),X29665))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29666,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29666,tc_HOL_Obool),X29665)),X29664) = c_Orderings_Obot__class_Obot(tc_fun(X29666,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29666,tc_HOL_Obool)),esk365_3(X29664,X29665,X29666)),X29664) != c_Orderings_Obot__class_Obot(tc_fun(X29666,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29666,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29666,tc_HOL_Obool),X29665)),X29664) = c_Orderings_Obot__class_Obot(tc_fun(X29666,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_8145,plain,
    ! [X23131,X23132,X23133] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23133))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23132))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23132),X23131))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23133),X23131)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23133),X23132))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2])]) ).

fof(i_0_8146,plain,
    ! [X27606,X27607,X27608,X27609] : hAPP(c_Relation_ODomain(X27609,X27608),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27609,X27608),tc_HOL_Obool)),X27607),X27606)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27609,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X27609,X27608),X27607)),hAPP(c_Relation_ODomain(X27609,X27608),X27606)),
    inference(variable_rename,[status(thm)],[fact_Domain__Un__eq]) ).

fof(i_0_8147,plain,
    ! [X27528,X27529,X27530,X27531] : hAPP(c_Relation_ORange(X27531,X27530),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27531,X27530),tc_HOL_Obool)),X27529),X27528)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27530,tc_HOL_Obool)),hAPP(c_Relation_ORange(X27531,X27530),X27529)),hAPP(c_Relation_ORange(X27531,X27530),X27528)),
    inference(variable_rename,[status(thm)],[fact_Range__Un__eq]) ).

fof(i_0_8148,plain,
    ! [X31137,X31138,X31139,X31140,X31141,X31142] : hAPP(hAPP(c_List_Omap(X31142,X31141),X31140),hAPP(hAPP(c_List_Olist__update(X31142,X31139),X31138),X31137)) = hAPP(hAPP(c_List_Olist__update(X31141,hAPP(hAPP(c_List_Omap(X31142,X31141),X31140),X31139)),X31138),hAPP(X31140,X31137)),
    inference(variable_rename,[status(thm)],[fact_map__update]) ).

fof(i_0_8149,plain,
    ! [X18288,X18289,X18290,X18291] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X18291)
      | X18290 != c_Inductive_Ocomplete__lattice__class_Ogfp(X18291,X18289)
      | ~ c_Orderings_Oorder__class_Omono(X18291,X18291,X18289)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18291),X18288),hAPP(X18289,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18291),X18288),X18290))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18291),X18288),X18290)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_def__coinduct])]) ).

fof(i_0_8150,plain,
    ! [X29958,X29959,X29960,X29961,X29962] : hAPP(c_Map_Omap__add(X29962,X29961,X29960,X29959),X29958) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X29961),X29961,hAPP(X29960,X29958),c_Option_Ooption_OSome(X29961)),hAPP(X29959,X29958)),
    inference(variable_rename,[status(thm)],[fact_map__add__def]) ).

fof(i_0_8151,plain,
    ! [X30308,X30309,X30310,X30311] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X30311),X30310),hAPP(c_List_Oset(X30311),hAPP(hAPP(c_List_Olist_OCons(X30311),X30309),X30308))))
      | X30310 = X30309
      | hBOOL(hAPP(hAPP(c_member(X30311),X30310),hAPP(c_List_Oset(X30311),X30308))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__ConsD])]) ).

fof(i_0_8152,plain,
    ! [X31312] :
      ( X31312 = 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,X31312)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,X31312))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral__decr])]) ).

fof(i_0_8153,plain,
    ! [X31788,X31789,X31790,X31791] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X31791),X31790),hAPP(c_List_Oset(X31791),hAPP(hAPP(c_List_Odrop(X31791),X31789),X31788))))
      | hBOOL(hAPP(hAPP(c_member(X31791),X31790),hAPP(c_List_Oset(X31791),X31788))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__dropD])]) ).

fof(i_0_8154,plain,
    ! [X31082,X31083,X31084,X31085] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X31085),X31084),hAPP(c_List_Oset(X31085),hAPP(hAPP(c_List_Otake(X31085),X31083),X31082))))
      | hBOOL(hAPP(hAPP(c_member(X31085),X31084),hAPP(c_List_Oset(X31085),X31082))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__takeD])]) ).

fof(i_0_8155,plain,
    ! [X19018,X19019,X19020,X19021,X19022] :
      ( ( X19022 != c_Option_Ooption_ONone(X19021)
        | c_Map_Odom(X19020,X19021,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X19020,tc_Option_Ooption(X19021)),X19019),X19018),X19022)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19020,tc_HOL_Obool)),c_Map_Odom(X19020,X19021,X19019)),hAPP(hAPP(c_Set_Oinsert(X19020),X19018),c_Orderings_Obot__class_Obot(tc_fun(X19020,tc_HOL_Obool)))) )
      & ( X19022 = c_Option_Ooption_ONone(X19021)
        | c_Map_Odom(X19020,X19021,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X19020,tc_Option_Ooption(X19021)),X19019),X19018),X19022)) = hAPP(hAPP(c_Set_Oinsert(X19020),X19018),c_Map_Odom(X19020,X19021,X19019)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dom__fun__upd])]) ).

fof(i_0_8156,plain,
    ! [X22762,X22763,X22764] :
      ( ~ class_Rings_Olinordered__semidom(X22764)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22764),c_Groups_Ozero__class_Ozero(X22764)),X22763))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22764),X22763),c_Groups_Oone__class_Oone(X22764)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22764),hAPP(hAPP(c_Power_Opower__class_Opower(X22764),X22763),hAPP(c_Nat_OSuc,X22762))),c_Groups_Oone__class_Oone(X22764))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less__one])]) ).

fof(i_0_8157,plain,
    ! [X30831,X30832,X30833,X30834,X30835] :
      ( ( hAPP(hAPP(c_Map_Omap__of(X30835,X30833),hAPP(hAPP(c_List_Ozip(X30835,X30833),X30834),X30832)),X30831) != c_Option_Ooption_ONone(X30833)
        | ~ hBOOL(hAPP(hAPP(c_member(X30835),X30831),hAPP(c_List_Oset(X30835),X30834)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30835)),X30834) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30833)),X30832) )
      & ( hBOOL(hAPP(hAPP(c_member(X30835),X30831),hAPP(c_List_Oset(X30835),X30834)))
        | hAPP(hAPP(c_Map_Omap__of(X30835,X30833),hAPP(hAPP(c_List_Ozip(X30835,X30833),X30834),X30832)),X30831) = c_Option_Ooption_ONone(X30833)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30835)),X30834) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30833)),X30832) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5733])])]) ).

fof(i_0_8158,plain,
    ! [X29936,X29937,X29938] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29938),X29937),esk387_3(X29936,X29937,X29938)))
        | ~ hBOOL(hAPP(hAPP(c_member(X29938),X29937),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29938,tc_HOL_Obool),X29936))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X29938,tc_HOL_Obool)),esk387_3(X29936,X29937,X29938)),X29936))
        | ~ hBOOL(hAPP(hAPP(c_member(X29938),X29937),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29938,tc_HOL_Obool),X29936))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5734])])])]) ).

fof(i_0_8159,plain,
    ! [X23120,X23121,X23122] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23122),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)),X23121))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23121),X23120))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23122),X23121)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23122),X23120))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg])]) ).

fof(i_0_8160,plain,
    ! [X20292,X20293,X20294] :
      ( ( hBOOL(hAPP(hAPP(c_member(X20294),esk74_3(X20292,X20293,X20294)),X20292))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20294,X20294)),X20293),c_Relation_OId__on(X20294,X20292))) )
      & ( X20293 = hAPP(hAPP(c_Product__Type_OPair(X20294,X20294),esk74_3(X20292,X20293,X20294)),esk74_3(X20292,X20293,X20294))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20294,X20294)),X20293),c_Relation_OId__on(X20294,X20292))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__onE])])])]) ).

fof(i_0_8161,plain,
    ! [X19086,X19087,X19088,X19089] :
      ( ~ c_Fun_Oinj__on(X19089,X19088,X19087,c_Orderings_Otop__class_Otop(tc_fun(X19089,tc_HOL_Obool)))
      | hAPP(c_Hilbert__Choice_Oinv__into(X19089,X19088,c_Orderings_Otop__class_Otop(tc_fun(X19089,tc_HOL_Obool)),X19087),hAPP(X19087,X19086)) = X19086 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__f])]) ).

fof(i_0_8162,plain,
    ! [X19272,X19273,X19274,X19275] :
      ( ~ c_Fun_Oinj__on(X19275,X19274,X19273,c_Orderings_Otop__class_Otop(tc_fun(X19275,tc_HOL_Obool)))
      | hAPP(c_Fun_Othe__inv__into(X19275,X19274,c_Orderings_Otop__class_Otop(tc_fun(X19275,tc_HOL_Obool)),X19273),hAPP(X19273,X19272)) = X19272 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__f__f])]) ).

fof(i_0_8163,plain,
    ! [X29184,X29185,X29186,X29187,X29188,X29189] :
      ( ~ c_Finite__Set_Ofun__left__comm(X29189,X29188,X29187)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29189),X29186))
      | hAPP(hAPP(X29187,X29185),hAPP(hAPP(c_Finite__Set_Ofold(X29189,X29188,X29187),X29184),X29186)) = hAPP(hAPP(c_Finite__Set_Ofold(X29189,X29188,X29187),hAPP(hAPP(X29187,X29185),X29184)),X29186) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__fun__comm])]) ).

fof(i_0_8164,plain,
    ! [X19081,X19082,X19083,X19084,X19085] :
      ( ~ c_Fun_Oinj__on(X19085,X19084,X19083,c_Orderings_Otop__class_Otop(tc_fun(X19085,tc_HOL_Obool)))
      | hAPP(X19083,X19082) != X19081
      | hAPP(c_Hilbert__Choice_Oinv__into(X19085,X19084,c_Orderings_Otop__class_Otop(tc_fun(X19085,tc_HOL_Obool)),X19083),X19081) = X19082 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__eq])]) ).

fof(i_0_8165,plain,
    ! [X28189,X28190,X28191] :
      ( ~ c_Wellfounded_OwfP(X28191,X28190)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28191,tc_fun(X28191,tc_HOL_Obool))),X28189),X28190))
      | c_Wellfounded_OwfP(X28191,X28189) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__subset])]) ).

fof(i_0_8166,plain,
    ! [X17434,X17435,X17436] :
      ( ( hAPP(hAPP(c_COMBC(X17436,tc_fun(X17436,tc_HOL_Obool),tc_HOL_Obool),c_member(X17436)),X17435) != hAPP(hAPP(c_COMBC(X17436,tc_fun(X17436,tc_HOL_Obool),tc_HOL_Obool),c_member(X17436)),X17434)
        | X17435 = X17434 )
      & ( X17435 != X17434
        | hAPP(hAPP(c_COMBC(X17436,tc_fun(X17436,tc_HOL_Obool),tc_HOL_Obool),c_member(X17436)),X17435) = hAPP(hAPP(c_COMBC(X17436,tc_fun(X17436,tc_HOL_Obool),tc_HOL_Obool),c_member(X17436)),X17434) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq])]) ).

fof(i_0_8167,plain,
    ! [X22357,X22358,X22359] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22359))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22359),X22358)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22359),X22357))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22358),X22357))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22359),X22358)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22359),X22357))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22359))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22358),X22357))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22359),X22358)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22359),X22357))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1])])]) ).

fof(i_0_8168,plain,
    ! [X22354,X22355,X22356] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22355))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22356),X22355)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22354),X22355))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22356),X22354))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22356),X22355)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22354),X22355))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22355))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22356),X22354))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22356),X22355)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22354),X22355))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2])])]) ).

fof(i_0_8169,plain,
    ! [X32640,X32641,X32642,X32643,X32644] :
      ( ~ class_Orderings_Olinorder(X32644)
      | c_List_Olinorder__class_Osort__key(X32643,X32644,X32642,hAPP(hAPP(c_List_Olist_OCons(X32643),X32641),X32640)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32643,X32644,X32642),X32641),c_List_Olinorder__class_Osort__key(X32643,X32644,X32642,X32640)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sort__key__simps_I2_J])]) ).

fof(i_0_8170,plain,
    ! [X33867,X33868,X33869,X33870,X33871] : c_Lazy__Sequence_Ohb__map(X33871,X33870,X33869,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X33871),X33868,X33867)) = c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X33870),hAPP(hAPP(c_Option_Omap(X33871,X33870),X33869),X33868),c_Lazy__Sequence_Ohb__map(X33871,X33870,X33869,X33867)),
    inference(variable_rename,[status(thm)],[fact_hb__map_Osimps_I2_J]) ).

fof(i_0_8171,plain,
    ! [X24320,X24321,X24322,X24323] :
      ( ~ class_Fields_Olinordered__field(X24323)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24323),X24322),X24321))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24323),c_Groups_Ozero__class_Ozero(X24323)),X24320))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24323),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24323),X24322),X24320)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24323),X24321),X24320))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono])]) ).

fof(i_0_8172,plain,
    ! [X22229,X22230,X22231,X22232] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22232)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22232),X22231),X22230))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22232),c_Groups_Ozero__class_Ozero(X22232)),X22229))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22232),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22232),X22231),X22229)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22232),X22230),X22229))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono])]) ).

fof(i_0_8173,plain,
    ! [X22225,X22226,X22227,X22228] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22228)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22228),X22227),X22226))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22228),c_Groups_Ozero__class_Ozero(X22228)),X22225))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22228),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22228),X22225),X22227)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22228),X22225),X22226))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono])]) ).

fof(i_0_8174,plain,
    ! [X22221,X22222,X22223,X22224] :
      ( ~ class_Rings_Olinordered__comm__semiring__strict(X22224)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22224),X22223),X22222))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22224),c_Groups_Ozero__class_Ozero(X22224)),X22221))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22224),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22224),X22221),X22223)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22224),X22221),X22222))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono])]) ).

fof(i_0_8175,plain,
    ! [X24292,X24293,X24294,X24295] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X24295)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24295),X24294),X24293))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24295),c_Groups_Ozero__class_Ozero(X24295)),X24292))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24295),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24295),X24294),X24292)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24295),X24293),X24292))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono])]) ).

fof(i_0_8176,plain,
    ! [X22669,X22670,X22671,X22672] :
      ( ~ class_Rings_Olinordered__semidom(X22672)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22672),X22671),X22670))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22672),c_Groups_Ozero__class_Ozero(X22672)),X22671))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22672),hAPP(hAPP(c_Power_Opower__class_Opower(X22672),X22671),X22669)),hAPP(hAPP(c_Power_Opower__class_Opower(X22672),X22670),X22669))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mono])]) ).

fof(i_0_8177,plain,
    ! [X22163,X22164,X22165,X22166] :
      ( ~ class_Rings_Oordered__semiring(X22166)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22166),X22165),X22164))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22166),c_Groups_Ozero__class_Ozero(X22166)),X22163))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22166),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22166),X22165),X22163)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22166),X22164),X22163))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono])]) ).

fof(i_0_8178,plain,
    ! [X22171,X22172,X22173,X22174] :
      ( ~ class_Rings_Oordered__comm__semiring(X22174)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22174),X22173),X22172))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22174),c_Groups_Ozero__class_Ozero(X22174)),X22171))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22174),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22174),X22171),X22173)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22174),X22171),X22172))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono])]) ).

fof(i_0_8179,plain,
    ! [X22167,X22168,X22169,X22170] :
      ( ~ class_Rings_Oordered__semiring(X22170)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22170),X22169),X22168))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22170),c_Groups_Ozero__class_Ozero(X22170)),X22167))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22170),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22170),X22167),X22169)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22170),X22167),X22168))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono])]) ).

fof(i_0_8180,plain,
    ! [X30774,X30775,X30776,X30777,X30778,X30779] : hAPP(hAPP(c_List_Ozip(X30779,X30778),hAPP(hAPP(c_List_Olist_OCons(X30779),X30777),X30776)),hAPP(hAPP(c_List_Olist_OCons(X30778),X30775),X30774)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(X30779,X30778)),hAPP(hAPP(c_Product__Type_OPair(X30779,X30778),X30777),X30775)),hAPP(hAPP(c_List_Ozip(X30779,X30778),X30776),X30774)),
    inference(variable_rename,[status(thm)],[fact_zip__Cons__Cons]) ).

fof(i_0_8181,plain,
    ! [X24305,X24306,X24307] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24307),X24306),c_Groups_Ozero__class_Ozero(X24307)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24307),c_Groups_Ozero__class_Ozero(X24307)),X24306))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24307),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24307),X24306),X24305)),c_Groups_Ozero__class_Ozero(X24307)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24307) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24307),c_Groups_Ozero__class_Ozero(X24307)),X24305))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24307),c_Groups_Ozero__class_Ozero(X24307)),X24306))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24307),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24307),X24306),X24305)),c_Groups_Ozero__class_Ozero(X24307)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24307) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24307),X24306),c_Groups_Ozero__class_Ozero(X24307)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24307),X24305),c_Groups_Ozero__class_Ozero(X24307)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24307),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24307),X24306),X24305)),c_Groups_Ozero__class_Ozero(X24307)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24307) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24307),c_Groups_Ozero__class_Ozero(X24307)),X24305))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24307),X24305),c_Groups_Ozero__class_Ozero(X24307)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24307),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24307),X24306),X24305)),c_Groups_Ozero__class_Ozero(X24307)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24307) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24307),c_Groups_Ozero__class_Ozero(X24307)),X24306))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24307),X24305),c_Groups_Ozero__class_Ozero(X24307)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24307),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24307),X24306),X24305)),c_Groups_Ozero__class_Ozero(X24307)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24307) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24307),X24306),c_Groups_Ozero__class_Ozero(X24307)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24307),c_Groups_Ozero__class_Ozero(X24307)),X24305))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24307),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24307),X24306),X24305)),c_Groups_Ozero__class_Ozero(X24307)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24307) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__less__0__iff])])]) ).

fof(i_0_8182,plain,
    ! [X24296,X24297,X24298] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24298),X24297),c_Groups_Ozero__class_Ozero(X24298)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24298),c_Groups_Ozero__class_Ozero(X24298)),X24297))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24298),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24298),X24297),X24296)),c_Groups_Ozero__class_Ozero(X24298)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24298),c_Groups_Ozero__class_Ozero(X24298)),X24296))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24298),c_Groups_Ozero__class_Ozero(X24298)),X24297))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24298),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24298),X24297),X24296)),c_Groups_Ozero__class_Ozero(X24298)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24298),X24297),c_Groups_Ozero__class_Ozero(X24298)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24298),X24296),c_Groups_Ozero__class_Ozero(X24298)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24298),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24298),X24297),X24296)),c_Groups_Ozero__class_Ozero(X24298)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24298) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24298),c_Groups_Ozero__class_Ozero(X24298)),X24296))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24298),X24296),c_Groups_Ozero__class_Ozero(X24298)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24298),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24298),X24297),X24296)),c_Groups_Ozero__class_Ozero(X24298)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24298) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24298),c_Groups_Ozero__class_Ozero(X24298)),X24297))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24298),X24296),c_Groups_Ozero__class_Ozero(X24298)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24298),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24298),X24297),X24296)),c_Groups_Ozero__class_Ozero(X24298)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24298) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24298),X24297),c_Groups_Ozero__class_Ozero(X24298)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24298),c_Groups_Ozero__class_Ozero(X24298)),X24296))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24298),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24298),X24297),X24296)),c_Groups_Ozero__class_Ozero(X24298)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24298) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__le__0__iff])])]) ).

fof(i_0_8183,plain,
    ! [X22145,X22146,X22147] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22147),X22146),c_Groups_Ozero__class_Ozero(X22147)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22147),c_Groups_Ozero__class_Ozero(X22147)),X22146))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22147),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22147),X22146),X22145)),c_Groups_Ozero__class_Ozero(X22147)))
        | ~ class_Rings_Olinordered__ring__strict(X22147) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22147),c_Groups_Ozero__class_Ozero(X22147)),X22145))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22147),c_Groups_Ozero__class_Ozero(X22147)),X22146))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22147),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22147),X22146),X22145)),c_Groups_Ozero__class_Ozero(X22147)))
        | ~ class_Rings_Olinordered__ring__strict(X22147) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22147),X22146),c_Groups_Ozero__class_Ozero(X22147)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22147),X22145),c_Groups_Ozero__class_Ozero(X22147)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22147),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22147),X22146),X22145)),c_Groups_Ozero__class_Ozero(X22147)))
        | ~ class_Rings_Olinordered__ring__strict(X22147) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22147),c_Groups_Ozero__class_Ozero(X22147)),X22145))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22147),X22145),c_Groups_Ozero__class_Ozero(X22147)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22147),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22147),X22146),X22145)),c_Groups_Ozero__class_Ozero(X22147)))
        | ~ class_Rings_Olinordered__ring__strict(X22147) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22147),c_Groups_Ozero__class_Ozero(X22147)),X22146))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22147),X22145),c_Groups_Ozero__class_Ozero(X22147)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22147),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22147),X22146),X22145)),c_Groups_Ozero__class_Ozero(X22147)))
        | ~ class_Rings_Olinordered__ring__strict(X22147) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22147),X22146),c_Groups_Ozero__class_Ozero(X22147)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22147),c_Groups_Ozero__class_Ozero(X22147)),X22145))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22147),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22147),X22146),X22145)),c_Groups_Ozero__class_Ozero(X22147)))
        | ~ class_Rings_Olinordered__ring__strict(X22147) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff])])]) ).

fof(i_0_8184,plain,
    ! [X25531,X25532] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25532),X25531))
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X25532)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25531)))
        | ~ c_Nat__Transfer_Onat__set(X25531)
        | ~ c_Nat__Transfer_Ois__nat(X25532) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X25532)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25531)))
        | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25532),X25531))
        | ~ c_Nat__Transfer_Onat__set(X25531)
        | ~ c_Nat__Transfer_Ois__nat(X25532) ) ),
    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_8185,plain,
    ! [X28390,X28391,X28392] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28392),esk322_3(X28390,X28391,X28392)),X28391))
        | ~ hBOOL(hAPP(hAPP(c_member(X28392),X28390),X28391))
        | c_Big__Operators_Olinorder__class_OMax(X28392,X28391) = X28390
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28392),X28391))
        | ~ class_Orderings_Olinorder(X28392) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28392),esk322_3(X28390,X28391,X28392)),X28390))
        | ~ hBOOL(hAPP(hAPP(c_member(X28392),X28390),X28391))
        | c_Big__Operators_Olinorder__class_OMax(X28392,X28391) = X28390
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28392),X28391))
        | ~ class_Orderings_Olinorder(X28392) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__eqI])])])]) ).

fof(i_0_8186,plain,
    ! [X33577,X33578,X33579,X33580,X33581,X33582,X33583] :
      ( ( ~ c_List_Olist__all(X33579,X33578,X33577)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33580),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33579)),X33577)))
        | hBOOL(hAPP(X33578,hAPP(hAPP(c_List_Onth(X33579),X33577),X33580))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk502_3(X33581,X33582,X33583)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33583)),X33581)))
        | c_List_Olist__all(X33583,X33582,X33581) )
      & ( ~ hBOOL(hAPP(X33582,hAPP(hAPP(c_List_Onth(X33583),X33581),esk502_3(X33581,X33582,X33583))))
        | c_List_Olist__all(X33583,X33582,X33581) ) ),
    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_8187,plain,
    ! [X23988] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23988)),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),X23988)) = 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),X23988))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__1__number__of])]) ).

fof(i_0_8188,plain,
    ! [X18758,X18759,X18760,X18761,X18762] :
      ( ~ c_Fun_Oinj__on(X18762,X18761,X18760,X18759)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18762,tc_HOL_Obool)),X18758),X18759))
      | c_Fun_Oinj__on(X18762,X18761,X18760,X18758) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__inj__on])]) ).

fof(i_0_8189,plain,
    ! [X32276,X32277,X32278] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32278)),hAPP(c_List_Ofilter(X32278,X32277),X32276))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32278)),X32276))),
    inference(variable_rename,[status(thm)],[fact_length__filter__le]) ).

fof(i_0_8190,plain,
    ! [X28538,X28539,X28540] : hBOOL(hAPP(hAPP(c_member(tc_prod(X28540,X28540)),hAPP(hAPP(c_Product__Type_OPair(X28540,X28540),X28539),X28539)),c_Transitive__Closure_Ortrancl(X28540,X28538))),
    inference(variable_rename,[status(thm)],[fact_rtrancl_Ortrancl__refl]) ).

cnf(i_0_8191,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5735]) ).

cnf(i_0_8192,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_5736]) ).

cnf(i_0_8193,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_5737]) ).

fof(i_0_8194,plain,
    ! [X21672,X21673,X21674] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21674),X21673)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21674),X21672)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21673),X21672)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21673),X21672))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21674),X21673)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21674),X21672))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).

cnf(i_0_8195,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_5738]) ).

cnf(i_0_8196,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_5739]) ).

fof(i_0_8197,plain,
    ! [X21731,X21732,X21733] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21733),X21732)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21733),X21731)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21732),X21731)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21732),X21731))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21733),X21732)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21733),X21731))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).

fof(i_0_8198,plain,
    ! [X19235,X19236,X19237,X19238,X19239] :
      ( ~ c_Fun_Oinj__on(X19239,X19238,X19237,X19236)
      | ~ hBOOL(hAPP(hAPP(c_member(X19239),X19235),X19236))
      | hAPP(c_Hilbert__Choice_Oinv__into(X19239,X19238,X19236,X19237),hAPP(X19237,X19235)) = X19235 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__f])]) ).

fof(i_0_8199,plain,
    ! [X18719,X18720,X18721,X18722,X18723] :
      ( ~ c_Fun_Oinj__on(X18723,X18722,X18721,X18720)
      | ~ hBOOL(hAPP(hAPP(c_member(X18723),X18719),X18720))
      | hAPP(c_Fun_Othe__inv__into(X18723,X18722,X18720,X18721),hAPP(X18721,X18719)) = X18719 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__f])]) ).

cnf(i_0_8200,plain,
    hAPP(c_List_OremoveAll(X1,X2),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_5740]) ).

fof(i_0_8201,plain,
    ! [X23987] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23987)),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),X23987)) = 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),X23987))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__neg__1__number__of])]) ).

fof(i_0_8202,plain,
    ! [X19240,X19241,X19242,X19243,X19244,X19245] :
      ( ~ c_Fun_Oinj__on(X19245,X19244,X19243,X19242)
      | ~ hBOOL(hAPP(hAPP(c_member(X19245),X19241),X19242))
      | hAPP(X19243,X19241) != X19240
      | hAPP(c_Hilbert__Choice_Oinv__into(X19245,X19244,X19242,X19243),X19240) = X19241 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__eq])]) ).

fof(i_0_8203,plain,
    ! [X18713,X18714,X18715,X18716,X18717,X18718] :
      ( ~ c_Fun_Oinj__on(X18718,X18717,X18716,X18715)
      | hAPP(X18716,X18714) != X18713
      | ~ hBOOL(hAPP(hAPP(c_member(X18718),X18714),X18715))
      | hAPP(c_Fun_Othe__inv__into(X18718,X18717,X18715,X18716),X18713) = X18714 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__eq])]) ).

fof(i_0_8204,plain,
    ! [X29265,X29266,X29267,X29268,X29269] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29268),X29269),X29267))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29266),hAPP(X29265,X29269)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X29266),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29268,tc_fun(X29266,tc_HOL_Obool)),X29267),X29265))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__INT])])]) ).

fof(i_0_8205,plain,
    ! [X22742,X22743,X22744,X22745] :
      ( ~ class_Rings_Olinordered__semidom(X22745)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22744),X22743))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),c_Groups_Oone__class_Oone(X22745)),X22742))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),hAPP(hAPP(c_Power_Opower__class_Opower(X22745),X22742),X22744)),hAPP(hAPP(c_Power_Opower__class_Opower(X22745),X22742),X22743))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing])]) ).

fof(i_0_8206,plain,
    ! [X22746,X22747,X22748,X22749] :
      ( ~ class_Rings_Olinordered__semidom(X22749)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22748),X22747))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),c_Groups_Oone__class_Oone(X22749)),X22746))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),hAPP(hAPP(c_Power_Opower__class_Opower(X22749),X22746),X22748)),hAPP(hAPP(c_Power_Opower__class_Opower(X22749),X22746),X22747))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing])]) ).

fof(i_0_8207,plain,
    ! [X24324,X24325,X24326,X24327] :
      ( ~ class_Fields_Olinordered__field(X24327)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24327),X24326),X24325))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24327),X24324),c_Groups_Ozero__class_Ozero(X24327)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24327),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24327),X24325),X24324)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24327),X24326),X24324))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono__neg])]) ).

fof(i_0_8208,plain,
    ! [X22217,X22218,X22219,X22220] :
      ( ~ class_Rings_Olinordered__ring__strict(X22220)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22220),X22219),X22218))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22220),X22217),c_Groups_Ozero__class_Ozero(X22220)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22220),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22220),X22218),X22217)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22220),X22219),X22217))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg])]) ).

fof(i_0_8209,plain,
    ! [X22213,X22214,X22215,X22216] :
      ( ~ class_Rings_Olinordered__ring__strict(X22216)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22216),X22215),X22214))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22216),X22213),c_Groups_Ozero__class_Ozero(X22216)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22216),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22216),X22213),X22214)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22216),X22213),X22215))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg])]) ).

fof(i_0_8210,plain,
    ! [X24288,X24289,X24290,X24291] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X24291)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24291),X24290),X24289))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24291),X24288),c_Groups_Ozero__class_Ozero(X24291)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24291),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24291),X24289),X24288)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24291),X24290),X24288))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono__neg])]) ).

fof(i_0_8211,plain,
    ! [X22175,X22176,X22177,X22178] :
      ( ~ class_Rings_Oordered__ring(X22178)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22178),X22177),X22176))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22178),X22175),c_Groups_Ozero__class_Ozero(X22178)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22178),X22176),X22175)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22178),X22177),X22175))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg])]) ).

fof(i_0_8212,plain,
    ! [X22179,X22180,X22181,X22182] :
      ( ~ class_Rings_Oordered__ring(X22182)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22182),X22181),X22180))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22182),X22179),c_Groups_Ozero__class_Ozero(X22182)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22182),X22179),X22180)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22182),X22179),X22181))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg])]) ).

cnf(i_0_8213,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_5687]) ).

fof(i_0_8214,plain,
    ! [X21336,X21337,X21338] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21338),X21337))
      | ~ hBOOL(hAPP(hAPP(c_member(X21338),X21336),X21337))
      | hAPP(c_Finite__Set_Ocard(X21338),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21338,tc_HOL_Obool)),X21337),hAPP(hAPP(c_Set_Oinsert(X21338),X21336),c_Orderings_Obot__class_Obot(tc_fun(X21338,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21338),X21337)),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_8215,plain,
    ! [X21339,X21340,X21341] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X21341),X21339),X21340))
        | hAPP(c_Finite__Set_Ocard(X21341),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21341,tc_HOL_Obool)),X21340),hAPP(hAPP(c_Set_Oinsert(X21341),X21339),c_Orderings_Obot__class_Obot(tc_fun(X21341,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21341),X21340)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21341),X21340)) )
      & ( hBOOL(hAPP(hAPP(c_member(X21341),X21339),X21340))
        | hAPP(c_Finite__Set_Ocard(X21341),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21341,tc_HOL_Obool)),X21340),hAPP(hAPP(c_Set_Oinsert(X21341),X21339),c_Orderings_Obot__class_Obot(tc_fun(X21341,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(X21341),X21340)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21341),X21340)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5741])])]) ).

fof(i_0_8216,plain,
    ! [X20475,X20476,X20477] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20477),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20477,tc_HOL_Obool)),X20475),X20476)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20477),X20475))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20477),X20476)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20477),X20475))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20477),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20477,tc_HOL_Obool)),X20475),X20476)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20477),X20476)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff2])])]) ).

cnf(i_0_8217,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_5742]) ).

fof(i_0_8218,plain,
    ! [X24015,X24016,X24017] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24017),hAPP(c_Int_Onumber__class_Onumber__of(X24017),X24016)),hAPP(c_Int_Onumber__class_Onumber__of(X24017),X24015)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24017),hAPP(c_Int_Onumber__class_Onumber__of(X24017),X24015)),hAPP(c_Int_Onumber__class_Onumber__of(X24017),X24016)))
        | ~ class_Int_Onumber(X24017)
        | ~ class_Orderings_Olinorder(X24017) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24017),hAPP(c_Int_Onumber__class_Onumber__of(X24017),X24015)),hAPP(c_Int_Onumber__class_Onumber__of(X24017),X24016)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24017),hAPP(c_Int_Onumber__class_Onumber__of(X24017),X24016)),hAPP(c_Int_Onumber__class_Onumber__of(X24017),X24015)))
        | ~ class_Int_Onumber(X24017)
        | ~ class_Orderings_Olinorder(X24017) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5743])])]) ).

fof(i_0_8219,plain,
    ! [X20135,X20136,X20137,X20138] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X20138,tc_fun(X20137,tc_HOL_Obool))),X20136),X20135)),
    inference(variable_rename,[status(thm)],[i_0_5744]) ).

fof(i_0_8220,plain,
    ! [X31122,X31123,X31124] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31124),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X31123)))
      | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X31123),X31124),X31122)) = 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),X31123)),X31122)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X31123),X31124)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__update__nat])]) ).

fof(i_0_8221,plain,
    ! [X18922,X18923,X18924,X18925,X18926,X18927] : hAPP(hAPP(c_Fun_Ocomp(X18927,X18926,X18925,X18924),X18923),X18922) = hAPP(X18924,hAPP(X18923,X18922)),
    inference(variable_rename,[status(thm)],[fact_o__def]) ).

fof(i_0_8222,plain,
    ! [X18884,X18885,X18886,X18887,X18888,X18889] : hAPP(hAPP(c_Fun_Ocomp(X18889,X18888,X18887,X18886),X18885),X18884) = hAPP(X18886,hAPP(X18885,X18884)),
    inference(variable_rename,[status(thm)],[fact_o__apply]) ).

fof(i_0_8223,plain,
    ! [X22105,X22106] :
      ( ~ hBOOL(hAPP(X22106,X22105))
      | hBOOL(hAPP(X22106,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X22106) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X22106),c_Nat_OSuc))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5745])]) ).

fof(i_0_8224,plain,
    ! [X21574,X21575,X21576,X21577,X21578] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X21578)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21578),X21577),X21576))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21578),X21575),X21574))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21578),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21578),X21577),X21575)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21578),X21576),X21574))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).

fof(i_0_8225,plain,
    ! [X21779,X21780,X21781,X21782,X21783] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X21783)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21783),X21782),X21781))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21783),X21780),X21779))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21783),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21783),X21782),X21780)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21783),X21781),X21779))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).

fof(i_0_8226,plain,
    ! [X21774,X21775,X21776,X21777,X21778] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X21778)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21778),X21777),X21776))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21778),X21775),X21774))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21778),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21778),X21777),X21775)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21778),X21776),X21774))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).

fof(i_0_8227,plain,
    ! [X25787,X25788,X25789,X25790,X25791] :
      ( ~ class_Orderings_Olinorder(X25791)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25791),X25790),X25789))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25791),X25788),X25787))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25791),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25791),X25790),X25788)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25791),X25789),X25787))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__mono])]) ).

fof(i_0_8228,plain,
    ! [X25380,X25381,X25382,X25383,X25384] :
      ( ~ class_Orderings_Olinorder(X25384)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25384),X25383),X25382))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25384),X25381),X25380))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25384),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25384),X25383),X25381)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25384),X25382),X25380))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__mono])]) ).

fof(i_0_8229,plain,
    ! [X21553,X21554,X21555,X21556,X21557] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X21557)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21557),X21556),X21555))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21557),X21554),X21553))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21557),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21557),X21556),X21554)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21557),X21555),X21553))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).

fof(i_0_8230,plain,
    ! [X17960,X17961,X17962,X17963,X17964] :
      ( ~ class_Lattices_Osemilattice__inf(X17964)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17964),X17963),X17962))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17964),X17961),X17960))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17964),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17964),X17963),X17961)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17964),X17962),X17960))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__mono])]) ).

fof(i_0_8231,plain,
    ! [X17643,X17644,X17645,X17646,X17647] :
      ( ~ class_Lattices_Osemilattice__sup(X17647)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17647),X17646),X17645))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17647),X17644),X17643))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17647),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17647),X17646),X17644)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17647),X17645),X17643))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__mono])]) ).

fof(i_0_8232,plain,
    ! [X24022,X24023,X24024,X24025] :
      ( ~ class_Int_Onumber(X24025)
      | ~ class_Rings_Osemiring(X24025)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24025),hAPP(c_Int_Onumber__class_Onumber__of(X24025),X24024)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24025),X24023),X24022)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24025),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24025),hAPP(c_Int_Onumber__class_Onumber__of(X24025),X24024)),X24023)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24025),hAPP(c_Int_Onumber__class_Onumber__of(X24025),X24024)),X24022)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__distrib__number__of])]) ).

fof(i_0_8233,plain,
    ! [X24026,X24027,X24028,X24029] :
      ( ~ class_Int_Onumber(X24029)
      | ~ class_Rings_Oring(X24029)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24029),hAPP(c_Int_Onumber__class_Onumber__of(X24029),X24028)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24029),X24027),X24026)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24029),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24029),hAPP(c_Int_Onumber__class_Onumber__of(X24029),X24028)),X24027)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24029),hAPP(c_Int_Onumber__class_Onumber__of(X24029),X24028)),X24026)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__diff__distrib__number__of])]) ).

fof(i_0_8234,plain,
    ! [X29058,X29059,X29060,X29061] :
      ( ~ class_Orderings_Olinorder(X29061)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29061),X29060))
      | hAPP(hAPP(c_Finite__Set_Ofold(X29061,X29061,c_Orderings_Oord__class_Omax(X29061)),X29059),hAPP(hAPP(c_Set_Oinsert(X29061),X29058),X29060)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X29061),X29058),hAPP(hAPP(c_Finite__Set_Ofold(X29061,X29061,c_Orderings_Oord__class_Omax(X29061)),X29059),X29060)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__insert])]) ).

fof(i_0_8235,plain,
    ! [X29054,X29055,X29056,X29057] :
      ( ~ class_Orderings_Olinorder(X29057)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29057),X29056))
      | hAPP(hAPP(c_Finite__Set_Ofold(X29057,X29057,c_Orderings_Oord__class_Omin(X29057)),X29055),hAPP(hAPP(c_Set_Oinsert(X29057),X29054),X29056)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X29057),X29054),hAPP(hAPP(c_Finite__Set_Ofold(X29057,X29057,c_Orderings_Oord__class_Omin(X29057)),X29055),X29056)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__insert])]) ).

fof(i_0_8236,plain,
    ! [X29050,X29051,X29052,X29053] :
      ( ~ class_Lattices_Osemilattice__inf(X29053)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29053),X29052))
      | hAPP(hAPP(c_Finite__Set_Ofold(X29053,X29053,c_Lattices_Osemilattice__inf__class_Oinf(X29053)),X29051),hAPP(hAPP(c_Set_Oinsert(X29053),X29050),X29052)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X29053),X29050),hAPP(hAPP(c_Finite__Set_Ofold(X29053,X29053,c_Lattices_Osemilattice__inf__class_Oinf(X29053)),X29051),X29052)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__inf__insert])]) ).

fof(i_0_8237,plain,
    ! [X29046,X29047,X29048,X29049] :
      ( ~ class_Lattices_Osemilattice__sup(X29049)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29049),X29048))
      | hAPP(hAPP(c_Finite__Set_Ofold(X29049,X29049,c_Lattices_Osemilattice__sup__class_Osup(X29049)),X29047),hAPP(hAPP(c_Set_Oinsert(X29049),X29046),X29048)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X29049),X29046),hAPP(hAPP(c_Finite__Set_Ofold(X29049,X29049,c_Lattices_Osemilattice__sup__class_Osup(X29049)),X29047),X29048)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__sup__insert])]) ).

fof(i_0_8238,plain,
    ! [X20596,X20597,X20598,X20599] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20599),X20598))
      | ~ c_Fun_Oinj__on(X20597,X20599,X20596,c_Orderings_Otop__class_Otop(tc_fun(X20597,tc_HOL_Obool)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20597),hAPP(c_Set_Ovimage(X20597,X20599,X20596),X20598))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__vimageI])]) ).

fof(i_0_8239,plain,
    ! [X29546,X29547,X29548,X29549,X29550] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29550)
      | ~ hBOOL(hAPP(hAPP(c_member(X29549),X29548),X29547))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29550),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29549,X29550),X29547),X29546)),hAPP(X29546,X29548))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__leI])]) ).

fof(i_0_8240,plain,
    ! [X24087,X24088,X24089,X24090] :
      ( ~ class_Int_Onumber__ring(X24090)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24090),hAPP(c_Int_Onumber__class_Onumber__of(X24090),X24089)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24090),X24088),hAPP(c_Int_Onumber__class_Onumber__of(X24090),X24087))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24090),hAPP(c_Int_Onumber__class_Onumber__of(X24090),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24089),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24087)))),X24088) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__diff2])]) ).

fof(i_0_8241,plain,
    ! [X24745,X24746] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24746)),X24745))
        | hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24746),X24745)) )
      & ( ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24746),X24745))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24746)),X24745)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I2_J])]) ).

fof(i_0_8242,plain,
    ! [X19382,X19383,X19384,X19385,X19386,X19387] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X19387),X19386),X19385))
      | ~ hBOOL(hAPP(hAPP(X19384,X19386),X19383))
      | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19387,tc_fun(X19382,tc_HOL_Obool)),X19385),X19384),X19383)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP1__I])]) ).

fof(i_0_8243,plain,
    ! [X29636,X29637,X29638,X29639] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29638),c_Complete__Lattice_OSup__class_OSup(X29638,X29637)),X29636))
        | ~ hBOOL(hAPP(hAPP(c_member(X29638),X29639),X29637))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29638),X29639),X29636))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X29638) )
      & ( hBOOL(hAPP(hAPP(c_member(X29638),esk361_3(X29636,X29637,X29638)),X29637))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29638),c_Complete__Lattice_OSup__class_OSup(X29638,X29637)),X29636))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X29638) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29638),esk361_3(X29636,X29637,X29638)),X29636))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29638),c_Complete__Lattice_OSup__class_OSup(X29638,X29637)),X29636))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X29638) ) ),
    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_8244,plain,
    ! [X29062,X29063,X29064,X29065,X29066,X29067] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X29067,X29066,X29065)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29067),X29064))
      | hAPP(hAPP(c_Finite__Set_Ofold(X29067,X29066,X29065),X29063),hAPP(hAPP(c_Set_Oinsert(X29067),X29062),X29064)) = hAPP(hAPP(X29065,X29062),hAPP(hAPP(c_Finite__Set_Ofold(X29067,X29066,X29065),X29063),X29064)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem])]) ).

fof(i_0_8245,plain,
    ! [X32041,X32042,X32043,X32044,X32045] :
      ( ( X32042 = 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),X32042),X32041) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X32043),hAPP(c_List_Oset(tc_Nat_Onat),X32041)))
        | X32043 = 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),X32042),X32041) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk433_2(X32044,X32045)),hAPP(c_List_Oset(tc_Nat_Onat),X32044)))
        | X32045 != 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),X32045),X32044) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( esk433_2(X32044,X32045) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X32045 != 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),X32045),X32044) = 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_8246,plain,
    ! [X22475,X22476] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22476))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22475))
      | 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),X22475),X22476))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__mult])]) ).

fof(i_0_8247,plain,
    ! [X22493,X22494] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22494))
        | ~ 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),X22494),X22493))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22493))
        | ~ 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),X22494),X22493))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22494))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22493))
        | 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),X22494),X22493))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff])])]) ).

fof(i_0_8248,plain,
    ! [X23674,X23675,X23676] : 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),X23676),X23675)),X23674)),X23675) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X23674),X23675),
    inference(variable_rename,[status(thm)],[fact_mod__mult__self4]) ).

fof(i_0_8249,plain,
    ! [X29728,X29729,X29730] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X29730,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X29730,tc_HOL_Obool),tc_HOL_Obool)),X29729),X29728)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29730,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29730,tc_HOL_Obool),X29729)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29730,tc_HOL_Obool),X29728)),
    inference(variable_rename,[status(thm)],[fact_Union__Un__distrib]) ).

fof(i_0_8250,plain,
    ! [X29749,X29750,X29751] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X29751,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X29751,tc_HOL_Obool),tc_HOL_Obool)),X29750),X29749)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29751,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X29751,tc_HOL_Obool),X29750)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X29751,tc_HOL_Obool),X29749)),
    inference(variable_rename,[status(thm)],[fact_Inter__Un__distrib]) ).

fof(i_0_8251,plain,
    ! [X23685,X23686,X23687,X23688,X23689,X23690,X23691,X23692] :
      ( ( X23685 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X23687,X23686))
        | ~ hBOOL(hAPP(X23687,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23686,X23685))) )
      & ( X23685 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23689),X23685))
        | X23686 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23685),X23688)),X23689)
        | hBOOL(hAPP(X23687,X23689))
        | ~ hBOOL(hAPP(X23687,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23686,X23685))) )
      & ( X23690 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X23690 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X23692,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23691,X23690))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk135_3(X23690,X23691,X23692)),X23690))
        | X23690 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X23692,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23691,X23690))) )
      & ( X23691 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23690),esk134_3(X23690,X23691,X23692))),esk135_3(X23690,X23691,X23692))
        | X23690 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X23692,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23691,X23690))) )
      & ( ~ hBOOL(hAPP(X23692,esk135_3(X23690,X23691,X23692)))
        | X23690 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X23692,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23691,X23690))) )
      & ( X23690 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X23692,X23691))
        | hBOOL(hAPP(X23692,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23691,X23690))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk135_3(X23690,X23691,X23692)),X23690))
        | ~ hBOOL(hAPP(X23692,X23691))
        | hBOOL(hAPP(X23692,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23691,X23690))) )
      & ( X23691 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23690),esk134_3(X23690,X23691,X23692))),esk135_3(X23690,X23691,X23692))
        | ~ hBOOL(hAPP(X23692,X23691))
        | hBOOL(hAPP(X23692,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23691,X23690))) )
      & ( ~ hBOOL(hAPP(X23692,esk135_3(X23690,X23691,X23692)))
        | ~ hBOOL(hAPP(X23692,X23691))
        | hBOOL(hAPP(X23692,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23691,X23690))) ) ),
    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_8252,plain,
    ! [X31016,X31017,X31018,X31019,X31020,X31021,X31022] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31018)),X31017),c_List_Olists(X31018,X31016)))
        | ~ hBOOL(hAPP(hAPP(c_member(X31018),X31019),hAPP(c_List_Oset(X31018),X31017)))
        | hBOOL(hAPP(hAPP(c_member(X31018),X31019),X31016)) )
      & ( hBOOL(hAPP(hAPP(c_member(X31022),esk416_3(X31020,X31021,X31022)),hAPP(c_List_Oset(X31022),X31021)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31022)),X31021),c_List_Olists(X31022,X31020))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X31022),esk416_3(X31020,X31021,X31022)),X31020))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31022)),X31021),c_List_Olists(X31022,X31020))) ) ),
    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_8253,plain,
    ! [X30584,X30585,X30586,X30587] : c_List_Olist_Olist__size(X30587,X30586,hAPP(hAPP(c_List_Olist_OCons(X30587),X30585),X30584)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X30586,X30585)),c_List_Olist_Olist__size(X30587,X30586,X30584))),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_8254,plain,
    ! [X20301,X20302,X20303,X20304] : c_Map_Orestrict__map(X20304,X20303,X20302,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20304,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X20304),X20301),c_Orderings_Obot__class_Obot(tc_fun(X20304,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X20304,tc_Option_Ooption(X20303)),X20302),X20301),c_Option_Ooption_ONone(X20303)),
    inference(variable_rename,[status(thm)],[fact_restrict__complement__singleton__eq]) ).

fof(i_0_8255,plain,
    ! [X30377,X30378,X30379] : c_Random_Oselect__weight(X30379,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X30379)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X30379),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X30378)),X30377)) = c_Random_Oselect__weight(X30379,X30377),
    inference(variable_rename,[status(thm)],[fact_select__weight__cons__zero]) ).

fof(i_0_8256,plain,
    ! [X23539,X23540,X23541,X23542] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23541))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23541))
        | X23541 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23542,X23541) = X23539
        | X23542 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23541),X23540)),X23539) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23541),X23539))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23539),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)),X23541))
        | X23541 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23542,X23541) = X23539
        | X23542 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23541),X23540)),X23539) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23541))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23539))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23539),X23541))
        | X23541 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23542,X23541) = X23539
        | X23542 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23541),X23540)),X23539) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23541),X23539))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23539),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)),X23539))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23539),X23541))
        | X23541 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23542,X23541) = X23539
        | X23542 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23541),X23540)),X23539) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5746])])]) ).

fof(i_0_8257,plain,
    ! [X32242,X32243] :
      ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X32243)),c_List_Otranspose__rel(X32243)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X32243)),c_List_Olist_ONil(X32243)),X32242)))
      | c_List_Otranspose(X32243,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X32243)),c_List_Olist_ONil(X32243)),X32242)) = c_List_Otranspose(X32243,X32242) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I2_J])]) ).

cnf(i_0_8258,plain,
    c_List_Ofoldr(X1,X2,X3,c_List_Olist_ONil(X1),X4) = X4,
    inference(split_conjunct,[status(thm)],[i_0_5747]) ).

fof(i_0_8259,plain,
    ! [X20570,X20571,X20572] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20572,tc_HOL_Obool)),X20571),X20570) != c_Orderings_Obot__class_Obot(tc_fun(X20572,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20572,tc_HOL_Obool)),X20571),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20572,tc_HOL_Obool)),X20570))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20572,tc_HOL_Obool)),X20571),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20572,tc_HOL_Obool)),X20570)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20572,tc_HOL_Obool)),X20571),X20570) = c_Orderings_Obot__class_Obot(tc_fun(X20572,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_disjoint__eq__subset__Compl])]) ).

cnf(i_0_8260,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_5748]) ).

cnf(i_0_8261,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_5749]) ).

fof(i_0_8262,plain,
    ! [X21227,X21228,X21229] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21229),X21228))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21229,tc_HOL_Obool)),X21227),X21228))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21229),X21228)),hAPP(c_Finite__Set_Ocard(X21229),X21227)))
      | X21227 = X21228 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__seteq])]) ).

fof(i_0_8263,plain,
    ! [X29700,X29701,X29702] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X29702,tc_HOL_Obool)),X29701),X29700))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29702,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X29702,tc_HOL_Obool),X29700)),X29701)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inter__lower])]) ).

fof(i_0_8264,plain,
    ! [X28729,X28730,X28731,X28732,X28733] : hAPP(c_Relation_Oconverse(X28733,X28732),hAPP(hAPP(c_Relation_Orel__comp(X28733,X28731,X28732),X28730),X28729)) = hAPP(hAPP(c_Relation_Orel__comp(X28732,X28731,X28733),hAPP(c_Relation_Oconverse(X28731,X28732),X28729)),hAPP(c_Relation_Oconverse(X28733,X28731),X28730)),
    inference(variable_rename,[status(thm)],[fact_converse__rel__comp]) ).

fof(i_0_8265,plain,
    ! [X23226,X23227,X23228,X23229] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23228))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23228))
        | X23228 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23229),X23228) = X23227
        | X23229 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23228),X23227)),X23226) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23228),X23226))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23226),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)),X23228))
        | X23228 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23229),X23228) = X23227
        | X23229 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23228),X23227)),X23226) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23228))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23226))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23226),X23228))
        | X23228 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23229),X23228) = X23227
        | X23229 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23228),X23227)),X23226) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23228),X23226))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23226),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)),X23226))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23226),X23228))
        | X23228 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23229),X23228) = X23227
        | X23229 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23228),X23227)),X23226) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5750])])]) ).

fof(i_0_8266,plain,
    ! [X25364,X25365,X25366,X25367] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25367),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25367),X25366),X25365)),X25364))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25367),X25366),X25364))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25367),X25365),X25364))
        | ~ class_Orderings_Olinorder(X25367) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25367),X25366),X25364))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25367),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25367),X25366),X25365)),X25364))
        | ~ class_Orderings_Olinorder(X25367) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25367),X25365),X25364))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25367),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25367),X25366),X25365)),X25364))
        | ~ class_Orderings_Olinorder(X25367) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__less__iff__disj])])]) ).

fof(i_0_8267,plain,
    ! [X25372,X25373,X25374,X25375] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25375),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25375),X25374),X25373)),X25372))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25375),X25374),X25372))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25375),X25373),X25372))
        | ~ class_Orderings_Olinorder(X25375) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25375),X25374),X25372))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25375),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25375),X25374),X25373)),X25372))
        | ~ class_Orderings_Olinorder(X25375) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25375),X25373),X25372))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25375),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25375),X25374),X25373)),X25372))
        | ~ class_Orderings_Olinorder(X25375) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__le__iff__disj])])]) ).

fof(i_0_8268,plain,
    ! [X23512,X23513,X23514,X23515,X23516,X23517,X23518,X23519] :
      ( ( X23512 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X23514,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X23514,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23513),X23512))) )
      & ( X23512 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23516),X23512))
        | X23513 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23512),X23515)),X23516)
        | hBOOL(hAPP(X23514,X23515))
        | ~ hBOOL(hAPP(X23514,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23513),X23512))) )
      & ( X23517 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X23517 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X23519,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23518),X23517))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk125_3(X23517,X23518,X23519)),X23517))
        | X23517 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X23519,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23518),X23517))) )
      & ( X23518 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23517),esk124_3(X23517,X23518,X23519))),esk125_3(X23517,X23518,X23519))
        | X23517 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X23519,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23518),X23517))) )
      & ( ~ hBOOL(hAPP(X23519,esk124_3(X23517,X23518,X23519)))
        | X23517 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X23519,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23518),X23517))) )
      & ( X23517 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X23519,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X23519,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23518),X23517))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk125_3(X23517,X23518,X23519)),X23517))
        | ~ hBOOL(hAPP(X23519,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X23519,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23518),X23517))) )
      & ( X23518 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23517),esk124_3(X23517,X23518,X23519))),esk125_3(X23517,X23518,X23519))
        | ~ hBOOL(hAPP(X23519,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X23519,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23518),X23517))) )
      & ( ~ hBOOL(hAPP(X23519,esk124_3(X23517,X23518,X23519)))
        | ~ hBOOL(hAPP(X23519,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X23519,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23518),X23517))) ) ),
    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_8269,plain,
    ! [X25961,X25962,X25963] :
      ( ~ class_Orderings_Olinorder(X25963)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25963),X25962))
      | X25961 = c_Orderings_Obot__class_Obot(tc_fun(X25963,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25963,tc_HOL_Obool)),X25961),X25962))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25963),c_Big__Operators_Olattice_OSup__fin(X25963,c_Orderings_Oord__class_Omax(X25963),X25961)),c_Big__Operators_Olattice_OSup__fin(X25963,c_Orderings_Oord__class_Omax(X25963),X25962)) = c_Big__Operators_Olattice_OSup__fin(X25963,c_Orderings_Oord__class_Omax(X25963),X25962) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osubset__idem])]) ).

fof(i_0_8270,plain,
    ! [X25675,X25676,X25677] :
      ( ~ class_Orderings_Olinorder(X25677)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25677),X25676))
      | X25675 = c_Orderings_Obot__class_Obot(tc_fun(X25677,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25677,tc_HOL_Obool)),X25675),X25676))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25677),c_Big__Operators_Olattice_OInf__fin(X25677,c_Orderings_Oord__class_Omin(X25677),X25675)),c_Big__Operators_Olattice_OInf__fin(X25677,c_Orderings_Oord__class_Omin(X25677),X25676)) = c_Big__Operators_Olattice_OInf__fin(X25677,c_Orderings_Oord__class_Omin(X25677),X25676) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osubset__idem])]) ).

cnf(i_0_8271,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_5751]) ).

fof(i_0_8272,plain,
    ! [X29207,X29208,X29209,X29210,X29211,X29212] :
      ( ~ c_Finite__Set_Ofun__left__comm(X29212,X29211,X29210)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29212),X29209))
      | hBOOL(hAPP(hAPP(c_member(X29212),X29208),X29209))
      | hAPP(hAPP(c_Finite__Set_Ofold(X29212,X29211,X29210),X29207),hAPP(hAPP(c_Set_Oinsert(X29212),X29208),X29209)) = hAPP(hAPP(c_Finite__Set_Ofold(X29212,X29211,X29210),hAPP(hAPP(X29210,X29208),X29207)),X29209) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5752])]) ).

fof(i_0_8273,plain,
    ! [X29979,X29980,X29981,X29982,X29983] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29983),X29982),c_Map_Odom(X29983,X29981,X29980)))
      | hAPP(c_Map_Omap__add(X29983,X29981,X29979,X29980),X29982) = hAPP(X29980,X29982) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__dom__app__simps_I1_J])]) ).

cnf(i_0_8274,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_5753]) ).

fof(i_0_8275,plain,
    ! [X29719,X29720] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X29720,tc_HOL_Obool),tc_HOL_Obool)),X29719),hAPP(c_Set_OPow(X29720),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29720,tc_HOL_Obool),X29719)))),
    inference(variable_rename,[status(thm)],[fact_subset__Pow__Union]) ).

fof(i_0_8276,plain,
    ! [X17797,X17798,X17799,X17800] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17800),X17799),X17798))
      | ~ hBOOL(hAPP(hAPP(c_member(X17800),X17799),X17797))
      | hBOOL(hAPP(hAPP(c_member(X17800),X17799),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17800,tc_HOL_Obool)),X17798),X17797))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntI])]) ).

fof(i_0_8277,plain,
    ! [X30006,X30007,X30008,X30009] : c_Map_Odom(X30009,X30008,c_Map_Omap__add(X30009,X30008,X30007,X30006)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30009,tc_HOL_Obool)),c_Map_Odom(X30009,X30008,X30006)),c_Map_Odom(X30009,X30008,X30007)),
    inference(variable_rename,[status(thm)],[fact_dom__map__add]) ).

fof(i_0_8278,plain,
    ! [X26638,X26639,X26640,X26641] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26640),X26639))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26641),X26638),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26639),hAPP(c_Nat_OSuc,X26640))) = c_Groups_Ozero__class_Ozero(X26641)
        | ~ class_Groups_Ocomm__monoid__add(X26641) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26640),X26639))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26641),X26638),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26639),hAPP(c_Nat_OSuc,X26640))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26641),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26641),X26638),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26639),X26640))),hAPP(X26638,X26640))
        | ~ class_Groups_Ocomm__monoid__add(X26641) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5754])])]) ).

fof(i_0_8279,plain,
    ! [X23975,X23976,X23977,X23978,X23979,X23980] :
      ( ( hBOOL(hAPP(X23980,hAPP(c_Product__Type_Ofst(X23976,X23975),hAPP(hAPP(c_Product__Type_OPair(X23976,X23975),X23979),X23977))))
        | ~ hBOOL(hAPP(X23978,X23977))
        | ~ hBOOL(hAPP(X23980,X23979)) )
      & ( hBOOL(hAPP(X23978,hAPP(c_Product__Type_Osnd(X23976,X23975),hAPP(hAPP(c_Product__Type_OPair(X23976,X23975),X23979),X23977))))
        | ~ hBOOL(hAPP(X23978,X23977))
        | ~ hBOOL(hAPP(X23980,X23979)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conjI__realizer])])]) ).

fof(i_0_8280,plain,
    ! [X29356,X29357,X29358,X29359,X29360,X29361] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29361)
      | hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29360,tc_fun(X29359,X29361)),X29358),X29357),X29356) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29360,X29361),X29358),hAPP(hAPP(c_COMBC(X29360,X29359,X29361),X29357),X29356)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__apply])]) ).

fof(i_0_8281,plain,
    ! [X19757,X19758,X19759,X19760,X19761,X19762] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X19762)
      | hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19761,tc_fun(X19760,X19762)),X19759),X19758),X19757) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19761,X19762),X19759),hAPP(hAPP(c_COMBC(X19761,X19760,X19762),X19758),X19757)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUPR__apply])]) ).

fof(i_0_8282,plain,
    ! [X20469,X20470,X20471] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20471),X20470))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20471),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20471,tc_HOL_Obool)),X20470),X20469))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20471),X20469))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20471),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20471,tc_HOL_Obool)),X20470),X20469))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20471),X20470))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20471),X20469))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20471),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20471,tc_HOL_Obool)),X20470),X20469))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Un])])]) ).

fof(i_0_8283,plain,
    ! [X17269,X17270,X17271,X17272] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17272,tc_HOL_Obool)),X17271),X17270),X17269))
      | hBOOL(hAPP(X17271,X17269))
      | hBOOL(hAPP(X17270,X17269)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5755])]) ).

fof(i_0_8284,plain,
    ! [X17937,X17938,X17939] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17939,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17939,tc_HOL_Obool)),X17938),X17937)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17939,tc_HOL_Obool)),X17938),X17937)) = X17938,
    inference(variable_rename,[status(thm)],[fact_Un__Diff__Int]) ).

fof(i_0_8285,plain,
    ! [X33148,X33149,X33150] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33150,tc_HOL_Obool)),X33149),X33148))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X33150),tc_HOL_Obool)),c_List_Olistsp(X33150,X33149)),c_List_Olistsp(X33150,X33148))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__mono])]) ).

fof(i_0_8286,plain,
    ! [X30945,X30946,X30947] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30947,tc_HOL_Obool)),X30946),X30945))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X30947),tc_HOL_Obool)),c_List_Olists(X30947,X30946)),c_List_Olists(X30947,X30945))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__mono])]) ).

fof(i_0_8287,plain,
    ! [X24400,X24401,X24402,X24403] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24403),X24401),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24403),X24400),X24402)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24403),X24400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24403),X24401),X24402)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24403),X24402),c_Groups_Ozero__class_Ozero(X24403)))
        | ~ class_Fields_Olinordered__field(X24403) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24403),X24400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24403),X24401),X24402)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24403),X24401),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24403),X24400),X24402)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24403),X24402),c_Groups_Ozero__class_Ozero(X24403)))
        | ~ class_Fields_Olinordered__field(X24403) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__divide__eq])])]) ).

fof(i_0_8288,plain,
    ! [X24269,X24270,X24271,X24272] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24272),X24270),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24272),X24269),X24271)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24272),X24269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24272),X24270),X24271)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24272),X24271),c_Groups_Ozero__class_Ozero(X24272)))
        | ~ class_Fields_Olinordered__field(X24272) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24272),X24269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24272),X24270),X24271)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24272),X24270),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24272),X24269),X24271)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24272),X24271),c_Groups_Ozero__class_Ozero(X24272)))
        | ~ class_Fields_Olinordered__field(X24272) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__divide__eq])])]) ).

fof(i_0_8289,plain,
    ! [X28170,X28171] :
      ( ( ~ c_Wellfounded_OwfP(X28171,X28170)
        | c_Wellfounded_Owf(X28171,hAPP(c_Set_OCollect(tc_prod(X28171,X28171)),hAPP(c_Product__Type_Oprod_Oprod__case(X28171,X28171,tc_HOL_Obool),X28170))) )
      & ( ~ c_Wellfounded_Owf(X28171,hAPP(c_Set_OCollect(tc_prod(X28171,X28171)),hAPP(c_Product__Type_Oprod_Oprod__case(X28171,X28171,tc_HOL_Obool),X28170)))
        | c_Wellfounded_OwfP(X28171,X28170) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__def])]) ).

fof(i_0_8290,plain,
    ! [X23062,X23063] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23062),X23063)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23062),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)),X23063)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23062),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),X23062),X23063)),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)),X23063)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__neg__iff])])]) ).

cnf(i_0_8291,plain,
    ( c_List_OdropWhile(X3,X1,X2) = c_List_Olist_ONil(X3)
    | ~ hBOOL(hAPP(X1,esk463_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_5700]) ).

fof(i_0_8292,plain,
    ! [X27673,X27674,X27675,X27676,X27677,X27678] :
      ( ( hAPP(hAPP(c_Product__Type_OSigma(X27675,X27678),X27674),hAPP(c_COMBK(tc_fun(X27678,tc_HOL_Obool),X27675),X27676)) != hAPP(hAPP(c_Product__Type_OSigma(X27675,X27678),X27673),hAPP(c_COMBK(tc_fun(X27678,tc_HOL_Obool),X27675),X27676))
        | X27674 = X27673
        | ~ hBOOL(hAPP(hAPP(c_member(X27678),X27677),X27676)) )
      & ( X27674 != X27673
        | hAPP(hAPP(c_Product__Type_OSigma(X27675,X27678),X27674),hAPP(c_COMBK(tc_fun(X27678,tc_HOL_Obool),X27675),X27676)) = hAPP(hAPP(c_Product__Type_OSigma(X27675,X27678),X27673),hAPP(c_COMBK(tc_fun(X27678,tc_HOL_Obool),X27675),X27676))
        | ~ hBOOL(hAPP(hAPP(c_member(X27678),X27677),X27676)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__eq__cancel2])])]) ).

fof(i_0_8293,plain,
    ! [X23522,X23523] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23523))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23523),X23522)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23523,X23522) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23523),X23522) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__trivial])]) ).

fof(i_0_8294,plain,
    ! [X28337,X28338] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28338,tc_HOL_Obool)),esk311_2(X28337,X28338)),hAPP(c_Relation_OImage(X28338,X28338,X28337),esk311_2(X28337,X28338))))
        | c_Wellfounded_Owf(X28338,X28337) )
      & ( esk311_2(X28337,X28338) != c_Orderings_Obot__class_Obot(tc_fun(X28338,tc_HOL_Obool))
        | c_Wellfounded_Owf(X28338,X28337) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfI__pf])])])]) ).

fof(i_0_8295,plain,
    ! [X23817,X23818,X23819,X23820,X23821] :
      ( ~ hBOOL(hAPP(hAPP(X23821,X23820),X23819))
      | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X23818,X23817,tc_HOL_Obool),X23821),hAPP(hAPP(c_Product__Type_OPair(X23818,X23817),X23820),X23819))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_prod__caseI])]) ).

fof(i_0_8296,plain,
    ! [X23812,X23813,X23814,X23815,X23816] :
      ( ~ hBOOL(hAPP(hAPP(X23816,X23815),X23814))
      | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X23813,X23812,tc_HOL_Obool),X23816),hAPP(hAPP(c_Product__Type_OPair(X23813,X23812),X23815),X23814))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitI])]) ).

fof(i_0_8297,plain,
    ! [X23060,X23061] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23060),X23061)),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)),X23060))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23061),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)),X23060))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23060),X23061)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23061),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_8298,plain,
    ! [X21831,X21832,X21833] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21833),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21832),X21831)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21833),X21831)),X21832)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21833),X21831)),X21832))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21833),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21832),X21831))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__conv])]) ).

fof(i_0_8299,plain,
    ! [X21839,X21840,X21841] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21841),X21840)),X21839))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21841),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21839),X21840))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21841),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21839),X21840)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21841),X21840)),X21839)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv])]) ).

fof(i_0_8300,plain,
    ! [X21268,X21269,X21270] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21270),X21269))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21270,tc_HOL_Obool)),X21269),X21268))
      | hAPP(c_Finite__Set_Ocard(X21270),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21270,tc_HOL_Obool)),X21268),X21269)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21270),X21268)),hAPP(c_Finite__Set_Ocard(X21270),X21269)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff__subset])]) ).

fof(i_0_8301,plain,
    ! [X21086,X21087,X21088,X21089,X21090] :
      ( ~ c_Finite__Set_Ofolding__idem(X21090,X21089,X21088,X21087)
      | hAPP(c_Fun_Ocomp(X21089,X21089,X21089,hAPP(X21088,X21086)),hAPP(X21088,X21086)) = hAPP(X21088,X21086) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__comp])]) ).

cnf(i_0_8302,plain,
    c_Int_Opred(c_Int_OBit1(X1)) = c_Int_OBit0(X1),
    inference(split_conjunct,[status(thm)],[i_0_5756]) ).

fof(i_0_8303,plain,
    ! [X24516,X24517,X24518] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24518)))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24518)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24517)),X24516)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24517)),X24516) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24517)))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24518)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24517)),X24516)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24518)),X24516)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24518))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24517)))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24518)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24517)),X24516)) = 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),X24518),X24517))),X24516)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24518))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5757])])]) ).

cnf(i_0_8304,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_5758]) ).

cnf(i_0_8305,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_5759]) ).

cnf(i_0_8306,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_5760]) ).

fof(i_0_8307,plain,
    ! [X20273,X20274,X20275] : hAPP(c_Relation_OField(X20275),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X20275,X20275),tc_HOL_Obool)),X20274),X20273)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20275,tc_HOL_Obool)),hAPP(c_Relation_OField(X20275),X20274)),hAPP(c_Relation_OField(X20275),X20273)),
    inference(variable_rename,[status(thm)],[fact_Field__Un]) ).

fof(i_0_8308,plain,
    ! [X30420,X30421,X30422,X30423] : hAPP(c_List_Oset(tc_prod(X30423,X30422)),c_Enum_Oproduct(X30423,X30422,X30421,X30420)) = hAPP(hAPP(c_Product__Type_OSigma(X30423,X30422),hAPP(c_List_Oset(X30423),X30421)),hAPP(c_COMBK(tc_fun(X30422,tc_HOL_Obool),X30423),hAPP(c_List_Oset(X30422),X30420))),
    inference(variable_rename,[status(thm)],[fact_product__list__set]) ).

fof(i_0_8309,plain,
    ! [X30780,X30781,X30782,X30783,X30784] :
      ( ( hAPP(hAPP(c_List_Omap(tc_prod(X30784,X30782),X30784),c_Product__Type_Ofst(X30784,X30782)),X30780) = X30783
        | hAPP(hAPP(c_List_Ozip(X30784,X30782),X30783),X30781) != X30780
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30784)),X30783) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30782)),X30781) )
      & ( hAPP(hAPP(c_List_Omap(tc_prod(X30784,X30782),X30782),c_Product__Type_Osnd(X30784,X30782)),X30780) = X30781
        | hAPP(hAPP(c_List_Ozip(X30784,X30782),X30783),X30781) != X30780
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30784)),X30783) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30782)),X30781) )
      & ( hAPP(hAPP(c_List_Omap(tc_prod(X30784,X30782),X30784),c_Product__Type_Ofst(X30784,X30782)),X30780) != X30783
        | hAPP(hAPP(c_List_Omap(tc_prod(X30784,X30782),X30782),c_Product__Type_Osnd(X30784,X30782)),X30780) != X30781
        | hAPP(hAPP(c_List_Ozip(X30784,X30782),X30783),X30781) = X30780
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30784)),X30783) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30782)),X30781) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__eq__conv])])]) ).

fof(i_0_8310,plain,
    ! [X19928,X19929,X19930,X19931,X19932,X19933,X19934] :
      ( ( X19929 != X19931
        | X19929 = X19931
        | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X19934,tc_Option_Ooption(X19933)),X19932),X19931),hAPP(c_Option_Ooption_OSome(X19933),X19930)),X19929) != hAPP(c_Option_Ooption_OSome(X19933),X19928) )
      & ( hAPP(X19932,X19929) = hAPP(c_Option_Ooption_OSome(X19933),X19928)
        | X19929 = X19931
        | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X19934,tc_Option_Ooption(X19933)),X19932),X19931),hAPP(c_Option_Ooption_OSome(X19933),X19930)),X19929) != hAPP(c_Option_Ooption_OSome(X19933),X19928) )
      & ( X19929 != X19931
        | X19930 = X19928
        | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X19934,tc_Option_Ooption(X19933)),X19932),X19931),hAPP(c_Option_Ooption_OSome(X19933),X19930)),X19929) != hAPP(c_Option_Ooption_OSome(X19933),X19928) )
      & ( hAPP(X19932,X19929) = hAPP(c_Option_Ooption_OSome(X19933),X19928)
        | X19930 = X19928
        | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X19934,tc_Option_Ooption(X19933)),X19932),X19931),hAPP(c_Option_Ooption_OSome(X19933),X19930)),X19929) != hAPP(c_Option_Ooption_OSome(X19933),X19928) )
      & ( X19929 != X19931
        | X19930 != X19928
        | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X19934,tc_Option_Ooption(X19933)),X19932),X19931),hAPP(c_Option_Ooption_OSome(X19933),X19930)),X19929) = hAPP(c_Option_Ooption_OSome(X19933),X19928) )
      & ( X19929 = X19931
        | hAPP(X19932,X19929) != hAPP(c_Option_Ooption_OSome(X19933),X19928)
        | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X19934,tc_Option_Ooption(X19933)),X19932),X19931),hAPP(c_Option_Ooption_OSome(X19933),X19930)),X19929) = hAPP(c_Option_Ooption_OSome(X19933),X19928) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__upd__Some__unfold])])]) ).

fof(i_0_8311,plain,
    ! [X17785,X17786,X17787,X17788] :
      ( ( hBOOL(hAPP(X17787,X17785))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17788,tc_HOL_Obool)),X17787),X17786),X17785)) )
      & ( hBOOL(hAPP(X17786,X17785))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17788,tc_HOL_Obool)),X17787),X17786),X17785)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5761])])]) ).

fof(i_0_8312,plain,
    ! [X17882,X17883,X17884,X17885] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17885,tc_HOL_Obool)),X17884),X17883),X17882))
      | hBOOL(hAPP(X17884,X17882)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D1])]) ).

fof(i_0_8313,plain,
    ! [X17878,X17879,X17880,X17881] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17881,tc_HOL_Obool)),X17880),X17879),X17878))
      | hBOOL(hAPP(X17879,X17878)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D2])]) ).

cnf(i_0_8314,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_5762]) ).

fof(i_0_8315,plain,
    ! [X30721,X30722,X30723,X30724,X30725,X30726] :
      ( ~ hBOOL(hAPP(hAPP(X30726,X30725),X30724))
      | ~ c_List_Olistrelp(X30723,X30726,X30722,X30721)
      | c_List_Olistrelp(X30723,X30726,hAPP(hAPP(c_List_Olist_OCons(X30723),X30725),X30722),hAPP(hAPP(c_List_Olist_OCons(X30723),X30724),X30721)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp_OCons])]) ).

fof(i_0_8316,plain,
    ! [X30715,X30716,X30717,X30718,X30719,X30720] :
      ( ( hBOOL(hAPP(hAPP(X30719,X30718),X30716))
        | ~ c_List_Olistrelp(X30720,X30719,hAPP(hAPP(c_List_Olist_OCons(X30720),X30718),X30717),hAPP(hAPP(c_List_Olist_OCons(X30720),X30716),X30715)) )
      & ( c_List_Olistrelp(X30720,X30719,X30717,X30715)
        | ~ c_List_Olistrelp(X30720,X30719,hAPP(hAPP(c_List_Olist_OCons(X30720),X30718),X30717),hAPP(hAPP(c_List_Olist_OCons(X30720),X30716),X30715)) )
      & ( ~ hBOOL(hAPP(hAPP(X30719,X30718),X30716))
        | ~ c_List_Olistrelp(X30720,X30719,X30717,X30715)
        | c_List_Olistrelp(X30720,X30719,hAPP(hAPP(c_List_Olist_OCons(X30720),X30718),X30717),hAPP(hAPP(c_List_Olist_OCons(X30720),X30716),X30715)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp_Oequations_I2_J])])]) ).

cnf(i_0_8317,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_5763]) ).

fof(i_0_8318,plain,
    ! [X30758,X30759,X30760,X30761,X30762] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30762)),X30761) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30760)),X30759)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30762)),X30758) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30760)),X30759)
      | ~ hBOOL(hAPP(c_List_Odistinct(X30760),X30759))
      | hAPP(c_Map_Omap__of(X30760,X30762),hAPP(hAPP(c_List_Ozip(X30760,X30762),X30759),X30761)) != hAPP(c_Map_Omap__of(X30760,X30762),hAPP(hAPP(c_List_Ozip(X30760,X30762),X30759),X30758))
      | X30761 = X30758 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__zip__inject])]) ).

fof(i_0_8319,plain,
    ! [X28198] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X28198),c_Int_OInteg))
      | X28198 = hAPP(c_Int_ORep__Integ,esk290_1(X28198)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__cases])])]) ).

fof(i_0_8320,plain,
    ! [X29865,X29866,X29867] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X29867,tc_HOL_Obool)),esk379_3(X29865,X29866,X29867)),X29866))
        | hBOOL(hAPP(hAPP(c_member(X29867),X29865),c_Complete__Lattice_OInf__class_OInf(tc_fun(X29867,tc_HOL_Obool),X29866))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X29867),X29865),esk379_3(X29865,X29866,X29867)))
        | hBOOL(hAPP(hAPP(c_member(X29867),X29865),c_Complete__Lattice_OInf__class_OInf(tc_fun(X29867,tc_HOL_Obool),X29866))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InterI])])])]) ).

fof(i_0_8321,plain,
    ! [X32152,X32153,X32154,X32157,X32158,X32159,X32160,X32161] :
      ( ( X32153 = hAPP(hAPP(c_List_Olist_OCons(X32154),esk440_3(X32152,X32153,X32154)),esk441_3(X32152,X32153,X32154))
        | X32153 = c_List_Olist_ONil(X32154)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32154)),X32153),c_List_Olists(X32154,X32152))) )
      & ( hBOOL(hAPP(hAPP(c_member(X32154),esk440_3(X32152,X32153,X32154)),X32152))
        | X32153 = c_List_Olist_ONil(X32154)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32154)),X32153),c_List_Olists(X32154,X32152))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32154)),esk441_3(X32152,X32153,X32154)),c_List_Olists(X32154,X32152)))
        | X32153 = c_List_Olist_ONil(X32154)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32154)),X32153),c_List_Olists(X32154,X32152))) )
      & ( X32158 != c_List_Olist_ONil(X32159)
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32159)),X32158),c_List_Olists(X32159,X32157))) )
      & ( X32158 != hAPP(hAPP(c_List_Olist_OCons(X32159),X32160),X32161)
        | ~ hBOOL(hAPP(hAPP(c_member(X32159),X32160),X32157))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32159)),X32161),c_List_Olists(X32159,X32157)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32159)),X32158),c_List_Olists(X32159,X32157))) ) ),
    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_8322,plain,
    ! [X34043,X34044,X34045,X34046] :
      ( ( X34045 = X34043
        | ~ hBOOL(hAPP(hAPP(c_member(X34046),X34045),hAPP(c_List_Oset(X34046),c_List_Oreplicate(X34046,X34044,X34043)))) )
      & ( X34044 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X34046),X34045),hAPP(c_List_Oset(X34046),c_List_Oreplicate(X34046,X34044,X34043)))) )
      & ( X34045 != X34043
        | X34044 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_member(X34046),X34045),hAPP(c_List_Oset(X34046),c_List_Oreplicate(X34046,X34044,X34043)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__replicate])])]) ).

fof(i_0_8323,plain,
    ! [X20668,X20669,X20670,X20671,X20672] :
      ( ~ c_Finite__Set_Ofolding__one(X20672,X20671,X20670)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20672),X20669))
      | X20669 = c_Orderings_Obot__class_Obot(tc_fun(X20672,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20672),X20668))
      | X20668 = c_Orderings_Obot__class_Obot(tc_fun(X20672,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20672,tc_HOL_Obool)),X20669),X20668) != c_Orderings_Obot__class_Obot(tc_fun(X20672,tc_HOL_Obool))
      | hAPP(X20670,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20672,tc_HOL_Obool)),X20669),X20668)) = hAPP(hAPP(X20671,hAPP(X20670,X20669)),hAPP(X20670,X20668)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__disjoint])]) ).

fof(i_0_8324,plain,
    ! [X23282,X23283,X23284,X23285] :
      ( ~ class_Divides_Osemiring__div(X23285)
      | c_Divides_Odiv__class_Omod(X23285,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23285),X23284),X23283),X23282) = c_Divides_Odiv__class_Omod(X23285,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23285),c_Divides_Odiv__class_Omod(X23285,X23284,X23282)),c_Divides_Odiv__class_Omod(X23285,X23283,X23282)),X23282) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__eq])]) ).

fof(i_0_8325,plain,
    ! [X23318,X23319,X23320,X23321] :
      ( ~ class_Divides_Osemiring__div(X23321)
      | c_Divides_Odiv__class_Omod(X23321,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23321),X23320),X23319),X23318) = c_Divides_Odiv__class_Omod(X23321,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23321),c_Divides_Odiv__class_Omod(X23321,X23320,X23318)),c_Divides_Odiv__class_Omod(X23321,X23319,X23318)),X23318) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__eq])]) ).

fof(i_0_8326,plain,
    ! [X23345,X23346,X23347,X23348] :
      ( ~ class_Divides_Oring__div(X23348)
      | c_Divides_Odiv__class_Omod(X23348,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23348),X23347),X23346),X23345) = c_Divides_Odiv__class_Omod(X23348,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23348),c_Divides_Odiv__class_Omod(X23348,X23347,X23345)),c_Divides_Odiv__class_Omod(X23348,X23346,X23345)),X23345) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__eq])]) ).

fof(i_0_8327,plain,
    ! [X22723,X22724,X22725] :
      ( ~ class_Rings_Olinordered__semidom(X22725)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22725),c_Groups_Oone__class_Oone(X22725)),X22724))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22725),c_Groups_Oone__class_Oone(X22725)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22725),X22724),hAPP(hAPP(c_Power_Opower__class_Opower(X22725),X22724),X22723)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma])]) ).

fof(i_0_8328,plain,
    ! [X22205,X22206] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22206),X22205),X22205)),c_Groups_Ozero__class_Ozero(X22206)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22206),X22205),c_Groups_Ozero__class_Ozero(X22206)))
        | ~ class_Groups_Olinordered__ab__group__add(X22206) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22206),X22205),c_Groups_Ozero__class_Ozero(X22206)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22206),X22205),X22205)),c_Groups_Ozero__class_Ozero(X22206)))
        | ~ class_Groups_Olinordered__ab__group__add(X22206) ) ),
    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_8329,plain,
    ! [X22546,X22547] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22547),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22547),X22546),X22546)),c_Groups_Ozero__class_Ozero(X22547)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22547),X22546),c_Groups_Ozero__class_Ozero(X22547)))
        | ~ class_Rings_Olinordered__idom(X22547) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22547),X22546),c_Groups_Ozero__class_Ozero(X22547)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22547),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22547),X22546),X22546)),c_Groups_Ozero__class_Ozero(X22547)))
        | ~ class_Rings_Olinordered__idom(X22547) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).

fof(i_0_8330,plain,
    ! [X22121,X22122] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22122),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22122),X22121),X22121)),c_Groups_Ozero__class_Ozero(X22122)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22122),X22121),c_Groups_Ozero__class_Ozero(X22122)))
        | ~ class_Groups_Olinordered__ab__group__add(X22122) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22122),X22121),c_Groups_Ozero__class_Ozero(X22122)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22122),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22122),X22121),X22121)),c_Groups_Ozero__class_Ozero(X22122)))
        | ~ class_Groups_Olinordered__ab__group__add(X22122) ) ),
    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_8331,plain,
    ! [X28257,X28258] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk299_2(X28257,X28258)),X28258))
        | 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)),X28257),X28258) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28257),esk299_2(X28257,X28258)))
        | 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)),X28257),X28258) ) ),
    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_8332,plain,
    ! [X29582,X29583,X29584,X29585] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29585),X29584),c_Complete__Lattice_OInf__class_OInf(tc_fun(X29585,tc_HOL_Obool),X29583)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X29585,tc_HOL_Obool)),X29582),X29583))
      | hBOOL(hAPP(hAPP(c_member(X29585),X29584),X29582)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InterD])]) ).

fof(i_0_8333,plain,
    ! [X29578,X29579,X29580,X29581] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29581),X29580),c_Complete__Lattice_OInf__class_OInf(tc_fun(X29581,tc_HOL_Obool),X29579)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X29581,tc_HOL_Obool)),X29578),X29579))
      | hBOOL(hAPP(hAPP(c_member(X29581),X29580),X29578)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InterE])]) ).

fof(i_0_8334,plain,
    ! [X18164,X18165,X18166,X18167] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X18167),X18166),X18165))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18167,tc_HOL_Obool)),X18165),hAPP(X18164,X18165)))
      | hBOOL(hAPP(hAPP(c_member(X18167),X18166),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X18167,tc_HOL_Obool),X18164))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_weak__coinduct])]) ).

fof(i_0_8335,plain,
    ! [X25072,X25073] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25073))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25073),X25072)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25073),X25072) = 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_8336,plain,
    ! [X21996,X21997] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X21997,X21996)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X21997,X21996),tc_HOL_Obool))))
      | hAPP(c_Finite__Set_Ocard(X21996),c_Orderings_Otop__class_Otop(tc_fun(X21996,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X21997),c_Orderings_Otop__class_Otop(tc_fun(X21997,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD1])]) ).

fof(i_0_8337,plain,
    ! [X25967,X25968,X25969] :
      ( ~ class_Orderings_Olinorder(X25969)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25969),X25968))
      | X25968 = c_Orderings_Obot__class_Obot(tc_fun(X25969,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25969),X25967))
      | X25967 = c_Orderings_Obot__class_Obot(tc_fun(X25969,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OSup__fin(X25969,c_Orderings_Oord__class_Omax(X25969),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25969,tc_HOL_Obool)),X25968),X25967)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25969),c_Big__Operators_Olattice_OSup__fin(X25969,c_Orderings_Oord__class_Omax(X25969),X25968)),c_Big__Operators_Olattice_OSup__fin(X25969,c_Orderings_Oord__class_Omax(X25969),X25967)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__idem])]) ).

fof(i_0_8338,plain,
    ! [X25678,X25679,X25680] :
      ( ~ class_Orderings_Olinorder(X25680)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25680),X25679))
      | X25679 = c_Orderings_Obot__class_Obot(tc_fun(X25680,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25680),X25678))
      | X25678 = c_Orderings_Obot__class_Obot(tc_fun(X25680,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OInf__fin(X25680,c_Orderings_Oord__class_Omin(X25680),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25680,tc_HOL_Obool)),X25679),X25678)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25680),c_Big__Operators_Olattice_OInf__fin(X25680,c_Orderings_Oord__class_Omin(X25680),X25679)),c_Big__Operators_Olattice_OInf__fin(X25680,c_Orderings_Oord__class_Omin(X25680),X25678)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__idem])]) ).

fof(i_0_8339,plain,
    ! [X17805,X17806,X17807,X17808] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17808),X17807),X17806))
      | hBOOL(hAPP(hAPP(c_member(X17808),X17807),X17805))
      | hBOOL(hAPP(hAPP(c_member(X17808),X17807),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17808,tc_HOL_Obool)),X17806),X17805))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5764])]) ).

fof(i_0_8340,plain,
    ! [X22805,X22806,X22807] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22807),X22806))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22805))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22805),X22807)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22805),X22806))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2])]) ).

fof(i_0_8341,plain,
    ! [X22351,X22352,X22353] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22353),X22352))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22351))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22353),X22351)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22352),X22351))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono1])]) ).

fof(i_0_8342,plain,
    ! [X22348,X22349,X22350] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22350),X22349))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22348))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22348),X22350)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22348),X22349))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono2])]) ).

fof(i_0_8343,plain,
    ! [X23115,X23116,X23117] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23117),X23116))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23115))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23117),X23115)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23116),X23115))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1])]) ).

fof(i_0_8344,plain,
    ! [X23461,X23462,X23463] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23463))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23463),X23462))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23461),X23462)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23461),X23463))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono2])]) ).

fof(i_0_8345,plain,
    ! [X30127,X30128,X30129] :
      ( ( ~ c_Fun_Oinj__on(tc_List_Olist(X30129),tc_List_Olist(X30128),hAPP(c_List_Omap(X30129,X30128),X30127),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X30129),tc_HOL_Obool)))
        | c_Fun_Oinj__on(X30129,X30128,X30127,c_Orderings_Otop__class_Otop(tc_fun(X30129,tc_HOL_Obool))) )
      & ( ~ c_Fun_Oinj__on(X30129,X30128,X30127,c_Orderings_Otop__class_Otop(tc_fun(X30129,tc_HOL_Obool)))
        | c_Fun_Oinj__on(tc_List_Olist(X30129),tc_List_Olist(X30128),hAPP(c_List_Omap(X30129,X30128),X30127),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X30129),tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__map])]) ).

fof(i_0_8346,plain,
    ! [X30119,X30120,X30121] :
      ( ~ c_Fun_Oinj__on(tc_List_Olist(X30121),tc_List_Olist(X30120),hAPP(c_List_Omap(X30121,X30120),X30119),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X30121),tc_HOL_Obool)))
      | c_Fun_Oinj__on(X30121,X30120,X30119,c_Orderings_Otop__class_Otop(tc_fun(X30121,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__mapD])]) ).

fof(i_0_8347,plain,
    ! [X17027,X17028,X17029,X17030] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17030,tc_HOL_Obool)),X17029),X17028))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17030,tc_HOL_Obool)),X17029),hAPP(hAPP(c_Set_Oinsert(X17030),X17027),X17028))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__insertI2])]) ).

fof(i_0_8348,plain,
    ! [X33966,X33967,X33968,X33969] : hAPP(hAPP(c_List_Oappend(X33969),c_List_Oreplicate(X33969,X33968,X33967)),hAPP(hAPP(c_List_Olist_OCons(X33969),X33967),X33966)) = hAPP(hAPP(c_List_Olist_OCons(X33969),X33967),hAPP(hAPP(c_List_Oappend(X33969),c_List_Oreplicate(X33969,X33968,X33967)),X33966)),
    inference(variable_rename,[status(thm)],[fact_replicate__app__Cons__same]) ).

fof(i_0_8349,plain,
    ! [X29464,X29465,X29466,X29467,X29468] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29468,tc_fun(X29467,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X29468),X29466),X29465)),X29464) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29467,tc_HOL_Obool)),hAPP(X29464,X29466)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29468,tc_fun(X29467,tc_HOL_Obool)),X29465),X29464)),
    inference(variable_rename,[status(thm)],[fact_INT__insert]) ).

fof(i_0_8350,plain,
    ! [X19556,X19557,X19558,X19559,X19560] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19560,tc_fun(X19559,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X19560),X19558),X19557)),X19556) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19559,tc_HOL_Obool)),hAPP(X19556,X19558)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19560,tc_fun(X19559,tc_HOL_Obool)),X19557),X19556)),
    inference(variable_rename,[status(thm)],[fact_UN__insert]) ).

fof(i_0_8351,plain,
    ! [X25460,X25461,X25462,X25463] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25462),X25460),hAPP(c_Finite__Set_Ofold1(X25462,c_Orderings_Oord__class_Omin(X25462)),X25461)))
        | ~ hBOOL(hAPP(hAPP(c_member(X25462),X25463),X25461))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25462),X25460),X25463))
        | X25461 = c_Orderings_Obot__class_Obot(tc_fun(X25462,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25462),X25461))
        | ~ class_Orderings_Olinorder(X25462) )
      & ( hBOOL(hAPP(hAPP(c_member(X25462),esk161_3(X25460,X25461,X25462)),X25461))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25462),X25460),hAPP(c_Finite__Set_Ofold1(X25462,c_Orderings_Oord__class_Omin(X25462)),X25461)))
        | X25461 = c_Orderings_Obot__class_Obot(tc_fun(X25462,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25462),X25461))
        | ~ class_Orderings_Olinorder(X25462) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25462),X25460),esk161_3(X25460,X25461,X25462)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25462),X25460),hAPP(c_Finite__Set_Ofold1(X25462,c_Orderings_Oord__class_Omin(X25462)),X25461)))
        | X25461 = c_Orderings_Obot__class_Obot(tc_fun(X25462,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25462),X25461))
        | ~ class_Orderings_Olinorder(X25462) ) ),
    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_8352,plain,
    ! [X25450,X25451,X25452,X25453] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25452),X25450),hAPP(c_Finite__Set_Ofold1(X25452,c_Orderings_Oord__class_Omin(X25452)),X25451)))
        | ~ hBOOL(hAPP(hAPP(c_member(X25452),X25453),X25451))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25452),X25450),X25453))
        | X25451 = c_Orderings_Obot__class_Obot(tc_fun(X25452,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25452),X25451))
        | ~ class_Orderings_Olinorder(X25452) )
      & ( hBOOL(hAPP(hAPP(c_member(X25452),esk159_3(X25450,X25451,X25452)),X25451))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25452),X25450),hAPP(c_Finite__Set_Ofold1(X25452,c_Orderings_Oord__class_Omin(X25452)),X25451)))
        | X25451 = c_Orderings_Obot__class_Obot(tc_fun(X25452,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25452),X25451))
        | ~ class_Orderings_Olinorder(X25452) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25452),X25450),esk159_3(X25450,X25451,X25452)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25452),X25450),hAPP(c_Finite__Set_Ofold1(X25452,c_Orderings_Oord__class_Omin(X25452)),X25451)))
        | X25451 = c_Orderings_Obot__class_Obot(tc_fun(X25452,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25452),X25451))
        | ~ class_Orderings_Olinorder(X25452) ) ),
    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_8353,plain,
    ! [X21289,X21290,X21291,X21292] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21291),X21289),hAPP(c_Finite__Set_Ofold1(X21291,c_Lattices_Osemilattice__inf__class_Oinf(X21291)),X21290)))
        | ~ hBOOL(hAPP(hAPP(c_member(X21291),X21292),X21290))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21291),X21289),X21292))
        | X21290 = c_Orderings_Obot__class_Obot(tc_fun(X21291,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21291),X21290))
        | ~ class_Lattices_Osemilattice__inf(X21291) )
      & ( hBOOL(hAPP(hAPP(c_member(X21291),esk100_3(X21289,X21290,X21291)),X21290))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21291),X21289),hAPP(c_Finite__Set_Ofold1(X21291,c_Lattices_Osemilattice__inf__class_Oinf(X21291)),X21290)))
        | X21290 = c_Orderings_Obot__class_Obot(tc_fun(X21291,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21291),X21290))
        | ~ class_Lattices_Osemilattice__inf(X21291) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21291),X21289),esk100_3(X21289,X21290,X21291)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21291),X21289),hAPP(c_Finite__Set_Ofold1(X21291,c_Lattices_Osemilattice__inf__class_Oinf(X21291)),X21290)))
        | X21290 = c_Orderings_Obot__class_Obot(tc_fun(X21291,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21291),X21290))
        | ~ class_Lattices_Osemilattice__inf(X21291) ) ),
    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_8354,plain,
    ! [X33370,X33371,X33372,X33373,X33374] : c_List_Omaps(X33374,X33373,X33372,hAPP(hAPP(c_List_Olist_OCons(X33374),X33371),X33370)) = hAPP(hAPP(c_List_Oappend(X33373),hAPP(X33372,X33371)),c_List_Omaps(X33374,X33373,X33372,X33370)),
    inference(variable_rename,[status(thm)],[fact_maps__simps_I1_J]) ).

cnf(i_0_8355,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk448_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_5695]) ).

cnf(i_0_8356,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk449_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_5696]) ).

fof(i_0_8357,plain,
    ! [X22275,X22276,X22277] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22277),X22276),X22275))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22277),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22277),X22276),X22275)),c_Groups_Ozero__class_Ozero(X22277)))
        | ~ class_Groups_Oordered__ab__group__add(X22277) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22277),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22277),X22276),X22275)),c_Groups_Ozero__class_Ozero(X22277)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22277),X22276),X22275))
        | ~ class_Groups_Oordered__ab__group__add(X22277) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0])])]) ).

fof(i_0_8358,plain,
    ! [X22272,X22273,X22274] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22274),X22273),X22272))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22274),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22274),X22273),X22272)),c_Groups_Ozero__class_Ozero(X22274)))
        | ~ class_Groups_Oordered__ab__group__add(X22274) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22274),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22274),X22273),X22272)),c_Groups_Ozero__class_Ozero(X22274)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22274),X22273),X22272))
        | ~ class_Groups_Oordered__ab__group__add(X22274) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0])])]) ).

fof(i_0_8359,plain,
    ! [X23112,X23113,X23114] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23114),X23113))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23112),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),X23113),X23112)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23114),X23112))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1__neg])]) ).

cnf(i_0_8360,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_5765]) ).

cnf(i_0_8361,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_5766]) ).

fof(i_0_8362,plain,
    ! [X31003,X31004,X31005] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31005),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31004)),X31003)))
      | hBOOL(hAPP(hAPP(c_member(X31004),hAPP(hAPP(c_List_Onth(X31004),X31003),X31005)),hAPP(c_List_Oset(X31004),X31003))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__mem])]) ).

fof(i_0_8363,plain,
    ! [X22473,X22474] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22474))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22473))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22474),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22474),X22473))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__n__mult__m])]) ).

fof(i_0_8364,plain,
    ! [X22471,X22472] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22472))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22471))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22471),X22472))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__m__mult__n])]) ).

fof(i_0_8365,plain,
    ! [X22538,X22539] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22539),X22538))
      | hAPP(c_Finite__Set_Ocard(X22539),X22538) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X22539,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X22539),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22538) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oeq__fold__g])]) ).

fof(i_0_8366,plain,
    ! [X22536,X22537] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22537),X22536))
        | hAPP(c_Finite__Set_Ocard(X22537),X22536) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X22537,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X22537),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22536) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X22537),X22536))
        | hAPP(c_Finite__Set_Ocard(X22537),X22536) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5767])]) ).

fof(i_0_8367,plain,
    ! [X24421,X24422,X24423,X24424] :
      ( ~ class_Fields_Ofield(X24424)
      | X24423 = c_Groups_Ozero__class_Ozero(X24424)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24424),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24424),X24422),X24423)),X24421) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24424),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24424),X24422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24424),X24423),X24421))),X24423) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__add__eq__iff])]) ).

fof(i_0_8368,plain,
    ! [X24425,X24426,X24427,X24428] :
      ( ~ class_Fields_Ofield__inverse__zero(X24428)
      | X24427 = c_Groups_Ozero__class_Ozero(X24428)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24428),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24428),X24426),X24427)),X24425) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24428),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24428),X24426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24428),X24425),X24427))),X24427) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__num])]) ).

fof(i_0_8369,plain,
    ! [X24442,X24443,X24444,X24445] :
      ( ~ class_Fields_Ofield(X24445)
      | X24444 = c_Groups_Ozero__class_Ozero(X24445)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24445),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24445),X24443),X24444)),X24442) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24445),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24445),X24443),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24445),X24444),X24442))),X24444) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__diff__eq__iff])]) ).

fof(i_0_8370,plain,
    ! [X30995,X30996,X30997,X30999,X31000,X31001,X31002] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk415_3(X30995,X30996,X30997)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30997)),X30995)))
        | ~ hBOOL(hAPP(hAPP(c_member(X30997),X30996),hAPP(c_List_Oset(X30997),X30995))) )
      & ( hAPP(hAPP(c_List_Onth(X30997),X30995),esk415_3(X30995,X30996,X30997)) = X30996
        | ~ hBOOL(hAPP(hAPP(c_member(X30997),X30996),hAPP(c_List_Oset(X30997),X30995))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31002),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31001)),X30999)))
        | hAPP(hAPP(c_List_Onth(X31001),X30999),X31002) != X31000
        | hBOOL(hAPP(hAPP(c_member(X31001),X31000),hAPP(c_List_Oset(X31001),X30999))) ) ),
    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_8371,plain,
    ! [X22872,X22873,X22874,X22875] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22875),X22874))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22873),X22872))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22875),X22873)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22874),X22872))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono])]) ).

fof(i_0_8372,plain,
    ! [X21684,X21685,X21686,X21687] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21687),X21686))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21685),X21684))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21687),X21685)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21686),X21684))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).

fof(i_0_8373,plain,
    ! [X20953,X20954,X20955] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20955),X20954))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20953),X20955))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20955),X20953)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20954),X20953))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono])]) ).

fof(i_0_8374,plain,
    ! [X20968,X20969,X20970] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20970),X20969))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20970),X20968))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20968),X20969)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20968),X20970))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono2])]) ).

fof(i_0_8375,plain,
    ! [X21718,X21719,X21720,X21721] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21721),X21720))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21719),X21718))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21721),X21719)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21720),X21718))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).

fof(i_0_8376,plain,
    ! [X21021,X21022,X21023,X21024] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21024),X21023))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21022),X21021))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21024),X21022)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21023),X21021))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono])]) ).

fof(i_0_8377,plain,
    ! [X21898,X21899,X21900,X21901,X21902] :
      ( ~ class_Rings_Ocomm__semiring__1(X21902)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21902),X21901),X21900)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21902),X21899),X21898)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21902),X21899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21902),X21901),X21900)),X21898)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J])]) ).

fof(i_0_8378,plain,
    ! [X26406,X26407,X26408] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X26408,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X26408),X26407)),hAPP(c_SetInterval_Oord__class_OlessThan(X26408),X26406)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26408),X26407),X26406))
        | ~ class_Orderings_Olinorder(X26408) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26408),X26407),X26406))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X26408,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X26408),X26407)),hAPP(c_SetInterval_Oord__class_OlessThan(X26408),X26406)))
        | ~ class_Orderings_Olinorder(X26408) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__strict__subset__iff])])]) ).

fof(i_0_8379,plain,
    ! [X26807,X26808,X26809] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26809,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X26809),X26808)),hAPP(c_SetInterval_Oord__class_OatMost(X26809),X26807)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26809),X26808),X26807))
        | ~ class_Orderings_Oorder(X26809) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26809),X26808),X26807))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26809,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X26809),X26808)),hAPP(c_SetInterval_Oord__class_OatMost(X26809),X26807)))
        | ~ class_Orderings_Oorder(X26809) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__subset__iff])])]) ).

fof(i_0_8380,plain,
    ! [X26403,X26404,X26405] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26405,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X26405),X26404)),hAPP(c_SetInterval_Oord__class_OlessThan(X26405),X26403)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26405),X26404),X26403))
        | ~ class_Orderings_Olinorder(X26405) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26405),X26404),X26403))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26405,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X26405),X26404)),hAPP(c_SetInterval_Oord__class_OlessThan(X26405),X26403)))
        | ~ class_Orderings_Olinorder(X26405) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__subset__iff])])]) ).

fof(i_0_8381,plain,
    ! [X26918,X26919,X26920] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26920,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X26920),X26919)),hAPP(c_SetInterval_Oord__class_OatLeast(X26920),X26918)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26920),X26918),X26919))
        | ~ class_Orderings_Oorder(X26920) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26920),X26918),X26919))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26920,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X26920),X26919)),hAPP(c_SetInterval_Oord__class_OatLeast(X26920),X26918)))
        | ~ class_Orderings_Oorder(X26920) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeast__subset__iff])])]) ).

fof(i_0_8382,plain,
    ! [X26879,X26880,X26881] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26881,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26881),X26880)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26881),X26879)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26881),X26879),X26880))
        | ~ class_Orderings_Olinorder(X26881) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26881),X26879),X26880))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26881,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26881),X26880)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26881),X26879)))
        | ~ class_Orderings_Olinorder(X26881) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__subset__iff])])]) ).

cnf(i_0_8383,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X2),c_Relation_OId(X1)),X3) = X3,
    inference(split_conjunct,[status(thm)],[i_0_5768]) ).

fof(i_0_8384,plain,
    ! [X24314,X24315,X24316] :
      ( ~ class_Fields_Olinordered__field(X24316)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24316),X24315),c_Groups_Ozero__class_Ozero(X24316)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24316),c_Groups_Ozero__class_Ozero(X24316)),X24314))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24316),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24316),X24315),X24314)),c_Groups_Ozero__class_Ozero(X24316))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__pos])]) ).

fof(i_0_8385,plain,
    ! [X24311,X24312,X24313] :
      ( ~ class_Fields_Olinordered__field(X24313)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24313),c_Groups_Ozero__class_Ozero(X24313)),X24312))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24313),X24311),c_Groups_Ozero__class_Ozero(X24313)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24313),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24313),X24312),X24311)),c_Groups_Ozero__class_Ozero(X24313))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__neg])]) ).

fof(i_0_8386,plain,
    ! [X22236,X22237,X22238] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22238)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22238),X22237),c_Groups_Ozero__class_Ozero(X22238)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22238),c_Groups_Ozero__class_Ozero(X22238)),X22236))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22238),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22238),X22237),X22236)),c_Groups_Ozero__class_Ozero(X22238))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__pos])]) ).

fof(i_0_8387,plain,
    ! [X22252,X22253,X22254] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22254)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22254),c_Groups_Ozero__class_Ozero(X22254)),X22253))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22254),X22252),c_Groups_Ozero__class_Ozero(X22254)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22254),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22254),X22253),X22252)),c_Groups_Ozero__class_Ozero(X22254))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg])]) ).

fof(i_0_8388,plain,
    ! [X22249,X22250,X22251] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22251)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22251),c_Groups_Ozero__class_Ozero(X22251)),X22250))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22251),X22249),c_Groups_Ozero__class_Ozero(X22251)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22251),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22251),X22249),X22250)),c_Groups_Ozero__class_Ozero(X22251))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2])]) ).

fof(i_0_8389,plain,
    ! [X24370,X24371,X24372] :
      ( ~ class_Fields_Olinordered__field(X24372)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24372),c_Groups_Ozero__class_Ozero(X24372)),X24371))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24372),X24370),c_Groups_Ozero__class_Ozero(X24372)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24372),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24372),X24371),X24370)),c_Groups_Ozero__class_Ozero(X24372))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonneg__neg])]) ).

fof(i_0_8390,plain,
    ! [X24352,X24353,X24354] :
      ( ~ class_Fields_Olinordered__field(X24354)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24354),X24353),c_Groups_Ozero__class_Ozero(X24354)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24354),c_Groups_Ozero__class_Ozero(X24354)),X24352))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24354),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24354),X24353),X24352)),c_Groups_Ozero__class_Ozero(X24354))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonpos__pos])]) ).

fof(i_0_8391,plain,
    ! [X22196,X22197,X22198] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22198),c_Groups_Ozero__class_Ozero(X22198)),X22197))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22198),X22196),c_Groups_Ozero__class_Ozero(X22198)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22198),X22197),X22196)),c_Groups_Ozero__class_Ozero(X22198)))
        | ~ class_Rings_Oordered__cancel__semiring(X22198) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22198),X22197),c_Groups_Ozero__class_Ozero(X22198)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22198),c_Groups_Ozero__class_Ozero(X22198)),X22196))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22198),X22197),X22196)),c_Groups_Ozero__class_Ozero(X22198)))
        | ~ class_Rings_Oordered__cancel__semiring(X22198) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le])])]) ).

fof(i_0_8392,plain,
    ! [X22157,X22158,X22159] :
      ( ~ class_Rings_Oordered__cancel__semiring(X22159)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22159),X22158),c_Groups_Ozero__class_Ozero(X22159)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22159),c_Groups_Ozero__class_Ozero(X22159)),X22157))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22159),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22159),X22158),X22157)),c_Groups_Ozero__class_Ozero(X22159))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg])]) ).

fof(i_0_8393,plain,
    ! [X22151,X22152,X22153] :
      ( ~ class_Rings_Oordered__cancel__semiring(X22153)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22153),c_Groups_Ozero__class_Ozero(X22153)),X22152))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22153),X22151),c_Groups_Ozero__class_Ozero(X22153)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22153),X22152),X22151)),c_Groups_Ozero__class_Ozero(X22153))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos])]) ).

fof(i_0_8394,plain,
    ! [X22154,X22155,X22156] :
      ( ~ class_Rings_Oordered__cancel__semiring(X22156)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22156),c_Groups_Ozero__class_Ozero(X22156)),X22155))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22156),X22154),c_Groups_Ozero__class_Ozero(X22156)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22156),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22156),X22154),X22155)),c_Groups_Ozero__class_Ozero(X22156))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2])]) ).

fof(i_0_8395,plain,
    ! [X30312,X30313,X30314] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30314,tc_HOL_Obool)),hAPP(c_List_Oset(X30314),X30313)),hAPP(c_List_Oset(X30314),hAPP(hAPP(c_List_Olist_OCons(X30314),X30312),X30313)))),
    inference(variable_rename,[status(thm)],[fact_set__subset__Cons]) ).

fof(i_0_8396,plain,
    ! [X32232,X32233,X32234,X32235] : c_List_Otranspose(X32235,hAPP(hAPP(c_List_Omap(tc_List_Olist(X32234),tc_List_Olist(X32235)),hAPP(c_List_Omap(X32234,X32235),X32233)),X32232)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X32234),tc_List_Olist(X32235)),hAPP(c_List_Omap(X32234,X32235),X32233)),c_List_Otranspose(X32234,X32232)),
    inference(variable_rename,[status(thm)],[fact_transpose__map__map]) ).

cnf(i_0_8397,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_5769]) ).

cnf(i_0_8398,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_5770]) ).

fof(i_0_8399,plain,
    ! [X25771,X25772,X25773,X25774] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25774),X25773),X25771))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25774),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25774),X25773),X25772)),X25771))
        | ~ class_Orderings_Olinorder(X25774) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25774),X25772),X25771))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25774),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25774),X25773),X25772)),X25771))
        | ~ class_Orderings_Olinorder(X25774) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25774),X25773),X25771))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25774),X25772),X25771))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25774),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25774),X25773),X25772)),X25771))
        | ~ class_Orderings_Olinorder(X25774) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__less__iff__conj])])]) ).

fof(i_0_8400,plain,
    ! [X17723,X17724,X17725,X17726] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17726),X17725),X17723))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17726),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17726),X17725),X17724)),X17723))
        | ~ class_Lattices_Osemilattice__sup(X17726) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17726),X17724),X17723))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17726),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17726),X17725),X17724)),X17723))
        | ~ class_Lattices_Osemilattice__sup(X17726) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17726),X17725),X17723))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17726),X17724),X17723))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17726),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17726),X17725),X17724)),X17723))
        | ~ class_Lattices_Osemilattice__sup(X17726) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__sup__iff])])]) ).

fof(i_0_8401,plain,
    ! [X17639,X17640,X17641,X17642] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17642),X17641),X17639))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17642),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17642),X17641),X17640)),X17639))
        | ~ class_Lattices_Osemilattice__sup(X17642) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17642),X17640),X17639))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17642),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17642),X17641),X17640)),X17639))
        | ~ class_Lattices_Osemilattice__sup(X17642) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5771])])]) ).

fof(i_0_8402,plain,
    ! [X25814,X25815,X25816,X25817] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25817),X25816),X25814))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25817),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25817),X25816),X25815)),X25814))
        | ~ class_Orderings_Olinorder(X25817) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25817),X25815),X25814))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25817),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25817),X25816),X25815)),X25814))
        | ~ class_Orderings_Olinorder(X25817) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25817),X25816),X25814))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25817),X25815),X25814))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25817),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25817),X25816),X25815)),X25814))
        | ~ class_Orderings_Olinorder(X25817) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__sup__iff])])]) ).

fof(i_0_8403,plain,
    ! [X25783,X25784,X25785,X25786] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25786),X25785),X25783))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25786),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25786),X25785),X25784)),X25783))
        | ~ class_Orderings_Olinorder(X25786) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25786),X25784),X25783))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25786),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25786),X25785),X25784)),X25783))
        | ~ class_Orderings_Olinorder(X25786) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5772])])]) ).

fof(i_0_8404,plain,
    ! [X30982,X30983,X30984,X30985] :
      ( ( hAPP(hAPP(c_List_Onth(X30985),X30984),X30983) != hAPP(hAPP(c_List_Onth(X30985),X30984),X30982)
        | X30983 = X30982
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30982),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30985)),X30984)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30983),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30985)),X30984)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30985),X30984)) )
      & ( X30983 != X30982
        | hAPP(hAPP(c_List_Onth(X30985),X30984),X30983) = hAPP(hAPP(c_List_Onth(X30985),X30984),X30982)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30982),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30985)),X30984)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30983),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30985)),X30984)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30985),X30984)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__eq__iff__index__eq])])]) ).

fof(i_0_8405,plain,
    ! [X30974,X30975,X30976,X30977,X30978,X30979] :
      ( ( ~ hBOOL(hAPP(c_List_Odistinct(X30975),X30974))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30976),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30975)),X30974)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30977),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30975)),X30974)))
        | X30976 = X30977
        | hAPP(hAPP(c_List_Onth(X30975),X30974),X30976) != hAPP(hAPP(c_List_Onth(X30975),X30974),X30977) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk413_2(X30978,X30979)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30979)),X30978)))
        | hBOOL(hAPP(c_List_Odistinct(X30979),X30978)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk414_2(X30978,X30979)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30979)),X30978)))
        | hBOOL(hAPP(c_List_Odistinct(X30979),X30978)) )
      & ( esk413_2(X30978,X30979) != esk414_2(X30978,X30979)
        | hBOOL(hAPP(c_List_Odistinct(X30979),X30978)) )
      & ( hAPP(hAPP(c_List_Onth(X30979),X30978),esk413_2(X30978,X30979)) = hAPP(hAPP(c_List_Onth(X30979),X30978),esk414_2(X30978,X30979))
        | hBOOL(hAPP(c_List_Odistinct(X30979),X30978)) ) ),
    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_8406,plain,
    ! [X30440,X30441,X30442,X30443] :
      ( ( hBOOL(hAPP(c_List_Odistinct(X30442),X30440))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30443),hAPP(hAPP(c_List_Omap(X30442,X30443),X30441),X30440))) )
      & ( c_Fun_Oinj__on(X30442,X30443,X30441,hAPP(c_List_Oset(X30442),X30440))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30443),hAPP(hAPP(c_List_Omap(X30442,X30443),X30441),X30440))) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X30442),X30440))
        | ~ c_Fun_Oinj__on(X30442,X30443,X30441,hAPP(c_List_Oset(X30442),X30440))
        | hBOOL(hAPP(c_List_Odistinct(X30443),hAPP(hAPP(c_List_Omap(X30442,X30443),X30441),X30440))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__map])])]) ).

fof(i_0_8407,plain,
    ! [X25985,X25986] :
      ( ~ class_Orderings_Olinorder(X25986)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25986),X25985))
      | X25985 = c_Orderings_Obot__class_Obot(tc_fun(X25986,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25986),c_Big__Operators_Olattice_OInf__fin(X25986,c_Orderings_Oord__class_Omin(X25986),X25985)),c_Big__Operators_Olattice_OSup__fin(X25986,c_Orderings_Oord__class_Omax(X25986),X25985))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__le__Sup])]) ).

fof(i_0_8408,plain,
    ! [X18768,X18769,X18770,X18771,X18772] :
      ( ~ c_Fun_Oinj__on(X18772,X18771,X18770,X18769)
      | c_Fun_Oinj__on(X18772,X18771,X18770,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18772,tc_HOL_Obool)),X18769),X18768)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__diff])]) ).

fof(i_0_8409,plain,
    ! [X33754,X33755,X33756,X33757] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X33757,X33756),c_Lazy__Sequence_Olazy__sequence_OInsert(X33757,X33755,X33754)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X33756,X33755)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X33757,X33756),X33754))),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_8410,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_5773]) ).

cnf(i_0_8411,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_5774]) ).

cnf(i_0_8412,plain,
    c_List_Omember(X1) = c_List_Oset(X1),
    inference(split_conjunct,[status(thm)],[i_0_5775]) ).

fof(i_0_8413,plain,
    ! [X29068,X29069,X29070,X29071,X29072,X29073] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X29073,X29072,X29071)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29073),X29070))
      | hAPP(hAPP(c_Finite__Set_Ofold(X29073,X29072,X29071),X29069),hAPP(hAPP(c_Set_Oinsert(X29073),X29068),X29070)) = hAPP(hAPP(c_Finite__Set_Ofold(X29073,X29072,X29071),hAPP(hAPP(X29071,X29068),X29069)),X29070) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem2])]) ).

fof(i_0_8414,plain,
    ! [X18295,X18296,X18297] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X18297),X18296),X18295))
      | hAPP(hAPP(c_Set_Oinsert(X18297),X18296),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18297,tc_HOL_Obool)),X18295),hAPP(hAPP(c_Set_Oinsert(X18297),X18296),c_Orderings_Obot__class_Obot(tc_fun(X18297,tc_HOL_Obool))))) = X18295 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__Diff])]) ).

fof(i_0_8415,plain,
    ! [X20399,X20400] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20400),c_Orderings_Otop__class_Otop(tc_fun(X20400,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X20400,X20399)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X20400,X20399),tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20399),c_Orderings_Otop__class_Otop(tc_fun(X20399,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X20400,X20399)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X20400,X20399),tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20400),c_Orderings_Otop__class_Otop(tc_fun(X20400,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20399),c_Orderings_Otop__class_Otop(tc_fun(X20399,tc_HOL_Obool))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X20400,X20399)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X20400,X20399),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_8416,plain,
    ! [X20401,X20402] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20402),c_Orderings_Otop__class_Otop(tc_fun(X20402,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20401),c_Orderings_Otop__class_Otop(tc_fun(X20401,tc_HOL_Obool))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X20402,X20401)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X20402,X20401),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Prod__UNIV])]) ).

fof(i_0_8417,plain,
    ! [X26603,X26604,X26605,X26606] :
      ( ~ class_Groups_Ocomm__monoid__add(X26606)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26605),X26604))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26606),X26603),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26605,X26604)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26606),hAPP(X26603,X26605)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26606),X26603),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X26605),X26604))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__head__Suc])]) ).

fof(i_0_8418,plain,
    ! [X19429,X19430,X19431,X19432,X19433] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X19433),hAPP(X19432,X19431)),X19430))
      | hBOOL(hAPP(hAPP(c_member(X19429),X19431),hAPP(c_Set_Ovimage(X19429,X19433,X19432),X19430))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimageI2])]) ).

cnf(i_0_8419,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_5776]) ).

fof(i_0_8420,plain,
    ! [X32724,X32725,X32726] :
      ( ( ~ c_List_Olinorder__class_Osorted(X32726,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32726,X32726,c_COMBI(X32726)),X32725),X32724))
        | c_List_Olinorder__class_Osorted(X32726,X32724)
        | ~ class_Orderings_Olinorder(X32726) )
      & ( ~ c_List_Olinorder__class_Osorted(X32726,X32724)
        | c_List_Olinorder__class_Osorted(X32726,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32726,X32726,c_COMBI(X32726)),X32725),X32724))
        | ~ class_Orderings_Olinorder(X32726) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort])])]) ).

fof(i_0_8421,plain,
    ! [X26599,X26600,X26601,X26602] :
      ( ~ class_Groups_Ocomm__monoid__add(X26602)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26601),X26600))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26602),X26599),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26601),X26600)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26602),hAPP(X26599,X26601)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26602),X26599),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X26601)),X26600))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__head__upt__Suc])]) ).

fof(i_0_8422,plain,
    ! [X17117,X17118,X17119] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17117,tc_HOL_Obool)),X17119),X17118))
        | X17119 != X17118 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17117,tc_HOL_Obool)),X17118),X17119))
        | X17119 != X17118 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17117,tc_HOL_Obool)),X17119),X17118))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17117,tc_HOL_Obool)),X17118),X17119))
        | X17119 = X17118 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])]) ).

fof(i_0_8423,plain,
    ! [X17016,X17017,X17018] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17018,tc_HOL_Obool)),X17017),X17016))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17018,tc_HOL_Obool)),X17016),X17017))
      | X17017 = X17016 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityI])]) ).

fof(i_0_8424,plain,
    ! [X32943,X32944,X32945] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32945),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32944)),X32943)))
      | hAPP(hAPP(c_List_Onth(X32944),hAPP(c_List_Orev(X32944),X32943)),X32945) = hAPP(hAPP(c_List_Onth(X32944),X32943),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32944)),X32943)),hAPP(c_Nat_OSuc,X32945))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__nth])]) ).

fof(i_0_8425,plain,
    ! [X29398,X29399,X29400,X29401,X29402] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29402),X29401),X29400))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29399,tc_HOL_Obool)),hAPP(X29398,X29401)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29402,tc_fun(X29399,tc_HOL_Obool)),X29400),X29398)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29402,tc_fun(X29399,tc_HOL_Obool)),X29400),X29398) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__absorb])]) ).

fof(i_0_8426,plain,
    ! [X19800,X19801,X19802,X19803,X19804] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X19804),X19803),X19802))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19801,tc_HOL_Obool)),hAPP(X19800,X19803)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19804,tc_fun(X19801,tc_HOL_Obool)),X19802),X19800)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19804,tc_fun(X19801,tc_HOL_Obool)),X19802),X19800) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__absorb])]) ).

fof(i_0_8427,plain,
    ! [X31151,X31152,X31153,X31154,X31155] : hAPP(hAPP(c_List_Olist__update(X31155,hAPP(hAPP(c_List_Olist__update(X31155,X31154),X31153),X31152)),X31153),X31151) = hAPP(hAPP(c_List_Olist__update(X31155,X31154),X31153),X31151),
    inference(variable_rename,[status(thm)],[fact_list__update__overwrite]) ).

fof(i_0_8428,plain,
    ! [X25095,X25096] : 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,X25096)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25095))),
    inference(variable_rename,[status(thm)],[fact_negative__zless]) ).

fof(i_0_8429,plain,
    ! [X22210,X22211,X22212] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22212)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22212),X22211),c_Groups_Ozero__class_Ozero(X22212)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22212),X22210),c_Groups_Ozero__class_Ozero(X22212)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22212),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22212),X22211),X22210)),c_Groups_Ozero__class_Ozero(X22212))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).

fof(i_0_8430,plain,
    ! [X22400,X22401,X22402] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22402)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22402),X22401),c_Groups_Ozero__class_Ozero(X22402)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22402),X22400),c_Groups_Ozero__class_Ozero(X22402)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22402),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22402),X22401),X22400)),c_Groups_Ozero__class_Ozero(X22402))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).

fof(i_0_8431,plain,
    ! [X22397,X22398,X22399] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22399)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22399),X22398),c_Groups_Ozero__class_Ozero(X22399)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22399),X22397),c_Groups_Ozero__class_Ozero(X22399)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22399),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22399),X22398),X22397)),c_Groups_Ozero__class_Ozero(X22399))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).

fof(i_0_8432,plain,
    ! [X25658,X25659,X25660] :
      ( ~ class_Rings_Osemiring__1(X25660)
      | ~ hBOOL(hAPP(hAPP(c_member(X25660),X25659),c_Nat_Osemiring__1__class_ONats(X25660)))
      | ~ hBOOL(hAPP(hAPP(c_member(X25660),X25658),c_Nat_Osemiring__1__class_ONats(X25660)))
      | hBOOL(hAPP(hAPP(c_member(X25660),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25660),X25659),X25658)),c_Nat_Osemiring__1__class_ONats(X25660))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__add])]) ).

fof(i_0_8433,plain,
    ! [X22889,X22890,X22891] :
      ( ~ class_Rings_Oring__1(X22891)
      | ~ hBOOL(hAPP(hAPP(c_member(X22891),X22890),c_Int_Oring__1__class_OInts(X22891)))
      | ~ hBOOL(hAPP(hAPP(c_member(X22891),X22889),c_Int_Oring__1__class_OInts(X22891)))
      | hBOOL(hAPP(hAPP(c_member(X22891),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22891),X22890),X22889)),c_Int_Oring__1__class_OInts(X22891))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__add])]) ).

fof(i_0_8434,plain,
    ! [X25661,X25662,X25663] :
      ( ~ class_Rings_Osemiring__1(X25663)
      | ~ hBOOL(hAPP(hAPP(c_member(X25663),X25662),c_Nat_Osemiring__1__class_ONats(X25663)))
      | ~ hBOOL(hAPP(hAPP(c_member(X25663),X25661),c_Nat_Osemiring__1__class_ONats(X25663)))
      | hBOOL(hAPP(hAPP(c_member(X25663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25663),X25662),X25661)),c_Nat_Osemiring__1__class_ONats(X25663))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__mult])]) ).

fof(i_0_8435,plain,
    ! [X22892,X22893,X22894] :
      ( ~ class_Rings_Oring__1(X22894)
      | ~ hBOOL(hAPP(hAPP(c_member(X22894),X22893),c_Int_Oring__1__class_OInts(X22894)))
      | ~ hBOOL(hAPP(hAPP(c_member(X22894),X22892),c_Int_Oring__1__class_OInts(X22894)))
      | hBOOL(hAPP(hAPP(c_member(X22894),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22894),X22893),X22892)),c_Int_Oring__1__class_OInts(X22894))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__mult])]) ).

fof(i_0_8436,plain,
    ! [X22895,X22896,X22897] :
      ( ~ class_Rings_Oring__1(X22897)
      | ~ hBOOL(hAPP(hAPP(c_member(X22897),X22896),c_Int_Oring__1__class_OInts(X22897)))
      | ~ hBOOL(hAPP(hAPP(c_member(X22897),X22895),c_Int_Oring__1__class_OInts(X22897)))
      | hBOOL(hAPP(hAPP(c_member(X22897),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22897),X22896),X22895)),c_Int_Oring__1__class_OInts(X22897))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__diff])]) ).

fof(i_0_8437,plain,
    ! [X22137,X22138,X22139] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22139)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22139),X22138),c_Groups_Ozero__class_Ozero(X22139)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22139),X22137),c_Groups_Ozero__class_Ozero(X22139)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22139),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22139),X22138),X22137)),c_Groups_Ozero__class_Ozero(X22139))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).

fof(i_0_8438,plain,
    ! [X30647,X30648,X30649] : c_List_Olist_Olist__size(X30649,X30648,X30647) = 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(X30649,tc_Nat_Onat),X30648),X30647))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30649)),X30647)),
    inference(variable_rename,[status(thm)],[fact_list__size__conv__listsum]) ).

fof(i_0_8439,plain,
    ! [X18928,X18929,X18930,X18931] : c_Map_Odom(X18931,X18930,c_Map_Orestrict__map(X18931,X18930,X18929,X18928)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18931,tc_HOL_Obool)),c_Map_Odom(X18931,X18930,X18929)),X18928),
    inference(variable_rename,[status(thm)],[fact_dom__restrict]) ).

fof(i_0_8440,plain,
    ! [X17235,X17236,X17237] :
      ( ( hBOOL(hAPP(X17237,esk9_3(X17235,X17236,X17237)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17235,tc_HOL_Obool)),hAPP(c_Set_OCollect(X17235),X17237)),hAPP(c_Set_OCollect(X17235),X17236))) )
      & ( ~ hBOOL(hAPP(X17236,esk9_3(X17235,X17236,X17237)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17235,tc_HOL_Obool)),hAPP(c_Set_OCollect(X17235),X17237)),hAPP(c_Set_OCollect(X17235),X17236))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Collect__mono])])])]) ).

fof(i_0_8441,plain,
    ! [X20590,X20591] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20591),c_Orderings_Otop__class_Otop(tc_fun(X20591,tc_HOL_Obool))))
      | ~ c_Fun_Oinj__on(X20591,X20591,X20590,c_Orderings_Otop__class_Otop(tc_fun(X20591,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X20591,X20591,X20590),c_Orderings_Otop__class_Otop(tc_fun(X20591,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X20591,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj])]) ).

fof(i_0_8442,plain,
    ! [X30525,X30526,X30527,X30528] :
      ( ~ class_Rings_Osemiring__1(X30528)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30528),hAPP(hAPP(c_List_Omap(X30527,X30528),hAPP(c_COMBK(X30528,X30527),X30526)),X30525)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X30528),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X30528),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30527)),X30525))),X30526) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__triv])]) ).

fof(i_0_8443,plain,
    ! [X22750,X22751,X22752] :
      ( ~ class_Rings_Oring__1(X22752)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22752),hAPP(c_Groups_Ouminus__class_Ouminus(X22752),X22751)),X22750) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22752),hAPP(hAPP(c_Power_Opower__class_Opower(X22752),hAPP(c_Groups_Ouminus__class_Ouminus(X22752),c_Groups_Oone__class_Oone(X22752))),X22750)),hAPP(hAPP(c_Power_Opower__class_Opower(X22752),X22751),X22750)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus])]) ).

fof(i_0_8444,plain,
    ! [X19193,X19194,X19195,X19196] : hBOOL(hAPP(hAPP(c_member(X19196),hAPP(X19195,X19194)),hAPP(c_Set_Oimage(X19193,X19196,X19195),c_Orderings_Otop__class_Otop(tc_fun(X19193,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_rangeI]) ).

fof(i_0_8445,plain,
    ! [X24018,X24019,X24020,X24021] :
      ( ~ class_Int_Onumber(X24021)
      | ~ class_Rings_Osemiring(X24021)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24021),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24021),X24020),X24019)),hAPP(c_Int_Onumber__class_Onumber__of(X24021),X24018)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24021),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24021),X24020),hAPP(c_Int_Onumber__class_Onumber__of(X24021),X24018))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24021),X24019),hAPP(c_Int_Onumber__class_Onumber__of(X24021),X24018))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__distrib__number__of])]) ).

fof(i_0_8446,plain,
    ! [X24030,X24031,X24032,X24033] :
      ( ~ class_Int_Onumber(X24033)
      | ~ class_Rings_Oring(X24033)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24033),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24033),X24032),X24031)),hAPP(c_Int_Onumber__class_Onumber__of(X24033),X24030)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24033),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24033),X24032),hAPP(c_Int_Onumber__class_Onumber__of(X24033),X24030))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24033),X24031),hAPP(c_Int_Onumber__class_Onumber__of(X24033),X24030))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__diff__distrib__number__of])]) ).

fof(i_0_8447,plain,
    ! [X30000,X30001,X30002,X30003,X30004,X30005] :
      ( ( hAPP(X30002,X30001) = c_Option_Ooption_ONone(X30004)
        | hAPP(X30002,X30001) = hAPP(c_Option_Ooption_OSome(X30004),X30000)
        | hAPP(c_Map_Omap__add(X30005,X30004,X30003,X30002),X30001) != hAPP(c_Option_Ooption_OSome(X30004),X30000) )
      & ( hAPP(X30003,X30001) = hAPP(c_Option_Ooption_OSome(X30004),X30000)
        | hAPP(X30002,X30001) = hAPP(c_Option_Ooption_OSome(X30004),X30000)
        | hAPP(c_Map_Omap__add(X30005,X30004,X30003,X30002),X30001) != hAPP(c_Option_Ooption_OSome(X30004),X30000) )
      & ( hAPP(X30002,X30001) != hAPP(c_Option_Ooption_OSome(X30004),X30000)
        | hAPP(c_Map_Omap__add(X30005,X30004,X30003,X30002),X30001) = hAPP(c_Option_Ooption_OSome(X30004),X30000) )
      & ( hAPP(X30002,X30001) != c_Option_Ooption_ONone(X30004)
        | hAPP(X30003,X30001) != hAPP(c_Option_Ooption_OSome(X30004),X30000)
        | hAPP(c_Map_Omap__add(X30005,X30004,X30003,X30002),X30001) = hAPP(c_Option_Ooption_OSome(X30004),X30000) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__Some__iff])])]) ).

fof(i_0_8448,plain,
    ! [X29994,X29995,X29996,X29997,X29998,X29999] :
      ( ( hAPP(X29996,X29995) = c_Option_Ooption_ONone(X29998)
        | hAPP(X29996,X29995) = hAPP(c_Option_Ooption_OSome(X29998),X29994)
        | hAPP(c_Map_Omap__add(X29999,X29998,X29997,X29996),X29995) != hAPP(c_Option_Ooption_OSome(X29998),X29994) )
      & ( hAPP(X29997,X29995) = hAPP(c_Option_Ooption_OSome(X29998),X29994)
        | hAPP(X29996,X29995) = hAPP(c_Option_Ooption_OSome(X29998),X29994)
        | hAPP(c_Map_Omap__add(X29999,X29998,X29997,X29996),X29995) != hAPP(c_Option_Ooption_OSome(X29998),X29994) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__SomeD])])]) ).

fof(i_0_8449,plain,
    ! [X25491,X25492,X25493] :
      ( ~ class_Orderings_Olinorder(X25493)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25493),X25492))
      | X25492 = c_Orderings_Obot__class_Obot(tc_fun(X25493,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25493),X25491))
      | X25491 = c_Orderings_Obot__class_Obot(tc_fun(X25493,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25493,tc_HOL_Obool)),X25492),X25491) != c_Orderings_Obot__class_Obot(tc_fun(X25493,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMin(X25493,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25493,tc_HOL_Obool)),X25492),X25491)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25493),c_Big__Operators_Olinorder__class_OMin(X25493,X25492)),c_Big__Operators_Olinorder__class_OMin(X25493,X25491)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Ounion__disjoint])]) ).

fof(i_0_8450,plain,
    ! [X25912,X25913,X25914] :
      ( ~ class_Orderings_Olinorder(X25914)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25914),X25913))
      | X25913 = c_Orderings_Obot__class_Obot(tc_fun(X25914,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25914),X25912))
      | X25912 = c_Orderings_Obot__class_Obot(tc_fun(X25914,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25914,tc_HOL_Obool)),X25913),X25912) != c_Orderings_Obot__class_Obot(tc_fun(X25914,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMax(X25914,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25914,tc_HOL_Obool)),X25913),X25912)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25914),c_Big__Operators_Olinorder__class_OMax(X25914,X25913)),c_Big__Operators_Olinorder__class_OMax(X25914,X25912)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Ounion__disjoint])]) ).

fof(i_0_8451,plain,
    ! [X20885,X20886,X20887] :
      ( ~ class_Lattices_Olattice(X20887)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20887),X20886))
      | X20886 = c_Orderings_Obot__class_Obot(tc_fun(X20887,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20887),X20885))
      | X20885 = c_Orderings_Obot__class_Obot(tc_fun(X20887,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20887,tc_HOL_Obool)),X20886),X20885) != c_Orderings_Obot__class_Obot(tc_fun(X20887,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OSup__fin(X20887,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20887,tc_HOL_Obool)),X20886),X20885)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20887),c_Big__Operators_Olattice__class_OSup__fin(X20887,X20886)),c_Big__Operators_Olattice__class_OSup__fin(X20887,X20885)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__disjoint])]) ).

fof(i_0_8452,plain,
    ! [X20891,X20892,X20893] :
      ( ~ class_Lattices_Olattice(X20893)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20893),X20892))
      | X20892 = c_Orderings_Obot__class_Obot(tc_fun(X20893,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20893),X20891))
      | X20891 = c_Orderings_Obot__class_Obot(tc_fun(X20893,tc_HOL_Obool))
      | 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))
      | c_Big__Operators_Olattice__class_OInf__fin(X20893,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20893,tc_HOL_Obool)),X20892),X20891)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20893),c_Big__Operators_Olattice__class_OInf__fin(X20893,X20892)),c_Big__Operators_Olattice__class_OInf__fin(X20893,X20891)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__disjoint])]) ).

fof(i_0_8453,plain,
    ! [X21583,X21584,X21585,X21586] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X21586)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21586),X21585),X21584))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21586),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21586),X21585),X21583)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21586),X21584),X21583))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).

fof(i_0_8454,plain,
    ! [X21579,X21580,X21581,X21582] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X21582)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21582),X21581),X21580))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21582),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21582),X21579),X21581)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21582),X21579),X21580))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).

fof(i_0_8455,plain,
    ! [X21545,X21546,X21547,X21548] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X21548)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21548),X21547),X21546))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21548),X21547),X21545)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21548),X21546),X21545))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).

fof(i_0_8456,plain,
    ! [X21549,X21550,X21551,X21552] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X21552)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21552),X21551),X21550))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21552),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21552),X21549),X21551)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21552),X21549),X21550))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).

fof(i_0_8457,plain,
    ! [X21297,X21298,X21299] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X21299)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21299),X21298))
      | X21298 = c_Orderings_Obot__class_Obot(tc_fun(X21299,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21299),X21297))
      | X21297 = c_Orderings_Obot__class_Obot(tc_fun(X21299,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ofold1(X21299,c_Groups_Otimes__class_Otimes(X21299)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21299,tc_HOL_Obool)),X21298),X21297)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21299),hAPP(c_Finite__Set_Ofold1(X21299,c_Groups_Otimes__class_Otimes(X21299)),X21298)),hAPP(c_Finite__Set_Ofold1(X21299,c_Groups_Otimes__class_Otimes(X21299)),X21297)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__Un2])]) ).

fof(i_0_8458,plain,
    ! [X32934,X32935,X32936] : hAPP(c_List_Orev(X32936),hAPP(hAPP(c_List_Odrop(X32936),X32935),X32934)) = hAPP(hAPP(c_List_Otake(X32936),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32936)),X32934)),X32935)),hAPP(c_List_Orev(X32936),X32934)),
    inference(variable_rename,[status(thm)],[fact_rev__drop]) ).

fof(i_0_8459,plain,
    ! [X32937,X32938,X32939] : hAPP(c_List_Orev(X32939),hAPP(hAPP(c_List_Otake(X32939),X32938),X32937)) = hAPP(hAPP(c_List_Odrop(X32939),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32939)),X32937)),X32938)),hAPP(c_List_Orev(X32939),X32937)),
    inference(variable_rename,[status(thm)],[fact_rev__take]) ).

fof(i_0_8460,plain,
    ! [X26274,X26275,X26276] :
      ( ~ class_Orderings_Olinorder(X26276)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26276),X26275),X26274))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26276,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X26276),X26275),c_Orderings_Obot__class_Obot(tc_fun(X26276,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X26276,X26275,X26274)) = c_SetInterval_Oord__class_OatLeastAtMost(X26276,X26275,X26274) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I5_J])]) ).

fof(i_0_8461,plain,
    ! [X20516,X20517] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20517,tc_HOL_Obool)),X20516),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20517,tc_HOL_Obool)),X20516)))
        | X20516 = c_Orderings_Obot__class_Obot(tc_fun(X20517,tc_HOL_Obool)) )
      & ( X20516 != c_Orderings_Obot__class_Obot(tc_fun(X20517,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20517,tc_HOL_Obool)),X20516),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20517,tc_HOL_Obool)),X20516))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__Compl__self__eq])]) ).

fof(i_0_8462,plain,
    ! [X19940,X19941,X19942,X19943,X19944,X19945,X19946] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X19946,tc_Option_Ooption(X19945)),X19944),X19943),hAPP(c_Option_Ooption_OSome(X19945),X19942)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X19946,tc_Option_Ooption(X19945)),X19941),X19943),hAPP(c_Option_Ooption_OSome(X19945),X19940))
      | X19942 = X19940 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__upd__eqD1])]) ).

fof(i_0_8463,plain,
    ! [X24687,X24688,X24689] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24689),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24689)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24688)),X24687)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24689),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24689)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24688)),X24687)) = 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),X24689),X24688))),X24687) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5777])]) ).

fof(i_0_8464,plain,
    ! [X27190,X27191] : c_Divides_Opdivmod(X27191,X27190) = 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),X27191)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X27190))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X27191),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X27190))),
    inference(variable_rename,[status(thm)],[fact_pdivmod__def]) ).

fof(i_0_8465,plain,
    ! [X29633,X29634,X29635] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X29635,tc_HOL_Obool)),X29634),X29633))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29635,tc_HOL_Obool)),X29634),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29635,tc_HOL_Obool),X29633))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__upper])]) ).

fof(i_0_8466,plain,
    ! [X29028,X29029,X29030,X29031] : hAPP(c_Finite__Set_Ofold__image(X29031,X29030,X29029),X29028) = c_Finite__Set_Ofold(X29030,X29031,hAPP(hAPP(c_COMBB(X29031,tc_fun(X29031,X29031),X29030),X29029),X29028)),
    inference(variable_rename,[status(thm)],[fact_fold__image__def]) ).

fof(i_0_8467,plain,
    ! [X25868,X25869] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25869)),X25868) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X25869),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),X25869)),X25868),
    inference(variable_rename,[status(thm)],[fact_max__Suc1]) ).

fof(i_0_8468,plain,
    ! [X29656,X29657] : hAPP(c_Relation_OField(X29657),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X29657,X29657),tc_HOL_Obool),X29656)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X29657,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(X29657,X29657),tc_HOL_Obool),tc_fun(X29657,tc_HOL_Obool),c_Relation_OField(X29657)),X29656)),
    inference(variable_rename,[status(thm)],[fact_Field__Union]) ).

fof(i_0_8469,plain,
    ! [X18242,X18243,X18244] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18244,tc_HOL_Obool)),X18243),X18242))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18244,tc_HOL_Obool)),X18243),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18244,tc_HOL_Obool)),X18242),X18243)) = X18242 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__partition])]) ).

fof(i_0_8470,plain,
    ! [X30078,X30079,X30080] :
      ( ~ c_Fun_Oinj__on(X30080,X30079,X30078,c_Orderings_Otop__class_Otop(tc_fun(X30080,tc_HOL_Obool)))
      | c_Fun_Oinj__on(tc_List_Olist(X30080),tc_List_Olist(X30079),hAPP(c_List_Omap(X30080,X30079),X30078),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X30080),tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__mapI])]) ).

fof(i_0_8471,plain,
    ! [X20531,X20532,X20533] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20533,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20533,tc_HOL_Obool)),X20532),X20531)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20533,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20533,tc_HOL_Obool)),X20532)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20533,tc_HOL_Obool)),X20531)),
    inference(variable_rename,[status(thm)],[fact_Compl__Int]) ).

fof(i_0_8472,plain,
    ! [X20528,X20529,X20530] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20530,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20530,tc_HOL_Obool)),X20529),X20528)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20530,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20530,tc_HOL_Obool)),X20529)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20530,tc_HOL_Obool)),X20528)),
    inference(variable_rename,[status(thm)],[fact_Compl__Un]) ).

fof(i_0_8473,plain,
    ! [X33915,X33916,X33917,X33918,X33919] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X33919,X33918,X33917),X33916),X33915))
        | hBOOL(hAPP(hAPP(X33917,X33915),X33916)) )
      & ( ~ hBOOL(hAPP(hAPP(X33917,X33915),X33916))
        | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X33919,X33918,X33917),X33916),X33915)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__iff])]) ).

fof(i_0_8474,plain,
    ! [X33910,X33911,X33912,X33913,X33914] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X33914,X33913,X33912),X33911),X33910))
        | hBOOL(hAPP(hAPP(X33912,X33910),X33911)) )
      & ( ~ hBOOL(hAPP(hAPP(X33912,X33910),X33911))
        | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X33914,X33913,X33912),X33911),X33910)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep_Oequations])]) ).

fof(i_0_8475,plain,
    ! [X33900,X33901,X33902,X33903,X33904] :
      ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X33904,X33903,X33902),X33901),X33900))
      | hBOOL(hAPP(hAPP(X33902,X33900),X33901)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversepD])]) ).

fof(i_0_8476,plain,
    ! [X19388,X19389,X19390,X19391,X19392] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(X19392,X19391,X19390),X19389),X19388))
        | hBOOL(hAPP(X19389,hAPP(X19390,X19388))) )
      & ( ~ hBOOL(hAPP(X19389,hAPP(X19390,X19388)))
        | hBOOL(hAPP(hAPP(c_Set_Ovimage(X19392,X19391,X19390),X19389),X19388)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__code])]) ).

fof(i_0_8477,plain,
    ! [X29651,X29652,X29653,X29655] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29653),esk364_3(X29651,X29652,X29653)),X29652))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29653),c_Complete__Lattice_OInf__class_OInf(X29653,X29652)),X29651))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X29653)
        | ~ class_Orderings_Olinorder(X29653) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29653),esk364_3(X29651,X29652,X29653)),X29651))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29653),c_Complete__Lattice_OInf__class_OInf(X29653,X29652)),X29651))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X29653)
        | ~ class_Orderings_Olinorder(X29653) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X29653),X29655),X29652))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29653),X29655),X29651))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29653),c_Complete__Lattice_OInf__class_OInf(X29653,X29652)),X29651))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X29653)
        | ~ class_Orderings_Olinorder(X29653) ) ),
    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_8478,plain,
    ! [X24040,X24041,X24042,X24043] :
      ( ~ class_Int_Onumber__ring(X24043)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24043),hAPP(c_Int_Onumber__class_Onumber__of(X24043),X24042)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24043),hAPP(c_Int_Onumber__class_Onumber__of(X24043),X24041)),X24040)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24043),hAPP(c_Int_Onumber__class_Onumber__of(X24043),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24042),X24041))),X24040) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__left])]) ).

fof(i_0_8479,plain,
    ! [X24069,X24070,X24071,X24072] :
      ( ~ class_Int_Onumber__ring(X24072)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24072),hAPP(c_Int_Onumber__class_Onumber__of(X24072),X24071)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24072),hAPP(c_Int_Onumber__class_Onumber__of(X24072),X24070)),X24069)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24072),hAPP(c_Int_Onumber__class_Onumber__of(X24072),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24071),X24070))),X24069) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__diff1])]) ).

fof(i_0_8480,plain,
    ! [X24050,X24051,X24052,X24053] :
      ( ~ class_Int_Onumber__ring(X24053)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24053),hAPP(c_Int_Onumber__class_Onumber__of(X24053),X24052)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24053),hAPP(c_Int_Onumber__class_Onumber__of(X24053),X24051)),X24050)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24053),hAPP(c_Int_Onumber__class_Onumber__of(X24053),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24052),X24051))),X24050) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__number__of__left])]) ).

fof(i_0_8481,plain,
    ! [X30254,X30255,X30256] : hAPP(c_Option_Omap(X30256,X30255),X30254) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(X30255),X30256,c_Option_Ooption_ONone(X30255),hAPP(hAPP(c_COMBB(X30255,tc_Option_Ooption(X30255),X30256),c_Option_Ooption_OSome(X30255)),X30254)),
    inference(variable_rename,[status(thm)],[fact_Option_Omap__def]) ).

fof(i_0_8482,plain,
    ! [X26076,X26077,X26078] :
      ( ~ class_Orderings_Olinorder(X26078)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26078),X26077),X26076))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26078,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X26078),X26077),c_Orderings_Obot__class_Obot(tc_fun(X26078,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X26078,X26077,X26076)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26078,X26077),X26076) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I3_J])]) ).

fof(i_0_8483,plain,
    ! [X30969,X30970,X30971,X30972,X30973] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30973),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30972)),X30971)))
      | hAPP(hAPP(c_List_Onth(X30970),hAPP(hAPP(c_List_Omap(X30972,X30970),X30969),X30971)),X30973) = hAPP(X30969,hAPP(hAPP(c_List_Onth(X30972),X30971),X30973)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__map])]) ).

fof(i_0_8484,plain,
    ! [X27194,X27195] :
      ( ( X27194 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nitpick_Onat__gcd(X27195,X27194) = X27195
        | ~ 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),X27195),X27194))) )
      & ( X27194 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nitpick_Onat__gcd(X27195,X27194) = c_Nitpick_Onat__gcd(X27194,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X27195,X27194))
        | ~ 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),X27195),X27194))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__gcd_Opsimps])])]) ).

fof(i_0_8485,plain,
    ! [X29574,X29575,X29576,X29577] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X29577,tc_HOL_Obool)),X29576),X29575))
      | ~ hBOOL(hAPP(hAPP(c_member(X29577),X29574),X29576))
      | hBOOL(hAPP(hAPP(c_member(X29577),X29574),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29577,tc_HOL_Obool),X29575))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnionI])]) ).

fof(i_0_8486,plain,
    ! [X22243,X22244,X22245] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22245)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22245),c_Groups_Ozero__class_Ozero(X22245)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22245),X22244),X22243)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22245),c_Groups_Ozero__class_Ozero(X22245)),X22243))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22245),c_Groups_Ozero__class_Ozero(X22245)),X22244)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2])]) ).

fof(i_0_8487,plain,
    ! [X22246,X22247,X22248] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22248)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22248),c_Groups_Ozero__class_Ozero(X22248)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22248),X22247),X22246)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22248),c_Groups_Ozero__class_Ozero(X22248)),X22247))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22248),c_Groups_Ozero__class_Ozero(X22248)),X22246)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos])]) ).

fof(i_0_8488,plain,
    ! [X33541,X33542,X33543,X33546,X33547,X33548,X33549,X33550] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X33543),X33542),hAPP(c_List_Oset(X33543),X33541)))
        | X33541 = hAPP(hAPP(c_List_Oappend(X33543),esk499_3(X33541,X33542,X33543)),hAPP(hAPP(c_List_Olist_OCons(X33543),X33542),esk500_3(X33541,X33542,X33543))) )
      & ( X33546 != hAPP(hAPP(c_List_Oappend(X33548),X33549),hAPP(hAPP(c_List_Olist_OCons(X33548),X33547),X33550))
        | hBOOL(hAPP(hAPP(c_member(X33548),X33547),hAPP(c_List_Oset(X33548),X33546))) ) ),
    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_8489,plain,
    ! [X21942,X21943,X21944] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21944),X21943))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21944),X21942))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X21944,tc_HOL_Obool)),X21943),X21942) != c_Orderings_Obot__class_Obot(tc_fun(X21944,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ocard(X21944),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21944,tc_HOL_Obool)),X21943),X21942)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21944),X21943)),hAPP(c_Finite__Set_Ocard(X21944),X21942)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Un__disjoint])]) ).

fof(i_0_8490,plain,
    ! [X25443,X25444] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25444)),X25443) = 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),X25444)),X25443),
    inference(variable_rename,[status(thm)],[fact_min__Suc1]) ).

fof(i_0_8491,plain,
    ! [X32596,X32597,X32598] :
      ( ~ class_Orderings_Olinorder(X32598)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32598),X32597))
      | c_List_Olinorder__class_Osorted__list__of__set(X32598,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X32598,tc_HOL_Obool)),X32597),hAPP(hAPP(c_Set_Oinsert(X32598),X32596),c_Orderings_Obot__class_Obot(tc_fun(X32598,tc_HOL_Obool))))) = c_List_Oremove1(X32598,X32596,c_List_Olinorder__class_Osorted__list__of__set(X32598,X32597)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__remove])]) ).

fof(i_0_8492,plain,
    ! [X20460,X20461] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X20461,X20460)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X20461,X20460),tc_HOL_Obool))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20460),c_Orderings_Otop__class_Otop(tc_fun(X20460,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2])]) ).

fof(i_0_8493,plain,
    ! [X32698,X32699,X32700,X32701,X32702] :
      ( ~ class_Orderings_Olinorder(X32702)
      | hAPP(c_List_Ofilter(X32701,X32700),c_List_Olinorder__class_Osort__key(X32701,X32702,X32699,X32698)) = c_List_Olinorder__class_Osort__key(X32701,X32702,X32699,hAPP(c_List_Ofilter(X32701,X32700),X32698)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__sort])]) ).

fof(i_0_8494,plain,
    ! [X18152,X18153,X18154] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X18154,tc_HOL_Obool)),X18153),hAPP(c_Set_OPow(X18154),X18152)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18154,tc_HOL_Obool)),X18153),X18152)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_PowD])]) ).

fof(i_0_8495,plain,
    ! [X18149,X18150,X18151] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X18151,tc_HOL_Obool)),X18150),hAPP(c_Set_OPow(X18151),X18149)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18151,tc_HOL_Obool)),X18150),X18149)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18151,tc_HOL_Obool)),X18150),X18149))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X18151,tc_HOL_Obool)),X18150),hAPP(c_Set_OPow(X18151),X18149))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pow__iff])]) ).

fof(i_0_8496,plain,
    ! [X27144,X27145] :
      ( ( ~ 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),X27145)),X27144)))
        | X27145 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X27144 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X27145 = 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),X27145)),X27144))) )
      & ( X27144 != 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),X27145)),X27144))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__zpower__abs__iff])])]) ).

fof(i_0_8497,plain,
    ! [X26226,X26227,X26228,X26229] :
      ( ~ class_Orderings_Olinorder(X26229)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26229),X26228),X26227))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26229),X26227),X26226))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26229,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26229,X26228,X26227)),c_SetInterval_Oord__class_OgreaterThanAtMost(X26229,X26227,X26226)) = c_SetInterval_Oord__class_OatLeastAtMost(X26229,X26228,X26226) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I22_J])]) ).

fof(i_0_8498,plain,
    ! [X25640,X25641,X25642,X25643] :
      ( ~ class_Orderings_Olinorder(X25643)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25643),X25642),X25641))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25643),X25641),X25640))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25643,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25643,X25642,X25641)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25643,X25641,X25640)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X25643,X25642,X25640) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I20_J])]) ).

fof(i_0_8499,plain,
    ! [X25686,X25687,X25688,X25689] :
      ( ~ class_Orderings_Olinorder(X25689)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25689),X25688),X25687))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25689),X25687),X25686))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25689,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25689,X25688,X25687)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25689,X25687,X25686)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X25689,X25688,X25686) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I16_J])]) ).

fof(i_0_8500,plain,
    ! [X26072,X26073,X26074,X26075] :
      ( ~ class_Orderings_Olinorder(X26075)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26075),X26074),X26073))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26075),X26073),X26072))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26075,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X26075,X26074,X26073)),c_SetInterval_Oord__class_OatLeastAtMost(X26075,X26073,X26072)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X26075,X26074,X26072) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I19_J])]) ).

fof(i_0_8501,plain,
    ! [X17520,X17521,X17522] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17522,tc_HOL_Obool)),X17521),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17522,tc_HOL_Obool)),X17521),X17520))),
    inference(variable_rename,[status(thm)],[fact_Un__upper1]) ).

fof(i_0_8502,plain,
    ! [X17517,X17518,X17519] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17519,tc_HOL_Obool)),X17518),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17519,tc_HOL_Obool)),X17517),X17518))),
    inference(variable_rename,[status(thm)],[fact_Un__upper2]) ).

fof(i_0_8503,plain,
    ! [X28535,X28536,X28537] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28537,X28537)),X28536),X28535))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28537,X28537)),X28536),c_Transitive__Closure_Ortrancl(X28537,X28535))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__rtrancl])]) ).

fof(i_0_8504,plain,
    ! [X22618,X22619,X22620,X22621] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22621),X22620))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22619),X22618))
      | hAPP(c_Finite__Set_Ocard(tc_sum(X22621,X22619)),c_Sum__Type_OPlus(X22621,X22619,X22620,X22618)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X22621),X22620)),hAPP(c_Finite__Set_Ocard(X22619),X22618)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Plus])]) ).

fof(i_0_8505,plain,
    ! [X22569,X22570,X22571,X22572] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22572),X22571))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22570),X22569))
        | hAPP(c_Finite__Set_Ocard(tc_sum(X22572,X22570)),c_Sum__Type_OPlus(X22572,X22570,X22571,X22569)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X22572),X22571)),hAPP(c_Finite__Set_Ocard(X22570),X22569)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X22572),X22571))
        | hAPP(c_Finite__Set_Ocard(tc_sum(X22572,X22570)),c_Sum__Type_OPlus(X22572,X22570,X22571,X22569)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X22570),X22569))
        | hAPP(c_Finite__Set_Ocard(tc_sum(X22572,X22570)),c_Sum__Type_OPlus(X22572,X22570,X22571,X22569)) = 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_8506,plain,
    ! [X30337,X30338,X30339,X30340] :
      ( hAPP(c_Map_Omap__of(X30340,X30339),X30338) != hAPP(c_Map_Omap__of(X30340,X30339),X30337)
      | hAPP(c_Set_Oimage(tc_prod(X30340,X30339),X30340,c_Product__Type_Ofst(X30340,X30339)),hAPP(c_List_Oset(tc_prod(X30340,X30339)),X30338)) = hAPP(c_Set_Oimage(tc_prod(X30340,X30339),X30340,c_Product__Type_Ofst(X30340,X30339)),hAPP(c_List_Oset(tc_prod(X30340,X30339)),X30337)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__eq__dom])]) ).

fof(i_0_8507,plain,
    ! [X25796,X25797,X25798,X25799] :
      ( ~ class_Orderings_Olinorder(X25799)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25799),X25798),X25797))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25799),X25796),X25797))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25799),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25799),X25798),X25796)),X25797)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI])]) ).

fof(i_0_8508,plain,
    ! [X25792,X25793,X25794,X25795] :
      ( ~ class_Orderings_Olinorder(X25795)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25795),X25794),X25793))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25795),X25792),X25793))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25795),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25795),X25794),X25792)),X25793)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__least])]) ).

fof(i_0_8509,plain,
    ! [X17652,X17653,X17654,X17655] :
      ( ~ class_Lattices_Osemilattice__sup(X17655)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17655),X17654),X17653))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17655),X17652),X17653))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17655),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17655),X17654),X17652)),X17653)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI])]) ).

fof(i_0_8510,plain,
    ! [X17648,X17649,X17650,X17651] :
      ( ~ class_Lattices_Osemilattice__sup(X17651)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17651),X17650),X17649))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17651),X17648),X17649))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17651),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17651),X17650),X17648)),X17649)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__least])]) ).

fof(i_0_8511,plain,
    ! [X17909,X17910,X17911,X17912] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17912,tc_HOL_Obool)),X17911),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17912,tc_HOL_Obool)),X17910),X17909)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17912,tc_HOL_Obool)),X17910),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17912,tc_HOL_Obool)),X17911),X17909)),
    inference(variable_rename,[status(thm)],[fact_Int__left__commute]) ).

fof(i_0_8512,plain,
    ! [X17391,X17392,X17393,X17394] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17394,tc_HOL_Obool)),X17393),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17394,tc_HOL_Obool)),X17392),X17391)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17394,tc_HOL_Obool)),X17392),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17394,tc_HOL_Obool)),X17393),X17391)),
    inference(variable_rename,[status(thm)],[fact_Un__left__commute]) ).

fof(i_0_8513,plain,
    ! [X17902,X17903,X17904] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17904,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17904,tc_HOL_Obool)),X17903),X17902)),X17902) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17904,tc_HOL_Obool)),X17903),X17902),
    inference(variable_rename,[status(thm)],[fact_Diff__idemp]) ).

fof(i_0_8514,plain,
    ! [X18096,X18097,X18098] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18098,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18098,tc_HOL_Obool)),X18097),X18096)),X18096) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18098,tc_HOL_Obool)),X18097),X18096),
    inference(variable_rename,[status(thm)],[fact_Un__Diff__cancel2]) ).

cnf(i_0_8515,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_5778]) ).

fof(i_0_8516,plain,
    ! [X17337,X17338,X17339,X17340,X17341] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17341),X17340),X17339))
      | hBOOL(hAPP(hAPP(c_member(X17338),hAPP(X17337,X17340)),hAPP(c_Set_Oimage(X17341,X17338,X17337),X17339))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_imageI])]) ).

fof(i_0_8517,plain,
    ! [X17007,X17008,X17009,X17010] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X17010,X17009,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17010)),X17008),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17010),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(X17010,X17009,X17007)
      | c_Hoare__Mirabelle_Ohoare__derivs(X17010,X17009,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17010)),X17008),X17007)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hoare__derivs_Oinsert])]) ).

fof(i_0_8518,plain,
    ! [X29166,X29167,X29168,X29169,X29170] :
      ( ~ c_Finite__Set_Ofun__left__comm(X29170,X29169,X29168)
      | c_Finite__Set_Ofun__left__comm(X29167,X29169,hAPP(hAPP(c_COMBB(X29170,tc_fun(X29169,X29169),X29167),X29168),X29166)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm__apply])]) ).

fof(i_0_8519,plain,
    ! [X18917,X18918,X18919,X18920,X18921] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X18921,X18920,X18919)
      | c_Finite__Set_Ofun__left__comm__idem(X18918,X18920,hAPP(hAPP(c_COMBB(X18921,tc_fun(X18920,X18920),X18918),X18919),X18917)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__comm__idem__apply])]) ).

fof(i_0_8520,plain,
    ! [X18224,X18225,X18226,X18227] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X18227),X18226),X18225))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18227,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X18227),X18226),X18224)),X18225) = hAPP(hAPP(c_Set_Oinsert(X18227),X18226),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18227,tc_HOL_Obool)),X18224),X18225)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if1])]) ).

fof(i_0_8521,plain,
    ! [X18208,X18209,X18210,X18211] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X18211),X18210),X18209))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18211,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X18211),X18210),X18208)),X18209) = hAPP(hAPP(c_Set_Oinsert(X18211),X18210),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18211,tc_HOL_Obool)),X18208),X18209)) )
      & ( hBOOL(hAPP(hAPP(c_member(X18211),X18210),X18209))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18211,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X18211),X18210),X18208)),X18209) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18211,tc_HOL_Obool)),X18208),X18209) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5779])]) ).

fof(i_0_8522,plain,
    ! [X19225,X19226,X19227,X19228,X19229] :
      ( ( hAPP(c_Set_Oimage(X19229,X19228,X19227),X19226) != hAPP(c_Set_Oimage(X19229,X19228,X19227),X19225)
        | X19226 = X19225
        | ~ c_Fun_Oinj__on(X19229,X19228,X19227,c_Orderings_Otop__class_Otop(tc_fun(X19229,tc_HOL_Obool))) )
      & ( X19226 != X19225
        | hAPP(c_Set_Oimage(X19229,X19228,X19227),X19226) = hAPP(c_Set_Oimage(X19229,X19228,X19227),X19225)
        | ~ c_Fun_Oinj__on(X19229,X19228,X19227,c_Orderings_Otop__class_Otop(tc_fun(X19229,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_8523,plain,
    ! [X19327,X19328,X19329,X19330,X19331,X19332,X19333] :
      ( hAPP(c_Fun_Ocomp(X19333,X19332,X19331,X19330),X19329) != X19328
      | hAPP(X19330,hAPP(X19329,X19327)) = hAPP(X19328,X19327) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__dest__lhs])]) ).

fof(i_0_8524,plain,
    ! [X25264] : 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,X25264)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[fact_negative__zless__0]) ).

fof(i_0_8525,plain,
    ! [X31852,X31853,X31854] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31854),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31853)),X31852)))
      | hAPP(hAPP(c_List_Olist_OCons(X31853),hAPP(hAPP(c_List_Onth(X31853),X31852),X31854)),hAPP(hAPP(c_List_Odrop(X31853),hAPP(c_Nat_OSuc,X31854)),X31852)) = hAPP(hAPP(c_List_Odrop(X31853),X31854),X31852) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__drop_H])]) ).

fof(i_0_8526,plain,
    ! [X19505,X19506,X19507,X19508] : hAPP(c_Set_Oimage(X19508,X19507,X19506),hAPP(c_Set_Ovimage(X19508,X19507,X19506),X19505)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19507,tc_HOL_Obool)),X19505),hAPP(c_Set_Oimage(X19508,X19507,X19506),c_Orderings_Otop__class_Otop(tc_fun(X19508,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_image__vimage__eq]) ).

fof(i_0_8527,plain,
    ! [X22882,X22883] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22883),c_Groups_Oone__class_Oone(tc_Int_Oint))),X22882))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22883),X22882)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22883),X22882))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22883),c_Groups_Oone__class_Oone(tc_Int_Oint))),X22882)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add1__zle__eq])]) ).

fof(i_0_8528,plain,
    ! [X26136,X26137,X26138,X26139] :
      ( ~ class_Orderings_Olinorder(X26139)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26139),X26138),X26137))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26139),X26137),X26136))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26139,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26139,X26138,X26137)),c_SetInterval_Oord__class_OgreaterThanLessThan(X26139,X26137,X26136)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26139,X26138),X26136) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I18_J])]) ).

fof(i_0_8529,plain,
    ! [X25107] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X25107))
        | 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)),X25107))) )
      & ( ~ 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)),X25107)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X25107)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I1_J])]) ).

fof(i_0_8530,plain,
    ! [X21252,X21253,X21254] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21254),X21253))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X21254,tc_HOL_Obool)),X21252),X21253))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21254),X21252)),hAPP(c_Finite__Set_Ocard(X21254),X21253))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__card__mono])]) ).

fof(i_0_8531,plain,
    ! [X21230,X21231,X21232] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21232),X21231))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21232,tc_HOL_Obool)),X21230),X21231))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21232),X21230)),hAPP(c_Finite__Set_Ocard(X21232),X21231))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__mono])]) ).

fof(i_0_8532,plain,
    ! [X19284,X19285,X19286,X19287,X19288] :
      ( hAPP(X19288,X19287) != c_Option_Ooption_ONone(X19286)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19285,tc_HOL_Obool)),c_Map_Odom(X19285,X19286,X19288)),hAPP(hAPP(c_Set_Oinsert(X19285),X19287),X19284)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19285,tc_HOL_Obool)),c_Map_Odom(X19285,X19286,X19288)),X19284) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dom__minus])]) ).

fof(i_0_8533,plain,
    ! [X17346,X17347,X17348,X17349] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17349),X17348),X17347))
      | hBOOL(hAPP(hAPP(c_member(X17349),X17348),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17349,tc_HOL_Obool)),X17347),X17346))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnI1])]) ).

fof(i_0_8534,plain,
    ! [X17293,X17294,X17295,X17296] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17296),X17295),X17294))
        | hBOOL(hAPP(hAPP(c_member(X17296),X17295),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17296,tc_HOL_Obool)),X17293),X17294))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17296),X17295),X17293))
        | hBOOL(hAPP(hAPP(c_member(X17296),X17295),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17296,tc_HOL_Obool)),X17293),X17294))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5780])])]) ).

fof(i_0_8535,plain,
    ! [X17342,X17343,X17344,X17345] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17345),X17344),X17343))
      | hBOOL(hAPP(hAPP(c_member(X17345),X17344),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17345,tc_HOL_Obool)),X17342),X17343))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnI2])]) ).

fof(i_0_8536,plain,
    ! [X20588,X20589] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20589),c_Orderings_Otop__class_Otop(tc_fun(X20589,tc_HOL_Obool))))
      | hAPP(c_Set_Oimage(X20589,X20589,X20588),c_Orderings_Otop__class_Otop(tc_fun(X20589,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X20589,tc_HOL_Obool))
      | c_Fun_Oinj__on(X20589,X20589,X20588,c_Orderings_Otop__class_Otop(tc_fun(X20589,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__surj__inj])]) ).

fof(i_0_8537,plain,
    ! [X27090,X27091,X27092] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27092),X27091),X27090))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27092),hAPP(c_Groups_Oabs__class_Oabs(X27092),X27091)),X27090))
        | ~ class_Rings_Olinordered__idom(X27092) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27092),hAPP(c_Groups_Ouminus__class_Ouminus(X27092),X27091)),X27090))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27092),hAPP(c_Groups_Oabs__class_Oabs(X27092),X27091)),X27090))
        | ~ class_Rings_Olinordered__idom(X27092) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27092),X27091),X27090))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27092),hAPP(c_Groups_Ouminus__class_Ouminus(X27092),X27091)),X27090))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27092),hAPP(c_Groups_Oabs__class_Oabs(X27092),X27091)),X27090))
        | ~ class_Rings_Olinordered__idom(X27092) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__less__iff])])]) ).

fof(i_0_8538,plain,
    ! [X27084,X27085,X27086] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27086)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27086),X27085),X27084))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27086),hAPP(c_Groups_Ouminus__class_Ouminus(X27086),X27085)),X27084))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27086),hAPP(c_Groups_Oabs__class_Oabs(X27086),X27085)),X27084)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__leI])]) ).

fof(i_0_8539,plain,
    ! [X27081,X27082,X27083] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27083),X27082),X27081))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27083),hAPP(c_Groups_Oabs__class_Oabs(X27083),X27082)),X27081))
        | ~ class_Groups_Oordered__ab__group__add__abs(X27083) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27083),hAPP(c_Groups_Ouminus__class_Ouminus(X27083),X27082)),X27081))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27083),hAPP(c_Groups_Oabs__class_Oabs(X27083),X27082)),X27081))
        | ~ class_Groups_Oordered__ab__group__add__abs(X27083) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27083),X27082),X27081))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27083),hAPP(c_Groups_Ouminus__class_Ouminus(X27083),X27082)),X27081))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27083),hAPP(c_Groups_Oabs__class_Oabs(X27083),X27082)),X27081))
        | ~ class_Groups_Oordered__ab__group__add__abs(X27083) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__iff])])]) ).

fof(i_0_8540,plain,
    ! [X29989,X29990,X29991,X29992,X29993] :
      ( hBOOL(hAPP(hAPP(c_member(X29993),X29992),c_Map_Odom(X29993,X29991,X29990)))
      | hAPP(c_Map_Omap__add(X29993,X29991,X29990,X29989),X29992) = hAPP(X29989,X29992) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5781])]) ).

fof(i_0_8541,plain,
    ! [X29984,X29985,X29986,X29987,X29988] :
      ( hBOOL(hAPP(hAPP(c_member(X29988),X29987),c_Map_Odom(X29988,X29986,X29985)))
      | hAPP(c_Map_Omap__add(X29988,X29986,X29984,X29985),X29987) = hAPP(X29984,X29987) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5782])]) ).

fof(i_0_8542,plain,
    ! [X31048,X31049,X31050] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31050)),X31049),c_Wellfounded_Oacc(tc_List_Olist(X31050),c_List_Olistrel1(X31050,X31048))))
      | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31050)),X31049),c_List_Olists(X31050,c_Wellfounded_Oacc(X31050,X31048)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accI])]) ).

fof(i_0_8543,plain,
    ! [X22270,X22271] :
      ( ~ class_Rings_Olinordered__ring(X22271)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22271),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22271),X22270),X22270)),c_Groups_Ozero__class_Ozero(X22271))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5783])]) ).

fof(i_0_8544,plain,
    ! [X19509,X19510,X19511,X19512] :
      ( ~ c_Fun_Oinj__on(X19512,X19511,X19510,c_Orderings_Otop__class_Otop(tc_fun(X19512,tc_HOL_Obool)))
      | hAPP(c_Set_Ovimage(X19512,X19511,X19510),hAPP(c_Set_Oimage(X19512,X19511,X19510),X19509)) = X19509 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__vimage__image__eq])]) ).

fof(i_0_8545,plain,
    ! [X26265,X26266,X26267,X26268] :
      ( ~ class_Orderings_Olinorder(X26268)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26268),X26267),X26266))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26268),X26266),X26265))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26268,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X26268,X26267,X26266)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26268,X26266),X26265)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X26268,X26267,X26265) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I15_J])]) ).

fof(i_0_8546,plain,
    ! [X23161,X23162,X23163,X23164] :
      ( ~ class_Divides_Osemiring__div(X23164)
      | X23163 = c_Groups_Ozero__class_Ozero(X23164)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23164),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23164),X23162),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23164),X23163),X23161))),X23163) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23164),X23161),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23164),X23162),X23163)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2])]) ).

fof(i_0_8547,plain,
    ! [X23165,X23166,X23167,X23168] :
      ( ~ class_Divides_Osemiring__div(X23168)
      | X23167 = c_Groups_Ozero__class_Ozero(X23168)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23168),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23168),X23166),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23168),X23165),X23167))),X23167) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23168),X23165),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23168),X23166),X23167)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1])]) ).

fof(i_0_8548,plain,
    ! [X24433,X24434,X24435,X24436] :
      ( ~ class_Fields_Ofield__inverse__zero(X24436)
      | X24435 = c_Groups_Ozero__class_Ozero(X24436)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24436),X24434),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24436),X24433),X24435)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24436),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24436),X24433),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24436),X24434),X24435))),X24435) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__num__frac])]) ).

fof(i_0_8549,plain,
    ! [X27935,X27936,X27937,X27938] :
      ( ~ class_Groups_Ocomm__monoid__add(X27938)
      | ~ c_Fun_Oinj__on(X27937,X27938,X27936,X27935)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27937,X27938),X27936),X27935) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27938,X27938),c_Fun_Oid(X27938)),hAPP(c_Set_Oimage(X27937,X27938,X27936),X27935)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__reindex__id])]) ).

fof(i_0_8550,plain,
    ! [X27939,X27940,X27941,X27942] :
      ( ~ class_Groups_Ocomm__monoid__mult(X27942)
      | ~ c_Fun_Oinj__on(X27941,X27942,X27940,X27939)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27941,X27942),X27940),X27939) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27942,X27942),c_Fun_Oid(X27942)),hAPP(c_Set_Oimage(X27941,X27942,X27940),X27939)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__reindex__id])]) ).

fof(i_0_8551,plain,
    ! [X27395,X27396] :
      ( ( ~ c_Wellfounded_Owf(X27396,X27395)
        | c_Wellfounded_Owf(X27396,hAPP(hAPP(c_Relation_Orel__comp(X27396,X27396,X27396),X27395),X27395)) )
      & ( ~ c_Wellfounded_Owf(X27396,hAPP(hAPP(c_Relation_Orel__comp(X27396,X27396,X27396),X27395),X27395))
        | c_Wellfounded_Owf(X27396,X27395) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__comp__self])]) ).

fof(i_0_8552,plain,
    ! [X20205,X20206,X20207] :
      ( X20207 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X20206,X20206),tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X20206,X20206),tc_HOL_Obool)),X20207),X20205)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__by__empty])]) ).

fof(i_0_8553,plain,
    ! [X31686,X31687,X31688] :
      ( ( hBOOL(hAPP(c_List_Odistinct(X31688),X31687))
        | ~ hBOOL(hAPP(c_List_Odistinct(X31688),hAPP(hAPP(c_List_Oappend(X31688),X31687),X31686))) )
      & ( hBOOL(hAPP(c_List_Odistinct(X31688),X31686))
        | ~ hBOOL(hAPP(c_List_Odistinct(X31688),hAPP(hAPP(c_List_Oappend(X31688),X31687),X31686))) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31688,tc_HOL_Obool)),hAPP(c_List_Oset(X31688),X31687)),hAPP(c_List_Oset(X31688),X31686)) = c_Orderings_Obot__class_Obot(tc_fun(X31688,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(X31688),hAPP(hAPP(c_List_Oappend(X31688),X31687),X31686))) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X31688),X31687))
        | ~ hBOOL(hAPP(c_List_Odistinct(X31688),X31686))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31688,tc_HOL_Obool)),hAPP(c_List_Oset(X31688),X31687)),hAPP(c_List_Oset(X31688),X31686)) != c_Orderings_Obot__class_Obot(tc_fun(X31688,tc_HOL_Obool))
        | hBOOL(hAPP(c_List_Odistinct(X31688),hAPP(hAPP(c_List_Oappend(X31688),X31687),X31686))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__append])])]) ).

fof(i_0_8554,plain,
    ! [X32071,X32072,X32073] :
      ( ~ class_Orderings_Olinorder(X32073)
      | c_Big__Operators_Olattice_OSup__fin(X32073,c_Orderings_Oord__class_Omax(X32073),hAPP(c_List_Oset(X32073),hAPP(hAPP(c_List_Olist_OCons(X32073),X32072),X32071))) = hAPP(c_List_Ofoldl(X32073,X32073,c_Orderings_Oord__class_Omax(X32073),X32072),X32071) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin__set__fold])]) ).

fof(i_0_8555,plain,
    ! [X32068,X32069,X32070] :
      ( ~ class_Orderings_Olinorder(X32070)
      | c_Big__Operators_Olattice_OInf__fin(X32070,c_Orderings_Oord__class_Omin(X32070),hAPP(c_List_Oset(X32070),hAPP(hAPP(c_List_Olist_OCons(X32070),X32069),X32068))) = hAPP(c_List_Ofoldl(X32070,X32070,c_Orderings_Oord__class_Omin(X32070),X32069),X32068) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin__set__fold])]) ).

fof(i_0_8556,plain,
    ! [X26646,X26647,X26648,X26649] :
      ( ~ class_Groups_Ocomm__monoid__add(X26649)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26648),X26647))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26649),X26646),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26648,X26647)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26649),hAPP(X26646,X26648)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26649),X26646),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X26648,X26647))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__head])]) ).

fof(i_0_8557,plain,
    ! [X28910,X28911,X28912] : hAPP(hAPP(c_Nat_Ocompow(X28912,X28912),hAPP(c_Nat_OSuc,X28911)),X28910) = hAPP(c_Fun_Ocomp(X28912,X28912,X28912,X28910),hAPP(hAPP(c_Nat_Ocompow(X28912,X28912),X28911),X28910)),
    inference(variable_rename,[status(thm)],[fact_funpow_Osimps_I2_J]) ).

fof(i_0_8558,plain,
    ! [X30626,X30627,X30628,X30629,X30630] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X30630),X30629),hAPP(c_List_Oset(X30630),X30628)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30627),hAPP(X30626,X30629)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30627),c_List_Olist_Olist__size(X30630,X30626,X30628))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__size__estimation])]) ).

fof(i_0_8559,plain,
    ! [X30631,X30632,X30633,X30634,X30635] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X30635),X30634),hAPP(c_List_Oset(X30635),X30633)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30632),hAPP(X30631,X30634)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30632),c_List_Olist_Olist__size(X30635,X30631,X30633))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__size__estimation_H])]) ).

fof(i_0_8560,plain,
    ! [X30993,X30994] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30994),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X30993)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X30993),X30994)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X30993))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_elem__le__listsum__nat])]) ).

fof(i_0_8561,plain,
    ! [X23526,X23527] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23527))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23527),X23526))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23526),X23527) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23526),X23527)),X23527)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__div__geq])]) ).

fof(i_0_8562,plain,
    ! [X31045,X31046,X31047] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31047)),X31046),c_List_Olists(X31047,c_Wellfounded_Oacc(X31047,X31045))))
      | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31047)),X31046),c_Wellfounded_Oacc(tc_List_Olist(X31047),c_List_Olistrel1(X31047,X31045)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accD])]) ).

cnf(i_0_8563,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_5784]) ).

cnf(i_0_8564,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_5785]) ).

fof(i_0_8565,plain,
    ! [X25291,X25292] :
      ( ~ class_Rings_Osemiring__1(X25292)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25292),X25291) = c_Nat_Osemiring__1__class_Oof__nat__aux(X25292,hAPP(hAPP(c_COMBC(X25292,X25292,X25292),c_Groups_Oplus__class_Oplus(X25292)),c_Groups_Oone__class_Oone(X25292)),X25291,c_Groups_Ozero__class_Ozero(X25292)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__1__class_Oof__nat__code])]) ).

fof(i_0_8566,plain,
    ! [X30495,X30496,X30497,X30498] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30498)),X30497)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30498)),X30496)))
      | X30497 != hAPP(hAPP(c_List_Olist_OCons(X30498),X30495),X30496) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_impossible__Cons])]) ).

fof(i_0_8567,plain,
    ! [X17809,X17810,X17811] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17811,tc_HOL_Obool)),X17810),X17809))
      | hBOOL(hAPP(hAPP(c_member(tc_fun(X17811,tc_HOL_Obool)),X17810),hAPP(c_Set_OPow(X17811),X17809))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_PowI])]) ).

fof(i_0_8568,plain,
    ! [X22812,X22813,X22814,X22815,X22816] : hAPP(hAPP(c_Power_Opower_Opower(X22816,X22815,X22814),X22813),hAPP(c_Nat_OSuc,X22812)) = hAPP(hAPP(X22814,X22813),hAPP(hAPP(c_Power_Opower_Opower(X22816,X22815,X22814),X22813),X22812)),
    inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__Suc]) ).

fof(i_0_8569,plain,
    ! [X29963,X29964,X29965,X29966,X29967] :
      ( ( hAPP(X29964,X29963) = c_Option_Ooption_ONone(X29966)
        | hAPP(c_Map_Omap__add(X29967,X29966,X29965,X29964),X29963) != c_Option_Ooption_ONone(X29966) )
      & ( hAPP(X29965,X29963) = c_Option_Ooption_ONone(X29966)
        | hAPP(c_Map_Omap__add(X29967,X29966,X29965,X29964),X29963) != c_Option_Ooption_ONone(X29966) )
      & ( hAPP(X29964,X29963) != c_Option_Ooption_ONone(X29966)
        | hAPP(X29965,X29963) != c_Option_Ooption_ONone(X29966)
        | hAPP(c_Map_Omap__add(X29967,X29966,X29965,X29964),X29963) = c_Option_Ooption_ONone(X29966) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__None])])]) ).

fof(i_0_8570,plain,
    ! [X22533,X22534,X22535] :
      ( ~ class_Orderings_Olinorder(X22535)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22535,tc_HOL_Obool)),X22534),X22533))
      | X22534 = c_Orderings_Obot__class_Obot(tc_fun(X22535,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22535),X22533))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22535),c_Big__Operators_Olinorder__class_OMin(X22535,X22533)),c_Big__Operators_Olinorder__class_OMin(X22535,X22534))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__antimono])]) ).

fof(i_0_8571,plain,
    ! [X22530,X22531,X22532] :
      ( ~ class_Orderings_Olinorder(X22532)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22532,tc_HOL_Obool)),X22531),X22530))
      | X22531 = c_Orderings_Obot__class_Obot(tc_fun(X22532,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22532),X22530))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22532),c_Big__Operators_Olinorder__class_OMax(X22532,X22531)),c_Big__Operators_Olinorder__class_OMax(X22532,X22530))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__mono])]) ).

fof(i_0_8572,plain,
    ! [X22845,X22846] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22846),X22845))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X22846),X22845)),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),X22846),X22845)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22846),X22845)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__bin__lemma])]) ).

fof(i_0_8573,plain,
    ! [X17606,X17607,X17608] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17608),X17607),hAPP(hAPP(c_Set_Oinsert(X17608),X17606),c_Orderings_Obot__class_Obot(tc_fun(X17608,tc_HOL_Obool)))))
        | X17607 = X17606 )
      & ( X17607 != X17606
        | hBOOL(hAPP(hAPP(c_member(X17608),X17607),hAPP(hAPP(c_Set_Oinsert(X17608),X17606),c_Orderings_Obot__class_Obot(tc_fun(X17608,tc_HOL_Obool))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__iff])]) ).

fof(i_0_8574,plain,
    ! [X17603,X17604,X17605] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17605),X17604),hAPP(hAPP(c_Set_Oinsert(X17605),X17603),c_Orderings_Obot__class_Obot(tc_fun(X17605,tc_HOL_Obool)))))
      | X17604 = X17603 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singletonE])]) ).

fof(i_0_8575,plain,
    ! [X19188,X19189,X19190,X19191,X19192] :
      ( X19192 != hAPP(X19191,X19190)
      | hBOOL(hAPP(hAPP(c_member(X19189),X19192),hAPP(c_Set_Oimage(X19188,X19189,X19191),c_Orderings_Otop__class_Otop(tc_fun(X19188,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__eqI])]) ).

fof(i_0_8576,plain,
    ! [X27846,X27847,X27848,X27849] :
      ( ( X27849 != c_Orderings_Obot__class_Obot(tc_fun(X27848,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(tc_prod(X27848,X27847),X27847,c_Product__Type_Osnd(X27848,X27847)),hAPP(hAPP(c_Product__Type_OSigma(X27848,X27847),X27849),hAPP(c_COMBK(tc_fun(X27847,tc_HOL_Obool),X27848),X27846))) = c_Orderings_Obot__class_Obot(tc_fun(X27847,tc_HOL_Obool)) )
      & ( X27849 = c_Orderings_Obot__class_Obot(tc_fun(X27848,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(tc_prod(X27848,X27847),X27847,c_Product__Type_Osnd(X27848,X27847)),hAPP(hAPP(c_Product__Type_OSigma(X27848,X27847),X27849),hAPP(c_COMBK(tc_fun(X27847,tc_HOL_Obool),X27848),X27846))) = X27846 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snd__image__times])]) ).

fof(i_0_8577,plain,
    ! [X27842,X27843,X27844,X27845] :
      ( ( X27845 != c_Orderings_Obot__class_Obot(tc_fun(X27844,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(tc_prod(X27843,X27844),X27843,c_Product__Type_Ofst(X27843,X27844)),hAPP(hAPP(c_Product__Type_OSigma(X27843,X27844),X27842),hAPP(c_COMBK(tc_fun(X27844,tc_HOL_Obool),X27843),X27845))) = c_Orderings_Obot__class_Obot(tc_fun(X27843,tc_HOL_Obool)) )
      & ( X27845 = c_Orderings_Obot__class_Obot(tc_fun(X27844,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(tc_prod(X27843,X27844),X27843,c_Product__Type_Ofst(X27843,X27844)),hAPP(hAPP(c_Product__Type_OSigma(X27843,X27844),X27842),hAPP(c_COMBK(tc_fun(X27844,tc_HOL_Obool),X27843),X27845))) = X27842 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fst__image__times])]) ).

fof(i_0_8578,plain,
    ! [X17043,X17044,X17045,X17046,X17047] :
      ( ( X17046 = X17043
        | X17046 = X17044
        | hAPP(hAPP(c_Set_Oinsert(X17047),X17046),hAPP(hAPP(c_Set_Oinsert(X17047),X17045),c_Orderings_Obot__class_Obot(tc_fun(X17047,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X17047),X17044),hAPP(hAPP(c_Set_Oinsert(X17047),X17043),c_Orderings_Obot__class_Obot(tc_fun(X17047,tc_HOL_Obool)))) )
      & ( X17045 = X17044
        | X17046 = X17044
        | hAPP(hAPP(c_Set_Oinsert(X17047),X17046),hAPP(hAPP(c_Set_Oinsert(X17047),X17045),c_Orderings_Obot__class_Obot(tc_fun(X17047,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X17047),X17044),hAPP(hAPP(c_Set_Oinsert(X17047),X17043),c_Orderings_Obot__class_Obot(tc_fun(X17047,tc_HOL_Obool)))) )
      & ( X17046 = X17043
        | X17045 = X17043
        | hAPP(hAPP(c_Set_Oinsert(X17047),X17046),hAPP(hAPP(c_Set_Oinsert(X17047),X17045),c_Orderings_Obot__class_Obot(tc_fun(X17047,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X17047),X17044),hAPP(hAPP(c_Set_Oinsert(X17047),X17043),c_Orderings_Obot__class_Obot(tc_fun(X17047,tc_HOL_Obool)))) )
      & ( X17045 = X17044
        | X17045 = X17043
        | hAPP(hAPP(c_Set_Oinsert(X17047),X17046),hAPP(hAPP(c_Set_Oinsert(X17047),X17045),c_Orderings_Obot__class_Obot(tc_fun(X17047,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X17047),X17044),hAPP(hAPP(c_Set_Oinsert(X17047),X17043),c_Orderings_Obot__class_Obot(tc_fun(X17047,tc_HOL_Obool)))) )
      & ( X17046 != X17044
        | X17045 != X17043
        | hAPP(hAPP(c_Set_Oinsert(X17047),X17046),hAPP(hAPP(c_Set_Oinsert(X17047),X17045),c_Orderings_Obot__class_Obot(tc_fun(X17047,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X17047),X17044),hAPP(hAPP(c_Set_Oinsert(X17047),X17043),c_Orderings_Obot__class_Obot(tc_fun(X17047,tc_HOL_Obool)))) )
      & ( X17046 != X17043
        | X17045 != X17044
        | hAPP(hAPP(c_Set_Oinsert(X17047),X17046),hAPP(hAPP(c_Set_Oinsert(X17047),X17045),c_Orderings_Obot__class_Obot(tc_fun(X17047,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X17047),X17044),hAPP(hAPP(c_Set_Oinsert(X17047),X17043),c_Orderings_Obot__class_Obot(tc_fun(X17047,tc_HOL_Obool)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_doubleton__eq__iff])])]) ).

fof(i_0_8579,plain,
    ! [X31206,X31207,X31208,X31209,X31210] :
      ( ( X31210 != X31207
        | hAPP(hAPP(c_List_Onth(X31209),hAPP(hAPP(c_List_Olist__update(X31209,X31208),X31210),X31206)),X31207) = X31206
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31210),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31209)),X31208))) )
      & ( X31210 = X31207
        | hAPP(hAPP(c_List_Onth(X31209),hAPP(hAPP(c_List_Olist__update(X31209,X31208),X31210),X31206)),X31207) = hAPP(hAPP(c_List_Onth(X31209),X31208),X31207)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31210),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31209)),X31208))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__list__update])])]) ).

fof(i_0_8580,plain,
    ! [X21692,X21693,X21694] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21694),X21693)),X21692))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21694),X21692)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).

fof(i_0_8581,plain,
    ! [X21709,X21710,X21711] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21711),X21709))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21711),X21710)),X21709)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21710),X21709))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21711),X21710)),X21709)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5786])])]) ).

fof(i_0_8582,plain,
    ! [X21712,X21713,X21714] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21714),X21713)),X21712))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21714),X21712)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).

fof(i_0_8583,plain,
    ! [X21715,X21716,X21717] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21717),X21716)),X21715))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21716),X21715)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).

fof(i_0_8584,plain,
    ! [X22469,X22470] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22470))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22470),hAPP(c_Nat_OSuc,X22469))),X22470)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__less])]) ).

fof(i_0_8585,plain,
    ! [X20090,X20091,X20092,X20093,X20094] :
      ( hAPP(X20094,X20093) != c_Option_Ooption_ONone(X20092)
      | c_Map_Oran(X20091,X20092,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X20091,tc_Option_Ooption(X20092)),X20094),X20093),hAPP(c_Option_Ooption_OSome(X20092),X20090))) = hAPP(hAPP(c_Set_Oinsert(X20092),X20090),c_Map_Oran(X20091,X20092,X20094)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ran__map__upd])]) ).

fof(i_0_8586,plain,
    ! [X26122,X26123,X26124,X26125] :
      ( ~ class_Orderings_Olinorder(X26125)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26125),X26124),X26123))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26125),X26123),X26122))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26125,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26125,X26124),X26123)),c_SetInterval_Oord__class_OatLeastAtMost(X26125,X26123,X26122)) = c_SetInterval_Oord__class_OatLeastAtMost(X26125,X26124,X26122) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I21_J])]) ).

fof(i_0_8587,plain,
    ! [X26218,X26219,X26220] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26220),X26219))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26220),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26219),X26218)) = 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,X26220),X26219)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26219),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26219),X26218))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__add__Un])]) ).

fof(i_0_8588,plain,
    ! [X18193,X18194,X18195] : hAPP(hAPP(c_Set_Oinsert(X18195),X18194),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18195,tc_HOL_Obool)),X18193),hAPP(hAPP(c_Set_Oinsert(X18195),X18194),c_Orderings_Obot__class_Obot(tc_fun(X18195,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(X18195),X18194),X18193),
    inference(variable_rename,[status(thm)],[fact_insert__Diff__single]) ).

cnf(i_0_8589,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_5787]) ).

cnf(i_0_8590,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_5788]) ).

cnf(i_0_8591,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_5789]) ).

cnf(i_0_8592,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_5790]) ).

cnf(i_0_8593,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_5791]) ).

cnf(i_0_8594,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_5792]) ).

cnf(i_0_8595,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_5607]) ).

fof(i_0_8596,plain,
    ! [X21224,X21225,X21226] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21226),X21225))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21226),X21225)),hAPP(c_Finite__Set_Ocard(X21226),hAPP(hAPP(c_Set_Oinsert(X21226),X21224),X21225)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert__le])]) ).

fof(i_0_8597,plain,
    ! [X25141,X25142,X25143] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25143)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25142)),X25141)) = 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),X25143),X25142))),X25141),
    inference(variable_rename,[status(thm)],[fact_zadd__int__left]) ).

fof(i_0_8598,plain,
    ! [X29646,X29647,X29648,X29650] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29648),esk363_3(X29646,X29647,X29648)),X29646))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29648),X29647),c_Complete__Lattice_OSup__class_OSup(X29648,X29646)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X29648)
        | ~ class_Orderings_Olinorder(X29648) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29648),X29647),esk363_3(X29646,X29647,X29648)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29648),X29647),c_Complete__Lattice_OSup__class_OSup(X29648,X29646)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X29648)
        | ~ class_Orderings_Olinorder(X29648) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X29648),X29650),X29646))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29648),X29647),X29650))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29648),X29647),c_Complete__Lattice_OSup__class_OSup(X29648,X29646)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X29648)
        | ~ class_Orderings_Olinorder(X29648) ) ),
    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_8599,plain,
    ! [X25525] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X25525))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25525)))
        | ~ c_Nat__Transfer_Onat__set(X25525) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25525)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X25525))
        | ~ c_Nat__Transfer_Onat__set(X25525) ) ),
    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_8600,plain,
    hAPP(c_Relation_OImage(X1,X1,c_Relation_OId(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_5793]) ).

fof(i_0_8601,plain,
    ! [X24556,X24557] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X24557)),hAPP(c_Int_Onat,X24556)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24557),X24556))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24556))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24557)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24557),X24556))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X24557)),hAPP(c_Int_Onat,X24556)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24556))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24557)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I2_J])])]) ).

fof(i_0_8602,plain,
    ! [X24549,X24550] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X24550)),hAPP(c_Int_Onat,X24549)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24550),X24549))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24549))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24550)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24550),X24549))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X24550)),hAPP(c_Int_Onat,X24549)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24549))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24550)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I3_J])])]) ).

fof(i_0_8603,plain,
    ! [X25619,X25620,X25621] :
      ( ~ class_Orderings_Olinorder(X25621)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25621),X25620),X25619))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25621,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25621,X25620,X25619)),hAPP(hAPP(c_Set_Oinsert(X25621),X25619),c_Orderings_Obot__class_Obot(tc_fun(X25621,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(X25621,X25620,X25619) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I4_J])]) ).

fof(i_0_8604,plain,
    ! [X18185,X18186,X18187,X18188] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X18188),X18187),X18186))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18188,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X18188),X18187),X18185)),X18186) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18188,tc_HOL_Obool)),X18185),X18186) )
      & ( hBOOL(hAPP(hAPP(c_member(X18188),X18187),X18186))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18188,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X18188),X18187),X18185)),X18186) = hAPP(hAPP(c_Set_Oinsert(X18188),X18187),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18188,tc_HOL_Obool)),X18185),X18186)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5794])]) ).

fof(i_0_8605,plain,
    ! [X28386,X28387,X28388] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28388),esk321_3(X28386,X28387,X28388)),X28387))
        | ~ hBOOL(hAPP(hAPP(c_member(X28388),X28386),X28387))
        | c_Big__Operators_Olinorder__class_OMin(X28388,X28387) = X28386
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28388),X28387))
        | ~ class_Orderings_Olinorder(X28388) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28388),X28386),esk321_3(X28386,X28387,X28388)))
        | ~ hBOOL(hAPP(hAPP(c_member(X28388),X28386),X28387))
        | c_Big__Operators_Olinorder__class_OMin(X28388,X28387) = X28386
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28388),X28387))
        | ~ class_Orderings_Olinorder(X28388) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__eqI])])])]) ).

fof(i_0_8606,plain,
    ! [X31574,X31575,X31576,X31577,X31578] : hAPP(hAPP(c_List_Omap(X31578,X31577),X31576),hAPP(hAPP(c_List_Oappend(X31578),X31575),X31574)) = hAPP(hAPP(c_List_Oappend(X31577),hAPP(hAPP(c_List_Omap(X31578,X31577),X31576),X31575)),hAPP(hAPP(c_List_Omap(X31578,X31577),X31576),X31574)),
    inference(variable_rename,[status(thm)],[fact_map__append]) ).

fof(i_0_8607,plain,
    ! [X29823,X29824] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X29824,tc_HOL_Obool)),esk370_2(X29823,X29824)),X29823))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X29824),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29824,tc_HOL_Obool),X29823)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X29824,tc_HOL_Obool)),X29823)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29824),esk370_2(X29823,X29824)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X29824),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29824,tc_HOL_Obool),X29823)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X29824,tc_HOL_Obool)),X29823)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Union])])])]) ).

fof(i_0_8608,plain,
    ! [X23142,X23143] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23143))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X23142))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23143),X23142)),X23143)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__div__less__self])]) ).

fof(i_0_8609,plain,
    ! [X23471,X23472] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X23472))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23471))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23471),X23472)),X23471)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less__dividend])]) ).

fof(i_0_8610,plain,
    ! [X22346,X22347] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22347))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22346))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22346),X22347)),X22346)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less])]) ).

cnf(i_0_8611,plain,
    c_Map_Omap__comp(X1,X2,X3,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)),X4,X5) = c_Option_Ooption_ONone(X2),
    inference(split_conjunct,[status(thm)],[i_0_5795]) ).

cnf(i_0_8612,plain,
    c_Map_Omap__comp(X1,X2,X3,X4,hAPP(c_COMBK(tc_Option_Ooption(X1),X3),c_Option_Ooption_ONone(X1)),X5) = c_Option_Ooption_ONone(X2),
    inference(split_conjunct,[status(thm)],[i_0_5796]) ).

cnf(i_0_8613,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_5797]) ).

cnf(i_0_8614,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_5798]) ).

fof(i_0_8615,plain,
    ! [X18088,X18089,X18090,X18091] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18091,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X18091),X18090),X18089)),hAPP(hAPP(c_Set_Oinsert(X18091),X18090),X18088)) = hAPP(hAPP(c_Set_Oinsert(X18091),X18090),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18091,tc_HOL_Obool)),X18089),X18088)),
    inference(variable_rename,[status(thm)],[fact_insert__inter__insert]) ).

fof(i_0_8616,plain,
    ! [X23058,X23059] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23059),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)),X23058))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23059),X23058)),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_8617,plain,
    ! [X23129,X23130] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23130))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23129),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),X23130),X23129)),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_8618,plain,
    ! [X23123,X23124] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23124),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)),X23123))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23124),X23123)),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_8619,plain,
    ! [X23444,X23445,X23446] :
      ( ~ class_Divides_Osemiring__div(X23446)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23446),c_Divides_Odiv__class_Omod(X23446,X23445,X23444)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23446),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23446),X23445),X23444)),X23444)) = X23445 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__div__class_Omod__div__equality_H])]) ).

fof(i_0_8620,plain,
    ! [X24302,X24303,X24304] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24304),X24303),c_Groups_Ozero__class_Ozero(X24304)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24304),c_Groups_Ozero__class_Ozero(X24304)),X24303))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24304),c_Groups_Ozero__class_Ozero(X24304)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24304),X24303),X24302)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24304) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24304),X24302),c_Groups_Ozero__class_Ozero(X24304)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24304),c_Groups_Ozero__class_Ozero(X24304)),X24303))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24304),c_Groups_Ozero__class_Ozero(X24304)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24304),X24303),X24302)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24304) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24304),X24303),c_Groups_Ozero__class_Ozero(X24304)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24304),c_Groups_Ozero__class_Ozero(X24304)),X24302))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24304),c_Groups_Ozero__class_Ozero(X24304)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24304),X24303),X24302)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24304) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24304),X24302),c_Groups_Ozero__class_Ozero(X24304)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24304),c_Groups_Ozero__class_Ozero(X24304)),X24302))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24304),c_Groups_Ozero__class_Ozero(X24304)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24304),X24303),X24302)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24304) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24304),c_Groups_Ozero__class_Ozero(X24304)),X24303))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24304),c_Groups_Ozero__class_Ozero(X24304)),X24302))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24304),c_Groups_Ozero__class_Ozero(X24304)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24304),X24303),X24302)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24304) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24304),X24303),c_Groups_Ozero__class_Ozero(X24304)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24304),X24302),c_Groups_Ozero__class_Ozero(X24304)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24304),c_Groups_Ozero__class_Ozero(X24304)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24304),X24303),X24302)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24304) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__divide__iff])])]) ).

fof(i_0_8621,plain,
    ! [X24299,X24300,X24301] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24301),X24300),c_Groups_Ozero__class_Ozero(X24301)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24301),c_Groups_Ozero__class_Ozero(X24301)),X24300))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24301),c_Groups_Ozero__class_Ozero(X24301)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24301),X24300),X24299)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24301) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24301),X24299),c_Groups_Ozero__class_Ozero(X24301)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24301),c_Groups_Ozero__class_Ozero(X24301)),X24300))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24301),c_Groups_Ozero__class_Ozero(X24301)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24301),X24300),X24299)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24301) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24301),X24300),c_Groups_Ozero__class_Ozero(X24301)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24301),c_Groups_Ozero__class_Ozero(X24301)),X24299))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24301),c_Groups_Ozero__class_Ozero(X24301)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24301),X24300),X24299)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24301) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24301),X24299),c_Groups_Ozero__class_Ozero(X24301)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24301),c_Groups_Ozero__class_Ozero(X24301)),X24299))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24301),c_Groups_Ozero__class_Ozero(X24301)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24301),X24300),X24299)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24301) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24301),c_Groups_Ozero__class_Ozero(X24301)),X24300))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24301),c_Groups_Ozero__class_Ozero(X24301)),X24299))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24301),c_Groups_Ozero__class_Ozero(X24301)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24301),X24300),X24299)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24301) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24301),X24300),c_Groups_Ozero__class_Ozero(X24301)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24301),X24299),c_Groups_Ozero__class_Ozero(X24301)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24301),c_Groups_Ozero__class_Ozero(X24301)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24301),X24300),X24299)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X24301) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__divide__iff])])]) ).

fof(i_0_8622,plain,
    ! [X22142,X22143,X22144] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22144),X22143),c_Groups_Ozero__class_Ozero(X22144)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22144),c_Groups_Ozero__class_Ozero(X22144)),X22143))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22144),c_Groups_Ozero__class_Ozero(X22144)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22144),X22143),X22142)))
        | ~ class_Rings_Olinordered__ring__strict(X22144) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22144),X22142),c_Groups_Ozero__class_Ozero(X22144)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22144),c_Groups_Ozero__class_Ozero(X22144)),X22143))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22144),c_Groups_Ozero__class_Ozero(X22144)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22144),X22143),X22142)))
        | ~ class_Rings_Olinordered__ring__strict(X22144) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22144),X22143),c_Groups_Ozero__class_Ozero(X22144)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22144),c_Groups_Ozero__class_Ozero(X22144)),X22142))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22144),c_Groups_Ozero__class_Ozero(X22144)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22144),X22143),X22142)))
        | ~ class_Rings_Olinordered__ring__strict(X22144) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22144),X22142),c_Groups_Ozero__class_Ozero(X22144)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22144),c_Groups_Ozero__class_Ozero(X22144)),X22142))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22144),c_Groups_Ozero__class_Ozero(X22144)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22144),X22143),X22142)))
        | ~ class_Rings_Olinordered__ring__strict(X22144) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22144),c_Groups_Ozero__class_Ozero(X22144)),X22143))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22144),c_Groups_Ozero__class_Ozero(X22144)),X22142))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22144),c_Groups_Ozero__class_Ozero(X22144)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22144),X22143),X22142)))
        | ~ class_Rings_Olinordered__ring__strict(X22144) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22144),X22143),c_Groups_Ozero__class_Ozero(X22144)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22144),X22142),c_Groups_Ozero__class_Ozero(X22144)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22144),c_Groups_Ozero__class_Ozero(X22144)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22144),X22143),X22142)))
        | ~ class_Rings_Olinordered__ring__strict(X22144) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff])])]) ).

fof(i_0_8623,plain,
    ! [X34190,X34191,X34192,X34193,X34194,X34195,X34196] :
      ( ( ~ c_List_Oall__interval__int(X34192,X34191,X34190)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X34193),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X34191,X34190)))
        | hBOOL(hAPP(X34192,X34193)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk532_3(X34194,X34195,X34196)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X34195,X34194)))
        | c_List_Oall__interval__int(X34196,X34195,X34194) )
      & ( ~ hBOOL(hAPP(X34196,esk532_3(X34194,X34195,X34196)))
        | c_List_Oall__interval__int(X34196,X34195,X34194) ) ),
    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_8624,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5735]) ).

cnf(i_0_8625,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_5736]) ).

cnf(i_0_8626,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_5737]) ).

fof(i_0_8627,plain,
    ! [X22858,X22859,X22860] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22860),X22859))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22860),X22858)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22859),X22858))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono])]) ).

fof(i_0_8628,plain,
    ! [X21681,X21682,X21683] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21683),X21682))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21683),X21681)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21682),X21681))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).

cnf(i_0_8629,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_5738]) ).

cnf(i_0_8630,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_5739]) ).

fof(i_0_8631,plain,
    ! [X22869,X22870,X22871] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22871),X22870))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22869),X22871)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22869),X22870))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__left__mono])]) ).

fof(i_0_8632,plain,
    ! [X23364,X23365,X23366] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23366),X23365))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23366),X23364)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23365),X23364))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono])]) ).

fof(i_0_8633,plain,
    ! [X21722,X21723,X21724] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21724),X21723))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21724),X21722)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21723),X21722))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).

fof(i_0_8634,plain,
    ! [X21015,X21016,X21017] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21017),X21016))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21017),X21015)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21016),X21015))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono1])]) ).

fof(i_0_8635,plain,
    ! [X21018,X21019,X21020] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21020),X21019))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21018),X21020)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21018),X21019))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono2])]) ).

fof(i_0_8636,plain,
    ! [X20989,X20990,X20991] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20991),X20990))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20991),X20989)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20990),X20989))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono])]) ).

fof(i_0_8637,plain,
    ! [X20986,X20987,X20988] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20988),X20987))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20986),X20987)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20986),X20988))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono2])]) ).

fof(i_0_8638,plain,
    ! [X32062,X32063,X32064] :
      ( ~ class_Orderings_Olinorder(X32064)
      | c_Big__Operators_Olinorder__class_OMin(X32064,hAPP(c_List_Oset(X32064),hAPP(hAPP(c_List_Olist_OCons(X32064),X32063),X32062))) = hAPP(c_List_Ofoldl(X32064,X32064,c_Orderings_Oord__class_Omin(X32064),X32063),X32062) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__fin__set__fold])]) ).

fof(i_0_8639,plain,
    ! [X32065,X32066,X32067] :
      ( ~ class_Orderings_Olinorder(X32067)
      | c_Big__Operators_Olinorder__class_OMax(X32067,hAPP(c_List_Oset(X32067),hAPP(hAPP(c_List_Olist_OCons(X32067),X32066),X32065))) = hAPP(c_List_Ofoldl(X32067,X32067,c_Orderings_Oord__class_Omax(X32067),X32066),X32065) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__fin__set__fold])]) ).

fof(i_0_8640,plain,
    ! [X32056,X32057,X32058] :
      ( ~ class_Lattices_Olattice(X32058)
      | c_Big__Operators_Olattice__class_OSup__fin(X32058,hAPP(c_List_Oset(X32058),hAPP(hAPP(c_List_Olist_OCons(X32058),X32057),X32056))) = hAPP(c_List_Ofoldl(X32058,X32058,c_Lattices_Osemilattice__sup__class_Osup(X32058),X32057),X32056) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin__set__fold])]) ).

fof(i_0_8641,plain,
    ! [X32059,X32060,X32061] :
      ( ~ class_Lattices_Olattice(X32061)
      | c_Big__Operators_Olattice__class_OInf__fin(X32061,hAPP(c_List_Oset(X32061),hAPP(hAPP(c_List_Olist_OCons(X32061),X32060),X32059))) = hAPP(c_List_Ofoldl(X32061,X32061,c_Lattices_Osemilattice__inf__class_Oinf(X32061),X32060),X32059) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin__set__fold])]) ).

fof(i_0_8642,plain,
    ! [X21534,X21535,X21536] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21536),X21535))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21535),X21536))),X21534) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21535)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21536),X21534)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq2])]) ).

fof(i_0_8643,plain,
    ! [X23447,X23448,X23449] :
      ( ~ class_Divides_Osemiring__div(X23449)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23449),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23449),X23448),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23449),X23447),X23448))),c_Divides_Odiv__class_Omod(X23449,X23447,X23448)) = X23447 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__equality2])]) ).

cnf(i_0_8644,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_5799]) ).

fof(i_0_8645,plain,
    ! [X31180,X31181,X31182,X31183,X31184] : hAPP(hAPP(c_List_Olist__update(X31184,hAPP(hAPP(c_List_Olist_OCons(X31184),X31183),X31182)),hAPP(c_Nat_OSuc,X31181)),X31180) = hAPP(hAPP(c_List_Olist_OCons(X31184),X31183),hAPP(hAPP(c_List_Olist__update(X31184,X31182),X31181),X31180)),
    inference(variable_rename,[status(thm)],[fact_list__update__code_I3_J]) ).

fof(i_0_8646,plain,
    ! [X34104,X34105,X34106,X34107,X34108,X34109] :
      ( ( X34107 = X34105
        | c_Nitpick_Opair__box_OPairBox(X34109,X34108,X34107,X34106) != c_Nitpick_Opair__box_OPairBox(X34109,X34108,X34105,X34104) )
      & ( X34106 = X34104
        | c_Nitpick_Opair__box_OPairBox(X34109,X34108,X34107,X34106) != c_Nitpick_Opair__box_OPairBox(X34109,X34108,X34105,X34104) )
      & ( X34107 != X34105
        | X34106 != X34104
        | c_Nitpick_Opair__box_OPairBox(X34109,X34108,X34107,X34106) = c_Nitpick_Opair__box_OPairBox(X34109,X34108,X34105,X34104) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__box_Oinject])])]) ).

fof(i_0_8647,plain,
    ! [X19376,X19377,X19378,X19379,X19380,X19381] :
      ( hAPP(X19381,X19380) != X19379
      | ~ hBOOL(hAPP(hAPP(c_member(X19378),X19379),X19377))
      | hBOOL(hAPP(hAPP(c_member(X19376),X19380),hAPP(c_Set_Ovimage(X19376,X19378,X19381),X19377))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimageI])]) ).

fof(i_0_8648,plain,
    ! [X17287,X17288,X17289,X17290,X17291,X17292] :
      ( X17292 != hAPP(X17291,X17290)
      | ~ hBOOL(hAPP(hAPP(c_member(X17289),X17290),X17288))
      | hBOOL(hAPP(hAPP(c_member(X17287),X17292),hAPP(c_Set_Oimage(X17289,X17287,X17291),X17288))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eqI])]) ).

fof(i_0_8649,plain,
    ! [X17319,X17320,X17321,X17322,X17323,X17324] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17324),X17323),X17322))
      | X17321 != hAPP(X17320,X17323)
      | hBOOL(hAPP(hAPP(c_member(X17319),X17321),hAPP(c_Set_Oimage(X17324,X17319,X17320),X17322))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__image__eqI])]) ).

fof(i_0_8650,plain,
    ! [X18746,X18747,X18748,X18749,X18750,X18751] :
      ( ( hAPP(X18749,X18747) != hAPP(X18749,X18746)
        | X18747 = X18746
        | ~ hBOOL(hAPP(hAPP(c_member(X18751),X18746),X18748))
        | ~ hBOOL(hAPP(hAPP(c_member(X18751),X18747),X18748))
        | ~ c_Fun_Oinj__on(X18751,X18750,X18749,X18748) )
      & ( X18747 != X18746
        | hAPP(X18749,X18747) = hAPP(X18749,X18746)
        | ~ hBOOL(hAPP(hAPP(c_member(X18751),X18746),X18748))
        | ~ hBOOL(hAPP(hAPP(c_member(X18751),X18747),X18748))
        | ~ c_Fun_Oinj__on(X18751,X18750,X18749,X18748) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff])])]) ).

fof(i_0_8651,plain,
    ! [X18752,X18753,X18754,X18755,X18756,X18757] :
      ( ~ c_Fun_Oinj__on(X18757,X18756,X18755,X18754)
      | hAPP(X18755,X18753) != hAPP(X18755,X18752)
      | ~ hBOOL(hAPP(hAPP(c_member(X18757),X18753),X18754))
      | ~ hBOOL(hAPP(hAPP(c_member(X18757),X18752),X18754))
      | X18753 = X18752 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__onD])]) ).

fof(i_0_8652,plain,
    ! [X18740,X18741,X18742,X18743,X18744,X18745] :
      ( ~ c_Fun_Oinj__on(X18745,X18744,X18743,X18742)
      | X18741 = X18740
      | ~ hBOOL(hAPP(hAPP(c_member(X18745),X18741),X18742))
      | ~ hBOOL(hAPP(hAPP(c_member(X18745),X18740),X18742))
      | hAPP(X18743,X18741) != hAPP(X18743,X18740) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__contraD])]) ).

fof(i_0_8653,plain,
    ! [X23510,X23511] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23510),X23511))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23510),X23511) = 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)),X23511)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23510),X23511))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23510),X23511) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23510),X23511)),X23511))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23511)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5800])])]) ).

fof(i_0_8654,plain,
    ! [X23508,X23509] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23509))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23508),X23509))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23508),X23509) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23508),X23509)),X23509)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5801])]) ).

fof(i_0_8655,plain,
    ! [X23134,X23135] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23134),X23135))
        | ~ 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),X23135),X23134)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23135)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23134))
        | ~ 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),X23135),X23134)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23135)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23134),X23135))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23134))
        | 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),X23135),X23134)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23135)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonneg1__imp__zdiv__pos__iff])])]) ).

fof(i_0_8656,plain,
    ! [X33492,X33493,X33494,X33496,X33497,X33498,X33499] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk493_3(X33492,X33493,X33494)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33494)),X33492)))
        | ~ c_List_Olist__ex(X33494,X33493,X33492) )
      & ( hBOOL(hAPP(X33493,hAPP(hAPP(c_List_Onth(X33494),X33492),esk493_3(X33492,X33493,X33494))))
        | ~ c_List_Olist__ex(X33494,X33493,X33492) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33499),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33498)),X33496)))
        | ~ hBOOL(hAPP(X33497,hAPP(hAPP(c_List_Onth(X33498),X33496),X33499)))
        | c_List_Olist__ex(X33498,X33497,X33496) ) ),
    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_8657,plain,
    ! [X21128,X21129,X21130,X21131,X21132] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X21132,X21131,X21130)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21132),X21129))
      | X21128 = c_Orderings_Obot__class_Obot(tc_fun(X21132,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21132,tc_HOL_Obool)),X21128),X21129))
      | hAPP(hAPP(X21131,hAPP(X21130,X21128)),hAPP(X21130,X21129)) = hAPP(X21130,X21129) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Osubset__idem])]) ).

fof(i_0_8658,plain,
    ! [X28806,X28807,X28808] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X28808,X28808,X28808),hAPP(c_Relation_Oconverse(X28808,X28808),X28807)),X28807) != X28807
      | hAPP(c_Relation_ODomain(X28808,X28808),X28807) != X28806
      | c_Equiv__Relations_Oequiv(X28808,X28806,X28807) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__equivI])]) ).

fof(i_0_8659,plain,
    ! [X34047,X34048,X34049,X34050,X34051,X34052] : hAPP(hAPP(c_List_Ozip(X34052,X34051),c_List_Oreplicate(X34052,X34050,X34049)),c_List_Oreplicate(X34051,X34048,X34047)) = c_List_Oreplicate(tc_prod(X34052,X34051),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X34050),X34048),hAPP(hAPP(c_Product__Type_OPair(X34052,X34051),X34049),X34047)),
    inference(variable_rename,[status(thm)],[fact_zip__replicate]) ).

fof(i_0_8660,plain,
    ! [X17129,X17130,X17131,X17132,X17133] :
      ( ~ class_Orderings_Oord(X17133)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17132,X17133)),X17131),X17130))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17133),hAPP(X17131,X17129)),hAPP(X17130,X17129))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).

fof(i_0_8661,plain,
    ! [X17124,X17125,X17126,X17127,X17128] :
      ( ~ class_Orderings_Oord(X17128)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17127,X17128)),X17126),X17125))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17128),hAPP(X17126,X17124)),hAPP(X17125,X17124))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).

fof(i_0_8662,plain,
    ! [X30122,X30123,X30124,X30125,X30126] :
      ( ( hAPP(hAPP(c_List_Omap(X30126,X30125),X30124),X30123) != hAPP(hAPP(c_List_Omap(X30126,X30125),X30124),X30122)
        | X30123 = X30122
        | ~ c_Fun_Oinj__on(X30126,X30125,X30124,c_Orderings_Otop__class_Otop(tc_fun(X30126,tc_HOL_Obool))) )
      & ( X30123 != X30122
        | hAPP(hAPP(c_List_Omap(X30126,X30125),X30124),X30123) = hAPP(hAPP(c_List_Omap(X30126,X30125),X30124),X30122)
        | ~ c_Fun_Oinj__on(X30126,X30125,X30124,c_Orderings_Otop__class_Otop(tc_fun(X30126,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_8663,plain,
    ! [X30114,X30115,X30116,X30117,X30118] :
      ( hAPP(hAPP(c_List_Omap(X30118,X30117),X30116),X30115) != hAPP(hAPP(c_List_Omap(X30118,X30117),X30116),X30114)
      | ~ c_Fun_Oinj__on(X30118,X30117,X30116,c_Orderings_Otop__class_Otop(tc_fun(X30118,tc_HOL_Obool)))
      | X30115 = X30114 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__injective])]) ).

fof(i_0_8664,plain,
    ! [X31198,X31199,X31200,X31201] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31201),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31200)),X31199)))
      | hAPP(hAPP(c_List_Onth(X31200),hAPP(hAPP(c_List_Olist__update(X31200,X31199),X31201),X31198)),X31201) = X31198 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__list__update__eq])]) ).

fof(i_0_8665,plain,
    ! [X26810,X26811,X26812] :
      ( ~ class_Groups_Ocomm__monoid__add(X26812)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26812),X26811),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26810))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26812),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26812),X26811),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X26810))),hAPP(X26811,hAPP(c_Nat_OSuc,X26810))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__atMost__Suc])]) ).

fof(i_0_8666,plain,
    ! [X26177,X26178,X26179,X26180] :
      ( ~ class_Orderings_Olinorder(X26180)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26180),X26179),X26178))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26180),X26178),X26177))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26180,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26180,X26179),X26178)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26180,X26178),X26177)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26180,X26179),X26177) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I17_J])]) ).

fof(i_0_8667,plain,
    ! [X32210,X32211] : c_List_Obutlast(X32211,X32210) = hAPP(hAPP(c_List_Otake(X32211),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32211)),X32210)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X32210),
    inference(variable_rename,[status(thm)],[fact_butlast__conv__take]) ).

fof(i_0_8668,plain,
    ! [X25447,X25448,X25449] :
      ( ~ class_Orderings_Olinorder(X25449)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25449),X25448))
      | ~ hBOOL(hAPP(hAPP(c_member(X25449),X25447),X25448))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25449),hAPP(c_Finite__Set_Ofold1(X25449,c_Orderings_Oord__class_Omin(X25449)),X25448)),X25447)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold1__belowI])]) ).

fof(i_0_8669,plain,
    ! [X21286,X21287,X21288] :
      ( ~ class_Lattices_Osemilattice__inf(X21288)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21288),X21287))
      | ~ hBOOL(hAPP(hAPP(c_member(X21288),X21286),X21287))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21288),hAPP(c_Finite__Set_Ofold1(X21288,c_Lattices_Osemilattice__inf__class_Oinf(X21288)),X21287)),X21286)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__belowI])]) ).

fof(i_0_8670,plain,
    ! [X25263] : ~ 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,X25263))))),
    inference(variable_rename,[status(thm)],[i_0_5802]) ).

fof(i_0_8671,plain,
    ! [X33488,X33489,X33490] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33490),esk492_3(X33488,X33489,X33490)),hAPP(c_List_Oset(X33490),X33489)))
        | ~ c_List_Olinorder__class_Osorted(X33490,X33489)
        | c_List_Olinorder__class_Osorted(X33490,hAPP(hAPP(c_List_Olist_OCons(X33490),X33488),X33489))
        | ~ class_Orderings_Olinorder(X33490) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33490),X33488),esk492_3(X33488,X33489,X33490)))
        | ~ c_List_Olinorder__class_Osorted(X33490,X33489)
        | c_List_Olinorder__class_Osorted(X33490,hAPP(hAPP(c_List_Olist_OCons(X33490),X33488),X33489))
        | ~ class_Orderings_Olinorder(X33490) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted_OCons])])])]) ).

fof(i_0_8672,plain,
    ! [X32818,X32819,X32820,X32821] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X32820),X32821),hAPP(c_List_Oset(X32820),X32818)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32820),X32819),X32821))
        | ~ c_List_Olinorder__class_Osorted(X32820,hAPP(hAPP(c_List_Olist_OCons(X32820),X32819),X32818))
        | ~ class_Orderings_Olinorder(X32820) )
      & ( c_List_Olinorder__class_Osorted(X32820,X32818)
        | ~ c_List_Olinorder__class_Osorted(X32820,hAPP(hAPP(c_List_Olist_OCons(X32820),X32819),X32818))
        | ~ class_Orderings_Olinorder(X32820) )
      & ( hBOOL(hAPP(hAPP(c_member(X32820),esk457_3(X32818,X32819,X32820)),hAPP(c_List_Oset(X32820),X32818)))
        | ~ c_List_Olinorder__class_Osorted(X32820,X32818)
        | c_List_Olinorder__class_Osorted(X32820,hAPP(hAPP(c_List_Olist_OCons(X32820),X32819),X32818))
        | ~ class_Orderings_Olinorder(X32820) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32820),X32819),esk457_3(X32818,X32819,X32820)))
        | ~ c_List_Olinorder__class_Osorted(X32820,X32818)
        | c_List_Olinorder__class_Osorted(X32820,hAPP(hAPP(c_List_Olist_OCons(X32820),X32819),X32818))
        | ~ class_Orderings_Olinorder(X32820) ) ),
    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_8673,plain,
    ! [X32800,X32801,X32802,X32803] :
      ( ( c_List_Olinorder__class_Osorted(X32802,X32800)
        | ~ c_List_Olinorder__class_Osorted(X32802,hAPP(hAPP(c_List_Olist_OCons(X32802),X32801),X32800))
        | ~ class_Orderings_Olinorder(X32802) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32802),X32803),hAPP(c_List_Oset(X32802),X32800)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32802),X32801),X32803))
        | ~ c_List_Olinorder__class_Osorted(X32802,hAPP(hAPP(c_List_Olist_OCons(X32802),X32801),X32800))
        | ~ class_Orderings_Olinorder(X32802) )
      & ( hBOOL(hAPP(hAPP(c_member(X32802),esk454_3(X32800,X32801,X32802)),hAPP(c_List_Oset(X32802),X32800)))
        | ~ c_List_Olinorder__class_Osorted(X32802,X32800)
        | c_List_Olinorder__class_Osorted(X32802,hAPP(hAPP(c_List_Olist_OCons(X32802),X32801),X32800))
        | ~ class_Orderings_Olinorder(X32802) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32802),X32801),esk454_3(X32800,X32801,X32802)))
        | ~ c_List_Olinorder__class_Osorted(X32802,X32800)
        | c_List_Olinorder__class_Osorted(X32802,hAPP(hAPP(c_List_Olist_OCons(X32802),X32801),X32800))
        | ~ class_Orderings_Olinorder(X32802) ) ),
    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_8674,plain,
    ! [X22965,X22966] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22966))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22965))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X22965),X22966)),X22965) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X22965),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22966),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_8675,plain,
    ! [X24308,X24309,X24310] :
      ( ~ class_Fields_Olinordered__field(X24310)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24310),c_Groups_Ozero__class_Ozero(X24310)),X24309))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24310),c_Groups_Ozero__class_Ozero(X24310)),X24308))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24310),c_Groups_Ozero__class_Ozero(X24310)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24310),X24309),X24308))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__pos])]) ).

fof(i_0_8676,plain,
    ! [X22207,X22208,X22209] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22209)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22209),c_Groups_Ozero__class_Ozero(X22209)),X22208))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22209),c_Groups_Ozero__class_Ozero(X22209)),X22207))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22209),c_Groups_Ozero__class_Ozero(X22209)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22209),X22208),X22207))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).

fof(i_0_8677,plain,
    ! [X22386,X22387,X22388] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22388)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22388),c_Groups_Ozero__class_Ozero(X22388)),X22387))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22388),c_Groups_Ozero__class_Ozero(X22388)),X22386))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22388),c_Groups_Ozero__class_Ozero(X22388)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22388),X22387),X22386))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).

fof(i_0_8678,plain,
    ! [X22383,X22384,X22385] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22385)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22385),c_Groups_Ozero__class_Ozero(X22385)),X22384))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22385),c_Groups_Ozero__class_Ozero(X22385)),X22383))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22385),c_Groups_Ozero__class_Ozero(X22385)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22385),X22384),X22383))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).

fof(i_0_8679,plain,
    ! [X22255,X22256,X22257] :
      ( ~ class_Rings_Olinordered__semiring__strict(X22257)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22257),c_Groups_Ozero__class_Ozero(X22257)),X22256))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22257),c_Groups_Ozero__class_Ozero(X22257)),X22255))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22257),c_Groups_Ozero__class_Ozero(X22257)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22257),X22256),X22255))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__pos])]) ).

fof(i_0_8680,plain,
    ! [X21367,X21368,X21369] :
      ( ~ class_Rings_Olinordered__semidom(X21369)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21369),c_Groups_Oone__class_Oone(X21369)),X21368))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21369),c_Groups_Oone__class_Oone(X21369)),X21367))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21369),c_Groups_Oone__class_Oone(X21369)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21369),X21368),X21367))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__1__mult])]) ).

fof(i_0_8681,plain,
    ! [X24373,X24374,X24375] :
      ( ~ class_Fields_Olinordered__field(X24375)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24375),c_Groups_Ozero__class_Ozero(X24375)),X24374))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24375),c_Groups_Ozero__class_Ozero(X24375)),X24373))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24375),c_Groups_Ozero__class_Ozero(X24375)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24375),X24374),X24373))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonneg__pos])]) ).

fof(i_0_8682,plain,
    ! [X22123,X22124,X22125] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22125)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22125),c_Groups_Ozero__class_Ozero(X22125)),X22124))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22125),c_Groups_Ozero__class_Ozero(X22125)),X22123))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22125),c_Groups_Ozero__class_Ozero(X22125)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22125),X22124),X22123))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).

fof(i_0_8683,plain,
    ! [X22148,X22149,X22150] :
      ( ~ class_Rings_Oordered__cancel__semiring(X22150)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22150),c_Groups_Ozero__class_Ozero(X22150)),X22149))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22150),c_Groups_Ozero__class_Ozero(X22150)),X22148))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22150),c_Groups_Ozero__class_Ozero(X22150)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22150),X22149),X22148))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg])]) ).

fof(i_0_8684,plain,
    ! [X22193,X22194,X22195] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22195),c_Groups_Ozero__class_Ozero(X22195)),X22194))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22195),c_Groups_Ozero__class_Ozero(X22195)),X22193))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22195),c_Groups_Ozero__class_Ozero(X22195)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22195),X22194),X22193)))
        | ~ class_Rings_Oordered__ring(X22195) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22195),X22194),c_Groups_Ozero__class_Ozero(X22195)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22195),X22193),c_Groups_Ozero__class_Ozero(X22195)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22195),c_Groups_Ozero__class_Ozero(X22195)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22195),X22194),X22193)))
        | ~ class_Rings_Oordered__ring(X22195) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le])])]) ).

fof(i_0_8685,plain,
    ! [X21241,X21242,X21243,X21244] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21244),X21243))
      | hAPP(c_Finite__Set_Ocard(X21242),hAPP(c_Set_Oimage(X21244,X21242,X21241),X21243)) != hAPP(c_Finite__Set_Ocard(X21244),X21243)
      | c_Fun_Oinj__on(X21244,X21242,X21241,X21243) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__card__imp__inj__on])]) ).

fof(i_0_8686,plain,
    ! [X21237,X21238,X21239,X21240] :
      ( ( ~ c_Fun_Oinj__on(X21240,X21238,X21237,X21239)
        | hAPP(c_Finite__Set_Ocard(X21238),hAPP(c_Set_Oimage(X21240,X21238,X21237),X21239)) = hAPP(c_Finite__Set_Ocard(X21240),X21239)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21240),X21239)) )
      & ( hAPP(c_Finite__Set_Ocard(X21238),hAPP(c_Set_Oimage(X21240,X21238,X21237),X21239)) != hAPP(c_Finite__Set_Ocard(X21240),X21239)
        | c_Fun_Oinj__on(X21240,X21238,X21237,X21239)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21240),X21239)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__eq__card])])]) ).

fof(i_0_8687,plain,
    ! [X20536,X20537,X20538] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20538,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20538,tc_HOL_Obool)),X20537),X20536)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20538,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20538,tc_HOL_Obool)),X20537)),X20536),
    inference(variable_rename,[status(thm)],[fact_Compl__Diff__eq]) ).

cnf(i_0_8688,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_5803]) ).

fof(i_0_8689,plain,
    ! [X22758,X22759,X22760,X22761] :
      ( ~ class_Rings_Olinordered__semidom(X22761)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22761),X22760),X22759) != hAPP(hAPP(c_Power_Opower__class_Opower(X22761),X22758),X22759)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22761),c_Groups_Ozero__class_Ozero(X22761)),X22760))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22761),c_Groups_Ozero__class_Ozero(X22761)),X22758))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22759))
      | X22760 = X22758 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base])]) ).

cnf(i_0_8690,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_5804]) ).

cnf(i_0_8691,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_5805]) ).

fof(i_0_8692,plain,
    ! [X27679,X27680,X27681,X27682] : hAPP(c_Finite__Set_Ocard(tc_prod(X27682,X27681)),hAPP(hAPP(c_Product__Type_OSigma(X27682,X27681),X27680),hAPP(c_COMBK(tc_fun(X27681,tc_HOL_Obool),X27682),X27679))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X27682),X27680)),hAPP(c_Finite__Set_Ocard(X27681),X27679)),
    inference(variable_rename,[status(thm)],[fact_card__cartesian__product]) ).

fof(i_0_8693,plain,
    ! [X31588,X31589,X31590,X31591] : hAPP(c_Map_Omap__of(X31591,X31590),hAPP(hAPP(c_List_Oappend(tc_prod(X31591,X31590)),X31589),X31588)) = c_Map_Omap__add(X31591,X31590,hAPP(c_Map_Omap__of(X31591,X31590),X31588),hAPP(c_Map_Omap__of(X31591,X31590),X31589)),
    inference(variable_rename,[status(thm)],[fact_map__of__append]) ).

fof(i_0_8694,plain,
    ! [X18220,X18221,X18222,X18223] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X18223),X18222),X18221))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18223,tc_HOL_Obool)),X18221),hAPP(hAPP(c_Set_Oinsert(X18223),X18222),X18220)) = hAPP(hAPP(c_Set_Oinsert(X18223),X18222),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18223,tc_HOL_Obool)),X18221),X18220)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if1])]) ).

fof(i_0_8695,plain,
    ! [X18204,X18205,X18206,X18207] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X18207),X18206),X18205))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18207,tc_HOL_Obool)),X18205),hAPP(hAPP(c_Set_Oinsert(X18207),X18206),X18204)) = hAPP(hAPP(c_Set_Oinsert(X18207),X18206),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18207,tc_HOL_Obool)),X18205),X18204)) )
      & ( hBOOL(hAPP(hAPP(c_member(X18207),X18206),X18205))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18207,tc_HOL_Obool)),X18205),hAPP(hAPP(c_Set_Oinsert(X18207),X18206),X18204)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18207,tc_HOL_Obool)),X18205),X18204) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5806])]) ).

fof(i_0_8696,plain,
    ! [X30937,X30938,X30939,X30940,X30941,X30942,X30943] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30937)),X30939) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30937)),X30938)
        | X30939 != X30938 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30940),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30937)),X30939)))
        | hAPP(hAPP(c_List_Onth(X30937),X30939),X30940) = hAPP(hAPP(c_List_Onth(X30937),X30938),X30940)
        | X30939 != X30938 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk410_3(X30941,X30942,X30943)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30941)),X30943)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30941)),X30943) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30941)),X30942)
        | X30943 = X30942 )
      & ( hAPP(hAPP(c_List_Onth(X30941),X30943),esk410_3(X30941,X30942,X30943)) != hAPP(hAPP(c_List_Onth(X30941),X30942),esk410_3(X30941,X30942,X30943))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30941)),X30943) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30941)),X30942)
        | X30943 = X30942 ) ),
    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_8697,plain,
    ! [X29032,X29033,X29034,X29035,X29036,X29037] :
      ( ~ c_Finite__Set_Ofolding(X29037,X29036,X29035,X29034)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29037),X29033))
      | hAPP(hAPP(X29034,X29033),X29032) = hAPP(hAPP(c_Finite__Set_Ofold(X29037,X29036,X29035),X29032),X29033) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oeq__fold])]) ).

fof(i_0_8698,plain,
    ! [X16999,X17000,X17001,X17002] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X17002,X17001,X17000)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X17002),tc_HOL_Obool)),X16999),X17000))
      | c_Hoare__Mirabelle_Ohoare__derivs(X17002,X17001,X16999) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_weaken])]) ).

fof(i_0_8699,plain,
    ! [X19784,X19785,X19786,X19787,X19788] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X19788)
      | ~ hBOOL(hAPP(hAPP(c_member(X19787),X19786),X19785))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19788),hAPP(X19784,X19786)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19787,X19788),X19785),X19784))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SUPI])]) ).

fof(i_0_8700,plain,
    ! [X23274,X23275,X23276,X23277] :
      ( ~ class_Divides_Osemiring__div(X23277)
      | c_Divides_Odiv__class_Omod(X23277,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23277),c_Divides_Odiv__class_Omod(X23277,X23276,X23275)),X23274),X23275) = c_Divides_Odiv__class_Omod(X23277,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23277),X23276),X23274),X23275) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I1_J])]) ).

fof(i_0_8701,plain,
    ! [X23306,X23307,X23308,X23309] :
      ( ~ class_Divides_Osemiring__div(X23309)
      | c_Divides_Odiv__class_Omod(X23309,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23309),c_Divides_Odiv__class_Omod(X23309,X23308,X23307)),X23306),X23307) = c_Divides_Odiv__class_Omod(X23309,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23309),X23308),X23306),X23307) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I4_J])]) ).

fof(i_0_8702,plain,
    ! [X23286,X23287,X23288,X23289] :
      ( ~ class_Divides_Osemiring__div(X23289)
      | c_Divides_Odiv__class_Omod(X23289,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23289),X23288),X23287),X23286) = c_Divides_Odiv__class_Omod(X23289,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23289),c_Divides_Odiv__class_Omod(X23289,X23288,X23286)),X23287),X23286) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__left__eq])]) ).

fof(i_0_8703,plain,
    ! [X23322,X23323,X23324,X23325] :
      ( ~ class_Divides_Osemiring__div(X23325)
      | c_Divides_Odiv__class_Omod(X23325,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23325),X23324),X23323),X23322) = c_Divides_Odiv__class_Omod(X23325,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23325),c_Divides_Odiv__class_Omod(X23325,X23324,X23322)),X23323),X23322) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__left__eq])]) ).

fof(i_0_8704,plain,
    ! [X23349,X23350,X23351,X23352] :
      ( ~ class_Divides_Oring__div(X23352)
      | c_Divides_Odiv__class_Omod(X23352,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23352),X23351),X23350),X23349) = c_Divides_Odiv__class_Omod(X23352,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23352),c_Divides_Odiv__class_Omod(X23352,X23351,X23349)),X23350),X23349) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__left__eq])]) ).

fof(i_0_8705,plain,
    ! [X18586,X18587,X18588] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18588,tc_HOL_Obool)),X18587),X18586))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18588,tc_HOL_Obool)),X18587),X18586))
        | X18587 = X18586 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18588,tc_HOL_Obool)),X18587),X18586))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18588,tc_HOL_Obool)),X18587),X18586)) )
      & ( X18587 != X18586
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18588,tc_HOL_Obool)),X18587),X18586)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq])])]) ).

fof(i_0_8706,plain,
    ! [X18583,X18584,X18585] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18585,tc_HOL_Obool)),X18584),X18583))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18585,tc_HOL_Obool)),X18584),X18583)) )
      & ( X18584 != X18583
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18585,tc_HOL_Obool)),X18584),X18583)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18585,tc_HOL_Obool)),X18584),X18583))
        | X18584 = X18583
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18585,tc_HOL_Obool)),X18584),X18583)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__eq])])]) ).

fof(i_0_8707,plain,
    ! [X20472,X20473,X20474] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20474),X20473))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20474),X20472))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20474),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20474,tc_HOL_Obool)),X20473),X20472))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UnI])]) ).

fof(i_0_8708,plain,
    ! [X17921,X17922,X17923] : hAPP(c_Set_OPow(X17923),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17923,tc_HOL_Obool)),X17922),X17921)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X17923,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X17923),X17922)),hAPP(c_Set_OPow(X17923),X17921)),
    inference(variable_rename,[status(thm)],[fact_Pow__Int__eq]) ).

fof(i_0_8709,plain,
    ! [X34160,X34161,X34163] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X34161)),X34160))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X34161)),X34163),X34160))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34161)),X34163)),esk531_2(X34160,X34161))) ),
    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_8710,plain,
    ! [X26592,X26593,X26594,X26595] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26594),X26593))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26594,X26595),X26592),X26593) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26595,X26594,c_Groups_Oplus__class_Oplus(X26595)),X26592),c_Groups_Ozero__class_Ozero(X26595)),X26593)
        | ~ class_Groups_Ocomm__monoid__add(X26595) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X26594),X26593))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26594,X26595),X26592),X26593) = c_Groups_Ozero__class_Ozero(X26595)
        | ~ class_Groups_Ocomm__monoid__add(X26595) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5807])])]) ).

fof(i_0_8711,plain,
    ! [X26588,X26589,X26590,X26591] :
      ( ~ class_Groups_Ocomm__monoid__add(X26591)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26590),X26589))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26590,X26591),X26588),X26589) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26591,X26590,c_Groups_Oplus__class_Oplus(X26591)),X26588),c_Groups_Ozero__class_Ozero(X26591)),X26589) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oeq__fold])]) ).

fof(i_0_8712,plain,
    ! [X23204,X23205,X23206,X23207] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23206),X23205))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23206,X23207),X23204),X23205) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X23207,X23206,c_Groups_Otimes__class_Otimes(X23207)),X23204),c_Groups_Oone__class_Oone(X23207)),X23205)
        | ~ class_Groups_Ocomm__monoid__mult(X23207) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X23206),X23205))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23206,X23207),X23204),X23205) = c_Groups_Oone__class_Oone(X23207)
        | ~ class_Groups_Ocomm__monoid__mult(X23207) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5808])])]) ).

fof(i_0_8713,plain,
    ! [X23200,X23201,X23202,X23203] :
      ( ~ class_Groups_Ocomm__monoid__mult(X23203)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23202),X23201))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23202,X23203),X23200),X23201) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X23203,X23202,c_Groups_Otimes__class_Otimes(X23203)),X23200),c_Groups_Oone__class_Oone(X23203)),X23201) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oeq__fold])]) ).

fof(i_0_8714,plain,
    ! [X18589,X18590,X18591] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18591,tc_HOL_Obool)),X18590),X18589))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18591,tc_HOL_Obool)),X18590),X18589)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset])]) ).

fof(i_0_8715,plain,
    ! [X33977,X33978,X33979,X33980] : hAPP(hAPP(c_List_Oappend(X33980),c_List_Oreplicate(X33980,X33979,X33978)),c_List_Oreplicate(X33980,X33977,X33978)) = hAPP(hAPP(c_List_Oappend(X33980),c_List_Oreplicate(X33980,X33977,X33978)),c_List_Oreplicate(X33980,X33979,X33978)),
    inference(variable_rename,[status(thm)],[fact_append__replicate__commute]) ).

fof(i_0_8716,plain,
    ! [X23766,X23767] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23767))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23766),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23767,X23766) = 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),X23767),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23766)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg])]) ).

fof(i_0_8717,plain,
    ! [X31689,X31690,X31691,X31692] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31692),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31691)),X31690)))
        | hAPP(hAPP(c_List_Onth(X31691),hAPP(hAPP(c_List_Oappend(X31691),X31690),X31689)),X31692) = hAPP(hAPP(c_List_Onth(X31691),X31690),X31692) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31692),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31691)),X31690)))
        | hAPP(hAPP(c_List_Onth(X31691),hAPP(hAPP(c_List_Oappend(X31691),X31690),X31689)),X31692) = hAPP(hAPP(c_List_Onth(X31691),X31689),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31692),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31691)),X31690))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5809])]) ).

fof(i_0_8718,plain,
    ! [X20440,X20441,X20442] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20442),X20441),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20442,tc_HOL_Obool)),X20440)))
        | ~ hBOOL(hAPP(hAPP(c_member(X20442),X20441),X20440)) )
      & ( hBOOL(hAPP(hAPP(c_member(X20442),X20441),X20440))
        | hBOOL(hAPP(hAPP(c_member(X20442),X20441),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20442,tc_HOL_Obool)),X20440))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5810])]) ).

fof(i_0_8719,plain,
    ! [X20437,X20438,X20439] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20439),X20438),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20439,tc_HOL_Obool)),X20437)))
      | ~ hBOOL(hAPP(hAPP(c_member(X20439),X20438),X20437)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5811])]) ).

fof(i_0_8720,plain,
    ! [X20434,X20435,X20436] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20436),X20435),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20436,tc_HOL_Obool)),X20434)))
      | ~ hBOOL(hAPP(hAPP(c_member(X20436),X20435),X20434)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5812])]) ).

fof(i_0_8721,plain,
    ! [X26294,X26295,X26296,X26298,X26299,X26300] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk196_2(X26294,X26295)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26295)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26296),X26295))
        | ~ hBOOL(hAPP(X26294,X26296)) )
      & ( hBOOL(hAPP(X26294,esk196_2(X26294,X26295)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26296),X26295))
        | ~ hBOOL(hAPP(X26294,X26296)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk197_2(X26298,X26299)),X26299))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X26300),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26299)))
        | ~ hBOOL(hAPP(X26298,X26300)) )
      & ( hBOOL(hAPP(X26298,esk197_2(X26298,X26299)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X26300),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26299)))
        | ~ hBOOL(hAPP(X26298,X26300)) ) ),
    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_8722,plain,
    ! [X19162,X19163,X19164,X19165] : hAPP(c_Map_Orestrict__map(X19165,X19164,hAPP(c_COMBK(tc_Option_Ooption(X19164),X19165),c_Option_Ooption_ONone(X19164)),X19163),X19162) = c_Option_Ooption_ONone(X19164),
    inference(variable_rename,[status(thm)],[fact_restrict__map__empty]) ).

fof(i_0_8723,plain,
    ! [X31859,X31860,X31861,X31862] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31862) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Odrop(X31861),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31862)),hAPP(hAPP(c_List_Olist_OCons(X31861),X31860),X31859)) = hAPP(hAPP(c_List_Olist_OCons(X31861),X31860),X31859) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31862) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Odrop(X31861),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31862)),hAPP(hAPP(c_List_Olist_OCons(X31861),X31860),X31859)) = hAPP(hAPP(c_List_Odrop(X31861),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31862)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X31859) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__Cons__number__of])]) ).

fof(i_0_8724,plain,
    ! [X28226,X28227] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk294_2(X28226,X28227)),c_Int_OInteg))
        | hBOOL(hAPP(X28227,X28226)) )
      & ( ~ hBOOL(hAPP(X28227,hAPP(c_Int_OAbs__Integ,esk294_2(X28226,X28227))))
        | hBOOL(hAPP(X28227,X28226)) ) ),
    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_8725,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_5813]) ).

fof(i_0_8726,plain,
    ! [X27404,X27405,X27406] :
      ( ~ c_Wellfounded_Owf(X27406,X27405)
      | c_Wellfounded_Owf(X27406,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27406,X27406),tc_HOL_Obool)),X27405),X27404)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Int1])]) ).

fof(i_0_8727,plain,
    ! [X27401,X27402,X27403] :
      ( ~ c_Wellfounded_Owf(X27403,X27402)
      | c_Wellfounded_Owf(X27403,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27403,X27403),tc_HOL_Obool)),X27401),X27402)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Int2])]) ).

fof(i_0_8728,plain,
    ! [X23768,X23769] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23769))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23768),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23769),X23768) = 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),X23769),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23768)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__neg])]) ).

fof(i_0_8729,plain,
    ! [X31991,X31992] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X31992)
      | X31991 = c_List_Olist_ONil(X31992)
      | hAPP(c_Finite__Set_Ofold1(X31992,c_Groups_Otimes__class_Otimes(X31992)),hAPP(c_List_Oset(X31992),X31991)) = hAPP(c_List_Ofoldl(X31992,X31992,c_Groups_Otimes__class_Otimes(X31992),hAPP(c_List_Ohd(X31992),X31991)),hAPP(c_List_Otl(X31992),X31991)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__set])]) ).

fof(i_0_8730,plain,
    ! [X31792,X31793,X31794,X31795,X31796] : hAPP(hAPP(c_List_Odrop(tc_prod(X31796,X31795)),X31794),hAPP(hAPP(c_List_Ozip(X31796,X31795),X31793),X31792)) = hAPP(hAPP(c_List_Ozip(X31796,X31795),hAPP(hAPP(c_List_Odrop(X31796),X31794),X31793)),hAPP(hAPP(c_List_Odrop(X31795),X31794),X31792)),
    inference(variable_rename,[status(thm)],[fact_drop__zip]) ).

fof(i_0_8731,plain,
    ! [X31077,X31078,X31079,X31080,X31081] : hAPP(hAPP(c_List_Otake(tc_prod(X31081,X31080)),X31079),hAPP(hAPP(c_List_Ozip(X31081,X31080),X31078),X31077)) = hAPP(hAPP(c_List_Ozip(X31081,X31080),hAPP(hAPP(c_List_Otake(X31081),X31079),X31078)),hAPP(hAPP(c_List_Otake(X31080),X31079),X31077)),
    inference(variable_rename,[status(thm)],[fact_take__zip]) ).

fof(i_0_8732,plain,
    ! [X26129,X26130,X26131] :
      ( ~ class_Orderings_Olinorder(X26131)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26131),X26130),X26129))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26131,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26131,X26130),X26129)),hAPP(hAPP(c_Set_Oinsert(X26131),X26129),c_Orderings_Obot__class_Obot(tc_fun(X26131,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(X26131,X26130,X26129) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I6_J])]) ).

fof(i_0_8733,plain,
    ! [X23760,X23761] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23761),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23760),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23761,X23760) = 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),X23761),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23760)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__neg])]) ).

fof(i_0_8734,plain,
    ! [X28839,X28840,X28841,X28842,X28843] :
      ( ~ c_Relation_Osingle__valued(X28843,X28842,X28841)
      | ~ c_Relation_Osingle__valued(X28842,X28840,X28839)
      | c_Relation_Osingle__valued(X28843,X28840,hAPP(hAPP(c_Relation_Orel__comp(X28843,X28842,X28840),X28841),X28839)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__rel__comp])]) ).

fof(i_0_8735,plain,
    ! [X32930,X32931] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X32931),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X32931))),c_List_Otranspose(X32931,X32930)))),
    inference(variable_rename,[status(thm)],[fact_sorted__transpose]) ).

fof(i_0_8736,plain,
    ! [X26221,X26222,X26223,X26224,X26225] :
      ( ~ class_Orderings_Olinorder(X26225)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26225,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26225,X26224),X26223)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26225,X26222),X26221)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26225,hAPP(hAPP(c_Orderings_Oord__class_Omax(X26225),X26224),X26222)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X26225),X26223),X26221)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastLessThan])]) ).

fof(i_0_8737,plain,
    ! [X26208,X26209,X26210,X26211,X26212] :
      ( ~ class_Orderings_Olinorder(X26212)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26212,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26212,X26211,X26210)),c_SetInterval_Oord__class_OatLeastAtMost(X26212,X26209,X26208)) = c_SetInterval_Oord__class_OatLeastAtMost(X26212,hAPP(hAPP(c_Orderings_Oord__class_Omax(X26212),X26211),X26209),hAPP(hAPP(c_Orderings_Oord__class_Omin(X26212),X26210),X26208)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMost])]) ).

fof(i_0_8738,plain,
    ! [X25881,X25882,X25883,X25884,X25885] :
      ( ~ class_Orderings_Olinorder(X25885)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25885,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25885,X25884,X25883)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25885,X25882,X25881)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X25885,hAPP(hAPP(c_Orderings_Oord__class_Omax(X25885),X25884),X25882),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25885),X25883),X25881)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greaterThanAtMost])]) ).

fof(i_0_8739,plain,
    ! [X25886,X25887,X25888,X25889,X25890] :
      ( ~ class_Orderings_Olinorder(X25890)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25890,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25890,X25889,X25888)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25890,X25887,X25886)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X25890,hAPP(hAPP(c_Orderings_Oord__class_Omax(X25890),X25889),X25887),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25890),X25888),X25886)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greaterThanLessThan])]) ).

fof(i_0_8740,plain,
    ! [X17568,X17569,X17570,X17571] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17571),X17570),X17569))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17571,tc_HOL_Obool)),X17569),X17568))
      | hBOOL(hAPP(hAPP(c_member(X17571),X17570),X17568)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__rev__mp])]) ).

fof(i_0_8741,plain,
    ! [X18561,X18562,X18563,X18564] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18564,tc_HOL_Obool)),X18563),X18562))
      | ~ hBOOL(hAPP(hAPP(c_member(X18564),X18561),X18563))
      | hBOOL(hAPP(hAPP(c_member(X18564),X18561),X18562)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubsetD])]) ).

fof(i_0_8742,plain,
    ! [X17572,X17573,X17574,X17575] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17575,tc_HOL_Obool)),X17574),X17573))
      | ~ hBOOL(hAPP(hAPP(c_member(X17575),X17572),X17574))
      | hBOOL(hAPP(hAPP(c_member(X17575),X17572),X17573)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mono])]) ).

fof(i_0_8743,plain,
    ! [X17564,X17565,X17566,X17567] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17567,tc_HOL_Obool)),X17566),X17565))
      | ~ hBOOL(hAPP(hAPP(c_member(X17567),X17564),X17566))
      | hBOOL(hAPP(hAPP(c_member(X17567),X17564),X17565)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__mp])]) ).

fof(i_0_8744,plain,
    ! [X17283,X17284,X17285,X17286] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17286,tc_HOL_Obool)),X17285),X17284))
      | ~ hBOOL(hAPP(hAPP(c_member(X17286),X17283),X17285))
      | hBOOL(hAPP(hAPP(c_member(X17286),X17283),X17284)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetD])]) ).

fof(i_0_8745,plain,
    ! [X31653,X31654,X31655,X31656] : hAPP(hAPP(c_List_Onth(X31656),hAPP(hAPP(c_List_Oappend(X31656),X31655),hAPP(hAPP(c_List_Olist_OCons(X31656),X31654),X31653))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31656)),X31655)) = X31654,
    inference(variable_rename,[status(thm)],[fact_nth__append__length]) ).

fof(i_0_8746,plain,
    ! [X25849,X25850,X25851] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25851),hAPP(c_Int_Onumber__class_Onumber__of(X25851),X25850)),hAPP(c_Int_Onumber__class_Onumber__of(X25851),X25849)))
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25851),hAPP(c_Int_Onumber__class_Onumber__of(X25851),X25850)),hAPP(c_Int_Onumber__class_Onumber__of(X25851),X25849)) = hAPP(c_Int_Onumber__class_Onumber__of(X25851),X25849)
        | ~ class_Int_Onumber(X25851)
        | ~ class_Orderings_Oord(X25851) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25851),hAPP(c_Int_Onumber__class_Onumber__of(X25851),X25850)),hAPP(c_Int_Onumber__class_Onumber__of(X25851),X25849)))
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25851),hAPP(c_Int_Onumber__class_Onumber__of(X25851),X25850)),hAPP(c_Int_Onumber__class_Onumber__of(X25851),X25849)) = hAPP(c_Int_Onumber__class_Onumber__of(X25851),X25850)
        | ~ class_Int_Onumber(X25851)
        | ~ class_Orderings_Oord(X25851) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5814])])]) ).

fof(i_0_8747,plain,
    ! [X25423,X25424,X25425] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25425),hAPP(c_Int_Onumber__class_Onumber__of(X25425),X25424)),hAPP(c_Int_Onumber__class_Onumber__of(X25425),X25423)))
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25425),hAPP(c_Int_Onumber__class_Onumber__of(X25425),X25424)),hAPP(c_Int_Onumber__class_Onumber__of(X25425),X25423)) = hAPP(c_Int_Onumber__class_Onumber__of(X25425),X25424)
        | ~ class_Int_Onumber(X25425)
        | ~ class_Orderings_Oord(X25425) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25425),hAPP(c_Int_Onumber__class_Onumber__of(X25425),X25424)),hAPP(c_Int_Onumber__class_Onumber__of(X25425),X25423)))
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25425),hAPP(c_Int_Onumber__class_Onumber__of(X25425),X25424)),hAPP(c_Int_Onumber__class_Onumber__of(X25425),X25423)) = hAPP(c_Int_Onumber__class_Onumber__of(X25425),X25423)
        | ~ class_Int_Onumber(X25425)
        | ~ class_Orderings_Oord(X25425) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5815])])]) ).

fof(i_0_8748,plain,
    ! [X23762,X23763] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23763),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23762),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23763),X23762) = 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),X23763),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23762)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__neg])]) ).

fof(i_0_8749,plain,
    ! [X21428,X21429] : 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)),X21429),X21428),
    inference(variable_rename,[status(thm)],[fact_inj__on__add__nat]) ).

fof(i_0_8750,plain,
    ! [X23138,X23139] :
      ( ( ~ 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),X23138),X23139)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23138))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23139)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23138))
        | 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),X23138),X23139)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23139)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__nonneg__iff])])]) ).

fof(i_0_8751,plain,
    ! [X24277,X24278,X24279,X24280,X24281] :
      ( ~ class_Fields_Ofield__inverse__zero(X24281)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24281),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24281),X24280),X24279)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24281),X24278),X24277)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24281),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24281),X24280),X24278)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24281),X24279),X24277)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__times__eq])]) ).

fof(i_0_8752,plain,
    ! [X21457,X21458,X21459,X21460,X21461] :
      ( ~ class_Rings_Ocomm__semiring__1(X21461)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21461),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21461),X21460),X21459)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21461),X21458),X21457)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21461),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21461),X21460),X21458)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21461),X21459),X21457)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).

fof(i_0_8753,plain,
    ! [X21893,X21894,X21895,X21896,X21897] :
      ( ~ class_Rings_Ocomm__semiring__1(X21897)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21897),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21897),X21896),X21895)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21897),X21894),X21893)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21897),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21897),X21896),X21894)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21897),X21895),X21893)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])]) ).

fof(i_0_8754,plain,
    ! [X21903,X21904,X21905,X21906,X21907] :
      ( ~ class_Rings_Ocomm__semiring__1(X21907)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21907),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21907),X21906),X21905)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21907),X21904),X21903)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21907),X21906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21907),X21905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21907),X21904),X21903))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J])]) ).

fof(i_0_8755,plain,
    ! [X32743,X32744,X32745,X32746,X32747] :
      ( ~ class_Orderings_Olinorder(X32747)
      | ~ c_List_Olinorder__class_Osorted(X32747,hAPP(hAPP(c_List_Omap(X32746,X32747),X32745),X32744))
      | c_List_Olinorder__class_Osorted(X32747,hAPP(hAPP(c_List_Omap(X32746,X32747),X32745),c_List_Oremove1(X32746,X32743,X32744))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__map__remove1])]) ).

fof(i_0_8756,plain,
    ! [X29668,X29669,X29670] : hAPP(c_Relation_ODomain(X29670,X29669),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X29670,X29669),tc_HOL_Obool),X29668)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X29670,X29669),tc_HOL_Obool),tc_fun(X29670,tc_HOL_Obool)),X29668),c_Relation_ODomain(X29670,X29669)),
    inference(variable_rename,[status(thm)],[fact_Domain__Union]) ).

fof(i_0_8757,plain,
    ! [X29679,X29680,X29681] : hAPP(c_Relation_ORange(X29681,X29680),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X29681,X29680),tc_HOL_Obool),X29679)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X29681,X29680),tc_HOL_Obool),tc_fun(X29680,tc_HOL_Obool)),X29679),c_Relation_ORange(X29681,X29680)),
    inference(variable_rename,[status(thm)],[fact_Range__Union]) ).

fof(i_0_8758,plain,
    ! [X26302,X26303,X26305,X26306,X26307,X26309] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk198_2(X26302,X26303)),X26303))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X26305),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26303)))
        | hBOOL(hAPP(X26302,X26305)) )
      & ( ~ hBOOL(hAPP(X26302,esk198_2(X26302,X26303)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X26305),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26303)))
        | hBOOL(hAPP(X26302,X26305)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk199_2(X26306,X26307)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26307)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26309),X26307))
        | hBOOL(hAPP(X26306,X26309)) )
      & ( ~ hBOOL(hAPP(X26306,esk199_2(X26306,X26307)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26309),X26307))
        | hBOOL(hAPP(X26306,X26309)) ) ),
    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_8759,plain,
    ! [X22901,X22902,X22903] :
      ( ~ class_Rings_Oring__1(X22903)
      | ~ hBOOL(hAPP(hAPP(c_member(X22903),X22902),c_Int_Oring__1__class_OInts(X22903)))
      | hBOOL(hAPP(hAPP(c_member(X22903),hAPP(hAPP(c_Power_Opower__class_Opower(X22903),X22902),X22901)),c_Int_Oring__1__class_OInts(X22903))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__power])]) ).

fof(i_0_8760,plain,
    ! [X17595,X17596] : hAPP(c_Set_OCollect(X17596),hAPP(hAPP(c_COMBC(X17596,tc_fun(X17596,tc_HOL_Obool),tc_HOL_Obool),c_member(X17596)),X17595)) = X17595,
    inference(variable_rename,[status(thm)],[fact_Collect__mem__eq]) ).

fof(i_0_8761,plain,
    ! [X22753,X22754] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22754))
      | 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),X22754),X22753))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__one__le__power])]) ).

fof(i_0_8762,plain,
    ! [X22626,X22627,X22628] :
      ( ~ class_Rings_Olinordered__semidom(X22628)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22628),c_Groups_Oone__class_Oone(X22628)),X22627))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22626))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22628),c_Groups_Oone__class_Oone(X22628)),hAPP(hAPP(c_Power_Opower__class_Opower(X22628),X22627),X22626))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__power])]) ).

fof(i_0_8763,plain,
    ! [X24317,X24318,X24319] :
      ( ~ class_Fields_Olinordered__field(X24319)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24319),X24318),c_Groups_Ozero__class_Ozero(X24319)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24319),X24317),c_Groups_Ozero__class_Ozero(X24319)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24319),c_Groups_Ozero__class_Ozero(X24319)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24319),X24318),X24317))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__neg])]) ).

fof(i_0_8764,plain,
    ! [X22233,X22234,X22235] :
      ( ~ class_Rings_Olinordered__ring__strict(X22235)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22235),X22234),c_Groups_Ozero__class_Ozero(X22235)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22235),X22233),c_Groups_Ozero__class_Ozero(X22235)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22235),c_Groups_Ozero__class_Ozero(X22235)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22235),X22234),X22233))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__neg])]) ).

fof(i_0_8765,plain,
    ! [X24349,X24350,X24351] :
      ( ~ class_Fields_Olinordered__field(X24351)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24351),X24350),c_Groups_Ozero__class_Ozero(X24351)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24351),X24349),c_Groups_Ozero__class_Ozero(X24351)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24351),c_Groups_Ozero__class_Ozero(X24351)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24351),X24350),X24349))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonpos__neg])]) ).

fof(i_0_8766,plain,
    ! [X22160,X22161,X22162] :
      ( ~ class_Rings_Oordered__ring(X22162)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22162),X22161),c_Groups_Ozero__class_Ozero(X22162)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22162),X22160),c_Groups_Ozero__class_Ozero(X22162)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22162),c_Groups_Ozero__class_Ozero(X22162)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22162),X22161),X22160))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos])]) ).

fof(i_0_8767,plain,
    ! [X26560,X26561,X26562] :
      ( ~ class_Groups_Ocomm__monoid__add(X26562)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26562),X26561),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26560))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26562),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26562),X26561),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26560))),hAPP(X26561,X26560)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__lessThan__Suc])]) ).

fof(i_0_8768,plain,
    ! [X21668,X21669] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21669),X21668)),X21669)),
    inference(variable_rename,[status(thm)],[i_0_5816]) ).

fof(i_0_8769,plain,
    ! [X21670,X21671] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21671),X21670)),X21670)),
    inference(variable_rename,[status(thm)],[i_0_5817]) ).

fof(i_0_8770,plain,
    ! [X23601,X23602] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23602))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23601))
      | c_Divides_OposDivAlg(X23602,X23601) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23602),X23601)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23602,X23601)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg__div__mod])]) ).

fof(i_0_8771,plain,
    ! [X23136,X23137] :
      ( ( ~ 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),X23136),X23137)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23137),X23136))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23137)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23137),X23136))
        | 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),X23136),X23137)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23137)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__pos__iff])])]) ).

fof(i_0_8772,plain,
    ! [X27499,X27500] : c_List_Olex(X27500,X27499) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X27500),tc_List_Olist(X27500)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X27500,X27499)),
    inference(variable_rename,[status(thm)],[fact_lex__def]) ).

fof(i_0_8773,plain,
    ! [X32589,X32590,X32591,X32592] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X32592),X32591),hAPP(c_List_Oset(X32592),X32590)))
        | c_List_Oremove1(X32592,X32591,hAPP(hAPP(c_List_Oappend(X32592),X32590),X32589)) = hAPP(hAPP(c_List_Oappend(X32592),c_List_Oremove1(X32592,X32591,X32590)),X32589) )
      & ( hBOOL(hAPP(hAPP(c_member(X32592),X32591),hAPP(c_List_Oset(X32592),X32590)))
        | c_List_Oremove1(X32592,X32591,hAPP(hAPP(c_List_Oappend(X32592),X32590),X32589)) = hAPP(hAPP(c_List_Oappend(X32592),X32590),c_List_Oremove1(X32592,X32591,X32589)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5818])]) ).

cnf(i_0_8774,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_5819]) ).

fof(i_0_8775,plain,
    ! [X25775,X25776,X25777,X25778] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25778),X25777),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25778),X25776),X25775)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25778),X25777),X25776))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25778),X25777),X25775))
        | ~ class_Orderings_Olinorder(X25778) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25778),X25777),X25776))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25778),X25777),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25778),X25776),X25775)))
        | ~ class_Orderings_Olinorder(X25778) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25778),X25777),X25775))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25778),X25777),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25778),X25776),X25775)))
        | ~ class_Orderings_Olinorder(X25778) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__max__iff__disj])])]) ).

fof(i_0_8776,plain,
    ! [X25779,X25780,X25781,X25782] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25782),X25781),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25782),X25780),X25779)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25782),X25781),X25780))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25782),X25781),X25779))
        | ~ class_Orderings_Olinorder(X25782) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25782),X25781),X25780))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25782),X25781),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25782),X25780),X25779)))
        | ~ class_Orderings_Olinorder(X25782) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25782),X25781),X25779))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25782),X25781),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25782),X25780),X25779)))
        | ~ class_Orderings_Olinorder(X25782) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__max__iff__disj])])]) ).

cnf(i_0_8777,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin)),
    inference(split_conjunct,[status(thm)],[i_0_5820]) ).

fof(i_0_8778,plain,
    ! [X19181,X19182,X19183] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X19183,X19182,c_Orderings_Obot__class_Obot(tc_fun(X19183,tc_HOL_Obool))),X19181)),
    inference(variable_rename,[status(thm)],[i_0_5821]) ).

fof(i_0_8779,plain,
    ! [X23125,X23126] :
      ( ( ~ 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),X23125),X23126)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23125),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23126),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23125),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),X23125),X23126)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23126),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_8780,plain,
    ! [X31313,X31314] :
      ( X31314 = c_List_Olist_ONil(X31313)
      | c_Random_Oselect__weight(X31313,hAPP(hAPP(c_List_Omap(X31313,tc_prod(tc_Code__Numeral_Ocode__numeral,X31313)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X31313),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X31314)) = c_Random_Oselect(X31313,X31314) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_select__weigth__select])]) ).

fof(i_0_8781,plain,
    ! [X29571,X29572,X29573] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X29572,tc_HOL_Obool)),X29573),X29571))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29572),X29573))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X29572),c_Complete__Lattice_OInf__class_OInf(tc_fun(X29572,tc_HOL_Obool),X29571))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Inter])])]) ).

fof(i_0_8782,plain,
    ! [X27108,X27109,X27110] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27110),c_Groups_Ozero__class_Ozero(X27110)),X27108))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27110),c_Groups_Ozero__class_Ozero(X27110)),X27109))
        | hAPP(c_Groups_Oabs__class_Oabs(X27110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27110),X27109),X27108)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27110),hAPP(c_Groups_Oabs__class_Oabs(X27110),X27109)),hAPP(c_Groups_Oabs__class_Oabs(X27110),X27108))
        | ~ class_Rings_Oordered__ring__abs(X27110) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27110),X27108),c_Groups_Ozero__class_Ozero(X27110)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27110),c_Groups_Ozero__class_Ozero(X27110)),X27109))
        | hAPP(c_Groups_Oabs__class_Oabs(X27110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27110),X27109),X27108)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27110),hAPP(c_Groups_Oabs__class_Oabs(X27110),X27109)),hAPP(c_Groups_Oabs__class_Oabs(X27110),X27108))
        | ~ class_Rings_Oordered__ring__abs(X27110) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27110),c_Groups_Ozero__class_Ozero(X27110)),X27108))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27110),X27109),c_Groups_Ozero__class_Ozero(X27110)))
        | hAPP(c_Groups_Oabs__class_Oabs(X27110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27110),X27109),X27108)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27110),hAPP(c_Groups_Oabs__class_Oabs(X27110),X27109)),hAPP(c_Groups_Oabs__class_Oabs(X27110),X27108))
        | ~ class_Rings_Oordered__ring__abs(X27110) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27110),X27108),c_Groups_Ozero__class_Ozero(X27110)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27110),X27109),c_Groups_Ozero__class_Ozero(X27110)))
        | hAPP(c_Groups_Oabs__class_Oabs(X27110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27110),X27109),X27108)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27110),hAPP(c_Groups_Oabs__class_Oabs(X27110),X27109)),hAPP(c_Groups_Oabs__class_Oabs(X27110),X27108))
        | ~ class_Rings_Oordered__ring__abs(X27110) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__mult])])]) ).

cnf(i_0_8783,plain,
    ( X1 = X2
    | c_Int_OBit1(X1) != c_Int_OBit1(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5822]) ).

fof(i_0_8784,plain,
    ! [X32173,X32174,X32175] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32175),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32174)),X32173)))
      | c_List_Obutlast(X32174,hAPP(hAPP(c_List_Otake(X32174),X32175),X32173)) = hAPP(hAPP(c_List_Otake(X32174),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X32175),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X32173) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__take])]) ).

fof(i_0_8785,plain,
    ! [X26409,X26410] :
      ( ~ class_Orderings_Oorder(X26410)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26410,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X26410),X26409),c_Orderings_Obot__class_Obot(tc_fun(X26410,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X26410),X26409)) = hAPP(hAPP(c_Set_Oinsert(X26410),X26409),c_Orderings_Obot__class_Obot(tc_fun(X26410,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__Diff__lessThan])]) ).

fof(i_0_8786,plain,
    ! [X18062,X18063,X18064,X18065,X18066,X18067,X18068,X18069] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18064,tc_HOL_Obool)),X18063),X18062) != c_Orderings_Obot__class_Obot(tc_fun(X18064,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(X18064),X18065),X18063))
        | ~ hBOOL(hAPP(hAPP(c_member(X18064),X18066),X18062))
        | X18065 != X18066 )
      & ( hBOOL(hAPP(hAPP(c_member(X18069),esk23_3(X18067,X18068,X18069)),X18068))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18069,tc_HOL_Obool)),X18068),X18067) = c_Orderings_Obot__class_Obot(tc_fun(X18069,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X18069),esk24_3(X18067,X18068,X18069)),X18067))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18069,tc_HOL_Obool)),X18068),X18067) = c_Orderings_Obot__class_Obot(tc_fun(X18069,tc_HOL_Obool)) )
      & ( esk23_3(X18067,X18068,X18069) = esk24_3(X18067,X18068,X18069)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18069,tc_HOL_Obool)),X18068),X18067) = c_Orderings_Obot__class_Obot(tc_fun(X18069,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_8787,plain,
    ! [X32831,X32832,X32833] :
      ( ~ class_Orderings_Olinorder(X32833)
      | ~ hBOOL(hAPP(hAPP(c_member(X32833),X32832),hAPP(c_List_Oset(X32833),X32831)))
      | ~ c_List_Olinorder__class_Osorted(X32833,X32831)
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32833,X32833,c_COMBI(X32833)),X32832),c_List_Oremove1(X32833,X32832,X32831)) = X32831 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__remove1])]) ).

fof(i_0_8788,plain,
    ! [X23599,X23600] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23600),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)),X23599))
      | c_Divides_OnegDivAlg(X23600,X23599) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23600),X23599)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23600,X23599)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg__div__mod])]) ).

fof(i_0_8789,plain,
    ! [X25897,X25898,X25899] :
      ( ~ class_Orderings_Olinorder(X25899)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25899),X25898))
      | X25897 = c_Orderings_Obot__class_Obot(tc_fun(X25899,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25899,tc_HOL_Obool)),X25897),X25898))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25899),c_Big__Operators_Olinorder__class_OMax(X25899,X25897)),c_Big__Operators_Olinorder__class_OMax(X25899,X25898)) = c_Big__Operators_Olinorder__class_OMax(X25899,X25898) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Osubset__idem])]) ).

fof(i_0_8790,plain,
    ! [X25473,X25474,X25475] :
      ( ~ class_Orderings_Olinorder(X25475)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25475),X25474))
      | X25473 = c_Orderings_Obot__class_Obot(tc_fun(X25475,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25475,tc_HOL_Obool)),X25473),X25474))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25475),c_Big__Operators_Olinorder__class_OMin(X25475,X25473)),c_Big__Operators_Olinorder__class_OMin(X25475,X25474)) = c_Big__Operators_Olinorder__class_OMin(X25475,X25474) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Osubset__idem])]) ).

fof(i_0_8791,plain,
    ! [X20864,X20865,X20866] :
      ( ~ class_Lattices_Olattice(X20866)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20866),X20865))
      | X20864 = c_Orderings_Obot__class_Obot(tc_fun(X20866,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20866,tc_HOL_Obool)),X20864),X20865))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20866),c_Big__Operators_Olattice__class_OInf__fin(X20866,X20864)),c_Big__Operators_Olattice__class_OInf__fin(X20866,X20865)) = c_Big__Operators_Olattice__class_OInf__fin(X20866,X20865) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osubset__idem])]) ).

fof(i_0_8792,plain,
    ! [X20861,X20862,X20863] :
      ( ~ class_Lattices_Olattice(X20863)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20863),X20862))
      | X20861 = c_Orderings_Obot__class_Obot(tc_fun(X20863,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20863,tc_HOL_Obool)),X20861),X20862))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20863),c_Big__Operators_Olattice__class_OSup__fin(X20863,X20861)),c_Big__Operators_Olattice__class_OSup__fin(X20863,X20862)) = c_Big__Operators_Olattice__class_OSup__fin(X20863,X20862) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osubset__idem])]) ).

fof(i_0_8793,plain,
    ! [X23392,X23393,X23394] : 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,X23394,X23393)),X23392),X23393) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X23394),X23392),X23393),
    inference(variable_rename,[status(thm)],[fact_zpower__zmod]) ).

fof(i_0_8794,plain,
    ! [X23383,X23384,X23385] : 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,X23385,X23384)),X23383),X23384) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23385),X23383),X23384),
    inference(variable_rename,[status(thm)],[fact_zdiff__zmod__left]) ).

fof(i_0_8795,plain,
    ! [X29641,X29642,X29643,X29644] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29643),X29642),c_Complete__Lattice_OInf__class_OInf(X29643,X29641)))
        | ~ hBOOL(hAPP(hAPP(c_member(X29643),X29644),X29641))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29643),X29642),X29644))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X29643) )
      & ( hBOOL(hAPP(hAPP(c_member(X29643),esk362_3(X29641,X29642,X29643)),X29641))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29643),X29642),c_Complete__Lattice_OInf__class_OInf(X29643,X29641)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X29643) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29643),X29642),esk362_3(X29641,X29642,X29643)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29643),X29642),c_Complete__Lattice_OInf__class_OInf(X29643,X29641)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X29643) ) ),
    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_8796,plain,
    ! [X31449,X31450,X31451,X31452] :
      ( ( X31452 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(X31451),X31452),hAPP(hAPP(c_List_Olist_OCons(X31451),X31450),X31449)) = c_List_Olist_ONil(X31451) )
      & ( X31452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(X31451),X31452),hAPP(hAPP(c_List_Olist_OCons(X31451),X31450),X31449)) = hAPP(hAPP(c_List_Olist_OCons(X31451),X31450),hAPP(hAPP(c_List_Otake(X31451),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31452),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X31449)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Cons_H])]) ).

fof(i_0_8797,plain,
    ! [X17789,X17790,X17791,X17792] :
      ( ~ hBOOL(hAPP(X17792,X17791))
      | ~ hBOOL(hAPP(X17790,X17791))
      | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17789,tc_HOL_Obool)),X17792),X17790),X17791)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1I])]) ).

fof(i_0_8798,plain,
    ! [X33511,X33512,X33513,X33515,X33516,X33517,X33518] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33513),esk494_3(X33511,X33512,X33513)),hAPP(c_List_Oset(X33513),X33511)))
        | ~ c_List_Olist__ex(X33513,X33512,X33511) )
      & ( hBOOL(hAPP(X33512,esk494_3(X33511,X33512,X33513)))
        | ~ c_List_Olist__ex(X33513,X33512,X33511) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X33517),X33518),hAPP(c_List_Oset(X33517),X33515)))
        | ~ hBOOL(hAPP(X33516,X33518))
        | c_List_Olist__ex(X33517,X33516,X33515) ) ),
    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_8799,plain,
    ! [X25612] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X25612)),c_Int_OInteg)),
    inference(variable_rename,[status(thm)],[fact_Rep__Integ]) ).

fof(i_0_8800,plain,
    ! [X21117,X21118,X21119,X21120,X21121] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X21121,X21120,X21119)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21121),X21118))
      | X21118 = c_Orderings_Obot__class_Obot(tc_fun(X21121,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21121),X21117))
      | X21117 = c_Orderings_Obot__class_Obot(tc_fun(X21121,tc_HOL_Obool))
      | hAPP(X21119,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21121,tc_HOL_Obool)),X21118),X21117)) = hAPP(hAPP(X21120,hAPP(X21119,X21118)),hAPP(X21119,X21117)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ounion__idem])]) ).

fof(i_0_8801,plain,
    ! [X33140,X33141,X33142,X33143,X33144,X33145,X33146] :
      ( ( ~ hBOOL(hAPP(c_List_Olistsp(X33142,X33141),X33140))
        | ~ hBOOL(hAPP(hAPP(c_member(X33142),X33143),hAPP(c_List_Oset(X33142),X33140)))
        | hBOOL(hAPP(X33141,X33143)) )
      & ( hBOOL(hAPP(hAPP(c_member(X33146),esk467_3(X33144,X33145,X33146)),hAPP(c_List_Oset(X33146),X33144)))
        | hBOOL(hAPP(c_List_Olistsp(X33146,X33145),X33144)) )
      & ( ~ hBOOL(hAPP(X33145,esk467_3(X33144,X33145,X33146)))
        | hBOOL(hAPP(c_List_Olistsp(X33146,X33145),X33144)) ) ),
    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_8802,plain,
    ! [X22393,X22394,X22395,X22396] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22396)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22396),c_Groups_Ozero__class_Ozero(X22396)),X22395))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22396),X22394),X22393))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22396),X22394),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22396),X22395),X22393))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).

fof(i_0_8803,plain,
    ! [X22389,X22390,X22391,X22392] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22392)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22392),c_Groups_Ozero__class_Ozero(X22392)),X22391))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22392),X22390),X22389))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22392),X22390),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22392),X22391),X22389))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).

fof(i_0_8804,plain,
    ! [X22199,X22200,X22201,X22202] :
      ( ~ class_Rings_Olinordered__semidom(X22202)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22202),c_Groups_Ozero__class_Ozero(X22202)),X22201))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22202),X22200),X22199))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22202),X22200),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22202),X22201),X22199))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).

fof(i_0_8805,plain,
    ! [X22129,X22130,X22131,X22132] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22132)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22132),c_Groups_Ozero__class_Ozero(X22132)),X22131))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22132),X22130),X22129))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22132),X22130),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22132),X22131),X22129))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).

fof(i_0_8806,plain,
    ! [X22133,X22134,X22135,X22136] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X22136)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22136),c_Groups_Ozero__class_Ozero(X22136)),X22135))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22136),X22134),X22133))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22136),X22134),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22136),X22133),X22135))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).

fof(i_0_8807,plain,
    ! [X23489,X23490] : X23490 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23489),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23490),X23489))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23490,X23489)),
    inference(variable_rename,[status(thm)],[fact_zmod__zdiv__equality]) ).

cnf(i_0_8808,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_5823]) ).

fof(i_0_8809,plain,
    ! [X25360,X25361,X25362,X25363] :
      ( ~ class_Orderings_Olinorder(X25363)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25363),X25362),X25361))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25363),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25363),X25362),X25360)),X25361)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__infI1])]) ).

fof(i_0_8810,plain,
    ! [X25356,X25357,X25358,X25359] :
      ( ~ class_Orderings_Olinorder(X25359)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25359),X25358),X25357))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25359),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25359),X25356),X25358)),X25357)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__infI2])]) ).

fof(i_0_8811,plain,
    ! [X18575,X18576,X18577,X18578] :
      ( ~ class_Lattices_Osemilattice__inf(X18578)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18578),X18577),X18576))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18578),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18578),X18577),X18575)),X18576)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__infI1])]) ).

fof(i_0_8812,plain,
    ! [X18579,X18580,X18581,X18582] :
      ( ~ class_Lattices_Osemilattice__inf(X18582)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18582),X18581),X18580))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18582),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18582),X18579),X18581)),X18580)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__infI2])]) ).

fof(i_0_8813,plain,
    ! [X25403,X25404,X25405,X25406] :
      ( ~ class_Orderings_Olinorder(X25406)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25406),X25405),X25404))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25406),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25406),X25405),X25403)),X25404)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI1])]) ).

fof(i_0_8814,plain,
    ! [X25399,X25400,X25401,X25402] :
      ( ~ class_Orderings_Olinorder(X25402)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25402),X25401),X25400))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25402),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25402),X25399),X25401)),X25400)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI2])]) ).

fof(i_0_8815,plain,
    ! [X17983,X17984,X17985,X17986] :
      ( ~ class_Lattices_Osemilattice__inf(X17986)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17986),X17985),X17984))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17986),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17986),X17985),X17983)),X17984)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI1])]) ).

fof(i_0_8816,plain,
    ! [X17979,X17980,X17981,X17982] :
      ( ~ class_Lattices_Osemilattice__inf(X17982)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17982),X17981),X17980))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17982),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17982),X17979),X17981)),X17980)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI2])]) ).

fof(i_0_8817,plain,
    ! [X31458,X31459] : hAPP(c_Relation_OImage(tc_List_Olist(X31459),tc_List_Olist(X31459),c_List_Olistrel(X31459,X31458)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X31459)),c_List_Olist_ONil(X31459)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X31459),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X31459)),c_List_Olist_ONil(X31459)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X31459),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_listrel__Nil]) ).

fof(i_0_8818,plain,
    ! [X26712,X26713,X26714,X26715] :
      ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26714,tc_Nat_Onat),X26712),X26713) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X26714),X26715),X26713))
        | hAPP(X26712,X26715) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26714),X26713)) )
      & ( hBOOL(hAPP(hAPP(c_member(X26714),esk232_3(X26712,X26713,X26714)),X26713))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26714,tc_Nat_Onat),X26712),X26713) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26714),X26713)) )
      & ( hAPP(X26712,esk232_3(X26712,X26713,X26714)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26714,tc_Nat_Onat),X26712),X26713) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26714),X26713)) ) ),
    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_8819,plain,
    ! [X23051,X23052,X23053,X23054] :
      ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23053,tc_Nat_Onat),X23051),X23052) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X23053),X23054),X23052))
        | hAPP(X23051,X23054) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23053),X23052)) )
      & ( hBOOL(hAPP(hAPP(c_member(X23053),esk119_3(X23051,X23052,X23053)),X23052))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23053,tc_Nat_Onat),X23051),X23052) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23053),X23052)) )
      & ( hAPP(X23051,esk119_3(X23051,X23052,X23053)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23053,tc_Nat_Onat),X23051),X23052) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23053),X23052)) ) ),
    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_8820,plain,
    ! [X19267,X19268,X19269,X19270,X19271] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X19271),X19270),X19269))
        | hAPP(c_Map_Orestrict__map(X19271,X19268,X19267,X19269),X19270) = hAPP(X19267,X19270) )
      & ( hBOOL(hAPP(hAPP(c_member(X19271),X19270),X19269))
        | hAPP(c_Map_Orestrict__map(X19271,X19268,X19267,X19269),X19270) = c_Option_Ooption_ONone(X19268) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5824])]) ).

fof(i_0_8821,plain,
    ! [X18932,X18933,X18934,X18935,X18936] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X18936),X18935),X18934))
      | hAPP(c_Map_Orestrict__map(X18936,X18933,X18932,X18934),X18935) = hAPP(X18932,X18935) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_restrict__in])]) ).

fof(i_0_8822,plain,
    ! [X22485,X22486,X22487,X22488,X22489,X22490,X22491] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22486),X22485))
        | hBOOL(hAPP(X22487,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X22487,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22486),X22485))) )
      & ( X22486 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22485),X22488)
        | hBOOL(hAPP(X22487,X22488))
        | ~ hBOOL(hAPP(X22487,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22486),X22485))) )
      & ( X22490 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22489),esk113_3(X22489,X22490,X22491))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22490),X22489))
        | hBOOL(hAPP(X22491,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22490),X22489))) )
      & ( ~ hBOOL(hAPP(X22491,esk113_3(X22489,X22490,X22491)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22490),X22489))
        | hBOOL(hAPP(X22491,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22490),X22489))) )
      & ( X22490 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22489),esk113_3(X22489,X22490,X22491))
        | ~ hBOOL(hAPP(X22491,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X22491,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22490),X22489))) )
      & ( ~ hBOOL(hAPP(X22491,esk113_3(X22489,X22490,X22491)))
        | ~ hBOOL(hAPP(X22491,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X22491,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22490),X22489))) ) ),
    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_8823,plain,
    ! [X22477,X22478,X22479,X22480,X22481,X22482,X22483] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22478),X22477))
        | hBOOL(hAPP(X22479,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X22479,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22478),X22477))) )
      & ( X22478 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22477),X22480)
        | hBOOL(hAPP(X22479,X22480))
        | ~ hBOOL(hAPP(X22479,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22478),X22477))) )
      & ( X22482 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22481),esk112_3(X22481,X22482,X22483))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22482),X22481))
        | hBOOL(hAPP(X22483,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22482),X22481))) )
      & ( ~ hBOOL(hAPP(X22483,esk112_3(X22481,X22482,X22483)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22482),X22481))
        | hBOOL(hAPP(X22483,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22482),X22481))) )
      & ( X22482 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22481),esk112_3(X22481,X22482,X22483))
        | ~ hBOOL(hAPP(X22483,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X22483,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22482),X22481))) )
      & ( ~ hBOOL(hAPP(X22483,esk112_3(X22481,X22482,X22483)))
        | ~ hBOOL(hAPP(X22483,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X22483,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22482),X22481))) ) ),
    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_5825])])])])])]) ).

fof(i_0_8824,plain,
    ! [X20403,X20404] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20404),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20404,tc_HOL_Obool)),X20403)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20404),c_Orderings_Otop__class_Otop(tc_fun(X20404,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20404),X20403)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20404),c_Orderings_Otop__class_Otop(tc_fun(X20404,tc_HOL_Obool))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20404),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20404,tc_HOL_Obool)),X20403)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20404),X20403)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__compl])])]) ).

fof(i_0_8825,plain,
    ! [X24647,X24648] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24648),X24647))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X24647))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24648)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24647))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24648),X24647))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24648)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24647))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24648),X24647))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24648),X24647))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24648)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24647))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X24647))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24648),X24647))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24648)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24647))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__nat__number__of])])]) ).

fof(i_0_8826,plain,
    ! [X17491,X17492,X17493,X17494] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17494,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17494),X17493),X17492)),X17491) = hAPP(hAPP(c_Set_Oinsert(X17494),X17493),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17494,tc_HOL_Obool)),X17492),X17491)),
    inference(variable_rename,[status(thm)],[fact_Un__insert__left]) ).

cnf(i_0_8827,plain,
    ( c_Map_Omap__comp(X3,X6,X8,X5,X1,X2) = hAPP(c_Option_Ooption_OSome(X6),X7)
    | hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4)
    | hAPP(X5,X4) != hAPP(c_Option_Ooption_OSome(X6),X7) ),
    inference(split_conjunct,[status(thm)],[i_0_5326]) ).

fof(i_0_8828,plain,
    ! [X18913,X18914,X18915,X18916] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X18916,X18915,X18914)
      | hAPP(c_Fun_Ocomp(X18915,X18915,X18915,hAPP(X18914,X18913)),hAPP(X18914,X18913)) = hAPP(X18914,X18913) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__comp__idem])]) ).

fof(i_0_8829,plain,
    ! [X30863,X30864,X30865,X30866] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30866)),X30865) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30864)),X30863)
      | ~ hBOOL(hAPP(c_List_Odistinct(X30866),X30865))
      | c_Map_Odom(X30866,X30864,hAPP(c_Map_Omap__of(X30866,X30864),hAPP(hAPP(c_List_Ozip(X30866,X30864),X30865),X30863))) = hAPP(c_List_Oset(X30866),X30865) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dom__map__of__zip])]) ).

cnf(i_0_8830,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_5774]) ).

fof(i_0_8831,plain,
    ! [X23504,X23505,X23506,X23507] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X23507,X23506),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X23505),X23504)))
      | X23506 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23507,X23506) = X23504 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__mod])]) ).

fof(i_0_8832,plain,
    ! [X23940,X23941,X23942] : hAPP(c_Product__Type_Osnd(X23942,X23941),X23940) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X23942,X23941,X23941),hAPP(c_COMBK(tc_fun(X23941,X23941),X23942),c_COMBI(X23941))),X23940),
    inference(variable_rename,[status(thm)],[fact_snd__def]) ).

fof(i_0_8833,plain,
    ! [X22906,X22907] :
      ( ~ class_Int_Oring__char__0(X22907)
      | ~ hBOOL(hAPP(hAPP(c_member(X22907),X22906),c_Int_Oring__1__class_OInts(X22907)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22907),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22907),c_Groups_Oone__class_Oone(X22907)),X22906)),X22906) != c_Groups_Ozero__class_Ozero(X22907) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__nonzero])]) ).

fof(i_0_8834,plain,
    ! [X20333,X20334,X20335] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20335),X20334))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20335),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20335,tc_HOL_Obool)),X20334),X20333))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20335),X20333))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20335),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20335,tc_HOL_Obool)),X20334),X20333))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Int])])]) ).

fof(i_0_8835,plain,
    ! [X20336,X20337,X20338] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20338),X20337))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20338),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20338,tc_HOL_Obool)),X20337),X20336))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff])]) ).

fof(i_0_8836,plain,
    ! [X32791,X32792,X32793,X32794] :
      ( ~ class_Orderings_Olinorder(X32794)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32794),X32793),X32792))
      | ~ c_List_Olinorder__class_Osorted(X32794,hAPP(hAPP(c_List_Olist_OCons(X32794),X32792),X32791))
      | c_List_Olinorder__class_Osorted(X32794,hAPP(hAPP(c_List_Olist_OCons(X32794),X32793),hAPP(hAPP(c_List_Olist_OCons(X32794),X32792),X32791))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__many])]) ).

fof(i_0_8837,plain,
    ! [X32787,X32788,X32789,X32790] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32790),X32789),X32788))
        | ~ c_List_Olinorder__class_Osorted(X32790,hAPP(hAPP(c_List_Olist_OCons(X32790),X32789),hAPP(hAPP(c_List_Olist_OCons(X32790),X32788),X32787)))
        | ~ class_Orderings_Olinorder(X32790) )
      & ( c_List_Olinorder__class_Osorted(X32790,hAPP(hAPP(c_List_Olist_OCons(X32790),X32788),X32787))
        | ~ c_List_Olinorder__class_Osorted(X32790,hAPP(hAPP(c_List_Olist_OCons(X32790),X32789),hAPP(hAPP(c_List_Olist_OCons(X32790),X32788),X32787)))
        | ~ class_Orderings_Olinorder(X32790) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32790),X32789),X32788))
        | ~ c_List_Olinorder__class_Osorted(X32790,hAPP(hAPP(c_List_Olist_OCons(X32790),X32788),X32787))
        | c_List_Olinorder__class_Osorted(X32790,hAPP(hAPP(c_List_Olist_OCons(X32790),X32789),hAPP(hAPP(c_List_Olist_OCons(X32790),X32788),X32787)))
        | ~ class_Orderings_Olinorder(X32790) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__many__eq])])]) ).

fof(i_0_8838,plain,
    ! [X23722,X23723,X23724,X23725] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23725,X23724),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X23723),X23722)))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23725,X23724) = X23722 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__eq])]) ).

fof(i_0_8839,plain,
    ! [X23475,X23476] :
      ( ( 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,X23475,X23476)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23476)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23475,X23476)),X23476))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23476)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__conj])])]) ).

fof(i_0_8840,plain,
    ! [X23424,X23425] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23425))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23424,X23425)),X23425)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__bound])]) ).

fof(i_0_8841,plain,
    ! [X23643,X23644] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23644))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23643,X23644)),X23644)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__less__divisor])]) ).

fof(i_0_8842,plain,
    ! [X23420,X23421] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23421))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23421,X23420)),X23421)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__le__nonneg__dividend])]) ).

fof(i_0_8843,plain,
    ! [X23672,X23673] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23673))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23672,X23673)),X23673)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__le__divisor])]) ).

fof(i_0_8844,plain,
    ! [X32498,X32499] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32499)),c_List_Oremdups(X32499,X32498))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32499)),X32498))),
    inference(variable_rename,[status(thm)],[fact_length__remdups__leq]) ).

fof(i_0_8845,plain,
    ! [X30504,X30505] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X30505),hAPP(c_List_Oset(X30505),X30504))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30505)),X30504))),
    inference(variable_rename,[status(thm)],[fact_card__length]) ).

fof(i_0_8846,plain,
    ! [X18155,X18156,X18157,X18158,X18159] :
      ( hAPP(c_Set_Oimage(X18159,X18158,X18157),X18156) != X18155
      | hAPP(c_Set_Oimage(tc_fun(X18159,tc_HOL_Obool),tc_fun(X18158,tc_HOL_Obool),c_Set_Oimage(X18159,X18158,X18157)),hAPP(c_Set_OPow(X18159),X18156)) = hAPP(c_Set_OPow(X18158),X18155) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Pow__surj])]) ).

fof(i_0_8847,plain,
    ! [X30437,X30438,X30439] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X30439),X30438),hAPP(c_List_Oset(X30439),X30437)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30439),hAPP(hAPP(c_List_Olist_OCons(X30439),X30438),X30437))) )
      & ( hBOOL(hAPP(c_List_Odistinct(X30439),X30437))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30439),hAPP(hAPP(c_List_Olist_OCons(X30439),X30438),X30437))) )
      & ( hBOOL(hAPP(hAPP(c_member(X30439),X30438),hAPP(c_List_Oset(X30439),X30437)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30439),X30437))
        | hBOOL(hAPP(c_List_Odistinct(X30439),hAPP(hAPP(c_List_Olist_OCons(X30439),X30438),X30437))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5826])])]) ).

fof(i_0_8848,plain,
    ! [X19474,X19475,X19476,X19477] :
      ( hAPP(c_Set_Oimage(X19477,X19476,X19475),c_Orderings_Otop__class_Otop(tc_fun(X19477,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X19476,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(X19477,X19476,X19475),hAPP(c_Set_Ovimage(X19477,X19476,X19475),X19474)) = X19474 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__image__vimage__eq])]) ).

cnf(i_0_8849,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_5753]) ).

fof(i_0_8850,plain,
    ! [X22987,X22988,X22989,X22990] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22990,X22989),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22988),X22987)))
      | X22989 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22990),X22989) = X22988 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div])]) ).

fof(i_0_8851,plain,
    ! [X28266,X28267,X28268] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28268),c_Map_Odom(X28268,X28267,X28266)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X28268),c_Orderings_Otop__class_Otop(tc_fun(X28268,tc_HOL_Obool))))
      | hAPP(X28266,esk303_3(X28266,X28267,X28268)) = c_Option_Ooption_ONone(X28267) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5827])])]) ).

fof(i_0_8852,plain,
    ! [X20428,X20429,X20430] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20430),hAPP(c_Groups_Ouminus__class_Ouminus(X20430),X20429)),X20428))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20430),hAPP(c_Groups_Ouminus__class_Ouminus(X20430),X20428)),X20429))
        | ~ class_Groups_Oordered__ab__group__add(X20430) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20430),hAPP(c_Groups_Ouminus__class_Ouminus(X20430),X20428)),X20429))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20430),hAPP(c_Groups_Ouminus__class_Ouminus(X20430),X20429)),X20428))
        | ~ class_Groups_Oordered__ab__group__add(X20430) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__less__iff])])]) ).

fof(i_0_8853,plain,
    ! [X27087,X27088,X27089] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27089)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27089),hAPP(c_Groups_Oabs__class_Oabs(X27089),X27088)),X27087))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27089),hAPP(c_Groups_Ouminus__class_Ouminus(X27089),X27088)),X27087)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D2])]) ).

fof(i_0_8854,plain,
    ! [X20419,X20420,X20421] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20421),hAPP(c_Groups_Ouminus__class_Ouminus(X20421),X20420)),X20419))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20421),hAPP(c_Groups_Ouminus__class_Ouminus(X20421),X20419)),X20420))
        | ~ class_Groups_Oordered__ab__group__add(X20421) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20421),hAPP(c_Groups_Ouminus__class_Ouminus(X20421),X20419)),X20420))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20421),hAPP(c_Groups_Ouminus__class_Ouminus(X20421),X20420)),X20419))
        | ~ class_Groups_Oordered__ab__group__add(X20421) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__iff])])]) ).

fof(i_0_8855,plain,
    ! [X23481,X23482] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23481,X23482)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23482),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23482),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23481,X23482)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23482),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_8856,plain,
    ! [X23479,X23480] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23480),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,X23479,X23480)),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_8857,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_5828]) ).

fof(i_0_8858,plain,
    ! [X19466,X19467,X19468,X19469] : hAPP(c_Set_Ovimage(X19469,X19468,X19467),hAPP(c_Set_OCollect(X19468),X19466)) = hAPP(c_Set_OCollect(X19469),hAPP(hAPP(c_COMBB(X19468,tc_HOL_Obool,X19469),X19466),X19467)),
    inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq]) ).

fof(i_0_8859,plain,
    ! [X23739,X23740,X23741,X23742] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23742,X23741),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X23740),X23739)))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23742),X23741) = X23740 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__eq])]) ).

fof(i_0_8860,plain,
    ! [X21195,X21196,X21197,X21198] :
      ( ~ c_Fun_Oinj__on(X21198,X21197,X21196,X21195)
      | hAPP(c_Finite__Set_Ocard(X21197),hAPP(c_Set_Oimage(X21198,X21197,X21196),X21195)) = hAPP(c_Finite__Set_Ocard(X21198),X21195) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image])]) ).

fof(i_0_8861,plain,
    ! [X31797,X31798,X31799,X31800] : hAPP(hAPP(c_List_Otake(X31800),X31799),hAPP(hAPP(c_List_Odrop(X31800),X31798),X31797)) = hAPP(hAPP(c_List_Odrop(X31800),X31798),hAPP(hAPP(c_List_Otake(X31800),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31799),X31798)),X31797)),
    inference(variable_rename,[status(thm)],[fact_take__drop]) ).

fof(i_0_8862,plain,
    ! [X32753,X32754,X32755,X32756,X32757] :
      ( ~ class_Orderings_Olinorder(X32757)
      | ~ c_List_Olinorder__class_Osorted(X32757,hAPP(hAPP(c_List_Omap(X32756,X32757),X32755),X32754))
      | c_List_Olinorder__class_Osorted(X32757,hAPP(hAPP(c_List_Omap(X32756,X32757),X32755),hAPP(c_List_Ofilter(X32756,X32753),X32754))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__filter])]) ).

fof(i_0_8863,plain,
    ! [X28333,X28334,X28335] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X28335,X28334) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X28333,X28334)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28333),X28335))
      | X28335 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28333),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28334),esk310_3(X28333,X28334,X28335))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mod__eq__lemma])])]) ).

fof(i_0_8864,plain,
    ! [X32986,X32987,X32988,X32989,X32990,X32991,X32992] :
      ( ( c_List_OtakeWhile(X32988,X32987,X32986) != X32986
        | ~ hBOOL(hAPP(hAPP(c_member(X32988),X32989),hAPP(c_List_Oset(X32988),X32986)))
        | hBOOL(hAPP(X32987,X32989)) )
      & ( hBOOL(hAPP(hAPP(c_member(X32992),esk462_3(X32990,X32991,X32992)),hAPP(c_List_Oset(X32992),X32990)))
        | c_List_OtakeWhile(X32992,X32991,X32990) = X32990 )
      & ( ~ hBOOL(hAPP(X32991,esk462_3(X32990,X32991,X32992)))
        | c_List_OtakeWhile(X32992,X32991,X32990) = X32990 ) ),
    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_8865,plain,
    ! [X22203,X22204] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22204),c_Groups_Ozero__class_Ozero(X22204)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22204),X22203),X22203)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22204),c_Groups_Ozero__class_Ozero(X22204)),X22203))
        | ~ class_Groups_Olinordered__ab__group__add(X22204) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22204),c_Groups_Ozero__class_Ozero(X22204)),X22203))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22204),c_Groups_Ozero__class_Ozero(X22204)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22204),X22203),X22203)))
        | ~ class_Groups_Olinordered__ab__group__add(X22204) ) ),
    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_8866,plain,
    ! [X22119,X22120] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22120),c_Groups_Ozero__class_Ozero(X22120)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22120),X22119),X22119)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22120),c_Groups_Ozero__class_Ozero(X22120)),X22119))
        | ~ class_Groups_Olinordered__ab__group__add(X22120) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22120),c_Groups_Ozero__class_Ozero(X22120)),X22119))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22120),c_Groups_Ozero__class_Ozero(X22120)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22120),X22119),X22119)))
        | ~ class_Groups_Olinordered__ab__group__add(X22120) ) ),
    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_8867,plain,
    ! [X33602,X33603,X33604,X33606,X33607,X33608,X33609] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33604),esk504_3(X33602,X33603,X33604)),hAPP(c_List_Oset(X33604),X33603)))
        | c_List_Olist__all(X33604,X33602,X33603) )
      & ( ~ hBOOL(hAPP(X33602,esk504_3(X33602,X33603,X33604)))
        | c_List_Olist__all(X33604,X33602,X33603) )
      & ( ~ c_List_Olist__all(X33608,X33606,X33607)
        | ~ hBOOL(hAPP(hAPP(c_member(X33608),X33609),hAPP(c_List_Oset(X33608),X33607)))
        | hBOOL(hAPP(X33606,X33609)) ) ),
    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_8868,plain,
    ! [X33614,X33615,X33616,X33617,X33618,X33619,X33620] :
      ( ( ~ c_List_Olist__all(X33616,X33615,X33614)
        | ~ hBOOL(hAPP(hAPP(c_member(X33616),X33617),hAPP(c_List_Oset(X33616),X33614)))
        | hBOOL(hAPP(X33615,X33617)) )
      & ( hBOOL(hAPP(hAPP(c_member(X33620),esk505_3(X33618,X33619,X33620)),hAPP(c_List_Oset(X33620),X33618)))
        | c_List_Olist__all(X33620,X33619,X33618) )
      & ( ~ hBOOL(hAPP(X33619,esk505_3(X33618,X33619,X33620)))
        | c_List_Olist__all(X33620,X33619,X33618) ) ),
    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_8869,plain,
    ! [X33587,X33588,X33589,X33590,X33591,X33592,X33593] :
      ( ( ~ c_List_Olist__all(X33589,X33588,X33587)
        | ~ hBOOL(hAPP(hAPP(c_member(X33589),X33590),hAPP(c_List_Oset(X33589),X33587)))
        | hBOOL(hAPP(X33588,X33590)) )
      & ( hBOOL(hAPP(hAPP(c_member(X33593),esk503_3(X33591,X33592,X33593)),hAPP(c_List_Oset(X33593),X33591)))
        | c_List_Olist__all(X33593,X33592,X33591) )
      & ( ~ hBOOL(hAPP(X33592,esk503_3(X33591,X33592,X33593)))
        | c_List_Olist__all(X33593,X33592,X33591) ) ),
    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_8870,plain,
    ! [X22337,X22338] :
      ( ( ~ 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),X22338),X22337)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22338))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22337)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22338))
        | 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),X22338),X22337))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22337))
        | 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),X22338),X22337))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).

fof(i_0_8871,plain,
    ! [X16996,X16997,X16998] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X16998),tc_HOL_Obool)),X16997),X16996))
      | c_Hoare__Mirabelle_Ohoare__derivs(X16998,X16996,X16997) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_asm])]) ).

cnf(i_0_8872,plain,
    c_List_OdropWhile(X1,X2,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_5829]) ).

fof(i_0_8873,plain,
    ! [X23268,X23269,X23270,X23271,X23272,X23273] :
      ( ~ class_Divides_Osemiring__div(X23273)
      | c_Divides_Odiv__class_Omod(X23273,X23272,X23271) != c_Divides_Odiv__class_Omod(X23273,X23270,X23271)
      | c_Divides_Odiv__class_Omod(X23273,X23269,X23271) != c_Divides_Odiv__class_Omod(X23273,X23268,X23271)
      | c_Divides_Odiv__class_Omod(X23273,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23273),X23272),X23269),X23271) = c_Divides_Odiv__class_Omod(X23273,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23273),X23270),X23268),X23271) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__cong])]) ).

fof(i_0_8874,plain,
    ! [X23300,X23301,X23302,X23303,X23304,X23305] :
      ( ~ class_Divides_Osemiring__div(X23305)
      | c_Divides_Odiv__class_Omod(X23305,X23304,X23303) != c_Divides_Odiv__class_Omod(X23305,X23302,X23303)
      | c_Divides_Odiv__class_Omod(X23305,X23301,X23303) != c_Divides_Odiv__class_Omod(X23305,X23300,X23303)
      | c_Divides_Odiv__class_Omod(X23305,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23305),X23304),X23301),X23303) = c_Divides_Odiv__class_Omod(X23305,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23305),X23302),X23300),X23303) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__cong])]) ).

fof(i_0_8875,plain,
    ! [X23339,X23340,X23341,X23342,X23343,X23344] :
      ( ~ class_Divides_Oring__div(X23344)
      | c_Divides_Odiv__class_Omod(X23344,X23343,X23342) != c_Divides_Odiv__class_Omod(X23344,X23341,X23342)
      | c_Divides_Odiv__class_Omod(X23344,X23340,X23342) != c_Divides_Odiv__class_Omod(X23344,X23339,X23342)
      | c_Divides_Odiv__class_Omod(X23344,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23344),X23343),X23340),X23342) = c_Divides_Odiv__class_Omod(X23344,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23344),X23341),X23339),X23342) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__cong])]) ).

fof(i_0_8876,plain,
    ! [X24232,X24233,X24234,X24235] :
      ( ~ class_Fields_Ofield(X24235)
      | X24234 = c_Groups_Ozero__class_Ozero(X24235)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24233),X24232))
      | hAPP(hAPP(c_Power_Opower__class_Opower(X24235),X24234),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24232),X24233)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24235),hAPP(hAPP(c_Power_Opower__class_Opower(X24235),X24234),X24232)),hAPP(hAPP(c_Power_Opower__class_Opower(X24235),X24234),X24233)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__diff])]) ).

fof(i_0_8877,plain,
    ! [X18298,X18299,X18300] :
      ( hBOOL(hAPP(hAPP(c_member(X18300),X18299),X18298))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18300,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X18300),X18299),X18298)),hAPP(hAPP(c_Set_Oinsert(X18300),X18299),c_Orderings_Obot__class_Obot(tc_fun(X18300,tc_HOL_Obool)))) = X18298 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5830])]) ).

fof(i_0_8878,plain,
    ! [X26568,X26569,X26570,X26571,X26572] :
      ( ~ class_Groups_Ocomm__monoid__add(X26572)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26571),X26570))
      | hBOOL(hAPP(hAPP(c_member(X26571),X26569),X26570))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26571,X26572),X26568),hAPP(hAPP(c_Set_Oinsert(X26571),X26569),X26570)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26572),hAPP(X26568,X26569)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26571,X26572),X26568),X26570)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5831])]) ).

fof(i_0_8879,plain,
    ! [X26563,X26564,X26565,X26566,X26567] :
      ( ~ class_Groups_Ocomm__monoid__add(X26567)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26566),X26565))
      | hBOOL(hAPP(hAPP(c_member(X26566),X26564),X26565))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26566,X26567),X26563),hAPP(hAPP(c_Set_Oinsert(X26566),X26564),X26565)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26567),hAPP(X26563,X26564)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26566,X26567),X26563),X26565)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5832])]) ).

fof(i_0_8880,plain,
    ! [X23180,X23181,X23182,X23183,X23184] :
      ( ~ class_Groups_Ocomm__monoid__mult(X23184)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23183),X23182))
      | hBOOL(hAPP(hAPP(c_member(X23183),X23181),X23182))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23183,X23184),X23180),hAPP(hAPP(c_Set_Oinsert(X23183),X23181),X23182)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23184),hAPP(X23180,X23181)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23183,X23184),X23180),X23182)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5833])]) ).

fof(i_0_8881,plain,
    ! [X23175,X23176,X23177,X23178,X23179] :
      ( ~ class_Groups_Ocomm__monoid__mult(X23179)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23178),X23177))
      | hBOOL(hAPP(hAPP(c_member(X23178),X23176),X23177))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23178,X23179),X23175),hAPP(hAPP(c_Set_Oinsert(X23178),X23176),X23177)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23179),hAPP(X23175,X23176)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23178,X23179),X23175),X23177)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5834])]) ).

fof(i_0_8882,plain,
    ! [X23750,X23751,X23752] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23752),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23751)),X23750))
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X23752,X23751),hAPP(c_Divides_OnegateSnd,X23750))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__neg])]) ).

fof(i_0_8883,plain,
    ! [X18189,X18190,X18191,X18192] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X18192),X18191),X18190))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18192,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X18192),X18191),X18189)),X18190) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18192,tc_HOL_Obool)),X18189),X18190) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__Diff1])]) ).

fof(i_0_8884,plain,
    ! [X20013,X20014,X20015] : c_Map_Odom(X20015,X20014,hAPP(hAPP(c_COMBB(X20014,tc_Option_Ooption(X20014),X20015),c_Option_Ooption_OSome(X20014)),X20013)) = c_Orderings_Otop__class_Otop(tc_fun(X20015,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_dom__const]) ).

fof(i_0_8885,plain,
    ! [X20997,X20998,X20999] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20999),X20998))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20999),X20997))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20998),X20999)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20997),X20999)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20998),X20997) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq])]) ).

fof(i_0_8886,plain,
    ! [X33006,X33007,X33008] : c_List_OtakeWhile(X33008,X33007,X33006) = hAPP(hAPP(c_List_Otake(X33008),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33008)),c_List_OtakeWhile(X33008,X33007,X33006))),X33006),
    inference(variable_rename,[status(thm)],[fact_takeWhile__eq__take]) ).

fof(i_0_8887,plain,
    ! [X26318,X26319,X26320,X26322,X26323,X26324] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk202_2(X26318,X26319)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26319)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26320),X26319))
        | ~ hBOOL(hAPP(X26318,X26320)) )
      & ( hBOOL(hAPP(X26318,esk202_2(X26318,X26319)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26320),X26319))
        | ~ hBOOL(hAPP(X26318,X26320)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk203_2(X26322,X26323)),X26323))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X26324),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26323)))
        | ~ hBOOL(hAPP(X26322,X26324)) )
      & ( hBOOL(hAPP(X26322,esk203_2(X26322,X26323)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X26324),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26323)))
        | ~ hBOOL(hAPP(X26322,X26324)) ) ),
    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_8888,plain,
    ! [X21697,X21698,X21699] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21699)),X21698)),hAPP(c_Nat_OSuc,X21697)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21699),X21698)),X21697),
    inference(variable_rename,[status(thm)],[fact_Suc__diff__diff]) ).

fof(i_0_8889,plain,
    ! [X22719,X22720,X22721,X22722] :
      ( ~ class_Rings_Olinordered__semidom(X22722)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22722),X22721),hAPP(c_Nat_OSuc,X22720)) != hAPP(hAPP(c_Power_Opower__class_Opower(X22722),X22719),hAPP(c_Nat_OSuc,X22720))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22722),c_Groups_Ozero__class_Ozero(X22722)),X22721))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22722),c_Groups_Ozero__class_Ozero(X22722)),X22719))
      | X22721 = X22719 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__base])]) ).

cnf(i_0_8890,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_5835]) ).

fof(i_0_8891,plain,
    ! [X25232,X25233] :
      ( ( X25233 = 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),X25233)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25232)))) )
      & ( X25232 = 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),X25233)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25232)))) )
      & ( X25233 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X25232 != 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),X25233)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25232)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__zle__neg])])]) ).

fof(i_0_8892,plain,
    ! [X27474] :
      ( ~ class_Orderings_Owellorder(X27474)
      | c_Wellfounded_Owf(X27474,hAPP(c_Set_OCollect(tc_prod(X27474,X27474)),hAPP(c_Product__Type_Oprod_Oprod__case(X27474,X27474,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X27474)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf])]) ).

fof(i_0_8893,plain,
    ! [X32260,X32261,X32262,X32263,X32264,X32265,X32266] :
      ( ( hAPP(c_List_Ofilter(X32262,X32261),X32260) != c_List_Olist_ONil(X32262)
        | ~ hBOOL(hAPP(hAPP(c_member(X32262),X32263),hAPP(c_List_Oset(X32262),X32260)))
        | ~ hBOOL(hAPP(X32261,X32263)) )
      & ( hBOOL(hAPP(hAPP(c_member(X32266),esk446_3(X32264,X32265,X32266)),hAPP(c_List_Oset(X32266),X32264)))
        | hAPP(c_List_Ofilter(X32266,X32265),X32264) = c_List_Olist_ONil(X32266) )
      & ( hBOOL(hAPP(X32265,esk446_3(X32264,X32265,X32266)))
        | hAPP(c_List_Ofilter(X32266,X32265),X32264) = c_List_Olist_ONil(X32266) ) ),
    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_5836])])])])])]) ).

fof(i_0_8894,plain,
    ! [X25368,X25369,X25370,X25371] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25371),X25370),X25369))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25371),X25370),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25371),X25369),X25368)))
        | ~ class_Orderings_Olinorder(X25371) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25371),X25370),X25368))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25371),X25370),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25371),X25369),X25368)))
        | ~ class_Orderings_Olinorder(X25371) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25371),X25370),X25369))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25371),X25370),X25368))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25371),X25370),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25371),X25369),X25368)))
        | ~ class_Orderings_Olinorder(X25371) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__less__iff__conj])])]) ).

fof(i_0_8895,plain,
    ! [X25407,X25408,X25409,X25410] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25410),X25409),X25408))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25410),X25409),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25410),X25408),X25407)))
        | ~ class_Orderings_Olinorder(X25410) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25410),X25409),X25407))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25410),X25409),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25410),X25408),X25407)))
        | ~ class_Orderings_Olinorder(X25410) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25410),X25409),X25408))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25410),X25409),X25407))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25410),X25409),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25410),X25408),X25407)))
        | ~ class_Orderings_Olinorder(X25410) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__inf__iff])])]) ).

fof(i_0_8896,plain,
    ! [X25389,X25390,X25391,X25392] :
      ( ~ class_Orderings_Olinorder(X25392)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25392),X25391),X25390))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25392),X25391),X25389))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25392),X25391),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25392),X25390),X25389))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI])]) ).

fof(i_0_8897,plain,
    ! [X25385,X25386,X25387,X25388] :
      ( ~ class_Orderings_Olinorder(X25388)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25388),X25387),X25386))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25388),X25387),X25385))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25388),X25387),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25388),X25386),X25385))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__greatest])]) ).

fof(i_0_8898,plain,
    ! [X17987,X17988,X17989,X17990] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17990),X17989),X17988))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17990),X17989),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17990),X17988),X17987)))
        | ~ class_Lattices_Osemilattice__inf(X17990) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17990),X17989),X17987))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17990),X17989),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17990),X17988),X17987)))
        | ~ class_Lattices_Osemilattice__inf(X17990) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17990),X17989),X17988))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17990),X17989),X17987))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17990),X17989),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17990),X17988),X17987)))
        | ~ class_Lattices_Osemilattice__inf(X17990) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__inf__iff])])]) ).

fof(i_0_8899,plain,
    ! [X17969,X17970,X17971,X17972] :
      ( ~ class_Lattices_Osemilattice__inf(X17972)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17972),X17971),X17970))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17972),X17971),X17969))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17972),X17971),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17972),X17970),X17969))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI])]) ).

fof(i_0_8900,plain,
    ! [X17965,X17966,X17967,X17968] :
      ( ~ class_Lattices_Osemilattice__inf(X17968)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17968),X17967),X17966))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17968),X17967),X17965))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17968),X17967),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17968),X17966),X17965))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__greatest])]) ).

fof(i_0_8901,plain,
    ! [X25160,X25161] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25161)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25160)))),
    inference(variable_rename,[status(thm)],[i_0_5837]) ).

fof(i_0_8902,plain,
    ! [X22911,X22912,X22913] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22913))
      | X22913 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22913),X22911))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22912))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22911),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_8903,plain,
    ! [X32286,X32287,X32288,X32289,X32290,X32291,X32292] :
      ( ( hAPP(c_List_Ofilter(X32288,X32287),X32286) != X32286
        | ~ hBOOL(hAPP(hAPP(c_member(X32288),X32289),hAPP(c_List_Oset(X32288),X32286)))
        | hBOOL(hAPP(X32287,X32289)) )
      & ( hBOOL(hAPP(hAPP(c_member(X32292),esk447_3(X32290,X32291,X32292)),hAPP(c_List_Oset(X32292),X32290)))
        | hAPP(c_List_Ofilter(X32292,X32291),X32290) = X32290 )
      & ( ~ hBOOL(hAPP(X32291,esk447_3(X32290,X32291,X32292)))
        | hAPP(c_List_Ofilter(X32292,X32291),X32290) = X32290 ) ),
    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_8904,plain,
    ! [X23422,X23423] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23423))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23422))
      | 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,X23423,X23422))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I2_J])]) ).

fof(i_0_8905,plain,
    ! [X31657,X31658,X31659,X31660] : hAPP(hAPP(c_List_Onth(X31660),hAPP(hAPP(c_List_Oappend(X31660),X31659),X31658)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31660)),X31659)),X31657)) = hAPP(hAPP(c_List_Onth(X31660),X31658),X31657),
    inference(variable_rename,[status(thm)],[fact_nth__append__length__plus]) ).

cnf(i_0_8906,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_5838]) ).

fof(i_0_8907,plain,
    ! [X31479,X31480,X31481,X31482,X31483,X31484] : hAPP(c_List_Olist_Olist__case(X31484,X31483,X31482,X31481),hAPP(hAPP(c_List_Olist_OCons(X31483),X31480),X31479)) = hAPP(hAPP(X31481,X31480),X31479),
    inference(variable_rename,[status(thm)],[fact_list_Osimps_I5_J]) ).

fof(i_0_8908,plain,
    ! [X17308,X17309,X17310,X17311] :
      ( ~ hBOOL(hAPP(X17311,X17310))
      | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17309,tc_HOL_Obool)),X17311),X17308),X17310)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup1I1])]) ).

fof(i_0_8909,plain,
    ! [X17265,X17266,X17267,X17268] :
      ( ( ~ hBOOL(hAPP(X17268,X17267))
        | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17265,tc_HOL_Obool)),X17266),X17268),X17267)) )
      & ( ~ hBOOL(hAPP(X17266,X17267))
        | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17265,tc_HOL_Obool)),X17266),X17268),X17267)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5839])])]) ).

fof(i_0_8910,plain,
    ! [X17304,X17305,X17306,X17307] :
      ( ~ hBOOL(hAPP(X17307,X17306))
      | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17305,tc_HOL_Obool)),X17304),X17307),X17306)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup1I2])]) ).

fof(i_0_8911,plain,
    ! [X27127,X27128,X27129] :
      ( ~ class_Rings_Olinordered__idom(X27129)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27129),c_Groups_Ozero__class_Ozero(X27129)),hAPP(hAPP(c_Power_Opower__class_Opower(X27129),hAPP(c_Groups_Oabs__class_Oabs(X27129),X27128)),X27127))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power__abs])]) ).

fof(i_0_8912,plain,
    ! [X21531,X21532,X21533] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21533),X21532))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21531),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21532),X21533))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21531),X21533)),hAPP(c_Nat_OSuc,X21532)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq1])]) ).

fof(i_0_8913,plain,
    ! [X17035,X17036] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17036,tc_HOL_Obool)),X17035),c_Orderings_Obot__class_Obot(tc_fun(X17036,tc_HOL_Obool))))
        | X17035 = c_Orderings_Obot__class_Obot(tc_fun(X17036,tc_HOL_Obool)) )
      & ( X17035 != c_Orderings_Obot__class_Obot(tc_fun(X17036,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17036,tc_HOL_Obool)),X17035),c_Orderings_Obot__class_Obot(tc_fun(X17036,tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__empty])]) ).

fof(i_0_8914,plain,
    ! [X28196,X28197] :
      ( ~ c_Wellfounded_OwfP(X28197,X28196)
      | c_Wellfounded_Oacyclic(X28197,hAPP(c_Set_OCollect(tc_prod(X28197,X28197)),hAPP(c_Product__Type_Oprod_Oprod__case(X28197,X28197,tc_HOL_Obool),X28196))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__acyclicP])]) ).

cnf(i_0_8915,plain,
    ( c_Map_Omap__comp(X3,X6,X7,X5,X1,X2) = c_Option_Ooption_ONone(X6)
    | hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4)
    | hAPP(X5,X4) != c_Option_Ooption_ONone(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_5420]) ).

fof(i_0_8916,plain,
    ! [X27277,X27278,X27279,X27280] : hAPP(hAPP(c_Relation_Orel__comp(X27280,X27279,X27278),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27280,X27279),tc_HOL_Obool))),X27277) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27280,X27278),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__empty1]) ).

fof(i_0_8917,plain,
    ! [X23565,X23566] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X23565,X23566) != 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),X23565)),X23566) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23565),X23566))
        | X23566 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X23565,X23566) = 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),X23565)),X23566) = 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),X23565),X23566))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | X23566 = 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_8918,plain,
    ! [X32613,X32614,X32615,X32616,X32617,X32618,X32619] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X32617),X32618),hAPP(c_List_Oset(X32617),X32614)))
        | hBOOL(hAPP(X32616,X32618))
        | c_List_Opartition(X32617,X32616,X32615) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32617),tc_List_Olist(X32617)),X32614),X32613) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32617),X32619),hAPP(c_List_Oset(X32617),X32613)))
        | ~ hBOOL(hAPP(X32616,X32619))
        | c_List_Opartition(X32617,X32616,X32615) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32617),tc_List_Olist(X32617)),X32614),X32613) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5840])])])]) ).

fof(i_0_8919,plain,
    ! [X20431,X20432,X20433] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20433),hAPP(c_Groups_Ouminus__class_Ouminus(X20433),X20432)),hAPP(c_Groups_Ouminus__class_Ouminus(X20433),X20431)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20433),X20431),X20432))
        | ~ class_Groups_Oordered__ab__group__add(X20433) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20433),X20431),X20432))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20433),hAPP(c_Groups_Ouminus__class_Ouminus(X20433),X20432)),hAPP(c_Groups_Ouminus__class_Ouminus(X20433),X20431)))
        | ~ class_Groups_Oordered__ab__group__add(X20433) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less])])]) ).

fof(i_0_8920,plain,
    ! [X20410,X20411,X20412] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20412),hAPP(c_Groups_Ouminus__class_Ouminus(X20412),X20411)),hAPP(c_Groups_Ouminus__class_Ouminus(X20412),X20410)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20412),X20410),X20411))
        | ~ class_Lattices_Oboolean__algebra(X20412) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20412),X20410),X20411))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20412),hAPP(c_Groups_Ouminus__class_Ouminus(X20412),X20411)),hAPP(c_Groups_Ouminus__class_Ouminus(X20412),X20410)))
        | ~ class_Lattices_Oboolean__algebra(X20412) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff])])]) ).

fof(i_0_8921,plain,
    ! [X20416,X20417,X20418] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20418),hAPP(c_Groups_Ouminus__class_Ouminus(X20418),X20417)),hAPP(c_Groups_Ouminus__class_Ouminus(X20418),X20416)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20418),X20416),X20417))
        | ~ class_Groups_Oordered__ab__group__add(X20418) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20418),X20416),X20417))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20418),hAPP(c_Groups_Ouminus__class_Ouminus(X20418),X20417)),hAPP(c_Groups_Ouminus__class_Ouminus(X20418),X20416)))
        | ~ class_Groups_Oordered__ab__group__add(X20418) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le])])]) ).

fof(i_0_8922,plain,
    ! [X26310,X26311,X26313,X26314,X26315,X26317] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk200_2(X26310,X26311)),X26311))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X26313),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26311)))
        | hBOOL(hAPP(X26310,X26313)) )
      & ( ~ hBOOL(hAPP(X26310,esk200_2(X26310,X26311)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X26313),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26311)))
        | hBOOL(hAPP(X26310,X26313)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk201_2(X26314,X26315)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26315)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26317),X26315))
        | hBOOL(hAPP(X26314,X26317)) )
      & ( ~ hBOOL(hAPP(X26314,esk201_2(X26314,X26315)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26317),X26315))
        | hBOOL(hAPP(X26314,X26317)) ) ),
    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_8923,plain,
    ! [X22731,X22732,X22733] :
      ( ~ class_Rings_Olinordered__semidom(X22733)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22733),c_Groups_Oone__class_Oone(X22733)),X22732))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22733),c_Groups_Oone__class_Oone(X22733)),hAPP(hAPP(c_Power_Opower__class_Opower(X22733),X22732),hAPP(c_Nat_OSuc,X22731)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1])]) ).

fof(i_0_8924,plain,
    ! [X22908,X22909,X22910] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22910))
      | X22910 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22910),X22908))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22909),X22910))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X22908)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1])]) ).

fof(i_0_8925,plain,
    ! [X33905,X33906,X33907,X33908,X33909] :
      ( ~ hBOOL(hAPP(hAPP(X33909,X33908),X33907))
      | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X33906,X33905,X33909),X33907),X33908)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep_Ointros])]) ).

cnf(i_0_8926,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_5841]) ).

cnf(i_0_8927,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_5842]) ).

fof(i_0_8928,plain,
    ! [X24653,X24654] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24654)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24653)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24654),X24653))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24654),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24654),X24653))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24654)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24653))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24654),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),X24654)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24653))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5843])])]) ).

fof(i_0_8929,plain,
    ! [X24037,X24038,X24039] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24039),hAPP(c_Int_Onumber__class_Onumber__of(X24039),X24038)),hAPP(c_Int_Onumber__class_Onumber__of(X24039),X24037)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24038),X24037))
        | ~ class_Int_Onumber__ring(X24039)
        | ~ class_Rings_Olinordered__idom(X24039) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24038),X24037))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24039),hAPP(c_Int_Onumber__class_Onumber__of(X24039),X24038)),hAPP(c_Int_Onumber__class_Onumber__of(X24039),X24037)))
        | ~ class_Int_Onumber__ring(X24039)
        | ~ class_Rings_Olinordered__idom(X24039) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of])])]) ).

fof(i_0_8930,plain,
    ! [X24034,X24035,X24036] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24036),hAPP(c_Int_Onumber__class_Onumber__of(X24036),X24035)),hAPP(c_Int_Onumber__class_Onumber__of(X24036),X24034)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24035),X24034))
        | ~ class_Int_Onumber__ring(X24036)
        | ~ class_Rings_Olinordered__idom(X24036) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24035),X24034))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24036),hAPP(c_Int_Onumber__class_Onumber__of(X24036),X24035)),hAPP(c_Int_Onumber__class_Onumber__of(X24036),X24034)))
        | ~ class_Int_Onumber__ring(X24036)
        | ~ class_Rings_Olinordered__idom(X24036) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__number__of])])]) ).

fof(i_0_8931,plain,
    ! [X31147,X31148,X31149,X31150] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31150)),X31149)),X31148))
      | hAPP(hAPP(c_List_Olist__update(X31150,X31149),X31148),X31147) = X31149 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__beyond])]) ).

fof(i_0_8932,plain,
    ! [X21014] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21014),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21014),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21014),X21014)))),
    inference(variable_rename,[status(thm)],[fact_le__cube]) ).

fof(i_0_8933,plain,
    ! [X32192,X32193,X32194] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X32194),X32193),hAPP(c_List_Oset(X32194),c_List_Obutlast(X32194,X32192))))
      | hBOOL(hAPP(hAPP(c_member(X32194),X32193),hAPP(c_List_Oset(X32194),X32192))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__butlastD])]) ).

fof(i_0_8934,plain,
    ! [X17418,X17419,X17420,X17421,X17422] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17422),X17421),X17420))
      | hAPP(hAPP(c_Set_Oinsert(X17419),hAPP(X17418,X17421)),hAPP(c_Set_Oimage(X17422,X17419,X17418),X17420)) = hAPP(c_Set_Oimage(X17422,X17419,X17418),X17420) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__image])]) ).

cnf(i_0_8935,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_5844]) ).

cnf(i_0_8936,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_5845]) ).

fof(i_0_8937,plain,
    ! [X23109,X23110,X23111] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X23111,X23111),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X23110),X23109)))
      | X23111 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | X23110 = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient])]) ).

fof(i_0_8938,plain,
    ! [X23011,X23012,X23013] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X23013,X23013),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X23012),X23011)))
      | X23013 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | X23011 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__remainder])]) ).

fof(i_0_8939,plain,
    ! [X29124,X29125,X29126,X29127,X29128] :
      ( ~ c_Finite__Set_Ofolding__one(X29128,X29127,X29126)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29128),X29125))
      | hBOOL(hAPP(hAPP(c_member(X29128),X29124),X29125))
      | hAPP(X29126,hAPP(hAPP(c_Set_Oinsert(X29128),X29124),X29125)) = hAPP(hAPP(c_Finite__Set_Ofold(X29128,X29128,X29127),X29124),X29125) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5846])]) ).

fof(i_0_8940,plain,
    ! [X28844,X28845,X28846] :
      ( ~ c_Wellfounded_Owf(X28846,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28846,X28846),tc_HOL_Obool),X28845),X28844))
      | c_Wellfounded_Owf(X28846,X28844) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__exp])]) ).

fof(i_0_8941,plain,
    ! [X25017,X25018,X25019] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25019),hAPP(c_Int_Oring__1__class_Oof__int(X25019),X25018)),hAPP(c_Int_Oring__1__class_Oof__int(X25019),X25017)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25018),X25017))
        | ~ class_Rings_Olinordered__idom(X25019) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25018),X25017))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25019),hAPP(c_Int_Oring__1__class_Oof__int(X25019),X25018)),hAPP(c_Int_Oring__1__class_Oof__int(X25019),X25017)))
        | ~ class_Rings_Olinordered__idom(X25019) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__less__iff])])]) ).

fof(i_0_8942,plain,
    ! [X25175,X25176,X25177] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25177),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25177),X25176)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25177),X25175)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25176),X25175))
        | ~ class_Rings_Olinordered__semidom(X25177) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25176),X25175))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25177),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25177),X25176)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25177),X25175)))
        | ~ class_Rings_Olinordered__semidom(X25177) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__less__iff])])]) ).

fof(i_0_8943,plain,
    ! [X25169,X25170,X25171] :
      ( ~ class_Rings_Olinordered__semidom(X25171)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25171),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25171),X25170)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25171),X25169)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25170),X25169)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__less__imp__less])]) ).

fof(i_0_8944,plain,
    ! [X25014,X25015,X25016] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25016),hAPP(c_Int_Oring__1__class_Oof__int(X25016),X25015)),hAPP(c_Int_Oring__1__class_Oof__int(X25016),X25014)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25015),X25014))
        | ~ class_Rings_Olinordered__idom(X25016) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25015),X25014))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25016),hAPP(c_Int_Oring__1__class_Oof__int(X25016),X25015)),hAPP(c_Int_Oring__1__class_Oof__int(X25016),X25014)))
        | ~ class_Rings_Olinordered__idom(X25016) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__le__iff])])]) ).

fof(i_0_8945,plain,
    ! [X25178,X25179,X25180] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25180),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25180),X25179)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25180),X25178)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25179),X25178))
        | ~ class_Rings_Olinordered__semidom(X25180) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25179),X25178))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25180),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25180),X25179)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25180),X25178)))
        | ~ class_Rings_Olinordered__semidom(X25180) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__le__iff])])]) ).

fof(i_0_8946,plain,
    ! [X28250] :
      ( X28250 = hAPP(c_Int_OAbs__Integ,esk297_1(X28250))
      & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk297_1(X28250)),c_Int_OInteg)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5847])])]) ).

cnf(i_0_8947,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_5848]) ).

cnf(i_0_8948,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_5849]) ).

fof(i_0_8949,plain,
    ! [X24179,X24180,X24181,X24182] :
      ( ~ class_Fields_Ofield(X24182)
      | X24181 = c_Groups_Ozero__class_Ozero(X24182)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X24182),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24182),X24180),X24181)),X24179) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24182),hAPP(hAPP(c_Power_Opower__class_Opower(X24182),X24180),X24179)),hAPP(hAPP(c_Power_Opower__class_Opower(X24182),X24181),X24179)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__power__divide])]) ).

fof(i_0_8950,plain,
    ! [X22884,X22885] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22885),X22884))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22885),c_Groups_Oone__class_Oone(tc_Int_Oint))),X22884)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle])]) ).

fof(i_0_8951,plain,
    ! [X25476,X25477,X25478] :
      ( ~ class_Orderings_Olinorder(X25478)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25478),X25477))
      | X25477 = c_Orderings_Obot__class_Obot(tc_fun(X25478,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25478),X25476))
      | X25476 = c_Orderings_Obot__class_Obot(tc_fun(X25478,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMin(X25478,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25478,tc_HOL_Obool)),X25477),X25476)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25478),c_Big__Operators_Olinorder__class_OMin(X25478,X25477)),c_Big__Operators_Olinorder__class_OMin(X25478,X25476)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__Un])]) ).

fof(i_0_8952,plain,
    ! [X25903,X25904,X25905] :
      ( ~ class_Orderings_Olinorder(X25905)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25905),X25904))
      | X25904 = c_Orderings_Obot__class_Obot(tc_fun(X25905,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25905),X25903))
      | X25903 = c_Orderings_Obot__class_Obot(tc_fun(X25905,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMax(X25905,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25905,tc_HOL_Obool)),X25904),X25903)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25905),c_Big__Operators_Olinorder__class_OMax(X25905,X25904)),c_Big__Operators_Olinorder__class_OMax(X25905,X25903)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__Un])]) ).

fof(i_0_8953,plain,
    ! [X20867,X20868,X20869] :
      ( ~ class_Lattices_Olattice(X20869)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20869),X20868))
      | X20868 = c_Orderings_Obot__class_Obot(tc_fun(X20869,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20869),X20867))
      | X20867 = c_Orderings_Obot__class_Obot(tc_fun(X20869,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OSup__fin(X20869,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20869,tc_HOL_Obool)),X20868),X20867)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20869),c_Big__Operators_Olattice__class_OSup__fin(X20869,X20868)),c_Big__Operators_Olattice__class_OSup__fin(X20869,X20867)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__idem])]) ).

fof(i_0_8954,plain,
    ! [X20870,X20871,X20872] :
      ( ~ class_Lattices_Olattice(X20872)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20872),X20871))
      | X20871 = c_Orderings_Obot__class_Obot(tc_fun(X20872,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20872),X20870))
      | X20870 = c_Orderings_Obot__class_Obot(tc_fun(X20872,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OInf__fin(X20872,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20872,tc_HOL_Obool)),X20871),X20870)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20872),c_Big__Operators_Olattice__class_OInf__fin(X20872,X20871)),c_Big__Operators_Olattice__class_OInf__fin(X20872,X20870)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__idem])]) ).

fof(i_0_8955,plain,
    ! [X33932,X33933,X33934,X33935,X33936] : c_List_Osplice(X33936,hAPP(hAPP(c_List_Olist_OCons(X33936),X33935),X33934),hAPP(hAPP(c_List_Olist_OCons(X33936),X33933),X33932)) = hAPP(hAPP(c_List_Olist_OCons(X33936),X33935),hAPP(hAPP(c_List_Olist_OCons(X33936),X33933),c_List_Osplice(X33936,X33934,X33932))),
    inference(variable_rename,[status(thm)],[fact_splice_Osimps_I3_J]) ).

fof(i_0_8956,plain,
    ! [X31111,X31112] :
      ( ( hAPP(c_Code__Numeral_Oof__nat,X31112) != hAPP(c_Code__Numeral_Oof__nat,X31111)
        | X31112 = X31111
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X31111),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X31112),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) )
      & ( X31112 != X31111
        | hAPP(c_Code__Numeral_Oof__nat,X31112) = hAPP(c_Code__Numeral_Oof__nat,X31111)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X31111),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X31112),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_8957,plain,
    ! [X24547,X24548] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X24547)),hAPP(c_Int_Onat,X24548)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24547),X24548))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24548)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24547),X24548))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X24547)),hAPP(c_Int_Onat,X24548)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24548)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mono__iff])])]) ).

fof(i_0_8958,plain,
    ! [X24554,X24555] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X24555)),hAPP(c_Int_Onat,X24554)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24555),X24554))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24555)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24555),X24554))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X24555)),hAPP(c_Int_Onat,X24554)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24555)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__eq__zless])])]) ).

fof(i_0_8959,plain,
    ! [X24558,X24559] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X24559)),hAPP(c_Int_Onat,X24558)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24559),X24558))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24559)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24559),X24558))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X24559)),hAPP(c_Int_Onat,X24558)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24559)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X24559)),hAPP(c_Int_Onat,X24558)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24559),X24558))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24558)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24559),X24558))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X24559)),hAPP(c_Int_Onat,X24558)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24558)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__eq__zle])])]) ).

cnf(i_0_8960,plain,
    ( c_Map_Omap__comp(X3,X5,X6,X7,X1,X2) = hAPP(X7,X4)
    | hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_5850]) ).

fof(i_0_8961,plain,
    ! [X28847,X28848,X28849,X28850] : hAPP(X28850,hAPP(hAPP(hAPP(c_Nat_Ocompow(X28849,X28849),X28848),X28850),X28847)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(X28849,X28849),X28848),X28850),hAPP(X28850,X28847)),
    inference(variable_rename,[status(thm)],[fact_funpow__swap1]) ).

fof(i_0_8962,plain,
    ! [X32692,X32693,X32694,X32695,X32696,X32697] :
      ( ~ class_Orderings_Olinorder(X32697)
      | hBOOL(hAPP(X32696,X32695))
      | hAPP(c_List_Ofilter(X32694,X32696),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32694,X32697,X32693),X32695),X32692)) = hAPP(c_List_Ofilter(X32694,X32696),X32692) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5851])]) ).

fof(i_0_8963,plain,
    ! [X21510,X21511,X21512,X21513] :
      ( ~ class_Rings_Ocomm__semiring__1(X21513)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21513),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21513),X21512),X21511)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21513),X21510),X21511)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21513),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21513),X21512),X21510)),X21511) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J])]) ).

fof(i_0_8964,plain,
    ! [X25831,X25832,X25833,X25834] :
      ( ~ class_Orderings_Olinorder(X25834)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25834),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25834),X25833),X25832)),X25831) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25834),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25834),X25833),X25831)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25834),X25832),X25831)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__distrib2])]) ).

fof(i_0_8965,plain,
    ! [X25827,X25828,X25829,X25830] :
      ( ~ class_Orderings_Olinorder(X25830)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25830),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25830),X25829),X25828)),X25827) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25830),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25830),X25829),X25827)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25830),X25828),X25827)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__distrib2])]) ).

fof(i_0_8966,plain,
    ! [X24127,X24128,X24129,X24130] :
      ( ~ class_Rings_Odivision__ring(X24130)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24130),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24130),X24129),X24128)),X24127) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24130),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24130),X24129),X24127)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24130),X24128),X24127)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__distrib])]) ).

fof(i_0_8967,plain,
    ! [X24146,X24147,X24148,X24149] :
      ( ~ class_Rings_Odivision__ring(X24149)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24149),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24149),X24148),X24147)),X24146) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24149),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24149),X24148),X24146)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24149),X24147),X24146)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__divide__distrib])]) ).

fof(i_0_8968,plain,
    ! [X24137,X24138,X24139,X24140] :
      ( ~ class_Fields_Ofield__inverse__zero(X24140)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X24140),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24140),X24139),X24138)),X24137) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24140),hAPP(hAPP(c_Power_Opower__class_Opower(X24140),X24139),X24137)),hAPP(hAPP(c_Power_Opower__class_Opower(X24140),X24138),X24137)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__divide])]) ).

fof(i_0_8969,plain,
    ! [X22573,X22574,X22575,X22576] :
      ( ~ class_Rings_Ocomm__semiring__1(X22576)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22576),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22576),X22575),X22574)),X22573) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22576),hAPP(hAPP(c_Power_Opower__class_Opower(X22576),X22575),X22573)),hAPP(hAPP(c_Power_Opower__class_Opower(X22576),X22574),X22573)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J])]) ).

fof(i_0_8970,plain,
    ! [X22654,X22655,X22656,X22657] :
      ( ~ class_Groups_Ocomm__monoid__mult(X22657)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22657),X22656),X22655)),X22654) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22657),hAPP(hAPP(c_Power_Opower__class_Opower(X22657),X22656),X22654)),hAPP(hAPP(c_Power_Opower__class_Opower(X22657),X22655),X22654)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult__distrib])]) ).

fof(i_0_8971,plain,
    ! [X25751,X25752,X25753,X25754] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X25754)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25754),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25754),X25753),X25752)),X25751) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25754),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25754),X25753),X25751)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25754),X25752),X25751)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__add__distrib__left])]) ).

fof(i_0_8972,plain,
    ! [X25313,X25314,X25315,X25316] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X25316)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25316),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25316),X25315),X25314)),X25313) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25316),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25316),X25315),X25313)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25316),X25314),X25313)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__add__distrib__left])]) ).

fof(i_0_8973,plain,
    ! [X21599,X21600,X21601,X21602] :
      ( ~ class_Rings_Ocomm__semiring(X21602)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21602),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21602),X21601),X21600)),X21599) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21602),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21602),X21601),X21599)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21602),X21600),X21599)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib])]) ).

fof(i_0_8974,plain,
    ! [X21514,X21515,X21516,X21517] :
      ( ~ class_Rings_Ocomm__semiring__1(X21517)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21517),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21517),X21516),X21515)),X21514) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21517),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21517),X21516),X21514)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21517),X21515),X21514)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])]) ).

fof(i_0_8975,plain,
    ! [X18024,X18025,X18026,X18027] :
      ( ~ class_Lattices_Odistrib__lattice(X18027)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18027),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18027),X18026),X18025)),X18024) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18027),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18027),X18026),X18024)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18027),X18025),X18024)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib2])]) ).

fof(i_0_8976,plain,
    ! [X25712,X25713,X25714,X25715] :
      ( ~ class_Groups_Oordered__ab__group__add(X25715)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25715),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25715),X25714),X25713)),X25712) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25715),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25715),X25714),X25712)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25715),X25713),X25712)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__diff__distrib__left])]) ).

fof(i_0_8977,plain,
    ! [X25317,X25318,X25319,X25320] :
      ( ~ class_Groups_Oordered__ab__group__add(X25320)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25320),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25320),X25319),X25318)),X25317) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25320),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25320),X25319),X25317)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25320),X25318),X25317)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__diff__distrib__left])]) ).

fof(i_0_8978,plain,
    ! [X18028,X18029,X18030,X18031] :
      ( ~ class_Lattices_Odistrib__lattice(X18031)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18031),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18031),X18030),X18029)),X18028) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18031),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18031),X18030),X18028)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18031),X18029),X18028)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib2])]) ).

fof(i_0_8979,plain,
    ! [X32683,X32684,X32685,X32686,X32687] :
      ( ~ class_Orderings_Olinorder(X32687)
      | hAPP(c_List_Oset(X32686),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32686,X32687,X32685),X32684),X32683)) = hAPP(hAPP(c_Set_Oinsert(X32686),X32684),hAPP(c_List_Oset(X32686),X32683)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__insort])]) ).

fof(i_0_8980,plain,
    ! [X22360,X22361] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22361))
        | ~ 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),X22361),X22360))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22360))
        | ~ 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),X22361),X22360))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22361))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22360))
        | 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),X22361),X22360))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff])])]) ).

fof(i_0_8981,plain,
    ! [X23056,X23057] :
      ( ~ 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)),X23056))
      | 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),X23057),X23056))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I1_J])]) ).

fof(i_0_8982,plain,
    ! [X22961,X22962] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22962))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22961))
      | 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),X22962),X22961))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J])]) ).

fof(i_0_8983,plain,
    ! [X22959,X22960] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22960))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22959))
      | 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),X22960),X22959))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J])]) ).

fof(i_0_8984,plain,
    ! [X29018,X29019,X29020] :
      ( ~ class_Orderings_Olinorder(X29020)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29020),X29019))
      | hBOOL(hAPP(hAPP(c_member(X29020),X29018),X29019))
      | c_Big__Operators_Olattice_OSup__fin(X29020,c_Orderings_Oord__class_Omax(X29020),hAPP(hAPP(c_Set_Oinsert(X29020),X29018),X29019)) = hAPP(hAPP(c_Finite__Set_Ofold(X29020,X29020,c_Orderings_Oord__class_Omax(X29020)),X29018),X29019) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5852])]) ).

fof(i_0_8985,plain,
    ! [X29021,X29022,X29023] :
      ( ~ class_Orderings_Olinorder(X29023)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29023),X29022))
      | hBOOL(hAPP(hAPP(c_member(X29023),X29021),X29022))
      | c_Big__Operators_Olattice_OInf__fin(X29023,c_Orderings_Oord__class_Omin(X29023),hAPP(hAPP(c_Set_Oinsert(X29023),X29021),X29022)) = hAPP(hAPP(c_Finite__Set_Ofold(X29023,X29023,c_Orderings_Oord__class_Omin(X29023)),X29021),X29022) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5853])]) ).

fof(i_0_8986,plain,
    ! [X26950,X26951] :
      ( ~ class_Orderings_Olinorder(X26951)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26951,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X26951),X26950),c_Orderings_Obot__class_Obot(tc_fun(X26951,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26951),X26950)) = hAPP(c_SetInterval_Oord__class_OatLeast(X26951),X26950) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I1_J])]) ).

fof(i_0_8987,plain,
    ! [X28738,X28739,X28740] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28740,X28739)),hAPP(c_Relation_Oconverse(X28739,X28740),X28738)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28739,X28740)),X28738)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28739,X28740)),X28738))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28740,X28739)),hAPP(c_Relation_Oconverse(X28739,X28740),X28738))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__converse])]) ).

fof(i_0_8988,plain,
    ! [X22528] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22528),c_Orderings_Otop__class_Otop(tc_fun(X22528,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(X22528),c_Orderings_Otop__class_Otop(tc_fun(X22528,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0])]) ).

fof(i_0_8989,plain,
    ! [X32548,X32549,X32550] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X32550),X32549))
      | hAPP(c_List_Oset(X32550),c_List_Oremove1(X32550,X32548,X32549)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X32550,tc_HOL_Obool)),hAPP(c_List_Oset(X32550),X32549)),hAPP(hAPP(c_Set_Oinsert(X32550),X32548),c_Orderings_Obot__class_Obot(tc_fun(X32550,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__remove1__eq])]) ).

fof(i_0_8990,plain,
    ! [X29685,X29686,X29687] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29687,tc_HOL_Obool)),X29686),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29687,tc_HOL_Obool),X29685)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X29687,tc_HOL_Obool),tc_fun(X29687,tc_HOL_Obool)),X29685),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29687,tc_HOL_Obool)),X29686)),
    inference(variable_rename,[status(thm)],[fact_Int__Union]) ).

fof(i_0_8991,plain,
    ! [X29630,X29631,X29632] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29632,tc_HOL_Obool)),X29631),c_Complete__Lattice_OInf__class_OInf(tc_fun(X29632,tc_HOL_Obool),X29630)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X29632,tc_HOL_Obool),tc_fun(X29632,tc_HOL_Obool)),X29630),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29632,tc_HOL_Obool)),X29631)),
    inference(variable_rename,[status(thm)],[fact_Un__Inter]) ).

fof(i_0_8992,plain,
    ! [X18600,X18601,X18602,X18603,X18604] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18604),hAPP(X18602,X18601)),hAPP(X18602,X18600)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18603),X18601),X18600))
        | ~ c_Orderings_Oorder__class_Ostrict__mono(X18603,X18604,X18602)
        | ~ class_Orderings_Oorder(X18604)
        | ~ class_Orderings_Olinorder(X18603) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18603),X18601),X18600))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18604),hAPP(X18602,X18601)),hAPP(X18602,X18600)))
        | ~ c_Orderings_Oorder__class_Ostrict__mono(X18603,X18604,X18602)
        | ~ class_Orderings_Oorder(X18604)
        | ~ class_Orderings_Olinorder(X18603) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_strict__mono__less])])]) ).

fof(i_0_8993,plain,
    ! [X17168,X17169,X17170,X17171,X17172] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17172),hAPP(X17170,X17169)),hAPP(X17170,X17168)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17171),X17169),X17168))
        | ~ c_Orderings_Oorder__class_Ostrict__mono(X17171,X17172,X17170)
        | ~ class_Orderings_Oorder(X17172)
        | ~ class_Orderings_Olinorder(X17171) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17171),X17169),X17168))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17172),hAPP(X17170,X17169)),hAPP(X17170,X17168)))
        | ~ c_Orderings_Oorder__class_Ostrict__mono(X17171,X17172,X17170)
        | ~ class_Orderings_Oorder(X17172)
        | ~ class_Orderings_Olinorder(X17171) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_strict__mono__less__eq])])]) ).

fof(i_0_8994,plain,
    ! [X32663,X32664,X32665,X32666,X32667] :
      ( ~ class_Orderings_Olinorder(X32667)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32666)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32666,X32667,X32665),X32664),X32663)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32666)),X32663)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__insort])]) ).

fof(i_0_8995,plain,
    ! [X25272,X25273] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X25273)),X25272))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25273),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25272)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25273)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25273),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25272)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X25273)),X25272))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25273)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__iff])])]) ).

cnf(i_0_8996,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_5784]) ).

fof(i_0_8997,plain,
    ! [X18565,X18566] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18566,tc_HOL_Obool)),X18565),c_Orderings_Obot__class_Obot(tc_fun(X18566,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[i_0_5854]) ).

fof(i_0_8998,plain,
    ! [X19197,X19198,X19199,X19200,X19201] :
      ( hBOOL(hAPP(hAPP(c_member(X19201),X19200),X19199))
      | hAPP(c_Map_Orestrict__map(X19201,X19198,X19197,X19199),X19200) = c_Option_Ooption_ONone(X19198) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5855])]) ).

fof(i_0_8999,plain,
    ! [X32703,X32704,X32705] :
      ( ~ class_Orderings_Olinorder(X32705)
      | c_List_Oremove1(X32705,X32704,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32705,X32705,c_COMBI(X32705)),X32704),X32703)) = X32703 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remove1__insort])]) ).

fof(i_0_9000,plain,
    ! [X28232,X28233,X28234,X28235,X28236,X28237,X28238] :
      ( ( ~ hBOOL(hAPP(c_Predicate_OPowp(X28234,X28233),X28232))
        | ~ hBOOL(hAPP(hAPP(c_member(X28234),X28235),X28232))
        | hBOOL(hAPP(X28233,X28235)) )
      & ( hBOOL(hAPP(hAPP(c_member(X28238),esk295_3(X28236,X28237,X28238)),X28236))
        | hBOOL(hAPP(c_Predicate_OPowp(X28238,X28237),X28236)) )
      & ( ~ hBOOL(hAPP(X28237,esk295_3(X28236,X28237,X28238)))
        | hBOOL(hAPP(c_Predicate_OPowp(X28238,X28237),X28236)) ) ),
    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_9001,plain,
    ! [X19276,X19277,X19278,X19279] : hAPP(c_Map_Orestrict__map(X19279,X19278,X19277,c_Orderings_Obot__class_Obot(tc_fun(X19279,tc_HOL_Obool))),X19276) = c_Option_Ooption_ONone(X19278),
    inference(variable_rename,[status(thm)],[fact_restrict__map__to__empty]) ).

fof(i_0_9002,plain,
    ! [X24879,X24880,X24881] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X24881),X24880) != hAPP(c_Int_Onumber__class_Onumber__of(X24881),X24879)
        | c_Int_Oiszero(X24881,hAPP(c_Int_Onumber__class_Onumber__of(X24881),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24880),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24879))))
        | ~ class_Int_Onumber__ring(X24881) )
      & ( ~ c_Int_Oiszero(X24881,hAPP(c_Int_Onumber__class_Onumber__of(X24881),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24880),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24879))))
        | hAPP(c_Int_Onumber__class_Onumber__of(X24881),X24880) = hAPP(c_Int_Onumber__class_Onumber__of(X24881),X24879)
        | ~ class_Int_Onumber__ring(X24881) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__eq])])]) ).

fof(i_0_9003,plain,
    ! [X31831,X31832,X31833,X31834] :
      ( ( X31833 = hAPP(hAPP(c_List_Otake(X31834),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31834)),X31833)),X31831)
        | hAPP(hAPP(c_List_Oappend(X31834),X31833),X31832) != X31831 )
      & ( X31832 = hAPP(hAPP(c_List_Odrop(X31834),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31834)),X31833)),X31831)
        | hAPP(hAPP(c_List_Oappend(X31834),X31833),X31832) != X31831 )
      & ( X31833 != hAPP(hAPP(c_List_Otake(X31834),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31834)),X31833)),X31831)
        | X31832 != hAPP(hAPP(c_List_Odrop(X31834),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31834)),X31833)),X31831)
        | hAPP(hAPP(c_List_Oappend(X31834),X31833),X31832) = X31831 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__conv__conj])])]) ).

fof(i_0_9004,plain,
    ! [X29133,X29134,X29135] :
      ( ~ class_Groups_Oab__semigroup__mult(X29135)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29135),X29134))
      | hBOOL(hAPP(hAPP(c_member(X29135),X29133),X29134))
      | hAPP(c_Finite__Set_Ofold1(X29135,c_Groups_Otimes__class_Otimes(X29135)),hAPP(hAPP(c_Set_Oinsert(X29135),X29133),X29134)) = hAPP(hAPP(c_Finite__Set_Ofold(X29135,X29135,c_Groups_Otimes__class_Otimes(X29135)),X29133),X29134) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5856])]) ).

cnf(i_0_9005,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_5857]) ).

fof(i_0_9006,plain,
    ! [X23567,X23568] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X23567,X23568) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23567),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23568)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23567),X23568))
        | X23568 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X23567,X23568) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23567),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23568)) = 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),X23567),X23568))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | X23568 = 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_9007,plain,
    ! [X17181,X17182] : hAPP(c_Set_OCollect(X17182),hAPP(hAPP(c_COMBC(X17182,X17182,tc_HOL_Obool),c_fequal),X17181)) = hAPP(hAPP(c_Set_Oinsert(X17182),X17181),c_Orderings_Obot__class_Obot(tc_fun(X17182,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_singleton__conv]) ).

cnf(i_0_9008,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_5614]) ).

fof(i_0_9009,plain,
    ! [X17600,X17601,X17602] : hAPP(hAPP(c_Set_Oinsert(X17602),X17601),X17600) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17602,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17602),X17601),c_Orderings_Obot__class_Obot(tc_fun(X17602,tc_HOL_Obool)))),X17600),
    inference(variable_rename,[status(thm)],[fact_insert__is__Un]) ).

cnf(i_0_9010,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_5858]) ).

fof(i_0_9011,plain,
    ! [X20965,X20966,X20967] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20967),X20966))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20967),X20965)),X20966)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less])]) ).

fof(i_0_9012,plain,
    ! [X17956,X17957,X17958,X17959] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17959),X17958),X17957))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17959),X17958),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17959),X17957),X17956)))
        | ~ class_Lattices_Osemilattice__inf(X17959) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17959),X17958),X17956))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17959),X17958),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17959),X17957),X17956)))
        | ~ class_Lattices_Osemilattice__inf(X17959) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5859])])]) ).

fof(i_0_9013,plain,
    ! [X25376,X25377,X25378,X25379] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25379),X25378),X25377))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25379),X25378),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25379),X25377),X25376)))
        | ~ class_Orderings_Olinorder(X25379) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25379),X25378),X25376))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25379),X25378),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25379),X25377),X25376)))
        | ~ class_Orderings_Olinorder(X25379) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5860])])]) ).

fof(i_0_9014,plain,
    ! [X32593,X32594,X32595] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X32595),X32594),hAPP(c_List_Oset(X32595),X32593)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32595)),c_List_Oremove1(X32595,X32594,X32593)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32595)),X32593)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & ( hBOOL(hAPP(hAPP(c_member(X32595),X32594),hAPP(c_List_Oset(X32595),X32593)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32595)),c_List_Oremove1(X32595,X32594,X32593)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32595)),X32593) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5861])]) ).

fof(i_0_9015,plain,
    ! [X21864,X21865,X21866] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21866),X21865))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21865),X21864)),X21866) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21865),X21866)),X21864) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2])]) ).

fof(i_0_9016,plain,
    ! [X21861,X21862,X21863] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21863),X21862))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21862),X21863)),X21861) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21862),X21861)),X21863) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2])]) ).

fof(i_0_9017,plain,
    ! [X18114,X18115,X18116] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18116,tc_HOL_Obool)),X18115),X18114))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18116,tc_HOL_Obool)),X18115),X18114) = X18115 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb2])]) ).

fof(i_0_9018,plain,
    ! [X18111,X18112,X18113] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18113,tc_HOL_Obool)),X18112),X18111))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18113,tc_HOL_Obool)),X18111),X18112) = X18112 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb1])]) ).

fof(i_0_9019,plain,
    ! [X17514,X17515,X17516] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17516,tc_HOL_Obool)),X17515),X17514))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17516,tc_HOL_Obool)),X17515),X17514) = X17514 )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17516,tc_HOL_Obool)),X17515),X17514) != X17514
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17516,tc_HOL_Obool)),X17515),X17514)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__Un__eq])]) ).

fof(i_0_9020,plain,
    ! [X17511,X17512,X17513] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17513,tc_HOL_Obool)),X17512),X17511))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17513,tc_HOL_Obool)),X17512),X17511) = X17511 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__absorb1])]) ).

fof(i_0_9021,plain,
    ! [X17508,X17509,X17510] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17510,tc_HOL_Obool)),X17509),X17508))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17510,tc_HOL_Obool)),X17508),X17509) = X17508 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__absorb2])]) ).

fof(i_0_9022,plain,
    ! [X18216,X18217,X18218,X18219] :
      ( hBOOL(hAPP(hAPP(c_member(X18219),X18218),X18217))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18219,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X18219),X18218),X18216)),X18217) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18219,tc_HOL_Obool)),X18216),X18217) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5862])]) ).

fof(i_0_9023,plain,
    ! [X20491,X20492] : hAPP(c_Set_OCollect(X20492),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X20492),c_fNot),X20491)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20492,tc_HOL_Obool)),hAPP(c_Set_OCollect(X20492),X20491)),
    inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).

fof(i_0_9024,plain,
    ! [X31824,X31825,X31826] :
      ( ( hAPP(hAPP(c_List_Odrop(X31826),X31825),X31824) != c_List_Olist_ONil(X31826)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31826)),X31824)),X31825)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31826)),X31824)),X31825))
        | hAPP(hAPP(c_List_Odrop(X31826),X31825),X31824) = c_List_Olist_ONil(X31826) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__eq__Nil])]) ).

fof(i_0_9025,plain,
    ! [X31821,X31822,X31823] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31823)),X31822)),X31821))
      | hAPP(hAPP(c_List_Odrop(X31823),X31821),X31822) = c_List_Olist_ONil(X31823) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__all])]) ).

fof(i_0_9026,plain,
    ! [X17557,X17558,X17559,X17560] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17560),X17559),hAPP(hAPP(c_Set_Oinsert(X17560),X17558),X17557)))
        | X17559 = X17558
        | hBOOL(hAPP(hAPP(c_member(X17560),X17559),X17557)) )
      & ( X17559 != X17558
        | hBOOL(hAPP(hAPP(c_member(X17560),X17559),hAPP(hAPP(c_Set_Oinsert(X17560),X17558),X17557))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17560),X17559),X17557))
        | hBOOL(hAPP(hAPP(c_member(X17560),X17559),hAPP(hAPP(c_Set_Oinsert(X17560),X17558),X17557))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__iff])])]) ).

fof(i_0_9027,plain,
    ! [X17279,X17280,X17281,X17282] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17282),X17281),hAPP(hAPP(c_Set_Oinsert(X17282),X17280),X17279)))
      | X17281 = X17280
      | hBOOL(hAPP(hAPP(c_member(X17282),X17281),X17279)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertE])]) ).

cnf(i_0_9028,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_5787]) ).

cnf(i_0_9029,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_5789]) ).

cnf(i_0_9030,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_5788]) ).

cnf(i_0_9031,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_5790]) ).

cnf(i_0_9032,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_5791]) ).

cnf(i_0_9033,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_5792]) ).

fof(i_0_9034,plain,
    ! [X31106,X31107,X31108] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31108)),X31107)),X31106))
      | hAPP(hAPP(c_List_Otake(X31108),X31106),X31107) = X31107 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__all])]) ).

cnf(i_0_9035,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_5863]) ).

cnf(i_0_9036,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_5864]) ).

cnf(i_0_9037,plain,
    ( c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X2))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5865]) ).

fof(i_0_9038,plain,
    ! [X26184,X26185,X26186,X26187] :
      ( ~ class_Orderings_Olinorder(X26187)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26187),X26186),X26185))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26187,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26187,X26186),X26184)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26187,X26186),X26185)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26187,X26185),X26184) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__diff])]) ).

fof(i_0_9039,plain,
    ! [X23617,X23618,X23619,X23620,X23621,X23622,X23623] :
      ( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X23619,X23618),X23617))
        | ~ hBOOL(hAPP(hAPP(X23618,X23620),X23617))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X23619,X23618),X23620)) )
      & ( hBOOL(hAPP(hAPP(X23622,esk132_3(X23621,X23622,X23623)),X23621))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X23623,X23622),X23621)) )
      & ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X23623,X23622),esk132_3(X23621,X23622,X23623)))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X23623,X23622),X23621)) ) ),
    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])])])])])]) ).

fof(i_0_9040,plain,
    ! [X23609,X23610,X23611,X23612,X23613,X23614,X23615] :
      ( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X23611,X23610),X23609))
        | ~ hBOOL(hAPP(hAPP(X23610,X23612),X23609))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X23611,X23610),X23612)) )
      & ( hBOOL(hAPP(hAPP(X23614,esk131_3(X23613,X23614,X23615)),X23613))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X23615,X23614),X23613)) )
      & ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X23615,X23614),esk131_3(X23613,X23614,X23615)))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X23615,X23614),X23613)) ) ),
    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])])])])])]) ).

cnf(i_0_9041,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X2),X3),c_Relation_OId(X2)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_5866]) ).

fof(i_0_9042,plain,
    ! [X27692,X27693,X27694,X27695] :
      ( ( hAPP(hAPP(c_Product__Type_OSigma(X27695,X27694),X27693),hAPP(c_COMBK(tc_fun(X27694,tc_HOL_Obool),X27695),X27692)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27695,X27694),tc_HOL_Obool))
        | X27693 = c_Orderings_Obot__class_Obot(tc_fun(X27695,tc_HOL_Obool))
        | X27692 = c_Orderings_Obot__class_Obot(tc_fun(X27694,tc_HOL_Obool)) )
      & ( X27693 != c_Orderings_Obot__class_Obot(tc_fun(X27695,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(X27695,X27694),X27693),hAPP(c_COMBK(tc_fun(X27694,tc_HOL_Obool),X27695),X27692)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27695,X27694),tc_HOL_Obool)) )
      & ( X27692 != c_Orderings_Obot__class_Obot(tc_fun(X27694,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(X27695,X27694),X27693),hAPP(c_COMBK(tc_fun(X27694,tc_HOL_Obool),X27695),X27692)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27695,X27694),tc_HOL_Obool)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__empty])])]) ).

cnf(i_0_9043,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_5797]) ).

fof(i_0_9044,plain,
    ! [X26909,X26910,X26911] :
      ( ~ class_Orderings_Olinorder(X26911)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26911),X26910),X26909))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26911,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26911,X26910,X26909)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26911),X26909)) = hAPP(c_SetInterval_Oord__class_OatLeast(X26911),X26910) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I13_J])]) ).

fof(i_0_9045,plain,
    ! [X26889,X26890,X26891] :
      ( ~ class_Orderings_Olinorder(X26891)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26891),X26890),X26889))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26891,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X26891,X26890,X26889)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26891),X26889)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X26891),X26890) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I11_J])]) ).

fof(i_0_9046,plain,
    ! [X26900,X26901,X26902] :
      ( ~ class_Orderings_Olinorder(X26902)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26902),X26901),X26900))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26902,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X26902,X26901,X26900)),hAPP(c_SetInterval_Oord__class_OatLeast(X26902),X26900)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X26902),X26901) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I12_J])]) ).

fof(i_0_9047,plain,
    ! [X32052,X32053] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X32053)
      | c_Complete__Lattice_OSup__class_OSup(X32053,hAPP(c_List_Oset(X32053),X32052)) = hAPP(c_List_Ofoldl(X32053,X32053,c_Lattices_Osemilattice__sup__class_Osup(X32053),c_Orderings_Obot__class_Obot(X32053)),X32052) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__set__fold])]) ).

fof(i_0_9048,plain,
    ! [X32054,X32055] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X32055)
      | c_Complete__Lattice_OInf__class_OInf(X32055,hAPP(c_List_Oset(X32055),X32054)) = hAPP(c_List_Ofoldl(X32055,X32055,c_Lattices_Osemilattice__inf__class_Oinf(X32055),c_Orderings_Otop__class_Otop(X32055)),X32054) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__set__fold])]) ).

cnf(i_0_9049,plain,
    ( c_Map_Omap__comp(X3,X4,X5,X6,X1,X2) = c_Option_Ooption_ONone(X4)
    | hAPP(X1,X2) != c_Option_Ooption_ONone(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_5420]) ).

cnf(i_0_9050,plain,
    ( c_Map_Omap__comp(X3,X4,X5,X6,X1,X2) = c_Option_Ooption_ONone(X4)
    | hAPP(X1,X2) != c_Option_Ooption_ONone(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_5867]) ).

fof(i_0_9051,plain,
    ! [X26269,X26270] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X26270,X26269)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26269),X26270)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[fact_card__atLeastAtMost__int]) ).

fof(i_0_9052,plain,
    ! [X20329,X20330,X20331,X20332] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20332),X20331))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20330),hAPP(c_Set_Oimage(X20332,X20330,X20329),X20331))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])]) ).

cnf(i_0_9053,plain,
    ( c_List_Oconcat(X2,X1) = c_List_Olist_ONil(X2)
    | esk448_2(X1,X2) != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5695]) ).

cnf(i_0_9054,plain,
    ( c_List_Olist_ONil(X2) = c_List_Oconcat(X2,X1)
    | esk449_2(X1,X2) != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5696]) ).

fof(i_0_9055,plain,
    ! [X29788,X29789,X29790] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29790)
      | c_Complete__Lattice_OSup__class_OSup(X29790,hAPP(hAPP(c_Set_Oinsert(X29790),X29789),hAPP(hAPP(c_Set_Oinsert(X29790),X29788),c_Orderings_Obot__class_Obot(tc_fun(X29790,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X29790),X29789),X29788) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__binary])]) ).

fof(i_0_9056,plain,
    ! [X29791,X29792,X29793] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29793)
      | c_Complete__Lattice_OInf__class_OInf(X29793,hAPP(hAPP(c_Set_Oinsert(X29793),X29792),hAPP(hAPP(c_Set_Oinsert(X29793),X29791),c_Orderings_Obot__class_Obot(tc_fun(X29793,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X29793),X29792),X29791) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__binary])]) ).

fof(i_0_9057,plain,
    ! [X20913,X20914,X20915,X20916] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20916),X20915),c_SetInterval_Oord_OlessThan(X20916,X20914,X20913)))
        | hBOOL(hAPP(hAPP(X20914,X20915),X20913)) )
      & ( ~ hBOOL(hAPP(hAPP(X20914,X20915),X20913))
        | hBOOL(hAPP(hAPP(c_member(X20916),X20915),c_SetInterval_Oord_OlessThan(X20916,X20914,X20913))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OlessThan__iff])]) ).

fof(i_0_9058,plain,
    ! [X20905,X20906,X20907,X20908] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20908),X20907),c_SetInterval_Oord_OatMost(X20908,X20906,X20905)))
        | hBOOL(hAPP(hAPP(X20906,X20907),X20905)) )
      & ( ~ hBOOL(hAPP(hAPP(X20906,X20907),X20905))
        | hBOOL(hAPP(hAPP(c_member(X20908),X20907),c_SetInterval_Oord_OatMost(X20908,X20906,X20905))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatMost__iff])]) ).

fof(i_0_9059,plain,
    ! [X20917,X20918,X20919,X20920] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20920),X20919),c_SetInterval_Oord_OgreaterThan(X20920,X20918,X20917)))
        | hBOOL(hAPP(hAPP(X20918,X20917),X20919)) )
      & ( ~ hBOOL(hAPP(hAPP(X20918,X20917),X20919))
        | hBOOL(hAPP(hAPP(c_member(X20920),X20919),c_SetInterval_Oord_OgreaterThan(X20920,X20918,X20917))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThan__iff])]) ).

fof(i_0_9060,plain,
    ! [X20909,X20910,X20911,X20912] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20912),X20911),c_SetInterval_Oord_OatLeast(X20912,X20910,X20909)))
        | hBOOL(hAPP(hAPP(X20910,X20909),X20911)) )
      & ( ~ hBOOL(hAPP(hAPP(X20910,X20909),X20911))
        | hBOOL(hAPP(hAPP(c_member(X20912),X20911),c_SetInterval_Oord_OatLeast(X20912,X20910,X20909))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeast__iff])]) ).

fof(i_0_9061,plain,
    ! [X32599,X32600,X32601,X32602,X32603] :
      ( c_List_Opartition(X32603,X32602,X32601) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32603),tc_List_Olist(X32603)),X32600),X32599)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X32603,tc_HOL_Obool)),hAPP(c_List_Oset(X32603),X32600)),hAPP(c_List_Oset(X32603),X32599)) = hAPP(c_List_Oset(X32603),X32601) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_partition__set])]) ).

fof(i_0_9062,plain,
    ! [X31024,X31025,X31026,X31027] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31027) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Onth(X31026),hAPP(hAPP(c_List_Olist_OCons(X31026),X31025),X31024)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31027)) = X31025 )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31027) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Onth(X31026),hAPP(hAPP(c_List_Olist_OCons(X31026),X31025),X31024)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31027)) = hAPP(hAPP(c_List_Onth(X31026),X31024),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31027)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__Cons__number__of])]) ).

cnf(i_0_9063,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_5868]) ).

fof(i_0_9064,plain,
    ! [X28577,X28578] : hAPP(hAPP(c_Relation_Orel__comp(X28578,X28578,X28578),X28577),c_Transitive__Closure_Ortrancl(X28578,X28577)) = hAPP(hAPP(c_Relation_Orel__comp(X28578,X28578,X28578),c_Transitive__Closure_Ortrancl(X28578,X28577)),X28577),
    inference(variable_rename,[status(thm)],[fact_r__comp__rtrancl__eq]) ).

fof(i_0_9065,plain,
    ! [X34330,X34331,X34332,X34333,X34334,X34335] : hAPP(hAPP(hAPP(c_COMBS(X34335,X34334,X34333),X34332),X34331),X34330) = hAPP(hAPP(X34332,X34330),hAPP(X34331,X34330)),
    inference(variable_rename,[status(thm)],[help_c__COMBS__1]) ).

cnf(i_0_9066,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_5869]) ).

fof(i_0_9067,plain,
    ! [X27119,X27120] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27120)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27120),hAPP(c_Groups_Ouminus__class_Ouminus(X27120),hAPP(c_Groups_Oabs__class_Oabs(X27120),X27119))),c_Groups_Ozero__class_Ozero(X27120))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__le__zero])]) ).

fof(i_0_9068,plain,
    ! [X17495,X17496,X17497,X17498] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17498,tc_HOL_Obool)),X17497),hAPP(hAPP(c_Set_Oinsert(X17498),X17496),X17495)) = hAPP(hAPP(c_Set_Oinsert(X17498),X17496),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17498,tc_HOL_Obool)),X17497),X17495)),
    inference(variable_rename,[status(thm)],[fact_Un__insert__right]) ).

fof(i_0_9069,plain,
    ! [X22102,X22103,X22104] :
      ( ( X22103 = c_Groups_Ozero__class_Ozero(X22104)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22104),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22104),X22103),X22103)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22104),X22102),X22102)) != c_Groups_Ozero__class_Ozero(X22104)
        | ~ class_Rings_Olinordered__ring__strict(X22104) )
      & ( X22102 = c_Groups_Ozero__class_Ozero(X22104)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22104),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22104),X22103),X22103)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22104),X22102),X22102)) != c_Groups_Ozero__class_Ozero(X22104)
        | ~ class_Rings_Olinordered__ring__strict(X22104) )
      & ( X22103 != c_Groups_Ozero__class_Ozero(X22104)
        | X22102 != c_Groups_Ozero__class_Ozero(X22104)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22104),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22104),X22103),X22103)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22104),X22102),X22102)) = c_Groups_Ozero__class_Ozero(X22104)
        | ~ class_Rings_Olinordered__ring__strict(X22104) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff])])]) ).

fof(i_0_9070,plain,
    ! [X29968,X29969,X29970,X29971,X29972,X29973] :
      ( hAPP(X29973,X29972) != hAPP(c_Option_Ooption_OSome(X29971),X29970)
      | hAPP(c_Map_Omap__add(X29969,X29971,X29968,X29973),X29972) = hAPP(c_Option_Ooption_OSome(X29971),X29970) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__find__right])]) ).

fof(i_0_9071,plain,
    ! [X29043,X29044,X29045] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29045),X29044))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29045,tc_HOL_Obool)),X29044),X29043) = hAPP(hAPP(c_Finite__Set_Ofold(X29045,tc_fun(X29045,tc_HOL_Obool),c_Set_Oinsert(X29045)),X29043),X29044) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_union__fold__insert])]) ).

fof(i_0_9072,plain,
    ! [X24959,X24960] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X24960),X24959) != c_Groups_Ozero__class_Ozero(X24960)
        | c_Int_Oiszero(X24960,hAPP(c_Int_Onumber__class_Onumber__of(X24960),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24959),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
        | ~ class_Int_Onumber__ring(X24960) )
      & ( ~ c_Int_Oiszero(X24960,hAPP(c_Int_Onumber__class_Onumber__of(X24960),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24959),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
        | hAPP(c_Int_Onumber__class_Onumber__of(X24960),X24959) = c_Groups_Ozero__class_Ozero(X24960)
        | ~ class_Int_Onumber__ring(X24960) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I3_J])])]) ).

fof(i_0_9073,plain,
    ! [X24957,X24958] :
      ( ( c_Groups_Ozero__class_Ozero(X24958) != hAPP(c_Int_Onumber__class_Onumber__of(X24958),X24957)
        | c_Int_Oiszero(X24958,hAPP(c_Int_Onumber__class_Onumber__of(X24958),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24957))))
        | ~ class_Int_Onumber__ring(X24958) )
      & ( ~ c_Int_Oiszero(X24958,hAPP(c_Int_Onumber__class_Onumber__of(X24958),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24957))))
        | c_Groups_Ozero__class_Ozero(X24958) = hAPP(c_Int_Onumber__class_Onumber__of(X24958),X24957)
        | ~ class_Int_Onumber__ring(X24958) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I1_J])])]) ).

fof(i_0_9074,plain,
    ! [X27389,X27390,X27391,X27392] :
      ( ~ c_Wellfounded_Owf(X27392,X27391)
      | ~ c_Wellfounded_Owf(X27390,X27389)
      | c_Wellfounded_Owf(tc_prod(X27392,X27390),c_Wellfounded_Olex__prod(X27392,X27390,X27391,X27389)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lex__prod])]) ).

cnf(i_0_9075,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_5870]) ).

fof(i_0_9076,plain,
    ! [X30754,X30755,X30756,X30757] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30757),X30756))
      | hBOOL(hAPP(c_List_Odistinct(tc_prod(X30757,X30755)),hAPP(hAPP(c_List_Ozip(X30757,X30755),X30756),X30754))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__zipI1])]) ).

fof(i_0_9077,plain,
    ! [X30750,X30751,X30752,X30753] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30753),X30752))
      | hBOOL(hAPP(c_List_Odistinct(tc_prod(X30751,X30753)),hAPP(hAPP(c_List_Ozip(X30751,X30753),X30750),X30752))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__zipI2])]) ).

fof(i_0_9078,plain,
    ! [X29142,X29143,X29144] :
      ( ~ class_Orderings_Olinorder(X29144)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29144),X29143))
      | hBOOL(hAPP(hAPP(c_member(X29144),X29142),X29143))
      | c_Big__Operators_Olinorder__class_OMin(X29144,hAPP(hAPP(c_Set_Oinsert(X29144),X29142),X29143)) = hAPP(hAPP(c_Finite__Set_Ofold(X29144,X29144,c_Orderings_Oord__class_Omin(X29144)),X29142),X29143) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5871])]) ).

fof(i_0_9079,plain,
    ! [X29145,X29146,X29147] :
      ( ~ class_Orderings_Olinorder(X29147)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29147),X29146))
      | hBOOL(hAPP(hAPP(c_member(X29147),X29145),X29146))
      | c_Big__Operators_Olinorder__class_OMax(X29147,hAPP(hAPP(c_Set_Oinsert(X29147),X29145),X29146)) = hAPP(hAPP(c_Finite__Set_Ofold(X29147,X29147,c_Orderings_Oord__class_Omax(X29147)),X29145),X29146) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5872])]) ).

fof(i_0_9080,plain,
    ! [X29136,X29137,X29138] :
      ( ~ class_Lattices_Olattice(X29138)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29138),X29137))
      | hBOOL(hAPP(hAPP(c_member(X29138),X29136),X29137))
      | c_Big__Operators_Olattice__class_OSup__fin(X29138,hAPP(hAPP(c_Set_Oinsert(X29138),X29136),X29137)) = hAPP(hAPP(c_Finite__Set_Ofold(X29138,X29138,c_Lattices_Osemilattice__sup__class_Osup(X29138)),X29136),X29137) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5873])]) ).

fof(i_0_9081,plain,
    ! [X29139,X29140,X29141] :
      ( ~ class_Lattices_Olattice(X29141)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29141),X29140))
      | hBOOL(hAPP(hAPP(c_member(X29141),X29139),X29140))
      | c_Big__Operators_Olattice__class_OInf__fin(X29141,hAPP(hAPP(c_Set_Oinsert(X29141),X29139),X29140)) = hAPP(hAPP(c_Finite__Set_Ofold(X29141,X29141,c_Lattices_Osemilattice__inf__class_Oinf(X29141)),X29139),X29140) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5874])]) ).

fof(i_0_9082,plain,
    ! [X29688,X29689,X29690,X29691] : hAPP(c_Set_Ovimage(X29691,X29690,X29689),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29690,tc_HOL_Obool),X29688)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X29690,tc_HOL_Obool),tc_fun(X29691,tc_HOL_Obool)),X29688),c_Set_Ovimage(X29691,X29690,X29689)),
    inference(variable_rename,[status(thm)],[fact_vimage__Union]) ).

fof(i_0_9083,plain,
    ! [X29696,X29697,X29698,X29699] : hAPP(c_Set_Oimage(X29699,X29698,X29697),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29699,tc_HOL_Obool),X29696)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X29699,tc_HOL_Obool),tc_fun(X29698,tc_HOL_Obool)),X29696),c_Set_Oimage(X29699,X29698,X29697)),
    inference(variable_rename,[status(thm)],[fact_image__Union]) ).

fof(i_0_9084,plain,
    ! [X17231,X17232,X17233] :
      ( ( hBOOL(hAPP(X17232,esk8_3(X17231,X17232,X17233)))
        | c_Orderings_Oord__class_OLeast(X17233,X17232) = X17231
        | ~ hBOOL(hAPP(X17232,X17231))
        | ~ class_Orderings_Oorder(X17233) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17233),X17231),esk8_3(X17231,X17232,X17233)))
        | c_Orderings_Oord__class_OLeast(X17233,X17232) = X17231
        | ~ hBOOL(hAPP(X17232,X17231))
        | ~ class_Orderings_Oorder(X17233) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Least__equality])])])]) ).

fof(i_0_9085,plain,
    ! [X18143,X18144] : hBOOL(hAPP(hAPP(c_member(tc_fun(X18144,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X18144,tc_HOL_Obool))),hAPP(c_Set_OPow(X18144),X18143))),
    inference(variable_rename,[status(thm)],[fact_Pow__bottom]) ).

fof(i_0_9086,plain,
    ! [X30386,X30387,X30388] :
      ( ~ class_Groups_Omonoid__add(X30388)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30388),hAPP(hAPP(c_List_Omap(X30387,X30388),hAPP(c_COMBK(X30388,X30387),c_Groups_Ozero__class_Ozero(X30388))),X30386)) = c_Groups_Ozero__class_Ozero(X30388) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__0])]) ).

fof(i_0_9087,plain,
    ! [X17913,X17914,X17915] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17915,tc_HOL_Obool)),X17914),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17915,tc_HOL_Obool)),X17914),X17913)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17915,tc_HOL_Obool)),X17914),X17913),
    inference(variable_rename,[status(thm)],[fact_Int__left__absorb]) ).

fof(i_0_9088,plain,
    ! [X18099,X18100,X18101] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18101,tc_HOL_Obool)),X18100),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18101,tc_HOL_Obool)),X18099),X18100)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X18101,tc_HOL_Obool)),X18100),X18099),
    inference(variable_rename,[status(thm)],[fact_Un__Diff__cancel]) ).

fof(i_0_9089,plain,
    ! [X17407,X17408,X17409] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17409,tc_HOL_Obool)),X17408),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17409,tc_HOL_Obool)),X17408),X17407)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17409,tc_HOL_Obool)),X17408),X17407),
    inference(variable_rename,[status(thm)],[fact_Un__left__absorb]) ).

fof(i_0_9090,plain,
    ! [X31867,X31868] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31868)),X31867)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | hAPP(c_List_Orotate1(X31868),X31867) = X31867 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__length01])]) ).

fof(i_0_9091,plain,
    ! [X21188,X21189,X21190,X21191,X21192] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21192,X21191,X21190),X21189),X21188),c_Orderings_Obot__class_Obot(tc_fun(X21191,tc_HOL_Obool))) = X21188,
    inference(variable_rename,[status(thm)],[fact_fold__image__empty]) ).

fof(i_0_9092,plain,
    ! [X22455,X22456] :
      ( ( X22456 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22456),X22455) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22456 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22456),X22455) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22455),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22456),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X22455)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__if])]) ).

fof(i_0_9093,plain,
    ! [X33129,X33130,X33131] : c_List_Olistsp(X33131,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33131,tc_HOL_Obool)),X33130),X33129)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X33131),tc_HOL_Obool)),c_List_Olistsp(X33131,X33130)),c_List_Olistsp(X33131,X33129)),
    inference(variable_rename,[status(thm)],[fact_listsp__inf__eq]) ).

fof(i_0_9094,plain,
    ! [X27569,X27570,X27571,X27572,X27574,X27575,X27576,X27577,X27578] :
      ( ( ~ hBOOL(hAPP(c_Predicate_ORangeP(X27572,X27571,X27570),X27569))
        | hBOOL(hAPP(hAPP(X27570,esk266_2(X27569,X27570)),X27569)) )
      & ( ~ hBOOL(hAPP(hAPP(X27575,X27576),X27574))
        | hBOOL(hAPP(c_Predicate_ORangeP(X27578,X27577,X27575),X27574)) ) ),
    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_9095,plain,
    ! [X24514,X24515] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24515)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24514)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24515) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24514) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24514)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24515) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24515)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24515) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24514) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24514)))
        | X24515 = X24514
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24515)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24515) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24514) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24515)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24515)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24515) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24514) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24514)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24514)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24515)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24515) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24514) )
      & ( X24515 != X24514
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24514)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24515)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24515) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24514) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24514)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24515) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24515)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24515) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24514) )
      & ( X24515 != X24514
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24515) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24515)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24515) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24514) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24515)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24514)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24515) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24514) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24514)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24514)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24514)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24515) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24514) )
      & ( X24515 != X24514
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24514)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24514)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24515) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24514) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24514)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24515) != 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),X24514)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24515) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24514) )
      & ( X24515 != X24514
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24515) != 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),X24514)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24515) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24514) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5875])])]) ).

fof(i_0_9096,plain,
    ! [X24590,X24591] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24591),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24591),X24590)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24591))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24590))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__distrib__neg])]) ).

fof(i_0_9097,plain,
    ! [X30037,X30038,X30039] : hBOOL(hAPP(c_Finite__Set_Ofinite(X30039),c_Map_Odom(X30039,X30038,hAPP(c_Map_Omap__of(X30039,X30038),X30037)))),
    inference(variable_rename,[status(thm)],[fact_finite__dom__map__of]) ).

fof(i_0_9098,plain,
    ! [X34110,X34111,X34112,X34113] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X34113,X34112)),c_Nitpick_Opair__box_OPairBox(X34113,X34112,X34111,X34110)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_pair__box_Osize_I2_J]) ).

fof(i_0_9099,plain,
    ! [X32212,X32213,X32214,X32215] :
      ( ( X32215 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32214)),X32213)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_List_Obutlast(X32214,hAPP(hAPP(c_List_Olist__update(X32214,X32213),X32215),X32212)) = c_List_Obutlast(X32214,X32213) )
      & ( X32215 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32214)),X32213)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_List_Obutlast(X32214,hAPP(hAPP(c_List_Olist__update(X32214,X32213),X32215),X32212)) = hAPP(hAPP(c_List_Olist__update(X32214,c_List_Obutlast(X32214,X32213)),X32215),X32212) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__list__update])]) ).

fof(i_0_9100,plain,
    ! [X17457,X17458,X17459,X17460,X17461] : hAPP(c_Set_Oimage(X17461,X17460,X17459),hAPP(hAPP(c_Set_Oinsert(X17461),X17458),X17457)) = hAPP(hAPP(c_Set_Oinsert(X17460),hAPP(X17459,X17458)),hAPP(c_Set_Oimage(X17461,X17460,X17459),X17457)),
    inference(variable_rename,[status(thm)],[fact_image__insert]) ).

cnf(i_0_9101,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_5635]) ).

fof(i_0_9102,plain,
    ! [X20462,X20463,X20464] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20464,tc_HOL_Obool)),X20463),X20462))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20464),X20462))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20464),X20463)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__subset])]) ).

fof(i_0_9103,plain,
    ! [X20465,X20466,X20467] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20467),X20466))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20467,tc_HOL_Obool)),X20465),X20466))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20467),X20465)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__finite__subset])]) ).

fof(i_0_9104,plain,
    ! [X22298,X22299] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22299),hAPP(c_Groups_Ouminus__class_Ouminus(X22299),X22298)),c_Groups_Ozero__class_Ozero(X22299)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22299),c_Groups_Ozero__class_Ozero(X22299)),X22298))
        | ~ class_Groups_Oordered__ab__group__add(X22299) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22299),c_Groups_Ozero__class_Ozero(X22299)),X22298))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22299),hAPP(c_Groups_Ouminus__class_Ouminus(X22299),X22298)),c_Groups_Ozero__class_Ozero(X22299)))
        | ~ class_Groups_Oordered__ab__group__add(X22299) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less])])]) ).

fof(i_0_9105,plain,
    ! [X22290,X22291] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22291),hAPP(c_Groups_Ouminus__class_Ouminus(X22291),X22290)),c_Groups_Ozero__class_Ozero(X22291)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22291),c_Groups_Ozero__class_Ozero(X22291)),X22290))
        | ~ class_Groups_Oordered__ab__group__add(X22291) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22291),c_Groups_Ozero__class_Ozero(X22291)),X22290))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22291),hAPP(c_Groups_Ouminus__class_Ouminus(X22291),X22290)),c_Groups_Ozero__class_Ozero(X22291)))
        | ~ class_Groups_Oordered__ab__group__add(X22291) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le])])]) ).

fof(i_0_9106,plain,
    ! [X32668,X32669,X32670,X32671] :
      ( ~ class_Orderings_Olinorder(X32671)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32670)),c_List_Olinorder__class_Osort__key(X32670,X32671,X32669,X32668)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32670)),X32668) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__sort])]) ).

fof(i_0_9107,plain,
    ! [X18621,X18622] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X18622)
      | ~ c_Orderings_Oorder__class_Omono(X18622,X18622,X18621)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18622),hAPP(X18621,c_Inductive_Ocomplete__lattice__class_Olfp(X18622,X18621))),c_Inductive_Ocomplete__lattice__class_Olfp(X18622,X18621))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lfp__lemma2])]) ).

fof(i_0_9108,plain,
    ! [X18175,X18176] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X18176)
      | ~ c_Orderings_Oorder__class_Omono(X18176,X18176,X18175)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18176),hAPP(X18175,c_Inductive_Ocomplete__lattice__class_Ogfp(X18176,X18175))),c_Inductive_Ocomplete__lattice__class_Ogfp(X18176,X18175))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gfp__lemma3])]) ).

fof(i_0_9109,plain,
    ! [X32906,X32907,X32908,X32909] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32909)),X32908) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32907)),X32906)
      | hAPP(hAPP(c_List_Ozip(X32909,X32907),hAPP(c_List_Orev(X32909),X32908)),hAPP(c_List_Orev(X32907),X32906)) = hAPP(c_List_Orev(tc_prod(X32909,X32907)),hAPP(hAPP(c_List_Ozip(X32909,X32907),X32908),X32906)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__rev])]) ).

fof(i_0_9110,plain,
    ! [X22706,X22707] :
      ( ( ~ 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),X22707),X22706)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22707))
        | X22706 = 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)),X22707))
        | 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),X22707),X22706))) )
      & ( X22706 != 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),X22707),X22706))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff])])]) ).

fof(i_0_9111,plain,
    ! [X26932,X26933,X26934,X26935] :
      ( ~ class_Orderings_Olinorder(X26935)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26935,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26935,X26934,X26933)),hAPP(c_SetInterval_Oord__class_OatLeast(X26935),X26932)) = c_SetInterval_Oord__class_OatLeastAtMost(X26935,hAPP(hAPP(c_Orderings_Oord__class_Omax(X26935),X26934),X26932),X26933) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL2])]) ).

fof(i_0_9112,plain,
    ! [X26817,X26818,X26819,X26820] :
      ( ~ class_Orderings_Olinorder(X26820)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26820,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26820,X26819,X26818)),hAPP(c_SetInterval_Oord__class_OatMost(X26820),X26817)) = c_SetInterval_Oord__class_OatLeastAtMost(X26820,X26819,hAPP(hAPP(c_Orderings_Oord__class_Omin(X26820),X26818),X26817)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL1])]) ).

fof(i_0_9113,plain,
    ! [X31185,X31186,X31187,X31188] : hAPP(hAPP(c_List_Olist__update(X31188,hAPP(hAPP(c_List_Olist_OCons(X31188),X31187),X31186)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31185) = hAPP(hAPP(c_List_Olist_OCons(X31188),X31185),X31186),
    inference(variable_rename,[status(thm)],[fact_list__update__code_I2_J]) ).

fof(i_0_9114,plain,
    ! [X34324,X34325,X34326,X34327,X34328,X34329] : hAPP(hAPP(hAPP(c_COMBC(X34329,X34328,X34327),X34326),X34325),X34324) = hAPP(hAPP(X34326,X34324),X34325),
    inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).

fof(i_0_9115,plain,
    ! [X34318,X34319,X34320,X34321,X34322,X34323] : hAPP(hAPP(hAPP(c_COMBB(X34323,X34322,X34321),X34320),X34319),X34318) = hAPP(X34320,hAPP(X34319,X34318)),
    inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).

fof(i_0_9116,plain,
    ! [X20315,X20316,X20317,X20318,X20319] : hAPP(c_Option_Ooption_Ooption__case(X20319,X20318,X20317,X20316),hAPP(c_Option_Ooption_OSome(X20318),X20315)) = hAPP(X20316,X20315),
    inference(variable_rename,[status(thm)],[fact_option_Osimps_I5_J]) ).

fof(i_0_9117,plain,
    ! [X27140,X27141] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27141),hAPP(c_Int_Onumber__class_Onumber__of(X27141),X27140)),c_Groups_Ozero__class_Ozero(X27141)))
        | hAPP(c_Groups_Oabs__class_Oabs(X27141),hAPP(c_Int_Onumber__class_Onumber__of(X27141),X27140)) = hAPP(c_Groups_Ouminus__class_Ouminus(X27141),hAPP(c_Int_Onumber__class_Onumber__of(X27141),X27140))
        | ~ class_Int_Onumber__ring(X27141)
        | ~ class_Rings_Olinordered__idom(X27141) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27141),hAPP(c_Int_Onumber__class_Onumber__of(X27141),X27140)),c_Groups_Ozero__class_Ozero(X27141)))
        | hAPP(c_Groups_Oabs__class_Oabs(X27141),hAPP(c_Int_Onumber__class_Onumber__of(X27141),X27140)) = hAPP(c_Int_Onumber__class_Onumber__of(X27141),X27140)
        | ~ class_Int_Onumber__ring(X27141)
        | ~ class_Rings_Olinordered__idom(X27141) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5876])])]) ).

fof(i_0_9118,plain,
    ! [X20453,X20454,X20455,X20456] : hAPP(c_Set_Ovimage(X20456,X20455,X20454),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20455,tc_HOL_Obool)),X20453)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20456,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X20456,X20455,X20454),X20453)),
    inference(variable_rename,[status(thm)],[fact_vimage__Compl]) ).

fof(i_0_9119,plain,
    ! [X23655,X23656,X23657] : 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),X23657),X23656)),X23655),X23656) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23655,X23656),
    inference(variable_rename,[status(thm)],[fact_mod__mult__self3]) ).

fof(i_0_9120,plain,
    ! [X24576,X24577] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24577))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24576))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X24577)),hAPP(c_Int_Onat,X24576)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24577),X24576)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__functions_I1_J])]) ).

fof(i_0_9121,plain,
    ! [X24562,X24563] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24563))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24562))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X24563)),hAPP(c_Int_Onat,X24562)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24563),X24562)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J])]) ).

fof(i_0_9122,plain,
    ! [X24566,X24567] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24567))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24566))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X24567)),hAPP(c_Int_Onat,X24566)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24567),X24566)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J])]) ).

fof(i_0_9123,plain,
    ! [X24560,X24561] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24561))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24560))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24561),X24560)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X24561)),hAPP(c_Int_Onat,X24560)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__distrib])]) ).

fof(i_0_9124,plain,
    ! [X30744,X30745,X30746,X30747] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X30747,X30746))),hAPP(hAPP(c_List_Ozip(X30747,X30746),X30745),X30744)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30747)),X30745)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30746)),X30744)),
    inference(variable_rename,[status(thm)],[fact_length__zip]) ).

fof(i_0_9125,plain,
    ! [X29738,X29739,X29740,X29741] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X29741,tc_HOL_Obool),hAPP(c_Set_Oimage(X29740,tc_fun(X29741,tc_HOL_Obool),X29739),X29738)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29740,tc_fun(X29741,tc_HOL_Obool)),X29738),X29739),
    inference(variable_rename,[status(thm)],[fact_Union__image__eq]) ).

fof(i_0_9126,plain,
    ! [X29626,X29627,X29628,X29629] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X29629,tc_HOL_Obool),hAPP(c_Set_Oimage(X29628,tc_fun(X29629,tc_HOL_Obool),X29627),X29626)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29628,tc_fun(X29629,tc_HOL_Obool)),X29626),X29627),
    inference(variable_rename,[status(thm)],[fact_Inter__image__eq]) ).

fof(i_0_9127,plain,
    ! [X29622,X29623,X29624,X29625] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29625,tc_fun(X29624,tc_HOL_Obool)),X29623),X29622) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X29624,tc_HOL_Obool),hAPP(c_Set_Oimage(X29625,tc_fun(X29624,tc_HOL_Obool),X29622),X29623)),
    inference(variable_rename,[status(thm)],[fact_INTER__eq__Inter__image]) ).

fof(i_0_9128,plain,
    ! [X29734,X29735,X29736,X29737] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29737,tc_fun(X29736,tc_HOL_Obool)),X29735),X29734) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X29736,tc_HOL_Obool),hAPP(c_Set_Oimage(X29737,tc_fun(X29736,tc_HOL_Obool),X29734),X29735)),
    inference(variable_rename,[status(thm)],[fact_UNION__eq__Union__image]) ).

fof(i_0_9129,plain,
    ! [X25437,X25438,X25439,X25440] :
      ( ~ class_Rings_Osemiring__1(X25440)
      | c_Nat_Osemiring__1__class_Oof__nat__aux(X25440,X25439,hAPP(c_Nat_OSuc,X25438),X25437) = c_Nat_Osemiring__1__class_Oof__nat__aux(X25440,X25439,X25438,hAPP(X25439,X25437)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I2_J])]) ).

fof(i_0_9130,plain,
    ! [X24572,X24573] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24573))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24572))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X24573),hAPP(c_Int_Onat,X24572)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X24573,X24572)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__functions_I2_J])]) ).

fof(i_0_9131,plain,
    ! [X24570,X24571] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24571))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24570))
      | hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X24571,X24570)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X24571),hAPP(c_Int_Onat,X24570)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mod__distrib])]) ).

fof(i_0_9132,plain,
    ! [X23500,X23501] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X23501,X23500) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23501),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23501),X23500)),X23500)),
    inference(variable_rename,[status(thm)],[fact_zmod__zdiv__equality_H]) ).

fof(i_0_9133,plain,
    ! [X23666,X23667] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23667,X23666) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23667),X23666)),X23666)),
    inference(variable_rename,[status(thm)],[fact_Divides_Omod__div__equality_H]) ).

fof(i_0_9134,plain,
    ! [X22676,X22677,X22678] :
      ( ~ class_Rings_Olinordered__semidom(X22678)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22678),c_Groups_Ozero__class_Ozero(X22678)),X22677))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22678),c_Groups_Ozero__class_Ozero(X22678)),hAPP(hAPP(c_Power_Opower__class_Opower(X22678),X22677),X22676))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power])]) ).

fof(i_0_9135,plain,
    ! [X22673,X22674,X22675] :
      ( ~ class_Rings_Olinordered__semidom(X22675)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22675),c_Groups_Ozero__class_Ozero(X22675)),X22674))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22675),c_Groups_Ozero__class_Ozero(X22675)),hAPP(hAPP(c_Power_Opower__class_Opower(X22675),X22674),X22673))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power])]) ).

fof(i_0_9136,plain,
    ! [X22682,X22683,X22684] :
      ( ~ class_Rings_Olinordered__semidom(X22684)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22684),c_Groups_Oone__class_Oone(X22684)),X22683))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22684),c_Groups_Oone__class_Oone(X22684)),hAPP(hAPP(c_Power_Opower__class_Opower(X22684),X22683),X22682))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__power])]) ).

fof(i_0_9137,plain,
    ! [X18610,X18611,X18612] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X18612)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18612),hAPP(X18611,X18610)),X18610))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18612),c_Inductive_Ocomplete__lattice__class_Olfp(X18612,X18611)),X18610)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lfp__lowerbound])]) ).

fof(i_0_9138,plain,
    ! [X17479,X17480,X17481,X17482,X17483] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17483),X17482),X17481))
      | hAPP(c_Set_Oimage(X17483,X17480,hAPP(c_COMBK(X17480,X17483),X17479)),X17481) = hAPP(hAPP(c_Set_Oinsert(X17480),X17479),c_Orderings_Obot__class_Obot(tc_fun(X17480,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__constant])]) ).

fof(i_0_9139,plain,
    ! [X24545,X24546] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24545))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X24546)),hAPP(c_Int_Onat,X24545))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24546),X24545))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X24546)),hAPP(c_Int_Onat,X24545))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24545))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24546),X24545))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X24546)),hAPP(c_Int_Onat,X24545))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__nat__conj])])]) ).

fof(i_0_9140,plain,
    ! [X27784,X27785] : hAPP(hAPP(c_Product__Type_OSigma(X27785,X27784),c_Orderings_Otop__class_Otop(tc_fun(X27785,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X27784,tc_HOL_Obool),X27785),c_Orderings_Otop__class_Otop(tc_fun(X27784,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X27785,X27784),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_UNIV__Times__UNIV]) ).

fof(i_0_9141,plain,
    ! [X22886,X22887] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22887),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22886),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22887),X22886))
        | X22887 = X22886 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22887),X22886))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22887),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22886),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
      & ( X22887 != X22886
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22887),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22886),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_9142,plain,
    hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId(X1)) = c_Relation_OId(X1),
    inference(split_conjunct,[status(thm)],[i_0_5877]) ).

fof(i_0_9143,plain,
    ! [X22296,X22297] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22297),hAPP(c_Groups_Ouminus__class_Ouminus(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),hAPP(c_Groups_Ouminus__class_Ouminus(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_neg__less__nonneg])])]) ).

fof(i_0_9144,plain,
    ! [X22288,X22289] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22289),hAPP(c_Groups_Ouminus__class_Ouminus(X22289),X22288)),X22288))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22289),c_Groups_Ozero__class_Ozero(X22289)),X22288))
        | ~ class_Groups_Olinordered__ab__group__add(X22289) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22289),c_Groups_Ozero__class_Ozero(X22289)),X22288))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22289),hAPP(c_Groups_Ouminus__class_Ouminus(X22289),X22288)),X22288))
        | ~ class_Groups_Olinordered__ab__group__add(X22289) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff])])]) ).

fof(i_0_9145,plain,
    ! [X33119,X33120,X33121,X33122] :
      ( ( hBOOL(hAPP(c_List_Olistsp(X33122,X33121),X33120))
        | ~ hBOOL(hAPP(c_List_Olistsp(X33122,X33121),hAPP(hAPP(c_List_Oappend(X33122),X33120),X33119))) )
      & ( hBOOL(hAPP(c_List_Olistsp(X33122,X33121),X33119))
        | ~ hBOOL(hAPP(c_List_Olistsp(X33122,X33121),hAPP(hAPP(c_List_Oappend(X33122),X33120),X33119))) )
      & ( ~ hBOOL(hAPP(c_List_Olistsp(X33122,X33121),X33120))
        | ~ hBOOL(hAPP(c_List_Olistsp(X33122,X33121),X33119))
        | hBOOL(hAPP(c_List_Olistsp(X33122,X33121),hAPP(hAPP(c_List_Oappend(X33122),X33120),X33119))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__listsp__conv])])]) ).

fof(i_0_9146,plain,
    ! [X28851,X28852,X28853,X28854] : hAPP(hAPP(c_Nat_Ocompow(X28854,X28854),X28853),hAPP(hAPP(c_Nat_Ocompow(X28854,X28854),X28852),X28851)) = hAPP(hAPP(c_Nat_Ocompow(X28854,X28854),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28852),X28853)),X28851),
    inference(variable_rename,[status(thm)],[fact_funpow__mult]) ).

fof(i_0_9147,plain,
    ! [X33701,X33702] :
      ( ( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X33702)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X33701)))
        | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X33702),X33701)) )
      & ( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X33702),X33701))
        | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X33702)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X33701))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__int__code])]) ).

fof(i_0_9148,plain,
    ! [X24001,X24002] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24002)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24001)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24002),X24001)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24002),X24001))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24002)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24001))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of__int__code])]) ).

fof(i_0_9149,plain,
    ! [X25133,X25134] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25134)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25133)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25134),X25133)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25134),X25133))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25134)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25133))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I2_J])]) ).

fof(i_0_9150,plain,
    ! [X25131,X25132] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25132)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25131)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25132),X25131)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25132),X25131))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25132)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25131))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__int])]) ).

fof(i_0_9151,plain,
    ! [X23999,X24000] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24000)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23999)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24000),X23999)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24000),X23999))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24000)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23999))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__number__of__int__code])]) ).

fof(i_0_9152,plain,
    ! [X25137,X25138] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25138)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25137)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25138),X25137)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25138),X25137))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25138)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25137))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I3_J])]) ).

fof(i_0_9153,plain,
    ! [X25135,X25136] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25136)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25135)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25136),X25135)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25136),X25135))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25136)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25135))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__int])]) ).

fof(i_0_9154,plain,
    ! [X22344,X22345] :
      ( ( ~ 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),X22345),X22344)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22344),X22345)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22344),X22345))
        | 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),X22345),X22344))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__diff])]) ).

fof(i_0_9155,plain,
    ! [X22848,X22849] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22849),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X22848),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22849),X22848)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22849),X22848))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22849),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X22848),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_9156,plain,
    ! [X22880,X22881] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22881),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22880),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22881),X22880)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22881),X22880))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22881),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22880),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_9157,plain,
    ! [X24073,X24074,X24075] :
      ( ~ class_Int_Onumber__ring(X24075)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24075),hAPP(c_Groups_Ouminus__class_Ouminus(X24075),hAPP(c_Int_Onumber__class_Onumber__of(X24075),X24074))),X24073) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24075),hAPP(c_Int_Onumber__class_Onumber__of(X24075),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24074))),X24073) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__number__of__mult])]) ).

fof(i_0_9158,plain,
    ! [X21763,X21764,X21765] :
      ( ~ class_Rings_Ocomm__semiring__1(X21765)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21765),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21765),X21764),X21763)),X21763) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21765),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21765),X21764),c_Groups_Oone__class_Oone(X21765))),X21763) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])]) ).

fof(i_0_9159,plain,
    ! [X31202,X31203,X31204,X31205] :
      ( ( hAPP(hAPP(c_List_Olist__update(X31204,X31203),X31205),X31202) != X31203
        | hAPP(hAPP(c_List_Onth(X31204),X31203),X31205) = X31202
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31205),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31204)),X31203))) )
      & ( hAPP(hAPP(c_List_Onth(X31204),X31203),X31205) != X31202
        | hAPP(hAPP(c_List_Olist__update(X31204,X31203),X31205),X31202) = X31203
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31205),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31204)),X31203))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__same__conv])])]) ).

fof(i_0_9160,plain,
    ! [X24596,X24597] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24597)))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24597),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24596)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24596)))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24597),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24596)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24597)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24597))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24596)))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24597),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24596)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24597),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24596)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24597))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5878])])]) ).

fof(i_0_9161,plain,
    ! [X25970,X25971,X25972] :
      ( ~ class_Orderings_Olinorder(X25972)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25972),X25971))
      | hBOOL(hAPP(hAPP(c_member(X25972),X25970),X25971))
      | X25971 = c_Orderings_Obot__class_Obot(tc_fun(X25972,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OSup__fin(X25972,c_Orderings_Oord__class_Omax(X25972),hAPP(hAPP(c_Set_Oinsert(X25972),X25970),X25971)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25972),X25970),c_Big__Operators_Olattice_OSup__fin(X25972,c_Orderings_Oord__class_Omax(X25972),X25971)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5879])]) ).

fof(i_0_9162,plain,
    ! [X25683,X25684,X25685] :
      ( ~ class_Orderings_Olinorder(X25685)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25685),X25684))
      | hBOOL(hAPP(hAPP(c_member(X25685),X25683),X25684))
      | X25684 = c_Orderings_Obot__class_Obot(tc_fun(X25685,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OInf__fin(X25685,c_Orderings_Oord__class_Omin(X25685),hAPP(hAPP(c_Set_Oinsert(X25685),X25683),X25684)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25685),X25683),c_Big__Operators_Olattice_OInf__fin(X25685,c_Orderings_Oord__class_Omin(X25685),X25684)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5880])]) ).

fof(i_0_9163,plain,
    ! [X25093,X25094] : 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),X25094))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25093))),
    inference(variable_rename,[status(thm)],[fact_negative__zle]) ).

fof(i_0_9164,plain,
    ! [X27138,X27139] : 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),X27139)),X27138))),
    inference(variable_rename,[status(thm)],[fact_zero__le__zpower__abs]) ).

fof(i_0_9165,plain,
    ! [X25420,X25421,X25422] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25422),X25421)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25420),X25421)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X25422),X25420)),X25421),
    inference(variable_rename,[status(thm)],[fact_min__diff]) ).

cnf(i_0_9166,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_5881]) ).

fof(i_0_9167,plain,
    ! [X22782,X22783,X22784] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22784),X22783)),X22782) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22784),X22782)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22783),X22782)),
    inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib]) ).

fof(i_0_9168,plain,
    ! [X22795,X22796,X22797] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X22797),X22796)),X22795) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22797),X22795)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22796),X22795)),
    inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib]) ).

fof(i_0_9169,plain,
    ! [X21757,X21758,X21759] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21759),X21758)),X21757) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21759),X21757)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21758),X21757)),
    inference(variable_rename,[status(thm)],[fact_add__mult__distrib]) ).

fof(i_0_9170,plain,
    ! [X20962,X20963,X20964] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20964),X20963)),X20962) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20964),X20962)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20963),X20962)),
    inference(variable_rename,[status(thm)],[fact_diff__mult__distrib]) ).

fof(i_0_9171,plain,
    ! [X30948,X30949,X30950,X30951] : hAPP(hAPP(c_List_Onth(X30951),hAPP(hAPP(c_List_Olist_OCons(X30951),X30950),X30949)),X30948) = c_Nat_Onat_Onat__case(X30951,X30950,hAPP(c_List_Onth(X30951),X30949),X30948),
    inference(variable_rename,[status(thm)],[fact_nth_Osimps]) ).

fof(i_0_9172,plain,
    ! [X33957,X33958,X33959] : c_List_Oreplicate(X33959,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33959)),hAPP(c_List_Ofilter(X33959,hAPP(c_fequal,X33958)),X33957)),X33958) = hAPP(c_List_Ofilter(X33959,hAPP(c_fequal,X33958)),X33957),
    inference(variable_rename,[status(thm)],[fact_replicate__length__filter]) ).

fof(i_0_9173,plain,
    ! [X22772,X22773,X22774,X22775] :
      ( ( X22773 = c_Orderings_Obot__class_Obot(tc_fun(X22775,tc_HOL_Obool))
        | c_Sum__Type_OPlus(X22775,X22774,X22773,X22772) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X22775,X22774),tc_HOL_Obool)) )
      & ( X22772 = c_Orderings_Obot__class_Obot(tc_fun(X22774,tc_HOL_Obool))
        | c_Sum__Type_OPlus(X22775,X22774,X22773,X22772) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X22775,X22774),tc_HOL_Obool)) )
      & ( X22773 != c_Orderings_Obot__class_Obot(tc_fun(X22775,tc_HOL_Obool))
        | X22772 != c_Orderings_Obot__class_Obot(tc_fun(X22774,tc_HOL_Obool))
        | c_Sum__Type_OPlus(X22775,X22774,X22773,X22772) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X22775,X22774),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_9174,plain,
    ! [X32688,X32689,X32690,X32691] :
      ( ~ class_Orderings_Olinorder(X32691)
      | hAPP(c_List_Oset(X32690),c_List_Olinorder__class_Osort__key(X32690,X32691,X32689,X32688)) = hAPP(c_List_Oset(X32690),X32688) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__sort])]) ).

fof(i_0_9175,plain,
    ! [X33950,X33951,X33952] : hAPP(hAPP(c_List_Oappend(X33952),c_List_Oreplicate(X33952,X33951,X33950)),hAPP(hAPP(c_List_Olist_OCons(X33952),X33950),c_List_Olist_ONil(X33952))) = hAPP(hAPP(c_List_Olist_OCons(X33952),X33950),c_List_Oreplicate(X33952,X33951,X33950)),
    inference(variable_rename,[status(thm)],[fact_replicate__append__same]) ).

fof(i_0_9176,plain,
    ! [X29714,X29715,X29716] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X29716,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X29716,tc_HOL_Obool)),X29715),X29714)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29716,tc_HOL_Obool)),X29715),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29716,tc_HOL_Obool),X29714)),
    inference(variable_rename,[status(thm)],[fact_Union__insert]) ).

fof(i_0_9177,plain,
    ! [X29731,X29732,X29733] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X29733,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X29733,tc_HOL_Obool)),X29732),X29731)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29733,tc_HOL_Obool)),X29732),c_Complete__Lattice_OInf__class_OInf(tc_fun(X29733,tc_HOL_Obool),X29731)),
    inference(variable_rename,[status(thm)],[fact_Inter__insert]) ).

fof(i_0_9178,plain,
    ! [X27455,X27456] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X27456,X27456,X27456),X27455),X27455) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27456,X27456),tc_HOL_Obool))
      | c_Wellfounded_Owf(X27456,X27455) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__no__loop])]) ).

fof(i_0_9179,plain,
    ! [X22381,X22382] :
      ( ( X22382 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22382),X22381) = X22381 )
      & ( X22382 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22382),X22381) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22382),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X22381)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__if])]) ).

fof(i_0_9180,plain,
    ! [X20016,X20017,X20018,X20019,X20020] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X20020,tc_Option_Ooption(X20019)),X20018),X20017),hAPP(c_Option_Ooption_OSome(X20019),X20016)) != hAPP(c_COMBK(tc_Option_Ooption(X20019),X20020),c_Option_Ooption_ONone(X20019)),
    inference(variable_rename,[status(thm)],[fact_map__upd__nonempty]) ).

fof(i_0_9181,plain,
    ! [X26556,X26557,X26558,X26559] :
      ( ~ class_Rings_Osemiring__1(X26559)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26558,X26559),hAPP(c_COMBK(X26559,X26558),X26557)),X26556) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26559),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26559),hAPP(c_Finite__Set_Ocard(X26558),X26556))),X26557) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__constant])]) ).

fof(i_0_9182,plain,
    ! [X25069,X25070] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25070),hAPP(c_Int_Oring__1__class_Oof__int(X25070),X25069)),c_Groups_Ozero__class_Ozero(X25070)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25069),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ class_Rings_Olinordered__idom(X25070) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25069),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25070),hAPP(c_Int_Oring__1__class_Oof__int(X25070),X25069)),c_Groups_Ozero__class_Ozero(X25070)))
        | ~ class_Rings_Olinordered__idom(X25070) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__less__0__iff])])]) ).

fof(i_0_9183,plain,
    ! [X25063,X25064] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25064),hAPP(c_Int_Oring__1__class_Oof__int(X25064),X25063)),c_Groups_Ozero__class_Ozero(X25064)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25063),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ class_Rings_Olinordered__idom(X25064) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25063),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25064),hAPP(c_Int_Oring__1__class_Oof__int(X25064),X25063)),c_Groups_Ozero__class_Ozero(X25064)))
        | ~ class_Rings_Olinordered__idom(X25064) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__le__0__iff])])]) ).

fof(i_0_9184,plain,
    ! [X23278,X23279,X23280,X23281] :
      ( ~ class_Divides_Osemiring__div(X23281)
      | c_Divides_Odiv__class_Omod(X23281,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23281),X23280),c_Divides_Odiv__class_Omod(X23281,X23279,X23278)),X23278) = c_Divides_Odiv__class_Omod(X23281,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23281),X23280),X23279),X23278) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I2_J])]) ).

fof(i_0_9185,plain,
    ! [X23290,X23291,X23292,X23293] :
      ( ~ class_Divides_Osemiring__div(X23293)
      | c_Divides_Odiv__class_Omod(X23293,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23293),X23292),X23291),X23290) = c_Divides_Odiv__class_Omod(X23293,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23293),X23292),c_Divides_Odiv__class_Omod(X23293,X23291,X23290)),X23290) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__right__eq])]) ).

fof(i_0_9186,plain,
    ! [X23326,X23327,X23328,X23329] :
      ( ~ class_Divides_Osemiring__div(X23329)
      | c_Divides_Odiv__class_Omod(X23329,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23329),X23328),X23327),X23326) = c_Divides_Odiv__class_Omod(X23329,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23329),X23328),c_Divides_Odiv__class_Omod(X23329,X23327,X23326)),X23326) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__right__eq])]) ).

fof(i_0_9187,plain,
    ! [X23353,X23354,X23355,X23356] :
      ( ~ class_Divides_Oring__div(X23356)
      | c_Divides_Odiv__class_Omod(X23356,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23356),X23355),X23354),X23353) = c_Divides_Odiv__class_Omod(X23356,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23356),X23355),c_Divides_Odiv__class_Omod(X23356,X23354,X23353)),X23353) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__right__eq])]) ).

fof(i_0_9188,plain,
    ! [X17148,X17149,X17150,X17151] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17151,tc_HOL_Obool)),X17150),X17149))
      | ~ hBOOL(hAPP(X17150,X17148))
      | hBOOL(hAPP(X17149,X17148)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate1D])]) ).

fof(i_0_9189,plain,
    ! [X17152,X17153,X17154,X17155] :
      ( ~ hBOOL(hAPP(X17155,X17154))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17153,tc_HOL_Obool)),X17155),X17152))
      | hBOOL(hAPP(X17152,X17154)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])]) ).

fof(i_0_9190,plain,
    ! [X24568,X24569] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24569))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24569),X24568))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24568),X24569)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X24568)),hAPP(c_Int_Onat,X24569)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__distrib])]) ).

fof(i_0_9191,plain,
    ! [X33123,X33124,X33125,X33126] :
      ( ( hBOOL(hAPP(X33125,X33124))
        | ~ hBOOL(hAPP(c_List_Olistsp(X33126,X33125),hAPP(hAPP(c_List_Olist_OCons(X33126),X33124),X33123))) )
      & ( hBOOL(hAPP(c_List_Olistsp(X33126,X33125),X33123))
        | ~ hBOOL(hAPP(c_List_Olistsp(X33126,X33125),hAPP(hAPP(c_List_Olist_OCons(X33126),X33124),X33123))) )
      & ( ~ hBOOL(hAPP(X33125,X33124))
        | ~ hBOOL(hAPP(c_List_Olistsp(X33126,X33125),X33123))
        | hBOOL(hAPP(c_List_Olistsp(X33126,X33125),hAPP(hAPP(c_List_Olist_OCons(X33126),X33124),X33123))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp_Oequations_I2_J])])]) ).

fof(i_0_9192,plain,
    ! [X26926,X26927,X26928] :
      ( ~ class_Orderings_Olinorder(X26928)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26928),X26927),X26926))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26928,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26928,X26927),X26926)),hAPP(c_SetInterval_Oord__class_OatLeast(X26928),X26926)) = hAPP(c_SetInterval_Oord__class_OatLeast(X26928),X26927) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I14_J])]) ).

fof(i_0_9193,plain,
    ! [X24661,X24662] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24662),hAPP(c_Int_Onumber__class_Onumber__of(X24662),X24661)),c_Groups_Ozero__class_Ozero(X24662)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24661),c_Int_OPls))
        | ~ class_Int_Onumber__ring(X24662)
        | ~ class_Rings_Olinordered__idom(X24662) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24661),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24662),hAPP(c_Int_Onumber__class_Onumber__of(X24662),X24661)),c_Groups_Ozero__class_Ozero(X24662)))
        | ~ class_Int_Onumber__ring(X24662)
        | ~ class_Rings_Olinordered__idom(X24662) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I3_J])])]) ).

fof(i_0_9194,plain,
    ! [X24657,X24658] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24658),hAPP(c_Int_Onumber__class_Onumber__of(X24658),X24657)),c_Groups_Ozero__class_Ozero(X24658)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24657),c_Int_OPls))
        | ~ class_Int_Onumber__ring(X24658)
        | ~ class_Rings_Olinordered__idom(X24658) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24657),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24658),hAPP(c_Int_Onumber__class_Onumber__of(X24658),X24657)),c_Groups_Ozero__class_Ozero(X24658)))
        | ~ class_Int_Onumber__ring(X24658)
        | ~ class_Rings_Olinordered__idom(X24658) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I3_J])])]) ).

fof(i_0_9195,plain,
    ! [X19184,X19185,X19186,X19187] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X19187),X19186),c_Map_Odom(X19187,X19185,X19184)))
        | hAPP(X19184,X19186) != c_Option_Ooption_ONone(X19185) )
      & ( hAPP(X19184,X19186) = c_Option_Ooption_ONone(X19185)
        | hBOOL(hAPP(hAPP(c_member(X19187),X19186),c_Map_Odom(X19187,X19185,X19184))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_domIff])]) ).

fof(i_0_9196,plain,
    ! [X30763,X30764,X30765,X30766] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30766)),X30765) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30764)),X30763)
      | hAPP(hAPP(c_List_Omap(tc_prod(X30766,X30764),X30766),c_Product__Type_Ofst(X30766,X30764)),hAPP(hAPP(c_List_Ozip(X30766,X30764),X30765),X30763)) = X30765 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__fst__zip])]) ).

fof(i_0_9197,plain,
    ! [X30767,X30768,X30769,X30770] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30770)),X30769) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30768)),X30767)
      | hAPP(hAPP(c_List_Omap(tc_prod(X30770,X30768),X30768),c_Product__Type_Osnd(X30770,X30768)),hAPP(hAPP(c_List_Ozip(X30770,X30768),X30769),X30767)) = X30767 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__snd__zip])]) ).

fof(i_0_9198,plain,
    ! [X23169,X23170,X23171] :
      ( ~ class_Divides_Osemiring__div(X23171)
      | X23170 = c_Groups_Ozero__class_Ozero(X23171)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23171),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23171),X23170),X23169)),X23170) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23171),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23171),X23169),X23170)),c_Groups_Oone__class_Oone(X23171)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self1])]) ).

fof(i_0_9199,plain,
    ! [X23172,X23173,X23174] :
      ( ~ class_Divides_Osemiring__div(X23174)
      | X23173 = c_Groups_Ozero__class_Ozero(X23174)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23174),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23174),X23172),X23173)),X23173) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23174),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23174),X23172),X23173)),c_Groups_Oone__class_Oone(X23174)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self2])]) ).

fof(i_0_9200,plain,
    ! [X23310,X23311,X23312,X23313] :
      ( ~ class_Divides_Osemiring__div(X23313)
      | c_Divides_Odiv__class_Omod(X23313,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23313),X23312),X23311),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23313),X23310),X23311)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23313),c_Divides_Odiv__class_Omod(X23313,X23312,X23310)),X23311) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__mult2])]) ).

fof(i_0_9201,plain,
    ! [X27136,X27137] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X27137),X27136))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X27137))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X27136))),
    inference(variable_rename,[status(thm)],[fact_nat__abs__mult__distrib]) ).

fof(i_0_9202,plain,
    ! [X18605,X18606,X18607,X18608,X18609] :
      ( ~ class_Orderings_Oorder(X18609)
      | ~ class_Orderings_Oorder(X18608)
      | ~ c_Orderings_Oorder__class_Ostrict__mono(X18608,X18609,X18607)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18608),X18606),X18605))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18609),hAPP(X18607,X18606)),hAPP(X18607,X18605))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_strict__monoD])]) ).

fof(i_0_9203,plain,
    ! [X17579,X17580,X17581,X17582,X17583] :
      ( ~ class_Orderings_Oorder(X17583)
      | ~ class_Orderings_Oorder(X17582)
      | ~ c_Orderings_Oorder__class_Omono(X17582,X17583,X17581)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17582),X17580),X17579))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17583),hAPP(X17581,X17580)),hAPP(X17581,X17579))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monoD])]) ).

fof(i_0_9204,plain,
    ! [X23464,X23465,X23466] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23466))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23466),X23465)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23466),X23464)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23465),X23464) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel1])]) ).

fof(i_0_9205,plain,
    ! [X23144,X23145,X23146] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23146))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23145),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23144),X23146)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23145),X23144)),X23146) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__zmult2__eq])]) ).

fof(i_0_9206,plain,
    ! [X33018,X33019,X33020,X33021,X33022] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X33022),X33021),hAPP(c_List_Oset(X33022),X33020)))
      | hBOOL(hAPP(X33019,X33021))
      | c_List_OtakeWhile(X33022,X33019,hAPP(hAPP(c_List_Oappend(X33022),X33020),X33018)) = c_List_OtakeWhile(X33022,X33019,X33020) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5882])]) ).

fof(i_0_9207,plain,
    ! [X24598,X24599] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24599)))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24599)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24598)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24599)))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24599)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24598)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24599)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24598))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5883])]) ).

fof(i_0_9208,plain,
    ! [X24600,X24601] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24601)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24601)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24600)) = 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),X24600)) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24601)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24601)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24600)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24601)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24600))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5884])]) ).

fof(i_0_9209,plain,
    ! [X23965,X23966,X23967,X23968,X23969] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X23969,X23968,X23967),X23966),X23965) = hAPP(hAPP(X23966,hAPP(c_Product__Type_Ofst(X23969,X23968),X23965)),hAPP(c_Product__Type_Osnd(X23969,X23968),X23965)),
    inference(variable_rename,[status(thm)],[fact_split__beta]) ).

fof(i_0_9210,plain,
    ! [X23960,X23961,X23962,X23963,X23964] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X23964,X23963,X23962),X23961),X23960) = hAPP(hAPP(X23961,hAPP(c_Product__Type_Ofst(X23964,X23963),X23960)),hAPP(c_Product__Type_Osnd(X23964,X23963),X23960)),
    inference(variable_rename,[status(thm)],[fact_prod__case__beta]) ).

fof(i_0_9211,plain,
    ! [X23801,X23802,X23803,X23804,X23805] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X23805,X23804,X23803),X23802),X23801) = hAPP(hAPP(X23802,hAPP(c_Product__Type_Ofst(X23805,X23804),X23801)),hAPP(c_Product__Type_Osnd(X23805,X23804),X23801)),
    inference(variable_rename,[status(thm)],[fact_split__def]) ).

fof(i_0_9212,plain,
    ! [X32727,X32728] :
      ( ~ class_Orderings_Olinorder(X32728)
      | c_List_Olinorder__class_Osorted(X32728,c_List_Olinorder__class_Osort__key(X32728,X32728,c_COMBI(X32728),X32727)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__sort])]) ).

fof(i_0_9213,plain,
    ! [X31508,X31509,X31510,X31511,X31512] :
      ( ( X31511 = X31509
        | hAPP(hAPP(c_List_Oappend(X31512),X31511),hAPP(hAPP(c_List_Olist_OCons(X31512),X31510),c_List_Olist_ONil(X31512))) != hAPP(hAPP(c_List_Oappend(X31512),X31509),hAPP(hAPP(c_List_Olist_OCons(X31512),X31508),c_List_Olist_ONil(X31512))) )
      & ( X31510 = X31508
        | hAPP(hAPP(c_List_Oappend(X31512),X31511),hAPP(hAPP(c_List_Olist_OCons(X31512),X31510),c_List_Olist_ONil(X31512))) != hAPP(hAPP(c_List_Oappend(X31512),X31509),hAPP(hAPP(c_List_Olist_OCons(X31512),X31508),c_List_Olist_ONil(X31512))) )
      & ( X31511 != X31509
        | X31510 != X31508
        | hAPP(hAPP(c_List_Oappend(X31512),X31511),hAPP(hAPP(c_List_Olist_OCons(X31512),X31510),c_List_Olist_ONil(X31512))) = hAPP(hAPP(c_List_Oappend(X31512),X31509),hAPP(hAPP(c_List_Olist_OCons(X31512),X31508),c_List_Olist_ONil(X31512))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append1__eq__conv])])]) ).

fof(i_0_9214,plain,
    ! [X31885,X31886,X31887] :
      ( X31887 = c_List_Olist_ONil(X31886)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31885),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31886)),X31887)))
      | hAPP(c_List_Ohd(X31886),hAPP(hAPP(c_List_Odrop(X31886),X31885),X31887)) = hAPP(hAPP(c_List_Onth(X31886),X31887),X31885) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__drop__conv__nth])]) ).

fof(i_0_9215,plain,
    ! [X27048,X27049,X27050] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27050)
      | hAPP(c_Groups_Oabs__class_Oabs(X27050),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27050),hAPP(c_Groups_Oabs__class_Oabs(X27050),X27049)),hAPP(c_Groups_Oabs__class_Oabs(X27050),X27048))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27050),hAPP(c_Groups_Oabs__class_Oabs(X27050),X27049)),hAPP(c_Groups_Oabs__class_Oabs(X27050),X27048)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__add__abs])]) ).

fof(i_0_9216,plain,
    ! [X29079,X29080,X29081,X29082,X29083] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X29083,X29082,X29081)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29083),X29080))
      | hAPP(X29081,hAPP(hAPP(c_Set_Oinsert(X29083),X29079),X29080)) = hAPP(hAPP(c_Finite__Set_Ofold(X29083,X29083,X29082),X29079),X29080) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oeq__fold__idem_H])]) ).

fof(i_0_9217,plain,
    ! [X25417,X25418,X25419] :
      ( ~ class_Orderings_Olinorder(X25419)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25419),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25419),X25418),X25417)),X25418)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le1])]) ).

fof(i_0_9218,plain,
    ! [X25414,X25415,X25416] :
      ( ~ class_Orderings_Olinorder(X25416)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25416),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25416),X25415),X25414)),X25414)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le2])]) ).

fof(i_0_9219,plain,
    ! [X18000,X18001,X18002] :
      ( ~ class_Lattices_Osemilattice__inf(X18002)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18002),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18002),X18001),X18000)),X18001)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le1])]) ).

fof(i_0_9220,plain,
    ! [X18003,X18004,X18005] :
      ( ~ class_Lattices_Olattice(X18005)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18005),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18005),X18004),X18003)),X18004)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I1_J])]) ).

fof(i_0_9221,plain,
    ! [X17994,X17995,X17996] :
      ( ~ class_Lattices_Osemilattice__inf(X17996)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17996),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17996),X17995),X17994)),X17994)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le2])]) ).

fof(i_0_9222,plain,
    ! [X17997,X17998,X17999] :
      ( ~ class_Lattices_Olattice(X17999)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17999),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17999),X17998),X17997)),X17997)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I2_J])]) ).

fof(i_0_9223,plain,
    ! [X24256] :
      ( ~ 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),X24256)))
      | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24256) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24256)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_expand__Suc])]) ).

fof(i_0_9224,plain,
    ! [X26821,X26822,X26823] :
      ( ~ class_Orderings_Olinorder(X26823)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26823),X26822),X26821))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26823,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X26823),X26822)),c_SetInterval_Oord__class_OgreaterThanAtMost(X26823,X26822,X26821)) = hAPP(c_SetInterval_Oord__class_OatMost(X26823),X26821) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I9_J])]) ).

fof(i_0_9225,plain,
    ! [X26839,X26840,X26841] :
      ( ~ class_Orderings_Olinorder(X26841)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26841),X26840),X26839))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26841,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X26841),X26840)),c_SetInterval_Oord__class_OgreaterThanLessThan(X26841,X26840,X26839)) = hAPP(c_SetInterval_Oord__class_OlessThan(X26841),X26839) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I7_J])]) ).

fof(i_0_9226,plain,
    ! [X26836,X26837,X26838] :
      ( ~ class_Orderings_Olinorder(X26838)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26838),X26837),X26836))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26838,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X26838),X26837)),c_SetInterval_Oord__class_OatLeastAtMost(X26838,X26837,X26836)) = hAPP(c_SetInterval_Oord__class_OatMost(X26838),X26836) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I10_J])]) ).

fof(i_0_9227,plain,
    ! [X27057,X27058,X27059] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27059)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27059),hAPP(c_Groups_Oabs__class_Oabs(X27059),X27058)),X27057))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27059),X27058),X27057)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D1])]) ).

fof(i_0_9228,plain,
    ! [X25839,X25840,X25841,X25842] :
      ( ~ class_Orderings_Olinorder(X25842)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25842),X25841),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25842),X25840),X25839)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25842),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25842),X25841),X25840)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25842),X25841),X25839)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__distrib1])]) ).

fof(i_0_9229,plain,
    ! [X25835,X25836,X25837,X25838] :
      ( ~ class_Orderings_Olinorder(X25838)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25838),X25837),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25838),X25836),X25835)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25838),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25838),X25837),X25836)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25838),X25837),X25835)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__distrib1])]) ).

fof(i_0_9230,plain,
    ! [X21523,X21524,X21525,X21526] :
      ( ~ class_Rings_Ocomm__semiring__1(X21526)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21526),X21525),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21526),X21524),X21523)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21526),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21526),X21525),X21524)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21526),X21525),X21523)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J])]) ).

fof(i_0_9231,plain,
    ! [X18016,X18017,X18018,X18019] :
      ( ~ class_Lattices_Odistrib__lattice(X18019)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18019),X18018),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18019),X18017),X18016)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18019),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18019),X18018),X18017)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18019),X18018),X18016)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib1])]) ).

fof(i_0_9232,plain,
    ! [X18020,X18021,X18022,X18023] :
      ( ~ class_Lattices_Odistrib__lattice(X18023)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18023),X18022),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18023),X18021),X18020)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18023),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18023),X18022),X18021)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18023),X18022),X18020)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib1])]) ).

fof(i_0_9233,plain,
    ! [X21462,X21463,X21464,X21465] :
      ( ~ class_Rings_Ocomm__semiring__1(X21465)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21465),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21465),X21464),X21463)),X21462) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21465),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21465),X21464),X21462)),X21463) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).

fof(i_0_9234,plain,
    ! [X21908,X21909,X21910,X21911] :
      ( ~ class_Rings_Ocomm__semiring__1(X21911)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21911),X21910),X21909)),X21908) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21911),X21910),X21908)),X21909) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])]) ).

fof(i_0_9235,plain,
    ! [X20083] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X20083),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(X20083)),c_Option_Ooption_ONone(X20083)),hAPP(c_Set_Oimage(X20083,tc_Option_Ooption(X20083),c_Option_Ooption_OSome(X20083)),c_Orderings_Otop__class_Otop(tc_fun(X20083,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_UNIV__option__conv]) ).

fof(i_0_9236,plain,
    ! [X27912,X27913,X27914] : hAPP(c_Fun_Ocomp(X27914,X27914,X27913,c_Fun_Oid(X27914)),X27912) = X27912,
    inference(variable_rename,[status(thm)],[fact_id__o]) ).

fof(i_0_9237,plain,
    ! [X30513,X30514,X30515] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X30515),X30514),hAPP(c_List_Oset(X30515),X30513)))
      | 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(X30515)),X30513))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__pos__if__in__set])]) ).

cnf(i_0_9238,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_5774]) ).

fof(i_0_9239,plain,
    ! [X18682,X18683,X18684,X18685] :
      ( ( hBOOL(hAPP(hAPP(X18684,X18683),X18682))
        | ~ c_Partial__Function_Omk__less(X18685,X18684,X18683,X18682) )
      & ( ~ hBOOL(hAPP(hAPP(X18684,X18682),X18683))
        | ~ c_Partial__Function_Omk__less(X18685,X18684,X18683,X18682) )
      & ( ~ hBOOL(hAPP(hAPP(X18684,X18683),X18682))
        | hBOOL(hAPP(hAPP(X18684,X18682),X18683))
        | c_Partial__Function_Omk__less(X18685,X18684,X18683,X18682) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5885])])]) ).

fof(i_0_9240,plain,
    ! [X21185,X21186,X21187] :
      ( ~ class_Groups_Oab__semigroup__mult(X21187)
      | X21186 = c_Orderings_Obot__class_Obot(tc_fun(X21187,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21187),X21186))
      | hBOOL(hAPP(hAPP(c_member(X21187),X21185),X21186))
      | hAPP(c_Finite__Set_Ofold1(X21187,c_Groups_Otimes__class_Otimes(X21187)),hAPP(hAPP(c_Set_Oinsert(X21187),X21185),X21186)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21187),X21185),hAPP(c_Finite__Set_Ofold1(X21187,c_Groups_Otimes__class_Otimes(X21187)),X21186)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5886])]) ).

fof(i_0_9241,plain,
    ! [X28864,X28865,X28866] :
      ( ~ c_Relation_Osingle__valued(X28866,X28866,X28865)
      | c_Relation_Osingle__valued(X28866,X28866,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28866,X28866),tc_HOL_Obool),X28864),X28865)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__rel__pow])]) ).

fof(i_0_9242,plain,
    ! [X34212,X34213,X34214,X34215] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(X34215),X34214),X34213),X34212) = 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(X34215)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(X34215),X34214)),
    inference(variable_rename,[status(thm)],[fact_Random__Sequence_Osingle__def]) ).

fof(i_0_9243,plain,
    ! [X27774,X27775,X27776,X27777,X27779,X27780,X27781,X27782,X27783] :
      ( ( ~ hBOOL(hAPP(c_Predicate_ODomainP(X27777,X27776,X27775),X27774))
        | hBOOL(hAPP(hAPP(X27775,X27774),esk270_2(X27774,X27775))) )
      & ( ~ hBOOL(hAPP(hAPP(X27780,X27779),X27781))
        | hBOOL(hAPP(c_Predicate_ODomainP(X27783,X27782,X27780),X27779)) ) ),
    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_9244,plain,
    ! [X19128,X19129,X19130,X19131,X19132] :
      ( ( hAPP(X19130,X19129) != hAPP(X19130,X19128)
        | X19129 = X19128
        | ~ c_Fun_Oinj__on(X19132,X19131,X19130,c_Orderings_Otop__class_Otop(tc_fun(X19132,tc_HOL_Obool))) )
      & ( X19129 != X19128
        | hAPP(X19130,X19129) = hAPP(X19130,X19128)
        | ~ c_Fun_Oinj__on(X19132,X19131,X19130,c_Orderings_Otop__class_Otop(tc_fun(X19132,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__eq])])]) ).

fof(i_0_9245,plain,
    ! [X19123,X19124,X19125,X19126,X19127] :
      ( ~ c_Fun_Oinj__on(X19127,X19126,X19125,c_Orderings_Otop__class_Otop(tc_fun(X19127,tc_HOL_Obool)))
      | hAPP(X19125,X19124) != hAPP(X19125,X19123)
      | X19124 = X19123 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_injD])]) ).

fof(i_0_9246,plain,
    ! [X33973,X33974,X33975,X33976] : c_List_Oreplicate(X33976,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33975),X33974),X33973) = hAPP(hAPP(c_List_Oappend(X33976),c_List_Oreplicate(X33976,X33975,X33973)),c_List_Oreplicate(X33976,X33974,X33973)),
    inference(variable_rename,[status(thm)],[fact_replicate__add]) ).

fof(i_0_9247,plain,
    ! [X29118,X29119,X29120] :
      ( ~ class_Orderings_Olinorder(X29120)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29120),X29119))
      | c_Big__Operators_Olattice_OSup__fin(X29120,c_Orderings_Oord__class_Omax(X29120),hAPP(hAPP(c_Set_Oinsert(X29120),X29118),X29119)) = hAPP(hAPP(c_Finite__Set_Ofold(X29120,X29120,c_Orderings_Oord__class_Omax(X29120)),X29118),X29119) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold__idem_H])]) ).

fof(i_0_9248,plain,
    ! [X29115,X29116,X29117] :
      ( ~ class_Orderings_Olinorder(X29117)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29117),X29116))
      | c_Big__Operators_Olattice_OInf__fin(X29117,c_Orderings_Oord__class_Omin(X29117),hAPP(hAPP(c_Set_Oinsert(X29117),X29115),X29116)) = hAPP(hAPP(c_Finite__Set_Ofold(X29117,X29117,c_Orderings_Oord__class_Omin(X29117)),X29115),X29116) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold__idem_H])]) ).

cnf(i_0_9249,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_5887]) ).

fof(i_0_9250,plain,
    ! [X22977,X22978,X22980] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk117_2(X22977,X22978)),X22977))
        | ~ hBOOL(hAPP(X22978,X22977))
        | hBOOL(hAPP(X22978,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22980),esk117_2(X22977,X22978)))
        | ~ hBOOL(hAPP(X22978,X22980))
        | ~ hBOOL(hAPP(X22978,X22977))
        | hBOOL(hAPP(X22978,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
      & ( hBOOL(hAPP(X22978,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk117_2(X22977,X22978)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ hBOOL(hAPP(X22978,X22977))
        | hBOOL(hAPP(X22978,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_5888])])])])]) ).

fof(i_0_9251,plain,
    ! [X32018,X32019,X32020,X32021] : hAPP(c_List_Ofoldl(X32021,X32020,X32019,X32018),c_List_Olist_ONil(X32020)) = X32018,
    inference(variable_rename,[status(thm)],[fact_foldl__Nil]) ).

fof(i_0_9252,plain,
    ! [X31485,X31486,X31487,X31488] : hAPP(c_List_Olist_Olist__case(X31488,X31487,X31486,X31485),c_List_Olist_ONil(X31487)) = X31486,
    inference(variable_rename,[status(thm)],[fact_list_Osimps_I4_J]) ).

fof(i_0_9253,plain,
    ! [X20617,X20618,X20619,X20620] : hAPP(c_Option_Ooption_Ooption__case(X20620,X20619,X20618,X20617),c_Option_Ooption_ONone(X20619)) = X20618,
    inference(variable_rename,[status(thm)],[fact_option_Osimps_I4_J]) ).

fof(i_0_9254,plain,
    ! [X27915,X27916,X27917] : hAPP(c_Fun_Ocomp(X27917,X27916,X27917,X27915),c_Fun_Oid(X27917)) = X27915,
    inference(variable_rename,[status(thm)],[fact_o__id]) ).

fof(i_0_9255,plain,
    ! [X22126,X22127,X22128] :
      ( ( X22127 = c_Groups_Ozero__class_Ozero(X22128)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22128),X22127),X22126) != c_Groups_Ozero__class_Ozero(X22128)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22128),c_Groups_Ozero__class_Ozero(X22128)),X22126))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22128),c_Groups_Ozero__class_Ozero(X22128)),X22127))
        | ~ class_Groups_Oordered__comm__monoid__add(X22128) )
      & ( X22126 = c_Groups_Ozero__class_Ozero(X22128)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22128),X22127),X22126) != c_Groups_Ozero__class_Ozero(X22128)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22128),c_Groups_Ozero__class_Ozero(X22128)),X22126))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22128),c_Groups_Ozero__class_Ozero(X22128)),X22127))
        | ~ class_Groups_Oordered__comm__monoid__add(X22128) )
      & ( X22127 != c_Groups_Ozero__class_Ozero(X22128)
        | X22126 != c_Groups_Ozero__class_Ozero(X22128)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22128),X22127),X22126) = c_Groups_Ozero__class_Ozero(X22128)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22128),c_Groups_Ozero__class_Ozero(X22128)),X22126))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22128),c_Groups_Ozero__class_Ozero(X22128)),X22127))
        | ~ class_Groups_Oordered__comm__monoid__add(X22128) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).

cnf(i_0_9256,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_5889]) ).

fof(i_0_9257,plain,
    ! [X21858,X21859,X21860] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21860),X21859))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21858),X21859)),X21860) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21858),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21859),X21860)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc])]) ).

fof(i_0_9258,plain,
    ! [X21847,X21848,X21849] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21849),X21848))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21847),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21848),X21849)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21847),X21848)),X21849) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc])]) ).

fof(i_0_9259,plain,
    ! [X21836,X21837,X21838] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21838),X21837))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21836),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21837),X21838)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21836),X21838)),X21837) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__right])]) ).

fof(i_0_9260,plain,
    ! [X20407,X20408,X20409] :
      ( ~ class_Lattices_Oboolean__algebra(X20409)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20409),X20408),X20407))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20409),hAPP(c_Groups_Ouminus__class_Ouminus(X20409),X20407)),hAPP(c_Groups_Ouminus__class_Ouminus(X20409),X20408))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__mono])]) ).

fof(i_0_9261,plain,
    ! [X20413,X20414,X20415] :
      ( ~ class_Groups_Oordered__ab__group__add(X20415)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20415),X20414),X20413))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20415),hAPP(c_Groups_Ouminus__class_Ouminus(X20415),X20413)),hAPP(c_Groups_Ouminus__class_Ouminus(X20415),X20414))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__neg__le])]) ).

cnf(i_0_9262,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X1))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5890]) ).

cnf(i_0_9263,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_5891]) ).

cnf(i_0_9264,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_5892]) ).

cnf(i_0_9265,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_5893]) ).

cnf(i_0_9266,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_5894]) ).

fof(i_0_9267,plain,
    ! [X24586] :
      ( ( ~ 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,X24586)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X24586)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X24586))
        | 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,X24586))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__nat__eq])]) ).

fof(i_0_9268,plain,
    ! [X23632,X23633] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23633,X23632)),X23633)),
    inference(variable_rename,[status(thm)],[fact_mod__less__eq__dividend]) ).

fof(i_0_9269,plain,
    ! [X26899] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26899)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X26899)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26899)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_greaterThan__Suc]) ).

fof(i_0_9270,plain,
    ! [X22594,X22595,X22596,X22597] :
      ( ~ class_Rings_Ocomm__semiring__1(X22597)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22597),hAPP(hAPP(c_Power_Opower__class_Opower(X22597),X22596),X22595)),hAPP(hAPP(c_Power_Opower__class_Opower(X22597),X22596),X22594)) = hAPP(hAPP(c_Power_Opower__class_Opower(X22597),X22596),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22595),X22594)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J])]) ).

fof(i_0_9271,plain,
    ! [X22699,X22700,X22701,X22702] :
      ( ~ class_Groups_Omonoid__mult(X22702)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22702),X22701),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22700),X22699)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22702),hAPP(hAPP(c_Power_Opower__class_Opower(X22702),X22701),X22700)),hAPP(hAPP(c_Power_Opower__class_Opower(X22702),X22701),X22699)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__add])]) ).

fof(i_0_9272,plain,
    ! [X29100,X29101,X29102] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X29102)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29102),X29101))
      | hAPP(c_Finite__Set_Ofold1(X29102,c_Groups_Otimes__class_Otimes(X29102)),hAPP(hAPP(c_Set_Oinsert(X29102),X29100),X29101)) = hAPP(hAPP(c_Finite__Set_Ofold(X29102,X29102,c_Groups_Otimes__class_Otimes(X29102)),X29100),X29101) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__eq__fold__idem])]) ).

fof(i_0_9273,plain,
    ! [X22278,X22279,X22280,X22281,X22282,X22283] :
      ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X22283)
      | X22282 = c_Groups_Ozero__class_Ozero(X22283)
      | X22281 != X22280
      | X22279 = X22278
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22283),X22281),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22283),X22282),X22279)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22283),X22280),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22283),X22282),X22278)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq])]) ).

fof(i_0_9274,plain,
    ! [X28296,X28297] : c_Hilbert__Choice_OEps(X28297,hAPP(hAPP(c_COMBC(X28297,X28297,tc_HOL_Obool),c_fequal),X28296)) = X28296,
    inference(variable_rename,[status(thm)],[fact_some__eq__trivial]) ).

fof(i_0_9275,plain,
    ! [X17224,X17225] : c_HOL_OThe(X17225,hAPP(hAPP(c_COMBC(X17225,X17225,tc_HOL_Obool),c_fequal),X17224)) = X17224,
    inference(variable_rename,[status(thm)],[fact_the__eq__trivial]) ).

fof(i_0_9276,plain,
    ! [X21821,X21822] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21822),X21821)),hAPP(c_Nat_OSuc,X21822))),
    inference(variable_rename,[status(thm)],[fact_diff__less__Suc]) ).

fof(i_0_9277,plain,
    ! [X21426,X21427] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21427),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21427),X21426)))),
    inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).

fof(i_0_9278,plain,
    ! [X21424,X21425] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21425),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21424),X21425)))),
    inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).

fof(i_0_9279,plain,
    ! [X30351,X30352,X30353] : c_Map_Odom(X30353,X30352,hAPP(c_Map_Omap__of(X30353,X30352),X30351)) = hAPP(c_Set_Oimage(tc_prod(X30353,X30352),X30353,c_Product__Type_Ofst(X30353,X30352)),hAPP(c_List_Oset(tc_prod(X30353,X30352)),X30351)),
    inference(variable_rename,[status(thm)],[fact_dom__map__of__conv__image__fst]) ).

fof(i_0_9280,plain,
    ! [X26230,X26231,X26232,X26233] :
      ( ~ class_Orderings_Oorder(X26233)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26233,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26233,X26232,X26231)),c_SetInterval_Oord__class_OgreaterThanAtMost(X26233,X26231,X26230)) = c_Orderings_Obot__class_Obot(tc_fun(X26233,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I16_J])]) ).

fof(i_0_9281,plain,
    ! [X26234,X26235,X26236,X26237] :
      ( ~ class_Orderings_Oorder(X26237)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26237,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26237,X26236,X26235)),c_SetInterval_Oord__class_OgreaterThanLessThan(X26237,X26235,X26234)) = c_Orderings_Obot__class_Obot(tc_fun(X26237,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I12_J])]) ).

fof(i_0_9282,plain,
    ! [X25644,X25645,X25646,X25647] :
      ( ~ class_Orderings_Oorder(X25647)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25647,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25647,X25646,X25645)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25647,X25645,X25644)) = c_Orderings_Obot__class_Obot(tc_fun(X25647,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I14_J])]) ).

fof(i_0_9283,plain,
    ! [X25668,X25669,X25670,X25671] :
      ( ~ class_Orderings_Oorder(X25671)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25671,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25671,X25670,X25669)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25671,X25669,X25668)) = c_Orderings_Obot__class_Obot(tc_fun(X25671,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I10_J])]) ).

fof(i_0_9284,plain,
    ! [X26238,X26239,X26240,X26241] :
      ( ~ class_Orderings_Oorder(X26241)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26241,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X26241,X26240,X26239)),c_SetInterval_Oord__class_OatLeastAtMost(X26241,X26239,X26238)) = c_Orderings_Obot__class_Obot(tc_fun(X26241,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I13_J])]) ).

fof(i_0_9285,plain,
    ! [X17011,X17012] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17012,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X17012,tc_HOL_Obool))),X17011)),
    inference(variable_rename,[status(thm)],[fact_empty__subsetI]) ).

fof(i_0_9286,plain,
    ! [X28768,X28769,X28770] :
      ( ~ c_Equiv__Relations_Oequiv(X28770,X28769,X28768)
      | hAPP(hAPP(c_Relation_Orel__comp(X28770,X28770,X28770),hAPP(c_Relation_Oconverse(X28770,X28770),X28768)),X28768) = X28768 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__comp__eq])]) ).

fof(i_0_9287,plain,
    ! [X18212,X18213,X18214,X18215] :
      ( hBOOL(hAPP(hAPP(c_member(X18215),X18214),X18213))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18215,tc_HOL_Obool)),X18213),hAPP(hAPP(c_Set_Oinsert(X18215),X18214),X18212)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18215,tc_HOL_Obool)),X18213),X18212) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5895])]) ).

fof(i_0_9288,plain,
    ! [X23230,X23231] :
      ( ~ 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__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23230))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X23231,X23230))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J])]) ).

fof(i_0_9289,plain,
    ! [X17024,X17025,X17026] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17026,tc_HOL_Obool)),X17025),hAPP(hAPP(c_Set_Oinsert(X17026),X17024),X17025))),
    inference(variable_rename,[status(thm)],[fact_subset__insertI]) ).

fof(i_0_9290,plain,
    ! [X23377,X23378,X23379] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23379),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23378,X23377)),X23377) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23379),X23378),X23377),
    inference(variable_rename,[status(thm)],[fact_zmod__simps_I3_J]) ).

fof(i_0_9291,plain,
    ! [X23380,X23381,X23382] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23382),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23381,X23380)),X23380) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23382),X23381),X23380),
    inference(variable_rename,[status(thm)],[fact_zdiff__zmod__right]) ).

fof(i_0_9292,plain,
    ! [X23374,X23375,X23376] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23376),X23375),X23374) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23376),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23375,X23374)),X23374),
    inference(variable_rename,[status(thm)],[fact_zmod__zmult1__eq]) ).

fof(i_0_9293,plain,
    ! [X26411,X26412,X26413] :
      ( ~ class_Orderings_Olinorder(X26413)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26413),X26412),X26411))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26413,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X26413),X26412)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26413,X26412),X26411)) = hAPP(c_SetInterval_Oord__class_OlessThan(X26413),X26411) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I8_J])]) ).

cnf(i_0_9294,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_5896]) ).

fof(i_0_9295,plain,
    ! [X26203,X26204] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26204),hAPP(c_Nat_OSuc,X26203)))
      | c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26204,hAPP(c_Nat_OSuc,X26203)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26203)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26204,X26203)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMostSuc__conv])]) ).

cnf(i_0_9296,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_5897]) ).

fof(i_0_9297,plain,
    ! [X20493] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X20493)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X20493),tc_HOL_Obool))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20493),c_Orderings_Otop__class_Otop(tc_fun(X20493,tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20493),c_Orderings_Otop__class_Otop(tc_fun(X20493,tc_HOL_Obool))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X20493)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X20493),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV])]) ).

fof(i_0_9298,plain,
    ! [X25172,X25173,X25174] :
      ( ~ class_Rings_Olinordered__semidom(X25174)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25173),X25172))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25174),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25174),X25173)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25174),X25172))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__of__nat__less])]) ).

fof(i_0_9299,plain,
    ! [X26936,X26937,X26938,X26939] :
      ( ~ class_Orderings_Olinorder(X26939)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26939,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X26939),X26938)),c_SetInterval_Oord__class_OatLeastAtMost(X26939,X26937,X26936)) = c_SetInterval_Oord__class_OatLeastAtMost(X26939,hAPP(hAPP(c_Orderings_Oord__class_Omax(X26939),X26938),X26937),X26936) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR2])]) ).

fof(i_0_9300,plain,
    ! [X26813,X26814,X26815,X26816] :
      ( ~ class_Orderings_Olinorder(X26816)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26816,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X26816),X26815)),c_SetInterval_Oord__class_OatLeastAtMost(X26816,X26814,X26813)) = c_SetInterval_Oord__class_OatLeastAtMost(X26816,X26814,hAPP(hAPP(c_Orderings_Oord__class_Omin(X26816),X26815),X26813)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR1])]) ).

fof(i_0_9301,plain,
    ! [X25230,X25231] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25231),hAPP(c_Int_Onat,X25230)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25231)),X25230)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25231)),X25230))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25231),hAPP(c_Int_Onat,X25230))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__nat__eq__int__zless])]) ).

fof(i_0_9302,plain,
    ! [X26263,X26264] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26264),X26263))
        | c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X26263,X26264) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26264),X26263))
        | c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X26263,X26264) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X26263),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26263),c_Groups_Oone__class_Oone(tc_Int_Oint)),X26264)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5898])]) ).

fof(i_0_9303,plain,
    ! [X24582,X24583] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24583))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24582))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X24583)),hAPP(c_Int_Onat,X24582)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X24583,X24582)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J])]) ).

fof(i_0_9304,plain,
    ! [X31801,X31802,X31803,X31804] : hAPP(hAPP(c_List_Odrop(X31804),X31803),hAPP(hAPP(c_List_Otake(X31804),X31802),X31801)) = hAPP(hAPP(c_List_Otake(X31804),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31802),X31803)),hAPP(hAPP(c_List_Odrop(X31804),X31803),X31801)),
    inference(variable_rename,[status(thm)],[fact_drop__take]) ).

fof(i_0_9305,plain,
    ! [X27281,X27282,X27283,X27284] : hAPP(hAPP(c_Relation_Orel__comp(X27284,X27283,X27282),X27281),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27283,X27282),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27284,X27282),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__empty2]) ).

fof(i_0_9306,plain,
    ! [X24091] :
      ( ~ 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),X24091)))
      | 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),X24091)) = 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),X24091))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__1__number__of])]) ).

fof(i_0_9307,plain,
    ! [X23634,X23635,X23636] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23636,X23635)),X23634) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23636),X23634),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23635),X23634)),
    inference(variable_rename,[status(thm)],[fact_mod__mult__distrib]) ).

fof(i_0_9308,plain,
    ! [X25767,X25768,X25769,X25770] :
      ( ~ class_Orderings_Olinorder(X25770)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25770),X25769),X25768))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25770),X25769),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25770),X25768),X25767))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__supI1])]) ).

fof(i_0_9309,plain,
    ! [X25763,X25764,X25765,X25766] :
      ( ~ class_Orderings_Olinorder(X25766)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25766),X25765),X25764))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25766),X25765),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25766),X25763),X25764))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__supI2])]) ).

fof(i_0_9310,plain,
    ! [X18571,X18572,X18573,X18574] :
      ( ~ class_Lattices_Osemilattice__sup(X18574)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18574),X18573),X18572))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18574),X18573),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18574),X18572),X18571))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__supI1])]) ).

fof(i_0_9311,plain,
    ! [X18567,X18568,X18569,X18570] :
      ( ~ class_Lattices_Osemilattice__sup(X18570)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18570),X18569),X18568))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18570),X18569),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18570),X18567),X18568))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__supI2])]) ).

fof(i_0_9312,plain,
    ! [X25810,X25811,X25812,X25813] :
      ( ~ class_Orderings_Olinorder(X25813)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25813),X25812),X25811))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25813),X25812),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25813),X25811),X25810))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI1])]) ).

fof(i_0_9313,plain,
    ! [X25806,X25807,X25808,X25809] :
      ( ~ class_Orderings_Olinorder(X25809)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25809),X25808),X25807))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25809),X25808),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25809),X25806),X25807))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI2])]) ).

fof(i_0_9314,plain,
    ! [X17727,X17728,X17729,X17730] :
      ( ~ class_Lattices_Osemilattice__sup(X17730)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17730),X17729),X17728))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17730),X17729),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17730),X17728),X17727))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI1])]) ).

fof(i_0_9315,plain,
    ! [X17731,X17732,X17733,X17734] :
      ( ~ class_Lattices_Osemilattice__sup(X17734)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17734),X17733),X17732))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17734),X17733),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17734),X17731),X17732))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI2])]) ).

cnf(i_0_9316,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_5899]) ).

fof(i_0_9317,plain,
    ! [X25235] : 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),X25235))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[fact_negative__zle__0]) ).

fof(i_0_9318,plain,
    ! [X32236,X32237,X32238,X32239,X32240] :
      ( ( c_List_Otranspose(X32237,X32236) != c_List_Olist_ONil(tc_List_Olist(X32237))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32237)),X32238),hAPP(c_List_Oset(tc_List_Olist(X32237)),X32236)))
        | X32238 = c_List_Olist_ONil(X32237) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32240)),esk445_2(X32239,X32240)),hAPP(c_List_Oset(tc_List_Olist(X32240)),X32239)))
        | c_List_Otranspose(X32240,X32239) = c_List_Olist_ONil(tc_List_Olist(X32240)) )
      & ( esk445_2(X32239,X32240) != c_List_Olist_ONil(X32240)
        | c_List_Otranspose(X32240,X32239) = c_List_Olist_ONil(tc_List_Olist(X32240)) ) ),
    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_9319,plain,
    ! [X26596,X26597,X26598] :
      ( ~ class_Groups_Ocomm__monoid__add(X26598)
      | hAPP(X26597,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(X26598)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26598),X26597),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X26596)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26598),X26597),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26596)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0__upt])]) ).

fof(i_0_9320,plain,
    ! [X19672,X19673,X19674] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19674,tc_fun(X19673,tc_HOL_Obool)),X19672),hAPP(c_COMBK(tc_fun(X19673,tc_HOL_Obool),X19674),c_Orderings_Obot__class_Obot(tc_fun(X19673,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X19673,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_UN__empty2]) ).

fof(i_0_9321,plain,
    ! [X21640,X21641,X21642] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21642),X21641))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21641),X21640))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21642)),X21640)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).

fof(i_0_9322,plain,
    ! [X24092] :
      ( ~ 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),X24092)))
      | 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),X24092)) = 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),X24092))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos__1__number__of])]) ).

fof(i_0_9323,plain,
    ! [X23473,X23474] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23474))
      | 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,X23473,X23474))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__sign])]) ).

fof(i_0_9324,plain,
    ! [X30654,X30655] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X30655,X30654) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X30655),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X30654),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[fact_greaterThanLessThan__upto]) ).

fof(i_0_9325,plain,
    ! [X30279,X30280,X30281,X30282,X30283] : hAPP(hAPP(c_List_Omap(X30283,X30282),X30281),hAPP(hAPP(c_List_Olist_OCons(X30283),X30280),X30279)) = hAPP(hAPP(c_List_Olist_OCons(X30282),hAPP(X30281,X30280)),hAPP(hAPP(c_List_Omap(X30283,X30282),X30281),X30279)),
    inference(variable_rename,[status(thm)],[fact_map_Osimps_I2_J]) ).

fof(i_0_9326,plain,
    ! [X24183,X24184,X24185] :
      ( ~ class_Fields_Ofield__inverse__zero(X24185)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24185),c_Groups_Oone__class_Oone(X24185)),hAPP(hAPP(c_Power_Opower__class_Opower(X24185),X24184),X24183)) = hAPP(hAPP(c_Power_Opower__class_Opower(X24185),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24185),c_Groups_Oone__class_Oone(X24185)),X24184)),X24183) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__over])]) ).

fof(i_0_9327,plain,
    ! [X22841] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22841))
      | 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)),X22841))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__0__less])]) ).

fof(i_0_9328,plain,
    ! [X17549,X17550,X17551,X17552] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17552),X17551),X17550))
      | hBOOL(hAPP(hAPP(c_member(X17552),X17551),hAPP(hAPP(c_Set_Oinsert(X17552),X17549),X17550))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertI2])]) ).

fof(i_0_9329,plain,
    ! [X17275,X17276,X17277,X17278] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17278),X17277),X17276))
        | hBOOL(hAPP(hAPP(c_member(X17278),X17277),hAPP(hAPP(c_Set_Oinsert(X17278),X17275),X17276))) )
      & ( X17277 != X17275
        | hBOOL(hAPP(hAPP(c_member(X17278),X17277),hAPP(hAPP(c_Set_Oinsert(X17278),X17275),X17276))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5900])])]) ).

fof(i_0_9330,plain,
    ! [X20425,X20426,X20427] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20427),X20426),hAPP(c_Groups_Ouminus__class_Ouminus(X20427),X20425)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20427),X20425),hAPP(c_Groups_Ouminus__class_Ouminus(X20427),X20426)))
        | ~ class_Groups_Oordered__ab__group__add(X20427) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20427),X20425),hAPP(c_Groups_Ouminus__class_Ouminus(X20427),X20426)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20427),X20426),hAPP(c_Groups_Ouminus__class_Ouminus(X20427),X20425)))
        | ~ class_Groups_Oordered__ab__group__add(X20427) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__iff])])]) ).

fof(i_0_9331,plain,
    ! [X20422,X20423,X20424] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20424),X20423),hAPP(c_Groups_Ouminus__class_Ouminus(X20424),X20422)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20424),X20422),hAPP(c_Groups_Ouminus__class_Ouminus(X20424),X20423)))
        | ~ class_Groups_Oordered__ab__group__add(X20424) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20424),X20422),hAPP(c_Groups_Ouminus__class_Ouminus(X20424),X20423)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20424),X20423),hAPP(c_Groups_Ouminus__class_Ouminus(X20424),X20422)))
        | ~ class_Groups_Oordered__ab__group__add(X20424) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__iff])])]) ).

fof(i_0_9332,plain,
    ! [X32099,X32100,X32101,X32102] :
      ( ( X32100 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32101)),X32102)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_List_Olast(X32101,hAPP(hAPP(c_List_Olist__update(X32101,X32102),X32100),X32099)) = X32099
        | X32102 = c_List_Olist_ONil(X32101) )
      & ( X32100 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32101)),X32102)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_List_Olast(X32101,hAPP(hAPP(c_List_Olist__update(X32101,X32102),X32100),X32099)) = c_List_Olast(X32101,X32102)
        | X32102 = c_List_Olist_ONil(X32101) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__list__update])])]) ).

fof(i_0_9333,plain,
    ! [X26982,X26983] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26983),c_Groups_Osgn__class_Osgn(X26983,X26982)),c_Groups_Ozero__class_Ozero(X26983)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26983),X26982),c_Groups_Ozero__class_Ozero(X26983)))
        | ~ class_Rings_Olinordered__idom(X26983) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26983),X26982),c_Groups_Ozero__class_Ozero(X26983)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26983),c_Groups_Osgn__class_Osgn(X26983,X26982)),c_Groups_Ozero__class_Ozero(X26983)))
        | ~ class_Rings_Olinordered__idom(X26983) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__less])])]) ).

fof(i_0_9334,plain,
    ! [X32205,X32206,X32207] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32207),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32206)),X32205)))
      | hAPP(hAPP(c_List_Otake(X32206),X32207),c_List_Obutlast(X32206,X32205)) = hAPP(hAPP(c_List_Otake(X32206),X32207),X32205) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__butlast])]) ).

fof(i_0_9335,plain,
    ! [X32130,X32131,X32132] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32132),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32131)),X32130)))
      | c_List_Olast(X32131,hAPP(hAPP(c_List_Odrop(X32131),X32132),X32130)) = c_List_Olast(X32131,X32130) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__drop])]) ).

cnf(i_0_9336,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_5901]) ).

cnf(i_0_9337,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_5902]) ).

cnf(i_0_9338,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_5903]) ).

fof(i_0_9339,plain,
    ! [X23901,X23902,X23903,X23904,X23905,X23906] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X23906,X23905,X23904),X23903),hAPP(hAPP(c_Product__Type_OPair(X23906,X23905),X23902),X23901)) = hAPP(hAPP(X23903,X23902),X23901),
    inference(variable_rename,[status(thm)],[fact_split__conv]) ).

fof(i_0_9340,plain,
    ! [X23895,X23896,X23897,X23898,X23899,X23900] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X23900,X23899,X23898),X23897),hAPP(hAPP(c_Product__Type_OPair(X23900,X23899),X23896),X23895)) = hAPP(hAPP(X23897,X23896),X23895),
    inference(variable_rename,[status(thm)],[fact_prod_Osimps_I2_J]) ).

cnf(i_0_9341,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_5904]) ).

fof(i_0_9342,plain,
    ! [X25938,X25939,X25940] :
      ( ~ class_Orderings_Olinorder(X25940)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25940),X25939))
      | ~ hBOOL(hAPP(hAPP(c_member(X25940),X25938),X25939))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25940),X25938),c_Big__Operators_Olattice_OSup__fin(X25940,c_Orderings_Oord__class_Omax(X25940),X25939)) = c_Big__Operators_Olattice_OSup__fin(X25940,c_Orderings_Oord__class_Omax(X25940),X25939) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oin__idem])]) ).

fof(i_0_9343,plain,
    ! [X25650,X25651,X25652] :
      ( ~ class_Orderings_Olinorder(X25652)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25652),X25651))
      | ~ hBOOL(hAPP(hAPP(c_member(X25652),X25650),X25651))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25652),X25650),c_Big__Operators_Olattice_OInf__fin(X25652,c_Orderings_Oord__class_Omin(X25652),X25651)) = c_Big__Operators_Olattice_OInf__fin(X25652,c_Orderings_Oord__class_Omin(X25652),X25651) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oin__idem])]) ).

fof(i_0_9344,plain,
    ! [X20341,X20342,X20343] :
      ( hBOOL(hAPP(hAPP(c_member(X20343),X20342),X20341))
      | hBOOL(hAPP(hAPP(c_member(X20343),X20342),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20343,tc_HOL_Obool)),X20341))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5905])]) ).

fof(i_0_9345,plain,
    ! [X19513,X19514,X19515,X19516] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X19516),X19515),X19514))
        | hAPP(c_Set_Ovimage(X19513,X19516,hAPP(c_COMBK(X19516,X19513),X19515)),X19514) = c_Orderings_Otop__class_Otop(tc_fun(X19513,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X19516),X19515),X19514))
        | hAPP(c_Set_Ovimage(X19513,X19516,hAPP(c_COMBK(X19516,X19513),X19515)),X19514) = c_Orderings_Obot__class_Obot(tc_fun(X19513,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5906])]) ).

fof(i_0_9346,plain,
    ! [X26103,X26104,X26105,X26106,X26107] :
      ( ( X26106 = X26104
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26107,X26106),X26105) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26107,X26104),X26103)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26107),X26104),X26103))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26107),X26106),X26105))
        | ~ class_Orderings_Olinorder(X26107) )
      & ( X26105 = X26103
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26107,X26106),X26105) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26107,X26104),X26103)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26107),X26104),X26103))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26107),X26106),X26105))
        | ~ class_Orderings_Olinorder(X26107) )
      & ( X26106 != X26104
        | X26105 != X26103
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26107,X26106),X26105) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26107,X26104),X26103)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26107),X26104),X26103))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26107),X26106),X26105))
        | ~ class_Orderings_Olinorder(X26107) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__eq__iff])])]) ).

fof(i_0_9347,plain,
    ! [X26108,X26109,X26110,X26111,X26112] :
      ( ~ class_Orderings_Olinorder(X26112)
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26112,X26111),X26110) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26112,X26109),X26108)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26112),X26111),X26110))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26112),X26109),X26108))
      | X26111 = X26109 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I1_J])]) ).

fof(i_0_9348,plain,
    ! [X26113,X26114,X26115,X26116,X26117] :
      ( ~ class_Orderings_Olinorder(X26117)
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26117,X26116),X26115) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26117,X26114),X26113)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26117),X26116),X26115))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26117),X26114),X26113))
      | X26115 = X26113 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I2_J])]) ).

fof(i_0_9349,plain,
    ! [X20776,X20777,X20778,X20779,X20780] :
      ( ~ c_Finite__Set_Ofolding__one(X20780,X20779,X20778)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20780),X20777))
      | hBOOL(hAPP(hAPP(c_member(X20780),X20776),X20777))
      | X20777 = c_Orderings_Obot__class_Obot(tc_fun(X20780,tc_HOL_Obool))
      | hAPP(X20778,hAPP(hAPP(c_Set_Oinsert(X20780),X20776),X20777)) = hAPP(hAPP(X20779,X20776),hAPP(X20778,X20777)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5907])]) ).

cnf(i_0_9350,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_5819]) ).

fof(i_0_9351,plain,
    ! [X23701,X23702] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23702))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23701))
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X23702,X23701),c_Divides_OposDivAlg(X23702,X23701))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg__correct])]) ).

fof(i_0_9352,plain,
    ! [X31132,X31133,X31134,X31135,X31136] :
      ( X31136 = X31135
      | hAPP(hAPP(c_List_Onth(X31134),hAPP(hAPP(c_List_Olist__update(X31134,X31133),X31136),X31132)),X31135) = hAPP(hAPP(c_List_Onth(X31134),X31133),X31135) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__list__update__neq])]) ).

fof(i_0_9353,plain,
    ! [X26244,X26245,X26246,X26247] :
      ( ~ class_Orderings_Oorder(X26247)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26247,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X26247,X26246,X26245)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26247,X26245),X26244)) = c_Orderings_Obot__class_Obot(tc_fun(X26247,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I9_J])]) ).

fof(i_0_9354,plain,
    ! [X28755,X28756,X28757,X28758] : hAPP(c_Relation_Oconverse(X28758,X28758),hAPP(hAPP(c_Relation_Oinv__image(X28757,X28758),X28756),X28755)) = hAPP(hAPP(c_Relation_Oinv__image(X28757,X28758),hAPP(c_Relation_Oconverse(X28757,X28757),X28756)),X28755),
    inference(variable_rename,[status(thm)],[fact_converse__inv__image]) ).

fof(i_0_9355,plain,
    ! [X29109,X29110,X29111] :
      ( ~ class_Orderings_Olinorder(X29111)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29111),X29110))
      | c_Big__Operators_Olinorder__class_OMin(X29111,hAPP(hAPP(c_Set_Oinsert(X29111),X29109),X29110)) = hAPP(hAPP(c_Finite__Set_Ofold(X29111,X29111,c_Orderings_Oord__class_Omin(X29111)),X29109),X29110) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oeq__fold__idem_H])]) ).

fof(i_0_9356,plain,
    ! [X29112,X29113,X29114] :
      ( ~ class_Orderings_Olinorder(X29114)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29114),X29113))
      | c_Big__Operators_Olinorder__class_OMax(X29114,hAPP(hAPP(c_Set_Oinsert(X29114),X29112),X29113)) = hAPP(hAPP(c_Finite__Set_Ofold(X29114,X29114,c_Orderings_Oord__class_Omax(X29114)),X29112),X29113) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oeq__fold__idem_H])]) ).

fof(i_0_9357,plain,
    ! [X29103,X29104,X29105] :
      ( ~ class_Lattices_Olattice(X29105)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29105),X29104))
      | c_Big__Operators_Olattice__class_OSup__fin(X29105,hAPP(hAPP(c_Set_Oinsert(X29105),X29103),X29104)) = hAPP(hAPP(c_Finite__Set_Ofold(X29105,X29105,c_Lattices_Osemilattice__sup__class_Osup(X29105)),X29103),X29104) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oeq__fold__idem_H])]) ).

fof(i_0_9358,plain,
    ! [X29106,X29107,X29108] :
      ( ~ class_Lattices_Olattice(X29108)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29108),X29107))
      | c_Big__Operators_Olattice__class_OInf__fin(X29108,hAPP(hAPP(c_Set_Oinsert(X29108),X29106),X29107)) = hAPP(hAPP(c_Finite__Set_Ofold(X29108,X29108,c_Lattices_Osemilattice__inf__class_Oinf(X29108)),X29106),X29107) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oeq__fold__idem_H])]) ).

fof(i_0_9359,plain,
    ! [X28518,X28519] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X28519),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
        | c_Random_Olog(X28519,X28518) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X28518),X28519))
        | c_Random_Olog(X28519,X28518) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X28519),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X28518),X28519))
        | c_Random_Olog(X28519,X28518) = 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(X28519,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X28518),X28519))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_log_Osimps])])]) ).

fof(i_0_9360,plain,
    ! [X22899,X22900] :
      ( ~ class_Rings_Oring__1(X22900)
      | ~ hBOOL(hAPP(hAPP(c_member(X22900),X22899),c_Int_Oring__1__class_OInts(X22900)))
      | hBOOL(hAPP(hAPP(c_member(X22900),hAPP(c_Groups_Ouminus__class_Ouminus(X22900),X22899)),c_Int_Oring__1__class_OInts(X22900))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__minus])]) ).

fof(i_0_9361,plain,
    ! [X17584,X17585] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X17585,tc_HOL_Obool)),X17584))
        | hBOOL(hAPP(hAPP(c_member(X17585),X17584),c_Orderings_Obot__class_Obot(tc_fun(X17585,tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17585),X17584),c_Orderings_Obot__class_Obot(tc_fun(X17585,tc_HOL_Obool))))
        | hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X17585,tc_HOL_Obool)),X17584)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__empty__eq])]) ).

cnf(i_0_9362,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_5908]) ).

fof(i_0_9363,plain,
    ! [X27130,X27131,X27132] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X27132)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27132),c_Groups_Ozero__class_Ozero(X27132)),X27131))
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27132),hAPP(c_Groups_Oabs__class_Oabs(X27132),X27130)),X27131) = hAPP(c_Groups_Oabs__class_Oabs(X27132),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27132),X27130),X27131)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__div__pos])]) ).

fof(i_0_9364,plain,
    ! [X27105,X27106,X27107] :
      ( ~ class_Rings_Olinordered__idom(X27107)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27107),c_Groups_Ozero__class_Ozero(X27107)),X27106))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27107),hAPP(c_Groups_Oabs__class_Oabs(X27107),X27105)),X27106) = hAPP(c_Groups_Oabs__class_Oabs(X27107),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27107),X27105),X27106)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__pos])]) ).

fof(i_0_9365,plain,
    ! [X18145] : hAPP(c_Set_OPow(X18145),c_Orderings_Obot__class_Obot(tc_fun(X18145,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X18145,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X18145,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X18145,tc_HOL_Obool),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_Pow__empty]) ).

fof(i_0_9366,plain,
    ! [X26736,X26737] :
      ( hAPP(X26737,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),X26737),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26736)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X26737),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26736)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0])]) ).

fof(i_0_9367,plain,
    ! [X17864,X17865,X17866,X17867,X17868] :
      ( ~ class_Lattices_Olattice(X17868)
      | hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17867,X17868)),X17866),X17865),X17864) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17868),hAPP(X17866,X17864)),hAPP(X17865,X17864)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__fun__def])]) ).

fof(i_0_9368,plain,
    ! [X17812,X17813,X17814,X17815,X17816] :
      ( ~ class_Lattices_Olattice(X17816)
      | hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17815,X17816)),X17814),X17813),X17812) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17816),hAPP(X17814,X17812)),hAPP(X17813,X17812)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__apply])]) ).

fof(i_0_9369,plain,
    ! [X17869,X17870,X17871,X17872,X17873] :
      ( ~ class_Groups_Ominus(X17873)
      | hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17872,X17873)),X17871),X17870),X17869) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17873),hAPP(X17871,X17869)),hAPP(X17870,X17869)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__diff__def])]) ).

fof(i_0_9370,plain,
    ! [X17817,X17818,X17819,X17820,X17821] :
      ( ~ class_Groups_Ominus(X17821)
      | hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17820,X17821)),X17819),X17818),X17817) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17821),hAPP(X17819,X17817)),hAPP(X17818,X17817)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__apply])]) ).

fof(i_0_9371,plain,
    ! [X17627,X17628,X17629,X17630,X17631] :
      ( ~ class_Lattices_Olattice(X17631)
      | hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17630,X17631)),X17629),X17628),X17627) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17631),hAPP(X17629,X17627)),hAPP(X17628,X17627)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__apply])]) ).

fof(i_0_9372,plain,
    ! [X17622,X17623,X17624,X17625,X17626] :
      ( ~ class_Lattices_Olattice(X17626)
      | hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17625,X17626)),X17624),X17623),X17622) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17626),hAPP(X17624,X17622)),hAPP(X17623,X17622)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__fun__def])]) ).

fof(i_0_9373,plain,
    ! [X23697,X23698] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23698),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)),X23697))
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X23698,X23697),c_Divides_OnegDivAlg(X23698,X23697))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg__correct])]) ).

fof(i_0_9374,plain,
    ! [X23426,X23427] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23427),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23427),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23426,X23427))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__bound])]) ).

fof(i_0_9375,plain,
    ! [X27929,X27930,X27931,X27932] :
      ( ~ c_Finite__Set_Ofolding(X27932,X27931,X27930,X27929)
      | hAPP(X27929,c_Orderings_Obot__class_Obot(tc_fun(X27932,tc_HOL_Obool))) = c_Fun_Oid(X27931) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oempty])]) ).

fof(i_0_9376,plain,
    ! [X18623,X18624] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X18624)
      | ~ c_Orderings_Oorder__class_Omono(X18624,X18624,X18623)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18624),c_Inductive_Ocomplete__lattice__class_Olfp(X18624,X18623)),hAPP(X18623,c_Inductive_Ocomplete__lattice__class_Olfp(X18624,X18623)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lfp__lemma3])]) ).

fof(i_0_9377,plain,
    ! [X18173,X18174] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X18174)
      | ~ c_Orderings_Oorder__class_Omono(X18174,X18174,X18173)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18174),c_Inductive_Ocomplete__lattice__class_Ogfp(X18174,X18173)),hAPP(X18173,c_Inductive_Ocomplete__lattice__class_Ogfp(X18174,X18173)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gfp__lemma2])]) ).

fof(i_0_9378,plain,
    ! [X23703,X23704] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23703))
        | c_Divides_Odivmod__int(X23704,X23703) = c_Divides_OposDivAlg(X23704,X23703)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23704)) )
      & ( X23704 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X23704,X23703) = 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)),X23703))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23704)) )
      & ( X23704 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X23704,X23703) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23704),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23703)))
        | 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__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23704)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23703))
        | c_Divides_Odivmod__int(X23704,X23703) = c_Divides_OnegDivAlg(X23704,X23703)
        | 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(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23703))
        | c_Divides_Odivmod__int(X23704,X23703) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23704),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23703)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23704)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5909])])]) ).

fof(i_0_9379,plain,
    ! [X31289,X31290] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X31290),X31289))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X31290)),hAPP(c_Code__Numeral_Onat__of,X31289))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X31290)),hAPP(c_Code__Numeral_Onat__of,X31289)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X31290),X31289)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__code__numeral__def])]) ).

fof(i_0_9380,plain,
    ! [X31109,X31110] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X31110)),hAPP(c_Code__Numeral_Oof__nat,X31109)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31110),X31109)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31110),X31109))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X31110)),hAPP(c_Code__Numeral_Oof__nat,X31109))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__code__numeral__code])]) ).

fof(i_0_9381,plain,
    ! [X21647,X21648] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21648)),hAPP(c_Nat_OSuc,X21647)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21648),X21647)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).

fof(i_0_9382,plain,
    ! [X21630,X21631] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21631)),hAPP(c_Nat_OSuc,X21630)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21631),X21630)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21631),X21630))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21631)),hAPP(c_Nat_OSuc,X21630))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).

fof(i_0_9383,plain,
    ! [X31293,X31294] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X31294),X31293))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X31294)),hAPP(c_Code__Numeral_Onat__of,X31293))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X31294)),hAPP(c_Code__Numeral_Onat__of,X31293)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X31294),X31293)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__def])]) ).

fof(i_0_9384,plain,
    ! [X31119,X31120] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X31120)),hAPP(c_Code__Numeral_Oof__nat,X31119)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31120),X31119)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31120),X31119))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X31120)),hAPP(c_Code__Numeral_Oof__nat,X31119))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__code])]) ).

fof(i_0_9385,plain,
    ! [X21655,X21656] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21656)),hAPP(c_Nat_OSuc,X21655)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21656),X21655)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21656),X21655))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21656)),hAPP(c_Nat_OSuc,X21655))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).

fof(i_0_9386,plain,
    ! [X31064,X31065,X31066,X31067] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31067),X31066))
      | hAPP(hAPP(c_List_Onth(X31065),hAPP(hAPP(c_List_Otake(X31065),X31066),X31064)),X31067) = hAPP(hAPP(c_List_Onth(X31065),X31064),X31067) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__take])]) ).

fof(i_0_9387,plain,
    ! [X17931,X17932,X17933] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17933,tc_HOL_Obool)),X17932),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17933,tc_HOL_Obool)),X17931),X17932)) = c_Orderings_Obot__class_Obot(tc_fun(X17933,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Diff__disjoint]) ).

fof(i_0_9388,plain,
    ! [X32919,X32920,X32921,X32922] :
      ( ( hAPP(c_List_Orev(X32922),X32921) != hAPP(hAPP(c_List_Olist_OCons(X32922),X32920),X32919)
        | X32921 = hAPP(hAPP(c_List_Oappend(X32922),hAPP(c_List_Orev(X32922),X32919)),hAPP(hAPP(c_List_Olist_OCons(X32922),X32920),c_List_Olist_ONil(X32922))) )
      & ( X32921 != hAPP(hAPP(c_List_Oappend(X32922),hAPP(c_List_Orev(X32922),X32919)),hAPP(hAPP(c_List_Olist_OCons(X32922),X32920),c_List_Olist_ONil(X32922)))
        | hAPP(c_List_Orev(X32922),X32921) = hAPP(hAPP(c_List_Olist_OCons(X32922),X32920),X32919) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__eq__Cons__iff])]) ).

fof(i_0_9389,plain,
    ! [X22950,X22951] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22951))
      | 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),X22951),X22950))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J])]) ).

fof(i_0_9390,plain,
    ! [X23367,X23368] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23368),X23367)),X23368)),
    inference(variable_rename,[status(thm)],[fact_div__le__dividend]) ).

fof(i_0_9391,plain,
    ! [X20984,X20985] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20985),X20984)),X20985)),
    inference(variable_rename,[status(thm)],[fact_diff__le__self]) ).

fof(i_0_9392,plain,
    ! [X33769,X33770,X33771] : hAPP(c_Lazy__Sequence_Oyield(X33771),c_Lazy__Sequence_Olazy__sequence_OInsert(X33771,X33770,X33769)) = hAPP(c_Option_Ooption_OSome(tc_prod(X33771,tc_Lazy__Sequence_Olazy__sequence(X33771))),hAPP(hAPP(c_Product__Type_OPair(X33771,tc_Lazy__Sequence_Olazy__sequence(X33771)),X33770),X33769)),
    inference(variable_rename,[status(thm)],[fact__01]) ).

fof(i_0_9393,plain,
    ! [X26834,X26835] :
      ( ~ class_Orderings_Olinorder(X26835)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26835,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X26835),X26834)),hAPP(hAPP(c_Set_Oinsert(X26835),X26834),c_Orderings_Obot__class_Obot(tc_fun(X26835,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(X26835),X26834) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I2_J])]) ).

fof(i_0_9394,plain,
    ! [X22504,X22505,X22506] :
      ( ~ class_Orderings_Olinorder(X22506)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22506),X22505))
      | ~ hBOOL(hAPP(hAPP(c_member(X22506),X22504),X22505))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22506),c_Big__Operators_Olinorder__class_OMin(X22506,X22505)),X22504)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__le])]) ).

fof(i_0_9395,plain,
    ! [X22645,X22646,X22647] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X22647),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22646),X22645)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X22647),X22646)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X22647),X22645)),
    inference(variable_rename,[status(thm)],[fact_zpower__zadd__distrib]) ).

fof(i_0_9396,plain,
    ! [X22785,X22786,X22787] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22787),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22786),X22785)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22787),X22786)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22787),X22785)),
    inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib2]) ).

fof(i_0_9397,plain,
    ! [X22798,X22799,X22800] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22800),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X22799),X22798)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22800),X22799)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22800),X22798)),
    inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib2]) ).

fof(i_0_9398,plain,
    ! [X21760,X21761,X21762] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21762),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21761),X21760)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21762),X21761)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21762),X21760)),
    inference(variable_rename,[status(thm)],[fact_add__mult__distrib2]) ).

fof(i_0_9399,plain,
    ! [X20959,X20960,X20961] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20961),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20960),X20959)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20961),X20960)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20961),X20959)),
    inference(variable_rename,[status(thm)],[fact_diff__mult__distrib2]) ).

fof(i_0_9400,plain,
    ! [X20956,X20957,X20958] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20958),X20957)),X20956) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20958),X20956)),X20957),
    inference(variable_rename,[status(thm)],[fact_diff__commute]) ).

fof(i_0_9401,plain,
    ! [X22300,X22301] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22301),c_Groups_Ozero__class_Ozero(X22301)),hAPP(c_Groups_Ouminus__class_Ouminus(X22301),X22300)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22301),X22300),c_Groups_Ozero__class_Ozero(X22301)))
        | ~ class_Groups_Oordered__ab__group__add(X22301) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22301),X22300),c_Groups_Ozero__class_Ozero(X22301)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22301),c_Groups_Ozero__class_Ozero(X22301)),hAPP(c_Groups_Ouminus__class_Ouminus(X22301),X22300)))
        | ~ class_Groups_Oordered__ab__group__add(X22301) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less])])]) ).

fof(i_0_9402,plain,
    ! [X22294,X22295] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22295),c_Groups_Ozero__class_Ozero(X22295)),hAPP(c_Groups_Ouminus__class_Ouminus(X22295),X22294)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22295),X22294),c_Groups_Ozero__class_Ozero(X22295)))
        | ~ class_Groups_Oordered__ab__group__add(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)),hAPP(c_Groups_Ouminus__class_Ouminus(X22295),X22294)))
        | ~ class_Groups_Oordered__ab__group__add(X22295) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le])])]) ).

fof(i_0_9403,plain,
    ! [X18455,X18456,X18457,X18458] :
      ( ~ class_Orderings_Opreorder(X18458)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18458),X18457),X18456))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18458),X18456),X18455))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18458),X18457),X18455)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).

fof(i_0_9404,plain,
    ! [X18553,X18554,X18555,X18556] :
      ( ~ class_Orderings_Opreorder(X18556)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18556),X18555),X18554))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18556),X18554),X18553))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18556),X18555),X18553)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).

fof(i_0_9405,plain,
    ! [X18545,X18546,X18547,X18548] :
      ( ~ class_Orderings_Opreorder(X18548)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18548),X18547),X18546))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18548),X18546),X18545))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18548),X18547),X18545)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).

fof(i_0_9406,plain,
    ! [X18459,X18460,X18461,X18462] :
      ( ~ class_Orderings_Oorder(X18462)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18462),X18461),X18460))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18462),X18459),X18461))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18462),X18459),X18460)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).

fof(i_0_9407,plain,
    ! [X18557,X18558,X18559,X18560] :
      ( ~ class_Orderings_Oorder(X18560)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18560),X18559),X18558))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18560),X18557),X18559))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18560),X18557),X18558)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).

fof(i_0_9408,plain,
    ! [X18549,X18550,X18551,X18552] :
      ( ~ class_Orderings_Oorder(X18552)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18552),X18551),X18550))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18552),X18549),X18551))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18552),X18549),X18550)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).

fof(i_0_9409,plain,
    ! [X17058,X17059,X17060,X17061] :
      ( ~ class_Orderings_Opreorder(X17061)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17061),X17060),X17059))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17061),X17059),X17058))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17061),X17060),X17058)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).

fof(i_0_9410,plain,
    ! [X17051,X17052,X17053,X17054] :
      ( ~ class_Orderings_Oorder(X17054)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17054),X17053),X17052))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17054),X17051),X17053))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17054),X17051),X17052)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).

fof(i_0_9411,plain,
    ! [X23010] :
      ( X23010 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23010),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_9412,plain,
    ! [X23780,X23781] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23781))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23780))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23781,X23780) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X23781,X23780)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos])]) ).

fof(i_0_9413,plain,
    ! [X33013,X33014,X33015,X33016,X33017] :
      ( hBOOL(hAPP(X33017,X33016))
      | c_List_OtakeWhile(X33015,X33017,hAPP(hAPP(c_List_Oappend(X33015),X33014),hAPP(hAPP(c_List_Olist_OCons(X33015),X33016),X33013))) = c_List_OtakeWhile(X33015,X33017,X33014) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5910])]) ).

fof(i_0_9414,plain,
    ! [X18469,X18470,X18471,X18472,X18473] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18473),X18472),X18471))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18473),X18470),X18469))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18473),X18472),X18471) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18473),X18470),X18469)
        | ~ class_Groups_Oordered__ab__group__add(X18473) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18473),X18470),X18469))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18473),X18472),X18471))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18473),X18472),X18471) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18473),X18470),X18469)
        | ~ class_Groups_Oordered__ab__group__add(X18473) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less])])]) ).

fof(i_0_9415,plain,
    ! [X18319,X18320,X18321,X18322,X18323] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18323),X18322),X18321))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18323),X18320),X18319))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18323),X18322),X18321) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18323),X18320),X18319)
        | ~ class_Groups_Oordered__ab__group__add(X18323) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18323),X18320),X18319))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18323),X18322),X18321))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18323),X18322),X18321) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18323),X18320),X18319)
        | ~ class_Groups_Oordered__ab__group__add(X18323) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq])])]) ).

fof(i_0_9416,plain,
    ! [X20994,X20995,X20996] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20995),X20996) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20994),X20996)
        | X20995 = X20994
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20996),X20994))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20996),X20995)) )
      & ( X20995 != X20994
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20995),X20996) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20994),X20996)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20996),X20994))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20996),X20995)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__diff__iff])])]) ).

fof(i_0_9417,plain,
    ! [X27689,X27690,X27691] : hAPP(hAPP(c_Product__Type_OSigma(X27691,X27690),X27689),hAPP(c_COMBK(tc_fun(X27690,tc_HOL_Obool),X27691),c_Orderings_Obot__class_Obot(tc_fun(X27690,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27691,X27690),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Sigma__empty2]) ).

cnf(i_0_9418,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_5911]) ).

cnf(i_0_9419,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_9420,plain,
    ! [X32503,X32504,X32505,X32506] : c_List_Oremdups(X32506,hAPP(hAPP(c_List_Omap(X32505,X32506),X32504),c_List_Oremdups(X32505,X32503))) = c_List_Oremdups(X32506,hAPP(hAPP(c_List_Omap(X32505,X32506),X32504),X32503)),
    inference(variable_rename,[status(thm)],[fact_remdups__map__remdups]) ).

fof(i_0_9421,plain,
    ! [X21766,X21767,X21768] :
      ( ~ class_Rings_Ocomm__semiring__1(X21768)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21768),X21767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21768),X21766),X21767)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21768),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21768),X21766),c_Groups_Oone__class_Oone(X21768))),X21767) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])]) ).

cnf(i_0_9422,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_5912]) ).

cnf(i_0_9423,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_5913]) ).

fof(i_0_9424,plain,
    ! [X23778,X23779] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23779))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23778))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23779),X23778) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X23779,X23778)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos])]) ).

fof(i_0_9425,plain,
    ! [X21659,X21660] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21660),X21659))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21659)),X21660)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21659)),X21660))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21660),X21659)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5914])]) ).

fof(i_0_9426,plain,
    ! [X26118,X26119,X26120,X26121] :
      ( ~ class_Orderings_Oorder(X26121)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26121,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26121,X26120),X26119)),c_SetInterval_Oord__class_OatLeastAtMost(X26121,X26119,X26118)) = c_Orderings_Obot__class_Obot(tc_fun(X26121,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I15_J])]) ).

fof(i_0_9427,plain,
    ! [X25067,X25068] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25068),c_Groups_Ozero__class_Ozero(X25068)),hAPP(c_Int_Oring__1__class_Oof__int(X25068),X25067)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25067))
        | ~ class_Rings_Olinordered__idom(X25068) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25067))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25068),c_Groups_Ozero__class_Ozero(X25068)),hAPP(c_Int_Oring__1__class_Oof__int(X25068),X25067)))
        | ~ class_Rings_Olinordered__idom(X25068) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0__less__iff])])]) ).

fof(i_0_9428,plain,
    ! [X25267,X25268] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25268),c_Groups_Ozero__class_Ozero(X25268)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25268),X25267)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25267))
        | ~ class_Rings_Olinordered__semidom(X25268) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25267))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25268),c_Groups_Ozero__class_Ozero(X25268)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25268),X25267)))
        | ~ class_Rings_Olinordered__semidom(X25268) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0__less__iff])])]) ).

fof(i_0_9429,plain,
    ! [X25065,X25066] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25066),c_Groups_Ozero__class_Ozero(X25066)),hAPP(c_Int_Oring__1__class_Oof__int(X25066),X25065)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25065))
        | ~ class_Rings_Olinordered__idom(X25066) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25065))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25066),c_Groups_Ozero__class_Ozero(X25066)),hAPP(c_Int_Oring__1__class_Oof__int(X25066),X25065)))
        | ~ class_Rings_Olinordered__idom(X25066) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0__le__iff])])]) ).

fof(i_0_9430,plain,
    ! [X27020,X27021] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27021),hAPP(c_Groups_Oabs__class_Oabs(X27021),X27020)),c_Groups_Ozero__class_Ozero(X27021)))
        | X27020 = c_Groups_Ozero__class_Ozero(X27021)
        | ~ class_Groups_Oordered__ab__group__add__abs(X27021) )
      & ( X27020 != c_Groups_Ozero__class_Ozero(X27021)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27021),hAPP(c_Groups_Oabs__class_Oabs(X27021),X27020)),c_Groups_Ozero__class_Ozero(X27021)))
        | ~ class_Groups_Oordered__ab__group__add__abs(X27021) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff])])]) ).

fof(i_0_9431,plain,
    ! [X23776,X23777] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23777),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)),X23776))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23777,X23776) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X23777,X23776)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__pos])]) ).

fof(i_0_9432,plain,
    ! [X25958,X25959,X25960] :
      ( ~ class_Orderings_Olinorder(X25960)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25960),X25959))
      | X25959 = c_Orderings_Obot__class_Obot(tc_fun(X25960,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OSup__fin(X25960,c_Orderings_Oord__class_Omax(X25960),hAPP(hAPP(c_Set_Oinsert(X25960),X25958),X25959)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25960),X25958),c_Big__Operators_Olattice_OSup__fin(X25960,c_Orderings_Oord__class_Omax(X25960),X25959)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__idem])]) ).

fof(i_0_9433,plain,
    ! [X25672,X25673,X25674] :
      ( ~ class_Orderings_Olinorder(X25674)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25674),X25673))
      | X25673 = c_Orderings_Obot__class_Obot(tc_fun(X25674,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OInf__fin(X25674,c_Orderings_Oord__class_Omin(X25674),hAPP(hAPP(c_Set_Oinsert(X25674),X25672),X25673)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25674),X25672),c_Big__Operators_Olattice_OInf__fin(X25674,c_Orderings_Oord__class_Omin(X25674),X25673)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__idem])]) ).

fof(i_0_9434,plain,
    ! [X27012,X27013] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27013)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27013),hAPP(c_Groups_Oabs__class_Oabs(X27013),X27012)),c_Groups_Ozero__class_Ozero(X27013))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5915])]) ).

fof(i_0_9435,plain,
    ! [X25158,X25159] :
      ( ~ class_Rings_Olinordered__semidom(X25159)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25159),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25159),X25158)),c_Groups_Ozero__class_Ozero(X25159))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5916])]) ).

fof(i_0_9436,plain,
    ! [X25246,X25247,X25248] :
      ( ~ class_Rings_Oring__1(X25248)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25247),X25246))
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25248),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25246),X25247)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25248),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25248),X25246)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25248),X25247)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__diff])]) ).

cnf(i_0_9437,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_5917]) ).

fof(i_0_9438,plain,
    ! [X24667,X24668] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24668),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24668)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24667)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24667) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24667),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24668)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24667)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24668)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24668),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24667),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24668)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24667)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24668),X24667))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24668),c_Int_OPls)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5918])])]) ).

fof(i_0_9439,plain,
    ! [X24602,X24603] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24603)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24603)),X24602) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24602) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24603)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24603)),X24602) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24603)),X24602)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5919])]) ).

fof(i_0_9440,plain,
    ! [X23774,X23775] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23775),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)),X23774))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23775),X23774) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X23775,X23774)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__pos])]) ).

fof(i_0_9441,plain,
    ! [X20457,X20458,X20459] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20459),hAPP(hAPP(c_Set_Oinsert(X20459),X20458),X20457)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20459),X20457)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20459),X20457))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20459),hAPP(hAPP(c_Set_Oinsert(X20459),X20458),X20457))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__insert])]) ).

cnf(i_0_9442,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_5920]) ).

fof(i_0_9443,plain,
    ! [X29799,X29800,X29801] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29801)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29801),X29800))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X29801),X29799),c_Complete__Lattice_OInf__class_OInf(X29801,X29800)) = hAPP(hAPP(c_Finite__Set_Ofold(X29801,X29801,c_Lattices_Osemilattice__inf__class_Oinf(X29801)),X29799),X29800) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Inf__fold__inf])]) ).

fof(i_0_9444,plain,
    ! [X29794,X29795,X29796] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29796)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29796),X29795))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X29796),X29794),c_Complete__Lattice_OSup__class_OSup(X29796,X29795)) = hAPP(hAPP(c_Finite__Set_Ofold(X29796,X29796,c_Lattices_Osemilattice__sup__class_Osup(X29796)),X29794),X29795) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Sup__fold__sup])]) ).

cnf(i_0_9445,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_9446,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_9447,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_9448,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_9449,plain,
    ! [X20522,X20523] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20523,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20523,tc_HOL_Obool)),X20522)),X20522) = c_Orderings_Obot__class_Obot(tc_fun(X20523,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__disjoint2]) ).

fof(i_0_9450,plain,
    ! [X20526,X20527] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20527,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20527,tc_HOL_Obool)),X20526)),X20526) = c_Orderings_Otop__class_Otop(tc_fun(X20527,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__partition2]) ).

fof(i_0_9451,plain,
    ! [X22765,X22766] : c_Sum__Type_OPlus(X22766,X22765,c_Orderings_Otop__class_Otop(tc_fun(X22766,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X22765,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X22766,X22765),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_UNIV__Plus__UNIV]) ).

fof(i_0_9452,plain,
    ! [X26886,X26887,X26888] :
      ( ~ class_Orderings_Oorder(X26888)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26888,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26888,X26887,X26886)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26888),X26886)) = c_Orderings_Obot__class_Obot(tc_fun(X26888,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I7_J])]) ).

fof(i_0_9453,plain,
    ! [X26896,X26897,X26898] :
      ( ~ class_Orderings_Oorder(X26898)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26898,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X26898,X26897,X26896)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26898),X26896)) = c_Orderings_Obot__class_Obot(tc_fun(X26898,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I5_J])]) ).

fof(i_0_9454,plain,
    ! [X26940,X26941,X26942] :
      ( ~ class_Orderings_Oorder(X26942)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26942,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X26942,X26941,X26940)),hAPP(c_SetInterval_Oord__class_OatLeast(X26942),X26940)) = c_Orderings_Obot__class_Obot(tc_fun(X26942,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I6_J])]) ).

fof(i_0_9455,plain,
    ! [X28520,X28521,X28522] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X28522),X28521))
        | c_Random_Ominus__shift(X28520,X28522,X28521) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X28520),X28522)),X28521) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X28522),X28521))
        | c_Random_Ominus__shift(X28520,X28522,X28521) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X28522),X28521) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5921])]) ).

fof(i_0_9456,plain,
    ! [X24659,X24660] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24660),c_Groups_Ozero__class_Ozero(X24660)),hAPP(c_Int_Onumber__class_Onumber__of(X24660),X24659)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X24659))
        | ~ class_Int_Onumber__ring(X24660)
        | ~ class_Rings_Olinordered__idom(X24660) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X24659))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24660),c_Groups_Ozero__class_Ozero(X24660)),hAPP(c_Int_Onumber__class_Onumber__of(X24660),X24659)))
        | ~ class_Int_Onumber__ring(X24660)
        | ~ class_Rings_Olinordered__idom(X24660) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I1_J])])]) ).

fof(i_0_9457,plain,
    ! [X24655,X24656] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24656),c_Groups_Ozero__class_Ozero(X24656)),hAPP(c_Int_Onumber__class_Onumber__of(X24656),X24655)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X24655))
        | ~ class_Int_Onumber__ring(X24656)
        | ~ class_Rings_Olinordered__idom(X24656) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X24655))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24656),c_Groups_Ozero__class_Ozero(X24656)),hAPP(c_Int_Onumber__class_Onumber__of(X24656),X24655)))
        | ~ class_Int_Onumber__ring(X24656)
        | ~ class_Rings_Olinordered__idom(X24656) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I1_J])])]) ).

fof(i_0_9458,plain,
    ! [X23559,X23560,X23561] :
      ( ( ~ hBOOL(hAPP(X23561,c_Divides_Odiv__class_Omod(tc_Int_Oint,X23560,X23559)))
        | epred2_3(X23561,X23559,X23560) )
      & ( ~ epred2_3(X23561,X23559,X23560)
        | hBOOL(hAPP(X23561,c_Divides_Odiv__class_Omod(tc_Int_Oint,X23560,X23559))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5922])]) ).

fof(i_0_9459,plain,
    ! [X27610,X27611,X27612] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27612,X27611)),X27610))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27612),hAPP(c_Relation_ODomain(X27612,X27611),X27610))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Domain])]) ).

fof(i_0_9460,plain,
    ! [X27532,X27533,X27534] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27534,X27533)),X27532))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27533),hAPP(c_Relation_ORange(X27534,X27533),X27532))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Range])]) ).

fof(i_0_9461,plain,
    ! [X19177,X19178,X19179,X19180] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X19180,X19179,X19178),X19177))
      | X19178 != c_Orderings_Obot__class_Obot(tc_fun(X19180,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1Set__nonempty])]) ).

fof(i_0_9462,plain,
    ! [X27155,X27156] : hAPP(hAPP(c_Nitpick_Oint__gcd,X27156),X27155) = 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),X27156)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X27155)))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Oint__gcd__def]) ).

fof(i_0_9463,plain,
    ! [X31758,X31759,X31760,X31761,X31762] : hAPP(hAPP(c_List_Odrop(X31762),X31761),hAPP(hAPP(c_List_Omap(X31760,X31762),X31759),X31758)) = hAPP(hAPP(c_List_Omap(X31760,X31762),X31759),hAPP(hAPP(c_List_Odrop(X31760),X31761),X31758)),
    inference(variable_rename,[status(thm)],[fact_drop__map]) ).

fof(i_0_9464,plain,
    ! [X31068,X31069,X31070,X31071,X31072] : hAPP(hAPP(c_List_Otake(X31072),X31071),hAPP(hAPP(c_List_Omap(X31070,X31072),X31069),X31068)) = hAPP(hAPP(c_List_Omap(X31070,X31072),X31069),hAPP(hAPP(c_List_Otake(X31070),X31071),X31068)),
    inference(variable_rename,[status(thm)],[fact_take__map]) ).

fof(i_0_9465,plain,
    ! [X32246,X32247,X32248,X32249] : hAPP(c_List_Ofilter(X32249,X32248),hAPP(hAPP(c_List_Oappend(X32249),X32247),X32246)) = hAPP(hAPP(c_List_Oappend(X32249),hAPP(c_List_Ofilter(X32249,X32248),X32247)),hAPP(c_List_Ofilter(X32249,X32248),X32246)),
    inference(variable_rename,[status(thm)],[fact_filter__append]) ).

fof(i_0_9466,plain,
    ! [X31443,X31444] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X31444),X31443))
        | c_List_Oupto(X31444,X31443) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X31444),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X31444),c_Groups_Oone__class_Oone(tc_Int_Oint)),X31443)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X31444),X31443))
        | c_List_Oupto(X31444,X31443) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5923])]) ).

fof(i_0_9467,plain,
    ! [X27446,X27447,X27448,X27449,X27450] :
      ( ( ~ c_Wellfounded_Owf(X27447,X27446)
        | hBOOL(hAPP(hAPP(c_member(X27447),X27448),c_Wellfounded_Oacc(X27447,X27446))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27450),esk259_2(X27449,X27450)),c_Wellfounded_Oacc(X27450,X27449)))
        | c_Wellfounded_Owf(X27450,X27449) ) ),
    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_9468,plain,
    ! [X22304,X22305] :
      ( ~ class_Groups_Olinordered__ab__group__add(X22305)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22305),X22304))
      | X22304 = c_Orderings_Obot__class_Obot(tc_fun(X22305,tc_HOL_Obool))
      | hAPP(c_Groups_Ouminus__class_Ouminus(X22305),c_Big__Operators_Olinorder__class_OMin(X22305,X22304)) = c_Big__Operators_Olinorder__class_OMax(X22305,hAPP(c_Set_Oimage(X22305,X22305,c_Groups_Ouminus__class_Ouminus(X22305)),X22304)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__Min__eq__Max])]) ).

fof(i_0_9469,plain,
    ! [X22306,X22307] :
      ( ~ class_Groups_Olinordered__ab__group__add(X22307)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22307),X22306))
      | X22306 = c_Orderings_Obot__class_Obot(tc_fun(X22307,tc_HOL_Obool))
      | hAPP(c_Groups_Ouminus__class_Ouminus(X22307),c_Big__Operators_Olinorder__class_OMax(X22307,X22306)) = c_Big__Operators_Olinorder__class_OMin(X22307,hAPP(c_Set_Oimage(X22307,X22307,c_Groups_Ouminus__class_Ouminus(X22307)),X22306)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__Max__eq__Min])]) ).

fof(i_0_9470,plain,
    ! [X29717,X29718] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29718),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29718,tc_HOL_Obool),X29717)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X29718,tc_HOL_Obool)),X29717)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UnionD])]) ).

fof(i_0_9471,plain,
    ! [X23695,X23696] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X23696))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23696),X23695)),X23696) = 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_9472,plain,
    ! [X26984,X26985] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26985),c_Groups_Ozero__class_Ozero(X26985)),c_Groups_Osgn__class_Osgn(X26985,X26984)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26985),c_Groups_Ozero__class_Ozero(X26985)),X26984))
        | ~ class_Rings_Olinordered__idom(X26985) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26985),c_Groups_Ozero__class_Ozero(X26985)),X26984))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26985),c_Groups_Ozero__class_Ozero(X26985)),c_Groups_Osgn__class_Osgn(X26985,X26984)))
        | ~ class_Rings_Olinordered__idom(X26985) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__greater])])]) ).

cnf(i_0_9473,plain,
    c_Int_OBit0(X1) != c_Int_OBit1(X2),
    inference(split_conjunct,[status(thm)],[i_0_5924]) ).

cnf(i_0_9474,plain,
    c_Int_OBit1(X1) != c_Int_OBit0(X2),
    inference(split_conjunct,[status(thm)],[i_0_5925]) ).

fof(i_0_9475,plain,
    ! [X23314,X23315,X23316,X23317] :
      ( ~ class_Divides_Osemiring__div(X23317)
      | c_Divides_Odiv__class_Omod(X23317,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23317),X23316),X23315),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23317),X23316),X23314)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23317),X23316),c_Divides_Odiv__class_Omod(X23317,X23315,X23314)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__mult1])]) ).

fof(i_0_9476,plain,
    ! [X29420,X29421,X29422,X29423] :
      ( ( X29423 != c_Orderings_Obot__class_Obot(tc_fun(X29422,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29422,tc_fun(X29421,tc_HOL_Obool)),X29423),hAPP(c_COMBK(tc_fun(X29421,tc_HOL_Obool),X29422),X29420)) = c_Orderings_Otop__class_Otop(tc_fun(X29421,tc_HOL_Obool)) )
      & ( X29423 = c_Orderings_Obot__class_Obot(tc_fun(X29422,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29422,tc_fun(X29421,tc_HOL_Obool)),X29423),hAPP(c_COMBK(tc_fun(X29421,tc_HOL_Obool),X29422),X29420)) = X29420 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__constant])]) ).

fof(i_0_9477,plain,
    ! [X19668,X19669,X19670,X19671] :
      ( ( X19671 != c_Orderings_Obot__class_Obot(tc_fun(X19670,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19670,tc_fun(X19669,tc_HOL_Obool)),X19671),hAPP(c_COMBK(tc_fun(X19669,tc_HOL_Obool),X19670),X19668)) = c_Orderings_Obot__class_Obot(tc_fun(X19669,tc_HOL_Obool)) )
      & ( X19671 = c_Orderings_Obot__class_Obot(tc_fun(X19670,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19670,tc_fun(X19669,tc_HOL_Obool)),X19671),hAPP(c_COMBK(tc_fun(X19669,tc_HOL_Obool),X19670),X19668)) = X19668 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__constant])]) ).

fof(i_0_9478,plain,
    ! [X34209,X34210,X34211] : c_Random__Sequence_Oempty(X34211,X34210,X34209) = 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(X34211)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X34211)),
    inference(variable_rename,[status(thm)],[fact_Random__Sequence_Oempty__def]) ).

fof(i_0_9479,plain,
    ! [X23070,X23071,X23072,X23073] :
      ( ( X23072 != c_Groups_Ozero__class_Ozero(X23073)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23073),X23072),X23071)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23073),X23072),X23070)) = c_Groups_Ozero__class_Ozero(X23073)
        | ~ class_Divides_Osemiring__div(X23073) )
      & ( X23072 = c_Groups_Ozero__class_Ozero(X23073)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23073),X23072),X23071)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23073),X23072),X23070)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23073),X23071),X23070)
        | ~ class_Divides_Osemiring__div(X23073) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult1__if])])]) ).

fof(i_0_9480,plain,
    ! [X24333,X24334,X24335,X24336] :
      ( ~ class_Fields_Ofield__inverse__zero(X24336)
      | X24335 = c_Groups_Ozero__class_Ozero(X24336)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24336),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24336),X24335),X24334)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24336),X24335),X24333)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24336),X24334),X24333) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__left])]) ).

fof(i_0_9481,plain,
    ! [X24337,X24338,X24339,X24340] :
      ( ~ class_Fields_Ofield__inverse__zero(X24340)
      | X24339 = c_Groups_Ozero__class_Ozero(X24340)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24340),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24340),X24338),X24339)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24340),X24337),X24339)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24340),X24338),X24337) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__right])]) ).

fof(i_0_9482,plain,
    ! [X23084,X23085,X23086,X23087] :
      ( ~ class_Divides_Osemiring__div(X23087)
      | X23086 = c_Groups_Ozero__class_Ozero(X23087)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23087),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23087),X23086),X23085)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23087),X23086),X23084)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23087),X23085),X23084) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult1])]) ).

fof(i_0_9483,plain,
    ! [X23080,X23081,X23082,X23083] :
      ( ~ class_Divides_Osemiring__div(X23083)
      | X23082 = c_Groups_Ozero__class_Ozero(X23083)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23083),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23083),X23081),X23082)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23083),X23080),X23082)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23083),X23081),X23080) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult2])]) ).

cnf(i_0_9484,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_5926]) ).

fof(i_0_9485,plain,
    ! [X24734,X24735,X24736,X24737] : hAPP(c_Nat_Onat_Onat__rec(X24737,X24736,X24735),hAPP(c_Nat_OSuc,X24734)) = hAPP(hAPP(X24735,X24734),hAPP(c_Nat_Onat_Onat__rec(X24737,X24736,X24735),X24734)),
    inference(variable_rename,[status(thm)],[fact_nat__rec__Suc]) ).

fof(i_0_9486,plain,
    ! [X21675,X21676,X21677] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21677),X21676))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21676),X21675))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).

fof(i_0_9487,plain,
    ! [X21662,X21663,X21664] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21664),X21663))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21664),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21663),X21662))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).

fof(i_0_9488,plain,
    ! [X21678,X21679,X21680] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21680),X21679))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21680),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21678),X21679))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).

fof(i_0_9489,plain,
    ! [X21665,X21666,X21667] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21667),X21666))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21667),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21665),X21666))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).

fof(i_0_9490,plain,
    ! [X21728,X21729,X21730] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21730),X21729))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21730),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21729),X21728))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).

fof(i_0_9491,plain,
    ! [X21706,X21707,X21708] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21708),X21707))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21708),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21707),X21706))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).

fof(i_0_9492,plain,
    ! [X21725,X21726,X21727] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21727),X21726))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21727),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21725),X21726))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).

fof(i_0_9493,plain,
    ! [X21703,X21704,X21705] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21705),X21704))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21705),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21703),X21704))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).

fof(i_0_9494,plain,
    ! [X23405,X23406,X23407,X23408] :
      ( ~ class_Divides_Osemiring__div(X23408)
      | c_Divides_Odiv__class_Omod(X23408,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23408),X23407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23408),X23406),X23405)),X23406) = c_Divides_Odiv__class_Omod(X23408,X23407,X23406) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2])]) ).

fof(i_0_9495,plain,
    ! [X23401,X23402,X23403,X23404] :
      ( ~ class_Divides_Osemiring__div(X23404)
      | c_Divides_Odiv__class_Omod(X23404,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23404),X23403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23404),X23402),X23401)),X23401) = c_Divides_Odiv__class_Omod(X23404,X23403,X23401) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1])]) ).

fof(i_0_9496,plain,
    ! [X22322,X22323,X22325,X22326,X22327] :
      ( ( X22323 = hAPP(c_Nat_OSuc,esk110_2(X22322,X22323))
        | X22323 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22323),hAPP(c_Nat_OSuc,X22322))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk110_2(X22322,X22323)),X22322))
        | X22323 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22323),hAPP(c_Nat_OSuc,X22322))) )
      & ( X22326 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22326),hAPP(c_Nat_OSuc,X22325))) )
      & ( X22326 != hAPP(c_Nat_OSuc,X22327)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22327),X22325))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22326),hAPP(c_Nat_OSuc,X22325))) ) ),
    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_9497,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1))),
    inference(split_conjunct,[status(thm)],[i_0_5927]) ).

cnf(i_0_9498,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_5928]) ).

fof(i_0_9499,plain,
    ! [X31905,X31906] :
      ( X31906 = c_List_Olist_ONil(X31905)
      | hAPP(c_List_Orotate1(X31905),X31906) = hAPP(hAPP(c_List_Oappend(X31905),hAPP(c_List_Otl(X31905),X31906)),hAPP(hAPP(c_List_Olist_OCons(X31905),hAPP(c_List_Ohd(X31905),X31906)),c_List_Olist_ONil(X31905))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__hd__tl])]) ).

fof(i_0_9500,plain,
    ! [X18474,X18475,X18476,X18477,X18478,X18479] :
      ( ( X18479 != X18478
        | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18477,X18476),X18475),X18478),X18474),X18479) = X18474 )
      & ( X18479 = X18478
        | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18477,X18476),X18475),X18478),X18474),X18479) = hAPP(X18475,X18479) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__def])]) ).

fof(i_0_9501,plain,
    ! [X18386,X18387,X18388,X18389,X18390,X18391] :
      ( X18391 = X18390
      | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18389,X18388),X18387),X18390),X18386),X18391) = hAPP(X18387,X18391) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__other])]) ).

fof(i_0_9502,plain,
    ! [X18373,X18374,X18375,X18376,X18377,X18378] :
      ( ( X18378 != X18377
        | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18376,X18375),X18374),X18377),X18373),X18378) = X18373 )
      & ( X18378 = X18377
        | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18376,X18375),X18374),X18377),X18373),X18378) = hAPP(X18374,X18378) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__apply])]) ).

cnf(i_0_9503,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_5929]) ).

fof(i_0_9504,plain,
    ! [X30670,X30671,X30672,X30673] :
      ( ~ class_Groups_Ocomm__monoid__add(X30673)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X30673),X30672),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X30671,X30670))) = hAPP(c_List_Omonoid__add__class_Olistsum(X30673),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X30673),X30672),c_List_Oupto(X30671,X30670))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__set__upto__conv__listsum__int])]) ).

fof(i_0_9505,plain,
    ! [X30674,X30675,X30676,X30677] :
      ( ~ class_Groups_Ocomm__monoid__add(X30677)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30677),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X30677),X30676),c_List_Oupto(X30675,X30674))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X30677),X30676),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X30675,X30674))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_interv__listsum__conv__setsum__set__int])]) ).

fof(i_0_9506,plain,
    ! [X25723,X25724,X25725,X25726] :
      ( ~ class_Orderings_Olinorder(X25726)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25726),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25726),X25725),X25724)),X25723) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25726),X25725),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25726),X25724),X25723)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oassoc])]) ).

fof(i_0_9507,plain,
    ! [X25719,X25720,X25721,X25722] :
      ( ~ class_Orderings_Olinorder(X25722)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25722),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25722),X25721),X25720)),X25719) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25722),X25721),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25722),X25720),X25719)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__assoc])]) ).

fof(i_0_9508,plain,
    ! [X25350,X25351,X25352,X25353] :
      ( ~ class_Orderings_Olinorder(X25353)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25353),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25353),X25352),X25351)),X25350) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25353),X25352),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25353),X25351),X25350)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__assoc])]) ).

fof(i_0_9509,plain,
    ! [X25346,X25347,X25348,X25349] :
      ( ~ class_Orderings_Olinorder(X25349)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25349),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25349),X25348),X25347)),X25346) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25349),X25348),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25349),X25347),X25346)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oassoc])]) ).

fof(i_0_9510,plain,
    ! [X21481,X21482,X21483,X21484] :
      ( ~ class_Groups_Oab__semigroup__add(X21484)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21484),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21484),X21483),X21482)),X21481) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21484),X21483),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21484),X21482),X21481)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).

fof(i_0_9511,plain,
    ! [X21466,X21467,X21468,X21469] :
      ( ~ class_Rings_Ocomm__semiring__1(X21469)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21469),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21469),X21468),X21467)),X21466) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21469),X21468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21469),X21467),X21466)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).

fof(i_0_9512,plain,
    ! [X22658,X22659,X22660] :
      ( ~ class_Groups_Omonoid__mult(X22660)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22660),hAPP(hAPP(c_Power_Opower__class_Opower(X22660),X22659),X22658)),X22659) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22660),X22659),hAPP(hAPP(c_Power_Opower__class_Opower(X22660),X22659),X22658)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__commutes])]) ).

fof(i_0_9513,plain,
    ! [X21912,X21913,X21914,X21915] :
      ( ~ class_Rings_Ocomm__semiring__1(X21915)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21915),X21914),X21913)),X21912) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21915),X21914),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21915),X21913),X21912)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])]) ).

fof(i_0_9514,plain,
    ! [X20355,X20356,X20357,X20358] :
      ( ~ class_Groups_Oab__semigroup__mult(X20358)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20358),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20358),X20357),X20356)),X20355) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20358),X20357),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20358),X20356),X20355)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J])]) ).

fof(i_0_9515,plain,
    ! [X17830,X17831,X17832,X17833] :
      ( ~ class_Lattices_Osemilattice__inf(X17833)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17833),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17833),X17832),X17831)),X17830) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17833),X17832),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17833),X17831),X17830)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oassoc])]) ).

fof(i_0_9516,plain,
    ! [X17822,X17823,X17824,X17825] :
      ( ~ class_Lattices_Osemilattice__inf(X17825)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17825),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17825),X17824),X17823)),X17822) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17825),X17824),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17825),X17823),X17822)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__assoc])]) ).

fof(i_0_9517,plain,
    ! [X17826,X17827,X17828,X17829] :
      ( ~ class_Lattices_Olattice(X17829)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17829),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17829),X17828),X17827)),X17826) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17829),X17828),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17829),X17827),X17826)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I2_J])]) ).

fof(i_0_9518,plain,
    ! [X17666,X17667,X17668,X17669] :
      ( ~ class_Lattices_Olattice(X17669)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17669),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17669),X17668),X17667)),X17666) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17669),X17668),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17669),X17667),X17666)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I6_J])]) ).

fof(i_0_9519,plain,
    ! [X17670,X17671,X17672,X17673] :
      ( ~ class_Lattices_Osemilattice__sup(X17673)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17673),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17673),X17672),X17671)),X17670) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17673),X17672),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17673),X17671),X17670)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oassoc])]) ).

fof(i_0_9520,plain,
    ! [X17662,X17663,X17664,X17665] :
      ( ~ class_Lattices_Osemilattice__sup(X17665)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17665),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17665),X17664),X17663)),X17662) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17665),X17664),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17665),X17663),X17662)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__assoc])]) ).

fof(i_0_9521,plain,
    ! [X21470,X21471,X21472,X21473] :
      ( ~ class_Rings_Ocomm__semiring__1(X21473)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21473),X21472),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21473),X21471),X21470)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21473),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21473),X21472),X21471)),X21470) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).

fof(i_0_9522,plain,
    ! [X24131,X24132,X24133,X24134] :
      ( ~ class_Rings_Odivision__ring(X24134)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24134),X24133),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24134),X24132),X24131)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24134),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24134),X24133),X24132)),X24131) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__eq__right])]) ).

fof(i_0_9523,plain,
    ! [X21916,X21917,X21918,X21919] :
      ( ~ class_Rings_Ocomm__semiring__1(X21919)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21919),X21918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21919),X21917),X21916)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21919),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21919),X21918),X21917)),X21916) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J])]) ).

fof(i_0_9524,plain,
    ! [X32522,X32523,X32524] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X32524),X32523),hAPP(c_List_Oset(X32524),X32522)))
        | c_List_Oremdups(X32524,hAPP(hAPP(c_List_Olist_OCons(X32524),X32523),X32522)) = c_List_Oremdups(X32524,X32522) )
      & ( hBOOL(hAPP(hAPP(c_member(X32524),X32523),hAPP(c_List_Oset(X32524),X32522)))
        | c_List_Oremdups(X32524,hAPP(hAPP(c_List_Olist_OCons(X32524),X32523),X32522)) = hAPP(hAPP(c_List_Olist_OCons(X32524),X32523),c_List_Oremdups(X32524,X32522)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5930])]) ).

fof(i_0_9525,plain,
    ! [X32133,X32134] :
      ( X32134 = c_List_Olist_ONil(X32133)
      | c_List_Olast(X32133,X32134) = hAPP(hAPP(c_List_Onth(X32133),X32134),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32133)),X32134)),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_9526,plain,
    ! [X25282,X25283] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25282),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Oring__1__class_Oof__int(X25283),X25282) = hAPP(c_Groups_Ouminus__class_Ouminus(X25283),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25283),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25282))))
        | ~ class_Rings_Oring__1(X25283) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25282),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Oring__1__class_Oof__int(X25283),X25282) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25283),hAPP(c_Int_Onat,X25282))
        | ~ class_Rings_Oring__1(X25283) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5931])])]) ).

fof(i_0_9527,plain,
    ! [X25617,X25618] :
      ( ~ class_Int_Onumber__ring(X25618)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X25617))
      | hBOOL(hAPP(hAPP(c_member(X25618),hAPP(c_Int_Onumber__class_Onumber__of(X25618),X25617)),c_Nat_Osemiring__1__class_ONats(X25618))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__number__of])]) ).

fof(i_0_9528,plain,
    ! [X22565,X22566] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22566),X22565))
      | hAPP(c_Finite__Set_Ocard(tc_fun(X22566,tc_HOL_Obool)),hAPP(c_Set_OPow(X22566),X22565)) = 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(X22566),X22565)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Pow])]) ).

fof(i_0_9529,plain,
    ! [X26947] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26947)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X26947)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X26947),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_atLeast__Suc]) ).

fof(i_0_9530,plain,
    ! [X20539,X20540,X20541] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20541,tc_HOL_Obool)),X20540),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20541,tc_HOL_Obool)),X20539)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20541,tc_HOL_Obool)),X20540),X20539),
    inference(variable_rename,[status(thm)],[fact_Diff__Compl]) ).

fof(i_0_9531,plain,
    ! [X20542,X20543,X20544] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20544,tc_HOL_Obool)),X20543),X20542) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20544,tc_HOL_Obool)),X20543),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20544,tc_HOL_Obool)),X20542)),
    inference(variable_rename,[status(thm)],[fact_Diff__eq]) ).

fof(i_0_9532,plain,
    ! [X22463] :
      ( ~ class_Rings_Olinordered__semidom(X22463)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22463),c_Groups_Ozero__class_Ozero(X22463)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22463),c_Groups_Oone__class_Oone(X22463)),c_Groups_Oone__class_Oone(X22463)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).

fof(i_0_9533,plain,
    ! [X25558,X25559] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X25559,X25558)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25558),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25559),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[fact_card__greaterThanLessThan__int]) ).

fof(i_0_9534,plain,
    ! [X33995,X33996,X33997,X33998] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33998),X33997))
      | hAPP(hAPP(c_List_Onth(X33996),c_List_Oreplicate(X33996,X33997,X33995)),X33998) = X33995 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__replicate])]) ).

fof(i_0_9535,plain,
    ! [X17948,X17949,X17950] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X17950)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17950),X17949),hAPP(X17948,X17949)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17950),X17949),c_Inductive_Ocomplete__lattice__class_Ogfp(X17950,X17948))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gfp__upperbound])]) ).

fof(i_0_9536,plain,
    ! [X25900,X25901,X25902] :
      ( ~ class_Orderings_Olinorder(X25902)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25902),X25901))
      | ~ hBOOL(hAPP(hAPP(c_member(X25902),X25900),X25901))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25902),X25900),c_Big__Operators_Olattice_OInf__fin(X25902,c_Orderings_Oord__class_Omin(X25902),X25901)) = X25900 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf__absorb])]) ).

fof(i_0_9537,plain,
    ! [X25964,X25965,X25966] :
      ( ~ class_Orderings_Olinorder(X25966)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25966),X25965))
      | ~ hBOOL(hAPP(hAPP(c_member(X25966),X25964),X25965))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25966),X25964),c_Big__Operators_Olattice_OSup__fin(X25966,c_Orderings_Oord__class_Omax(X25966),X25965)) = X25964 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup__absorb])]) ).

fof(i_0_9538,plain,
    ! [X22302,X22303] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22303),X22302),hAPP(c_Groups_Ouminus__class_Ouminus(X22303),X22302)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22303),X22302),c_Groups_Ozero__class_Ozero(X22303)))
        | ~ class_Rings_Olinordered__idom(X22303) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22303),X22302),c_Groups_Ozero__class_Ozero(X22303)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22303),X22302),hAPP(c_Groups_Ouminus__class_Ouminus(X22303),X22302)))
        | ~ class_Rings_Olinordered__idom(X22303) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff])])]) ).

fof(i_0_9539,plain,
    ! [X22292,X22293] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22293),X22292),hAPP(c_Groups_Ouminus__class_Ouminus(X22293),X22292)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22293),X22292),c_Groups_Ozero__class_Ozero(X22293)))
        | ~ class_Groups_Olinordered__ab__group__add(X22293) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22293),X22292),c_Groups_Ozero__class_Ozero(X22293)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22293),X22292),hAPP(c_Groups_Ouminus__class_Ouminus(X22293),X22292)))
        | ~ class_Groups_Olinordered__ab__group__add(X22293) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff])])]) ).

fof(i_0_9540,plain,
    ! [X17934,X17935,X17936] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17936,tc_HOL_Obool)),X17935),X17934) != c_Orderings_Obot__class_Obot(tc_fun(X17936,tc_HOL_Obool))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17936,tc_HOL_Obool)),X17935),X17934) = X17935 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__triv])]) ).

fof(i_0_9541,plain,
    ! [X32655,X32656,X32657,X32658,X32659] :
      ( ~ class_Orderings_Olinorder(X32659)
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32658,X32659,X32657),X32656),X32655) != c_List_Olist_ONil(X32658) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__not__Nil])]) ).

fof(i_0_9542,plain,
    ! [X23157,X23158,X23159,X23160] :
      ( ~ class_Groups_Ocomm__monoid__mult(X23160)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23159),X23158))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23159,X23160),hAPP(c_COMBK(X23160,X23159),X23157)),X23158) = hAPP(hAPP(c_Power_Opower__class_Opower(X23160),X23157),hAPP(c_Finite__Set_Ocard(X23159),X23158)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__constant])]) ).

fof(i_0_9543,plain,
    ! [X33846,X33847] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33847),X33846))
        | c_Lazy__Sequence_Osmall__lazy_H(X33847,X33846) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33847),X33846))
        | c_Lazy__Sequence_Osmall__lazy_H(X33847,X33846) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X33846),c_Lazy__Sequence_Osmall__lazy_H(X33847,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X33846),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5932])]) ).

fof(i_0_9544,plain,
    ! [X21294,X21295,X21296] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X21296)
      | X21295 = c_Orderings_Obot__class_Obot(tc_fun(X21296,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21296),X21295))
      | hAPP(c_Finite__Set_Ofold1(X21296,c_Groups_Otimes__class_Otimes(X21296)),hAPP(hAPP(c_Set_Oinsert(X21296),X21294),X21295)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21296),X21294),hAPP(c_Finite__Set_Ofold1(X21296,c_Groups_Otimes__class_Otimes(X21296)),X21295)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__insert__idem])]) ).

fof(i_0_9545,plain,
    ! [X26190,X26191,X26192,X26193] :
      ( ~ class_Orderings_Oorder(X26193)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26193,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26193,X26192),X26191)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26193,X26191),X26190)) = c_Orderings_Obot__class_Obot(tc_fun(X26193,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I11_J])]) ).

fof(i_0_9546,plain,
    ! [X24747,X24748] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24748),hAPP(c_Nat_OSuc,X24747)) = 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),X24748),X24747)),
    inference(variable_rename,[status(thm)],[fact_diff__Suc]) ).

fof(i_0_9547,plain,
    ! [X31592,X31593,X31594,X31595] : hAPP(hAPP(c_List_Oappend(X31595),hAPP(hAPP(c_List_Oappend(X31595),X31594),X31593)),X31592) = hAPP(hAPP(c_List_Oappend(X31595),X31594),hAPP(hAPP(c_List_Oappend(X31595),X31593),X31592)),
    inference(variable_rename,[status(thm)],[fact_append__assoc]) ).

fof(i_0_9548,plain,
    ! [X31646,X31647,X31648,X31649] : hAPP(hAPP(c_List_Oappend(X31649),hAPP(hAPP(c_List_Olist_OCons(X31649),X31648),X31647)),X31646) = hAPP(hAPP(c_List_Olist_OCons(X31649),X31648),hAPP(hAPP(c_List_Oappend(X31649),X31647),X31646)),
    inference(variable_rename,[status(thm)],[fact_append__Cons]) ).

fof(i_0_9549,plain,
    ! [X31985,X31986,X31987] :
      ( X31987 = c_List_Olist_ONil(X31986)
      | hAPP(hAPP(c_List_Otake(X31986),hAPP(c_Nat_OSuc,X31985)),X31987) = hAPP(hAPP(c_List_Olist_OCons(X31986),hAPP(c_List_Ohd(X31986),X31987)),hAPP(hAPP(c_List_Otake(X31986),X31985),hAPP(c_List_Otl(X31986),X31987))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Suc])]) ).

fof(i_0_9550,plain,
    ! [X26392] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26392))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26392) = 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,X26392))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__atLeastZeroLessThan__int])]) ).

fof(i_0_9551,plain,
    ! [X31006,X31007,X31008,X31009] :
      ( ( X31009 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Onth(X31008),hAPP(hAPP(c_List_Olist_OCons(X31008),X31007),X31006)),X31009) = X31007 )
      & ( X31009 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Onth(X31008),hAPP(hAPP(c_List_Olist_OCons(X31008),X31007),X31006)),X31009) = hAPP(hAPP(c_List_Onth(X31008),X31006),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31009),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_9552,plain,
    ! [X17254,X17255,X17256,X17257] :
      ( ( X17257 != c_Orderings_Obot__class_Obot(tc_fun(X17256,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(X17256,X17255,hAPP(c_COMBK(X17255,X17256),X17254)),X17257) = c_Orderings_Obot__class_Obot(tc_fun(X17255,tc_HOL_Obool)) )
      & ( X17257 = c_Orderings_Obot__class_Obot(tc_fun(X17256,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(X17256,X17255,hAPP(c_COMBK(X17255,X17256),X17254)),X17257) = hAPP(hAPP(c_Set_Oinsert(X17255),X17254),c_Orderings_Obot__class_Obot(tc_fun(X17255,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__constant__conv])]) ).

cnf(i_0_9553,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5890]) ).

cnf(i_0_9554,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_5891]) ).

cnf(i_0_9555,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_5893]) ).

cnf(i_0_9556,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_5892]) ).

cnf(i_0_9557,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_5894]) ).

fof(i_0_9558,plain,
    ! [X30446,X30447,X30448,X30449] :
      ( ~ class_Groups_Ocomm__monoid__add(X30449)
      | ~ hBOOL(hAPP(c_List_Odistinct(X30448),X30447))
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30449),hAPP(hAPP(c_List_Omap(X30448,X30449),X30446),X30447)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X30448,X30449),X30446),hAPP(c_List_Oset(X30448),X30447)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__distinct__conv__setsum__set])]) ).

fof(i_0_9559,plain,
    ! [X22663,X22664,X22665,X22666] :
      ( ~ class_Groups_Omonoid__mult(X22666)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22666),X22665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22664),X22663)) = hAPP(hAPP(c_Power_Opower__class_Opower(X22666),hAPP(hAPP(c_Power_Opower__class_Opower(X22666),X22665),X22664)),X22663) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult])]) ).

fof(i_0_9560,plain,
    ! [X22577,X22578,X22579,X22580] :
      ( ~ class_Rings_Ocomm__semiring__1(X22580)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22580),hAPP(hAPP(c_Power_Opower__class_Opower(X22580),X22579),X22578)),X22577) = hAPP(hAPP(c_Power_Opower__class_Opower(X22580),X22579),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22578),X22577)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J])]) ).

fof(i_0_9561,plain,
    ! [X23357,X23358,X23359] :
      ( ~ class_Divides_Oring__div(X23359)
      | c_Divides_Odiv__class_Omod(X23359,hAPP(c_Groups_Ouminus__class_Ouminus(X23359),X23358),X23357) = c_Divides_Odiv__class_Omod(X23359,hAPP(c_Groups_Ouminus__class_Ouminus(X23359),c_Divides_Odiv__class_Omod(X23359,X23358,X23357)),X23357) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__minus__eq])]) ).

fof(i_0_9562,plain,
    ! [X31982,X31983,X31984] : hAPP(c_List_Otl(X31984),hAPP(hAPP(c_List_Otake(X31984),X31983),X31982)) = hAPP(hAPP(c_List_Otake(X31984),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31983),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X31984),X31982)),
    inference(variable_rename,[status(thm)],[fact_tl__take]) ).

fof(i_0_9563,plain,
    ! [X27096,X27097,X27098] :
      ( ~ class_Rings_Olinordered__idom(X27098)
      | hAPP(c_Groups_Oabs__class_Oabs(X27098),hAPP(hAPP(c_Power_Opower__class_Opower(X27098),hAPP(c_Groups_Ouminus__class_Ouminus(X27098),X27097)),X27096)) = hAPP(c_Groups_Oabs__class_Oabs(X27098),hAPP(hAPP(c_Power_Opower__class_Opower(X27098),X27097),X27096)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power__minus])]) ).

cnf(i_0_9564,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_5933]) ).

cnf(i_0_9565,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_5934]) ).

fof(i_0_9566,plain,
    ! [X18368,X18369,X18370,X18371,X18372] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18372,X18371),X18370),X18369),X18368),X18369) = X18368,
    inference(variable_rename,[status(thm)],[fact_fun__upd__same]) ).

fof(i_0_9567,plain,
    ! [X25479,X25480,X25481] :
      ( ~ class_Orderings_Olinorder(X25481)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25481),X25480))
      | hBOOL(hAPP(hAPP(c_member(X25481),X25479),X25480))
      | X25480 = c_Orderings_Obot__class_Obot(tc_fun(X25481,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMin(X25481,hAPP(hAPP(c_Set_Oinsert(X25481),X25479),X25480)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25481),X25479),c_Big__Operators_Olinorder__class_OMin(X25481,X25480)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5935])]) ).

fof(i_0_9568,plain,
    ! [X25906,X25907,X25908] :
      ( ~ class_Orderings_Olinorder(X25908)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25908),X25907))
      | hBOOL(hAPP(hAPP(c_member(X25908),X25906),X25907))
      | X25907 = c_Orderings_Obot__class_Obot(tc_fun(X25908,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMax(X25908,hAPP(hAPP(c_Set_Oinsert(X25908),X25906),X25907)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25908),X25906),c_Big__Operators_Olinorder__class_OMax(X25908,X25907)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5936])]) ).

fof(i_0_9569,plain,
    ! [X20873,X20874,X20875] :
      ( ~ class_Lattices_Olattice(X20875)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20875),X20874))
      | hBOOL(hAPP(hAPP(c_member(X20875),X20873),X20874))
      | X20874 = c_Orderings_Obot__class_Obot(tc_fun(X20875,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OSup__fin(X20875,hAPP(hAPP(c_Set_Oinsert(X20875),X20873),X20874)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20875),X20873),c_Big__Operators_Olattice__class_OSup__fin(X20875,X20874)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5937])]) ).

fof(i_0_9570,plain,
    ! [X20876,X20877,X20878] :
      ( ~ class_Lattices_Olattice(X20878)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20878),X20877))
      | hBOOL(hAPP(hAPP(c_member(X20878),X20876),X20877))
      | X20877 = c_Orderings_Obot__class_Obot(tc_fun(X20878,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OInf__fin(X20878,hAPP(hAPP(c_Set_Oinsert(X20878),X20876),X20877)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20878),X20876),c_Big__Operators_Olattice__class_OInf__fin(X20878,X20877)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5938])]) ).

fof(i_0_9571,plain,
    ! [X21193,X21194] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21194),c_Orderings_Otop__class_Otop(tc_fun(X21194,tc_HOL_Obool))))
      | hAPP(c_Finite__Set_Ocard(X21194),X21193) != hAPP(c_Finite__Set_Ocard(X21194),c_Orderings_Otop__class_Otop(tc_fun(X21194,tc_HOL_Obool)))
      | X21193 = c_Orderings_Otop__class_Otop(tc_fun(X21194,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV])]) ).

fof(i_0_9572,plain,
    ! [X31839,X31840,X31841,X31842] :
      ( ( X31842 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Odrop(X31841),X31842),hAPP(hAPP(c_List_Olist_OCons(X31841),X31840),X31839)) = hAPP(hAPP(c_List_Olist_OCons(X31841),X31840),X31839) )
      & ( X31842 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Odrop(X31841),X31842),hAPP(hAPP(c_List_Olist_OCons(X31841),X31840),X31839)) = hAPP(hAPP(c_List_Odrop(X31841),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31842),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X31839) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__Cons_H])]) ).

fof(i_0_9573,plain,
    ! [X25245] : 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,X25245))))),
    inference(variable_rename,[status(thm)],[fact_neg__zminus__int]) ).

fof(i_0_9574,plain,
    ! [X17093,X17094,X17095,X17096] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X17096),X17095),X17094),X17093))
        | X17095 = X17093
        | hBOOL(hAPP(X17094,X17093)) )
      & ( X17095 != X17093
        | hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X17096),X17095),X17094),X17093)) )
      & ( ~ hBOOL(hAPP(X17094,X17093))
        | hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X17096),X17095),X17094),X17093)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).

fof(i_0_9575,plain,
    ! [X26400,X26401,X26402] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26402),X26401),hAPP(c_SetInterval_Oord__class_OlessThan(X26402),X26400)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26402),X26401),X26400))
        | ~ class_Orderings_Oord(X26402) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26402),X26401),X26400))
        | hBOOL(hAPP(hAPP(c_member(X26402),X26401),hAPP(c_SetInterval_Oord__class_OlessThan(X26402),X26400)))
        | ~ class_Orderings_Oord(X26402) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__iff])])]) ).

fof(i_0_9576,plain,
    ! [X26876,X26877,X26878] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26878),X26877),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26878),X26876)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26878),X26876),X26877))
        | ~ class_Orderings_Oord(X26878) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26878),X26876),X26877))
        | hBOOL(hAPP(hAPP(c_member(X26878),X26877),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26878),X26876)))
        | ~ class_Orderings_Oord(X26878) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__iff])])]) ).

fof(i_0_9577,plain,
    ! [X26804,X26805,X26806] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26806),X26805),hAPP(c_SetInterval_Oord__class_OatMost(X26806),X26804)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26806),X26805),X26804))
        | ~ class_Orderings_Oord(X26806) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26806),X26805),X26804))
        | hBOOL(hAPP(hAPP(c_member(X26806),X26805),hAPP(c_SetInterval_Oord__class_OatMost(X26806),X26804)))
        | ~ class_Orderings_Oord(X26806) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__iff])])]) ).

fof(i_0_9578,plain,
    ! [X26915,X26916,X26917] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26917),X26916),hAPP(c_SetInterval_Oord__class_OatLeast(X26917),X26915)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26917),X26915),X26916))
        | ~ class_Orderings_Oord(X26917) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26917),X26915),X26916))
        | hBOOL(hAPP(hAPP(c_member(X26917),X26916),hAPP(c_SetInterval_Oord__class_OatLeast(X26917),X26915)))
        | ~ class_Orderings_Oord(X26917) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeast__iff])])]) ).

fof(i_0_9579,plain,
    ! [X26248,X26249,X26250] :
      ( ~ class_Groups_Oordered__ab__group__add(X26250)
      | hAPP(c_Set_Oimage(X26250,X26250,c_Groups_Ouminus__class_Ouminus(X26250)),c_SetInterval_Oord__class_OgreaterThanAtMost(X26250,X26249,X26248)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26250,hAPP(c_Groups_Ouminus__class_Ouminus(X26250),X26248)),hAPP(c_Groups_Ouminus__class_Ouminus(X26250),X26249)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanAtMost])]) ).

fof(i_0_9580,plain,
    ! [X21150,X21151,X21152,X21153,X21154] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X21154,X21153,X21152)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21154),X21151))
      | ~ hBOOL(hAPP(hAPP(c_member(X21154),X21150),X21151))
      | hAPP(hAPP(X21153,X21150),hAPP(X21152,X21151)) = hAPP(X21152,X21151) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oin__idem])]) ).

fof(i_0_9581,plain,
    ! [X22507,X22508,X22509] :
      ( ~ class_Orderings_Olinorder(X22509)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22509),X22508))
      | ~ hBOOL(hAPP(hAPP(c_member(X22509),X22507),X22508))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22509),X22507),c_Big__Operators_Olinorder__class_OMax(X22509,X22508))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__ge])]) ).

fof(i_0_9582,plain,
    ! [X31030,X31031] :
      ( ~ class_Groups_Ocomm__monoid__add(X31031)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X31031),X31030) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X31031),hAPP(c_List_Onth(X31031),X31030)),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(X31031)),X31030))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__setsum__nth])]) ).

fof(i_0_9583,plain,
    ! [X25241,X25242] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25242),X25241))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25241)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25242)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25241),X25242)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiff__int])]) ).

fof(i_0_9584,plain,
    ! [X22840] : 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)),X22840)),X22840) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_odd__nonzero]) ).

fof(i_0_9585,plain,
    ! [X27639,X27640] : hAPP(c_Relation_OField(X27640),X27639) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27640,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X27640,X27640),X27639)),hAPP(c_Relation_ORange(X27640,X27640),X27639)),
    inference(variable_rename,[status(thm)],[fact_Field__def]) ).

cnf(i_0_9586,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_5939]) ).

fof(i_0_9587,plain,
    ! [X26087,X26088] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26088,X26087) = 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),X26088),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X26087))),
    inference(variable_rename,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I2_J]) ).

fof(i_0_9588,plain,
    ! [X31445,X31446,X31447] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31447))
        | c_List_Osublist(X31446,hAPP(hAPP(c_List_Olist_OCons(X31446),X31445),c_List_Olist_ONil(X31446)),X31447) = hAPP(hAPP(c_List_Olist_OCons(X31446),X31445),c_List_Olist_ONil(X31446)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31447))
        | c_List_Osublist(X31446,hAPP(hAPP(c_List_Olist_OCons(X31446),X31445),c_List_Olist_ONil(X31446)),X31447) = c_List_Olist_ONil(X31446) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5940])]) ).

fof(i_0_9589,plain,
    ! [X23469,X23470] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23470))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23470),X23469)),X23470) = X23469 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__m])]) ).

fof(i_0_9590,plain,
    ! [X23467,X23468] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23468))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23467),X23468)),X23468) = X23467 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self__is__m])]) ).

cnf(i_0_9591,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_5941]) ).

cnf(i_0_9592,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_5942]) ).

fof(i_0_9593,plain,
    ! [X23487,X23488] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X23488,X23487) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23488,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23487)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X23488,X23487) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23488,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23487)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23488,X23487)),X23487) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus2__eq__if])]) ).

fof(i_0_9594,plain,
    ! [X19113,X19114] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19114,tc_HOL_Obool)),X19113),c_Orderings_Otop__class_Otop(tc_fun(X19114,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_subset__UNIV]) ).

fof(i_0_9595,plain,
    ! [X24523] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24523)))
        | 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),X24523)) = 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),X24523)))
        | 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),X24523)) = 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),X24523))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5943])]) ).

cnf(i_0_9596,plain,
    c_Relation_Osingle__valued(X1,X1,c_Relation_OId(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5944]) ).

fof(i_0_9597,plain,
    ! [X22933,X22934,X22935] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22935),X22934))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22934),X22933))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22935),X22933)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__trans])]) ).

fof(i_0_9598,plain,
    ! [X21005,X21006,X21007] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21007),X21006))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21006),X21005))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21007),X21005)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).

fof(i_0_9599,plain,
    ! [X21769,X21770] :
      ( ~ class_Rings_Ocomm__semiring__1(X21770)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21770),X21769),X21769) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21770),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21770),c_Groups_Oone__class_Oone(X21770)),c_Groups_Oone__class_Oone(X21770))),X21769) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J])]) ).

fof(i_0_9600,plain,
    ! [X18506,X18507,X18508] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18508),X18507),X18506))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18508),X18507),X18506))
        | ~ class_Orderings_Opreorder(X18508) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18508),X18506),X18507))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18508),X18507),X18506))
        | ~ class_Orderings_Opreorder(X18508) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18508),X18507),X18506))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18508),X18506),X18507))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18508),X18507),X18506))
        | ~ class_Orderings_Opreorder(X18508) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5945])])]) ).

fof(i_0_9601,plain,
    ! [X21688,X21689,X21690,X21691] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21691),X21690))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21689),X21690) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21691),X21688)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21689),X21688)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).

fof(i_0_9602,plain,
    ! [X21645,X21646] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21646)),X21645))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21646),X21645)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).

fof(i_0_9603,plain,
    ! [X21819,X21820] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21820),X21819))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21820)),X21819)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21820)),X21819))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21820),X21819)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])]) ).

fof(i_0_9604,plain,
    ! [X21815,X21816] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21816)),X21815))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21816),X21815)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21816),X21815))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21816)),X21815)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])]) ).

fof(i_0_9605,plain,
    ! [X21807,X21808] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21808)),X21807))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21808),X21807)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).

fof(i_0_9606,plain,
    ! [X21649,X21650] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21650)),X21649))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21650),X21649)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])]) ).

fof(i_0_9607,plain,
    ! [X21945,X21946,X21947] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21947),X21946))
      | hBOOL(hAPP(hAPP(c_member(X21947),X21945),X21946))
      | hAPP(c_Finite__Set_Ocard(X21947),hAPP(hAPP(c_Set_Oinsert(X21947),X21945),X21946)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X21947),X21946)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5946])]) ).

fof(i_0_9608,plain,
    ! [X31780,X31781,X31782,X31783] : hAPP(hAPP(c_List_Odrop(X31783),X31782),hAPP(hAPP(c_List_Odrop(X31783),X31781),X31780)) = hAPP(hAPP(c_List_Odrop(X31783),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31782),X31781)),X31780),
    inference(variable_rename,[status(thm)],[fact_drop__drop]) ).

fof(i_0_9609,plain,
    ! [X31096,X31097,X31098,X31099] : hAPP(hAPP(c_List_Otake(X31099),X31098),hAPP(hAPP(c_List_Otake(X31099),X31097),X31096)) = hAPP(hAPP(c_List_Otake(X31099),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X31098),X31097)),X31096),
    inference(variable_rename,[status(thm)],[fact_take__take]) ).

fof(i_0_9610,plain,
    ! [X23223,X23224,X23225] :
      ( ( ~ hBOOL(hAPP(X23225,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23224),X23223)))
        | epred1_3(X23225,X23223,X23224) )
      & ( ~ epred1_3(X23225,X23223,X23224)
        | hBOOL(hAPP(X23225,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23224),X23223))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5947])]) ).

fof(i_0_9611,plain,
    ! [X29746,X29747,X29748] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29748)
      | ~ hBOOL(hAPP(hAPP(c_member(X29748),X29747),X29746))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29748),c_Complete__Lattice_OInf__class_OInf(X29748,X29746)),X29747)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__lower])]) ).

fof(i_0_9612,plain,
    ! [X25117,X25119,X25120,X25122] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk150_1(X25117)))
        | hBOOL(hAPP(X25117,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25119))) )
      & ( ~ hBOOL(hAPP(X25117,esk150_1(X25117)))
        | hBOOL(hAPP(X25117,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25119))) )
      & ( ~ hBOOL(hAPP(X25120,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk151_1(X25120))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25122))
        | hBOOL(hAPP(X25120,X25122)) ) ),
    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_9613,plain,
    ! [X24574,X24575] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24575))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24575),X24574)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X24575)),hAPP(c_Int_Onat,X24574)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__div__distrib])]) ).

fof(i_0_9614,plain,
    ! [X24564,X24565] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24565))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24565),X24564)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X24565)),hAPP(c_Int_Onat,X24564)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__distrib])]) ).

fof(i_0_9615,plain,
    ! [X26126,X26127] :
      ( ~ c_Nat__Transfer_Ois__nat(X26127)
      | ~ c_Nat__Transfer_Ois__nat(X26126)
      | c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X26127,X26126) = 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,X26127),hAPP(c_Int_Onat,X26126))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__functions])]) ).

fof(i_0_9616,plain,
    ! [X32321] :
      ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X32321)),c_List_Otranspose__rel(X32321)),c_List_Olist_ONil(tc_List_Olist(X32321))))
      | c_List_Otranspose(X32321,c_List_Olist_ONil(tc_List_Olist(X32321))) = c_List_Olist_ONil(tc_List_Olist(X32321)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I1_J])]) ).

fof(i_0_9617,plain,
    ! [X23637,X23638,X23639] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23639),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23638,X23637)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23639),X23638),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23639),X23637)),
    inference(variable_rename,[status(thm)],[fact_mod__mult__distrib2]) ).

fof(i_0_9618,plain,
    ! [X25297,X25298] :
      ( ( X25298 != X25297
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25298) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25297) )
      & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25298) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25297)
        | X25298 = X25297 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I3_J])]) ).

fof(i_0_9619,plain,
    ! [X31633,X31634,X31635] : hAPP(c_List_Oset(X31635),hAPP(hAPP(c_List_Oappend(X31635),X31634),X31633)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31635,tc_HOL_Obool)),hAPP(c_List_Oset(X31635),X31634)),hAPP(c_List_Oset(X31635),X31633)),
    inference(variable_rename,[status(thm)],[fact_set__append]) ).

fof(i_0_9620,plain,
    ! [X21416,X21417] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21417),X21416))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21417)),hAPP(c_Nat_OSuc,X21416))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).

fof(i_0_9621,plain,
    ! [X17553,X17554,X17555,X17556] :
      ( ( hAPP(hAPP(c_Set_Oinsert(X17556),X17555),X17554) != hAPP(hAPP(c_Set_Oinsert(X17556),X17555),X17553)
        | X17554 = X17553
        | hBOOL(hAPP(hAPP(c_member(X17556),X17555),X17553))
        | hBOOL(hAPP(hAPP(c_member(X17556),X17555),X17554)) )
      & ( X17554 != X17553
        | hAPP(hAPP(c_Set_Oinsert(X17556),X17555),X17554) = hAPP(hAPP(c_Set_Oinsert(X17556),X17555),X17553)
        | hBOOL(hAPP(hAPP(c_member(X17556),X17555),X17553))
        | hBOOL(hAPP(hAPP(c_member(X17556),X17555),X17554)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5948])])]) ).

fof(i_0_9622,plain,
    ! [X22687,X22688,X22689,X22690] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X22690),X22689),X22688) != hAPP(hAPP(c_Power_Opower__class_Opower(X22690),X22689),X22687)
        | X22688 = X22687
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22690),c_Groups_Oone__class_Oone(X22690)),X22689))
        | ~ class_Rings_Olinordered__semidom(X22690) )
      & ( X22688 != X22687
        | hAPP(hAPP(c_Power_Opower__class_Opower(X22690),X22689),X22688) = hAPP(hAPP(c_Power_Opower__class_Opower(X22690),X22689),X22687)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22690),c_Groups_Oone__class_Oone(X22690)),X22689))
        | ~ class_Rings_Olinordered__semidom(X22690) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__exp])])]) ).

fof(i_0_9623,plain,
    ! [X31489,X31490,X31491] : c_List_Olistset(X31491,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X31491,tc_HOL_Obool)),X31490),X31489)) = c_List_Oset__Cons(X31491,X31490,c_List_Olistset(X31491,X31489)),
    inference(variable_rename,[status(thm)],[fact_listset_Osimps_I2_J]) ).

fof(i_0_9624,plain,
    ! [X29569,X29570] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29570)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29570),X29569))
      | c_Complete__Lattice_OSup__class_OSup(X29570,X29569) = hAPP(hAPP(c_Finite__Set_Ofold(X29570,X29570,c_Lattices_Osemilattice__sup__class_Osup(X29570)),c_Orderings_Obot__class_Obot(X29570)),X29569) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fold__sup])]) ).

fof(i_0_9625,plain,
    ! [X29567,X29568] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29568)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29568),X29567))
      | c_Complete__Lattice_OInf__class_OInf(X29568,X29567) = hAPP(hAPP(c_Finite__Set_Ofold(X29568,X29568,c_Lattices_Osemilattice__inf__class_Oinf(X29568)),c_Orderings_Otop__class_Otop(X29568)),X29567) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fold__inf])]) ).

fof(i_0_9626,plain,
    ! [X22600,X22601] :
      ( ( X22601 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22600),X22601) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X22601 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22600),X22601) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22600),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22600),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22601),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_9627,plain,
    ! [X26181,X26182,X26183] :
      ( ~ class_Groups_Oordered__ab__group__add(X26183)
      | hAPP(c_Set_Oimage(X26183,X26183,c_Groups_Ouminus__class_Ouminus(X26183)),c_SetInterval_Oord__class_OatLeastAtMost(X26183,X26182,X26181)) = c_SetInterval_Oord__class_OatLeastAtMost(X26183,hAPP(c_Groups_Ouminus__class_Ouminus(X26183),X26181),hAPP(c_Groups_Ouminus__class_Ouminus(X26183),X26182)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastAtMost])]) ).

fof(i_0_9628,plain,
    ! [X25571,X25572,X25573] :
      ( ~ class_Groups_Oordered__ab__group__add(X25573)
      | hAPP(c_Set_Oimage(X25573,X25573,c_Groups_Ouminus__class_Ouminus(X25573)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25573,X25572,X25571)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X25573,hAPP(c_Groups_Ouminus__class_Ouminus(X25573),X25571),hAPP(c_Groups_Ouminus__class_Ouminus(X25573),X25572)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanLessThan])]) ).

fof(i_0_9629,plain,
    ! [X21930,X21931,X21932] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X21932),X21930),X21931))
        | hAPP(c_Finite__Set_Ocard(X21932),hAPP(hAPP(c_Set_Oinsert(X21932),X21930),X21931)) = hAPP(c_Finite__Set_Ocard(X21932),X21931)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21932),X21931)) )
      & ( hBOOL(hAPP(hAPP(c_member(X21932),X21930),X21931))
        | hAPP(c_Finite__Set_Ocard(X21932),hAPP(hAPP(c_Set_Oinsert(X21932),X21930),X21931)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X21932),X21931))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21932),X21931)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5949])])]) ).

fof(i_0_9630,plain,
    ! [X26420] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26420)) = 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),X26420))),
    inference(variable_rename,[status(thm)],[fact_lessThan__Suc__eq__insert__0]) ).

fof(i_0_9631,plain,
    ! [X25284,X25285] : c_Code__Numeral_Odiv__mod__code__numeral(X25285,X25284) = 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),X25285),X25284)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X25285,X25284)),
    inference(variable_rename,[status(thm)],[fact_div__mod__code__numeral__def]) ).

fof(i_0_9632,plain,
    ! [X23603,X23604] : c_Divides_Odivmod__int(X23604,X23603) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23604),X23603)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23604,X23603)),
    inference(variable_rename,[status(thm)],[fact_divmod__int__mod__div]) ).

fof(i_0_9633,plain,
    ! [X23390,X23391] : 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,X23391,X23390)),X23390) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23391),X23390),
    inference(variable_rename,[status(thm)],[fact_zminus__zmod]) ).

fof(i_0_9634,plain,
    ! [X24526,X24527] :
      ( ( hAPP(c_Int_Onat,X24527) != hAPP(c_Int_Onat,X24526)
        | X24527 = X24526
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24526))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24527)) )
      & ( X24527 != X24526
        | hAPP(c_Int_Onat,X24527) = hAPP(c_Int_Onat,X24526)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24526))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24527)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I1_J])])]) ).

fof(i_0_9635,plain,
    ! [X24524,X24525] :
      ( ( hAPP(c_Int_Onat,X24525) != hAPP(c_Int_Onat,X24524)
        | X24525 = X24524
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24524))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24525)) )
      & ( X24525 != X24524
        | hAPP(c_Int_Onat,X24525) = hAPP(c_Int_Onat,X24524)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24524))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24525)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__nat__nat__iff])])]) ).

fof(i_0_9636,plain,
    ! [X25220,X25221,X25223,X25224,X25225] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25221),X25220))
        | X25220 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25221),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk155_2(X25220,X25221)))) )
      & ( X25223 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25224),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X25225)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25224),X25223)) ) ),
    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_9637,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_5950]) ).

fof(i_0_9638,plain,
    ! [X23670,X23671] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23671),X23670)),X23670) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23671),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23671,X23670)),
    inference(variable_rename,[status(thm)],[fact_div__mod__equality_H]) ).

fof(i_0_9639,plain,
    ! [X21853,X21854] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21854),X21853))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21853),X21854)),X21854) = X21853 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse2])]) ).

fof(i_0_9640,plain,
    ! [X25249] :
      ( ( ~ 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),X25249)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25249)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25249))
        | 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),X25249))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__int__conv])]) ).

fof(i_0_9641,plain,
    ! [X25265,X25266] :
      ( ( X25266 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25265))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25266) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25265) )
      & ( 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),X25265)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25266) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25265) )
      & ( X25266 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25265))
        | ~ 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),X25265)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25266) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25265) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__eq__iff__number__of])])]) ).

fof(i_0_9642,plain,
    ! [X20196,X20197,X20198,X20199,X20200] :
      ( hAPP(X20200,X20199) != hAPP(c_Option_Ooption_OSome(X20198),X20197)
      | hBOOL(hAPP(hAPP(c_member(X20198),X20197),c_Map_Oran(X20196,X20198,X20200))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ranI])]) ).

fof(i_0_9643,plain,
    ! [X19979,X19980,X19981,X19982,X19983] :
      ( hAPP(X19983,X19982) != hAPP(c_Option_Ooption_OSome(X19981),X19980)
      | hBOOL(hAPP(hAPP(c_member(X19979),X19982),c_Map_Odom(X19979,X19981,X19983))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_domI])]) ).

fof(i_0_9644,plain,
    ! [X20349,X20350] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X20350,tc_HOL_Obool)),hAPP(c_Set_OPow(X20350),X20349)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X20350),X20349)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20350),X20349))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X20350,tc_HOL_Obool)),hAPP(c_Set_OPow(X20350),X20349))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Pow__iff])]) ).

fof(i_0_9645,plain,
    ! [X27659,X27660,X27661,X27662,X27663] :
      ( ~ hBOOL(hAPP(hAPP(X27663,X27662),X27661))
      | hBOOL(hAPP(c_Predicate_ODomainP(X27660,X27659,X27663),X27662)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP_Ointros])]) ).

fof(i_0_9646,plain,
    ! [X27564,X27565,X27566,X27567,X27568] :
      ( ~ hBOOL(hAPP(hAPP(X27568,X27567),X27566))
      | hBOOL(hAPP(c_Predicate_ORangeP(X27565,X27564,X27568),X27566)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP_Ointros])]) ).

fof(i_0_9647,plain,
    ! [X30894] :
      ( ~ class_Enum_Oenum(X30894)
      | c_Enum_Oenum__class_Oenum(tc_Option_Ooption(X30894)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(X30894)),c_Option_Ooption_ONone(X30894)),hAPP(hAPP(c_List_Omap(X30894,tc_Option_Ooption(X30894)),c_Option_Ooption_OSome(X30894)),c_Enum_Oenum__class_Oenum(X30894))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__option__def])]) ).

fof(i_0_9648,plain,
    ! [X33883,X33884,X33885] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33885)),c_List_Osplice(X33885,X33884,X33883)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33885)),X33884)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33885)),X33883)),
    inference(variable_rename,[status(thm)],[fact_length__splice]) ).

fof(i_0_9649,plain,
    ! [X31417,X31418] :
      ( ( ~ 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(X31418)),X31417)))
        | X31417 != c_List_Olist_ONil(X31418) )
      & ( X31417 = c_List_Olist_ONil(X31418)
        | 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(X31418)),X31417))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__greater__0__conv])]) ).

fof(i_0_9650,plain,
    ! [X26929,X26930,X26931] :
      ( ~ class_Orderings_Oorder(X26931)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26931,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26931,X26930),X26929)),hAPP(c_SetInterval_Oord__class_OatLeast(X26931),X26929)) = c_Orderings_Obot__class_Obot(tc_fun(X26931,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I8_J])]) ).

fof(i_0_9651,plain,
    ! [X21809,X21810] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21809),hAPP(c_Nat_OSuc,X21810)))
        | X21809 = X21810
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21810),X21809)) )
      & ( X21809 != X21810
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21809),hAPP(c_Nat_OSuc,X21810)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21810),X21809)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])]) ).

cnf(i_0_9652,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_5951]) ).

fof(i_0_9653,plain,
    ! [X23477,X23478] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23478))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23478),X23477))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23478,X23477) = X23478 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__trivial])]) ).

fof(i_0_9654,plain,
    ! [X26948,X26949] :
      ( ~ class_Orderings_Oorder(X26949)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26949,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X26949),X26948)),hAPP(c_SetInterval_Oord__class_OatLeast(X26949),X26948)) = hAPP(hAPP(c_Set_Oinsert(X26949),X26948),c_Orderings_Obot__class_Obot(tc_fun(X26949,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__Int__atLeast])]) ).

fof(i_0_9655,plain,
    ! [X21626,X21627] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21627),X21626))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21626),hAPP(c_Nat_OSuc,X21627))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21626),hAPP(c_Nat_OSuc,X21627)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21627),X21626)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5952])]) ).

cnf(i_0_9656,plain,
    hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_5953]) ).

fof(i_0_9657,plain,
    ! [X31579,X31580,X31581] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31581)),hAPP(hAPP(c_List_Oappend(X31581),X31580),X31579)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31581)),X31580)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31581)),X31579)),
    inference(variable_rename,[status(thm)],[fact_length__append]) ).

fof(i_0_9658,plain,
    ! [X25517,X25518] :
      ( ( X25518 != X25517
        | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25518) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25517)
        | ~ c_Nat__Transfer_Onat__set(X25517)
        | ~ c_Nat__Transfer_Onat__set(X25518) )
      & ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25518) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25517)
        | X25518 = X25517
        | ~ c_Nat__Transfer_Onat__set(X25517)
        | ~ c_Nat__Transfer_Onat__set(X25518) ) ),
    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_9659,plain,
    ! [X23032,X23033,X23034,X23035,X23036] :
      ( ~ class_Rings_Ocomm__semiring__1(X23035)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23034),X23033))
      | ~ hBOOL(hAPP(hAPP(c_member(X23034),X23036),X23033))
      | hAPP(X23032,X23036) != c_Groups_Ozero__class_Ozero(X23035)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23034,X23035),X23032),X23033) = c_Groups_Ozero__class_Ozero(X23035) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__zero])])]) ).

fof(i_0_9660,plain,
    ! [X23417,X23418,X23419] :
      ( ( X23419 != 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),X23419),X23418)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23419),X23417)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X23419 = 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),X23419),X23418)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23419),X23417)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23418),X23417) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel__disj])]) ).

fof(i_0_9661,plain,
    ! [X17926,X17927] : hBOOL(hAPP(hAPP(c_member(tc_fun(X17927,tc_HOL_Obool)),X17926),hAPP(c_Set_OPow(X17927),X17926))),
    inference(variable_rename,[status(thm)],[fact_Pow__top]) ).

fof(i_0_9662,plain,
    ! [X32923,X32924,X32925] : hAPP(c_List_Orev(X32925),hAPP(hAPP(c_List_Olist_OCons(X32925),X32924),X32923)) = hAPP(hAPP(c_List_Oappend(X32925),hAPP(c_List_Orev(X32925),X32923)),hAPP(hAPP(c_List_Olist_OCons(X32925),X32924),c_List_Olist_ONil(X32925))),
    inference(variable_rename,[status(thm)],[fact_rev_Osimps_I2_J]) ).

cnf(i_0_9663,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_5954]) ).

fof(i_0_9664,plain,
    ! [X23140,X23141] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23141),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)),X23141))
        | X23140 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23141),X23140) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23140),X23141))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23141))
        | X23140 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23141),X23140) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23141),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23141),X23140))
        | X23140 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23141),X23140) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23140),X23141))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23141),X23140))
        | X23140 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23141),X23140) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X23140 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23141),X23140) = 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)),X23141))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23141),X23140))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23141),X23140) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23141),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23140),X23141))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23141),X23140) = 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_9665,plain,
    ! [X23127,X23128] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23128))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23128),X23127))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23128),X23127) = 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_9666,plain,
    ! [X20828,X20829] :
      ( ~ class_Lattices_Olattice(X20829)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20829),X20828))
      | X20828 = c_Orderings_Obot__class_Obot(tc_fun(X20829,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20829),c_Big__Operators_Olattice__class_OInf__fin(X20829,X20828)),c_Big__Operators_Olattice__class_OSup__fin(X20829,X20828))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__le__Sup])]) ).

fof(i_0_9667,plain,
    ! [X33953,X33954,X33955,X33956] : hAPP(hAPP(c_List_Omap(X33956,X33955),hAPP(c_COMBK(X33955,X33956),X33954)),X33953) = c_List_Oreplicate(X33955,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33956)),X33953),X33954),
    inference(variable_rename,[status(thm)],[fact_map__replicate__const]) ).

fof(i_0_9668,plain,
    ! [X20249,X20250,X20251,X20252,X20253] :
      ( ~ c_Equiv__Relations_Oequivp(X20253,X20252)
      | ~ hBOOL(hAPP(hAPP(X20252,X20251),X20250))
      | ~ hBOOL(hAPP(hAPP(X20252,X20250),X20249))
      | hBOOL(hAPP(hAPP(X20252,X20251),X20249)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__transp])]) ).

fof(i_0_9669,plain,
    ! [X21133,X21134,X21135,X21136,X21137] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X21137,X21136,X21135)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21137),X21134))
      | X21134 = c_Orderings_Obot__class_Obot(tc_fun(X21137,tc_HOL_Obool))
      | hAPP(X21135,hAPP(hAPP(c_Set_Oinsert(X21137),X21133),X21134)) = hAPP(hAPP(X21136,X21133),hAPP(X21135,X21134)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oinsert__idem])]) ).

fof(i_0_9670,plain,
    ! [X23360,X23361,X23362,X23363] :
      ( ~ class_Divides_Oring__div(X23363)
      | c_Divides_Odiv__class_Omod(X23363,X23362,X23361) != c_Divides_Odiv__class_Omod(X23363,X23360,X23361)
      | c_Divides_Odiv__class_Omod(X23363,hAPP(c_Groups_Ouminus__class_Ouminus(X23363),X23362),X23361) = c_Divides_Odiv__class_Omod(X23363,hAPP(c_Groups_Ouminus__class_Ouminus(X23363),X23360),X23361) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__minus__cong])]) ).

fof(i_0_9671,plain,
    ! [X30371,X30372] : hAPP(c_Set_Oimage(tc_List_Olist(X30372),tc_fun(X30372,tc_HOL_Obool),c_List_Oset(X30372)),hAPP(c_List_Oset(tc_List_Olist(X30372)),c_Enum_Osublists(X30372,X30371))) = hAPP(c_Set_OPow(X30372),hAPP(c_List_Oset(X30372),X30371)),
    inference(variable_rename,[status(thm)],[fact_sublists__powset]) ).

fof(i_0_9672,plain,
    ! [X29821,X29822] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X29822,tc_HOL_Obool),X29821) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X29822,tc_HOL_Obool),tc_fun(X29822,tc_HOL_Obool)),X29821),c_COMBI(tc_fun(X29822,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_Union__def]) ).

fof(i_0_9673,plain,
    ! [X29819,X29820] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X29820,tc_HOL_Obool),X29819) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X29820,tc_HOL_Obool),tc_fun(X29820,tc_HOL_Obool)),X29819),c_COMBI(tc_fun(X29820,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_Inter__def]) ).

fof(i_0_9674,plain,
    ! [X33009,X33010,X33011,X33012] :
      ( ( ~ hBOOL(hAPP(X33012,X33011))
        | c_List_OtakeWhile(X33010,X33012,hAPP(hAPP(c_List_Olist_OCons(X33010),X33011),X33009)) = hAPP(hAPP(c_List_Olist_OCons(X33010),X33011),c_List_OtakeWhile(X33010,X33012,X33009)) )
      & ( hBOOL(hAPP(X33012,X33011))
        | c_List_OtakeWhile(X33010,X33012,hAPP(hAPP(c_List_Olist_OCons(X33010),X33011),X33009)) = c_List_Olist_ONil(X33010) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5955])]) ).

fof(i_0_9675,plain,
    ! [X27134] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X27134)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | X27134 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X27134 != 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),X27134)),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_9676,plain,
    ! [X25219] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25219)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X25219 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X25219 != 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),X25219)),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_9677,plain,
    ! [X29952,X29953,X29954] : c_Map_Omap__add(X29954,X29953,hAPP(c_COMBK(tc_Option_Ooption(X29953),X29954),c_Option_Ooption_ONone(X29953)),X29952) = X29952,
    inference(variable_rename,[status(thm)],[fact_empty__map__add]) ).

fof(i_0_9678,plain,
    ! [X29955,X29956,X29957] : c_Map_Omap__add(X29957,X29956,X29955,hAPP(c_COMBK(tc_Option_Ooption(X29956),X29957),c_Option_Ooption_ONone(X29956))) = X29955,
    inference(variable_rename,[status(thm)],[fact_map__add__empty]) ).

fof(i_0_9679,plain,
    ! [X24578,X24579] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24579))
      | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X24579)),X24578) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X24579),X24578)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J])]) ).

fof(i_0_9680,plain,
    ! [X24580,X24581] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24581))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X24581),X24580)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X24581)),X24580) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__eq])]) ).

fof(i_0_9681,plain,
    ! [X21751,X21752,X21753] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21753),X21752)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21753),X21751)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21752),X21751),
    inference(variable_rename,[status(thm)],[fact_diff__cancel]) ).

fof(i_0_9682,plain,
    ! [X21754,X21755,X21756] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21756),X21755)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21754),X21755)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21756),X21754),
    inference(variable_rename,[status(thm)],[fact_diff__cancel2]) ).

fof(i_0_9683,plain,
    ! [X22648,X22649,X22650] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X22650),X22649)),X22648) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X22650),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22649),X22648)),
    inference(variable_rename,[status(thm)],[fact_zpower__zpower]) ).

fof(i_0_9684,plain,
    ! [X22866,X22867,X22868] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22868),X22867)),X22866) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22868),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22867),X22866)),
    inference(variable_rename,[status(thm)],[fact_zadd__assoc]) ).

fof(i_0_9685,plain,
    ! [X21446,X21447,X21448] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21448),X21447)),X21446) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21448),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21447),X21446)),
    inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).

fof(i_0_9686,plain,
    ! [X22790,X22791,X22792] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22792),X22791)),X22790) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22792),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22791),X22790)),
    inference(variable_rename,[status(thm)],[fact_zmult__assoc]) ).

fof(i_0_9687,plain,
    ! [X21064,X21065,X21066] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21066),X21065)),X21064) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21066),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21065),X21064)),
    inference(variable_rename,[status(thm)],[fact_nat__mult__assoc]) ).

fof(i_0_9688,plain,
    ! [X21748,X21749,X21750] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21750),X21749)),X21748) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21750),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21749),X21748)),
    inference(variable_rename,[status(thm)],[fact_diff__diff__left]) ).

fof(i_0_9689,plain,
    ! [X23369,X23370,X23371] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23371),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23370),X23369)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23371),X23370)),X23369),
    inference(variable_rename,[status(thm)],[fact_div__mult2__eq]) ).

fof(i_0_9690,plain,
    ! [X28229,X28230,X28231] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X28230),X28231),c_Orderings_Obot__class_Obot(tc_fun(X28230,tc_HOL_Obool))))
      | hBOOL(hAPP(X28229,X28231)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ball__empty])]) ).

fof(i_0_9691,plain,
    ! [X26828,X26829,X26830] :
      ( ~ class_Orderings_Oorder(X26830)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26830,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X26830),X26829)),c_SetInterval_Oord__class_OgreaterThanAtMost(X26830,X26829,X26828)) = c_Orderings_Obot__class_Obot(tc_fun(X26830,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I3_J])]) ).

fof(i_0_9692,plain,
    ! [X26831,X26832,X26833] :
      ( ~ class_Orderings_Oorder(X26833)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26833,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X26833),X26832)),c_SetInterval_Oord__class_OgreaterThanLessThan(X26833,X26832,X26831)) = c_Orderings_Obot__class_Obot(tc_fun(X26833,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I1_J])]) ).

fof(i_0_9693,plain,
    ! [X26414,X26415,X26416] :
      ( ~ class_Orderings_Oorder(X26416)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26416,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X26416),X26415)),c_SetInterval_Oord__class_OatLeastAtMost(X26416,X26415,X26414)) = c_Orderings_Obot__class_Obot(tc_fun(X26416,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I4_J])]) ).

fof(i_0_9694,plain,
    ! [X23483,X23484] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23484),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23483),X23484))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23484,X23483) = X23484 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__neg__trivial])]) ).

fof(i_0_9695,plain,
    ! [X30284,X30285,X30286,X30287] : hAPP(c_List_Oset(X30287),hAPP(hAPP(c_List_Omap(X30286,X30287),X30285),X30284)) = hAPP(c_Set_Oimage(X30286,X30287,X30285),hAPP(c_List_Oset(X30286),X30284)),
    inference(variable_rename,[status(thm)],[fact_set__map]) ).

fof(i_0_9696,plain,
    ! [X33629,X33630,X33631,X33634] :
      ( ( hBOOL(hAPP(X33629,esk506_3(X33629,X33630,X33631)))
        | ~ hBOOL(hAPP(X33629,X33631))
        | c_List_Olist__ex1(X33630,X33629,c_Enum_Oenum__class_Oenum(X33630))
        | ~ class_Enum_Oenum(X33630) )
      & ( esk506_3(X33629,X33630,X33631) != X33631
        | ~ hBOOL(hAPP(X33629,X33631))
        | c_List_Olist__ex1(X33630,X33629,c_Enum_Oenum__class_Oenum(X33630))
        | ~ class_Enum_Oenum(X33630) )
      & ( hBOOL(hAPP(X33629,esk507_2(X33629,X33630)))
        | ~ c_List_Olist__ex1(X33630,X33629,c_Enum_Oenum__class_Oenum(X33630))
        | ~ class_Enum_Oenum(X33630) )
      & ( ~ hBOOL(hAPP(X33629,X33634))
        | X33634 = esk507_2(X33629,X33630)
        | ~ c_List_Olist__ex1(X33630,X33629,c_Enum_Oenum__class_Oenum(X33630))
        | ~ class_Enum_Oenum(X33630) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exists1__code])])])])]) ).

fof(i_0_9697,plain,
    ! [X31755,X31756,X31757] : hAPP(hAPP(c_List_Oappend(X31757),hAPP(hAPP(c_List_Otake(X31757),X31756),X31755)),hAPP(hAPP(c_List_Odrop(X31757),X31756),X31755)) = X31755,
    inference(variable_rename,[status(thm)],[fact_append__take__drop__id]) ).

fof(i_0_9698,plain,
    ! [X25130] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25130)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[i_0_5956]) ).

fof(i_0_9699,plain,
    ! [X23625,X23626] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X23626),X23625) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23626,X23625)),X23625),
    inference(variable_rename,[status(thm)],[fact_mod__Suc__eq__Suc__mod]) ).

fof(i_0_9700,plain,
    ! [X24663] :
      ( ( ~ 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),X24663)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X24663)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X24663))
        | 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),X24663))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__0__number__of])]) ).

fof(i_0_9701,plain,
    ! [X33507,X33508,X33509,X33510] :
      ( ( ~ c_List_Olist__ex(X33510,X33509,hAPP(hAPP(c_List_Oappend(X33510),X33508),X33507))
        | c_List_Olist__ex(X33510,X33509,X33508)
        | c_List_Olist__ex(X33510,X33509,X33507) )
      & ( ~ c_List_Olist__ex(X33510,X33509,X33508)
        | c_List_Olist__ex(X33510,X33509,hAPP(hAPP(c_List_Oappend(X33510),X33508),X33507)) )
      & ( ~ c_List_Olist__ex(X33510,X33509,X33507)
        | c_List_Olist__ex(X33510,X33509,hAPP(hAPP(c_List_Oappend(X33510),X33508),X33507)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__append])])]) ).

fof(i_0_9702,plain,
    ! [X23118,X23119] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23119),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23118),X23119))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23119),X23118) = 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_9703,plain,
    ( c_Int_OMin = X1
    | c_Int_OMin != c_Int_OBit1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5957]) ).

cnf(i_0_9704,plain,
    ( X1 = c_Int_OMin
    | c_Int_OBit1(X1) != c_Int_OMin ),
    inference(split_conjunct,[status(thm)],[i_0_5958]) ).

fof(i_0_9705,plain,
    ! [X31073,X31074,X31075,X31076] : hAPP(hAPP(c_List_Otake(X31076),hAPP(c_Nat_OSuc,X31075)),hAPP(hAPP(c_List_Olist_OCons(X31076),X31074),X31073)) = hAPP(hAPP(c_List_Olist_OCons(X31076),X31074),hAPP(hAPP(c_List_Otake(X31076),X31075),X31073)),
    inference(variable_rename,[status(thm)],[fact_take__Suc__Cons]) ).

fof(i_0_9706,plain,
    ! [X33821,X33822,X33823] :
      ( ~ class_Lazy__Sequence_Osmall__lazy(X33823)
      | ~ class_Lazy__Sequence_Osmall__lazy(X33822)
      | c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(X33823,X33822),X33821) = c_Lazy__Sequence_Oproduct(X33823,X33822,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X33823,X33821),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X33822,X33821)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_small__lazy__prod__def])]) ).

fof(i_0_9707,plain,
    ! [X30479,X30480,X30481,X30482,X30483,X30484,X30485] :
      ( hAPP(hAPP(c_List_Omap(X30485,X30484),X30483),X30482) != hAPP(hAPP(c_List_Omap(X30481,X30484),X30480),X30479)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30485)),X30482) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30481)),X30479) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__eq__imp__length__eq])]) ).

cnf(i_0_9708,plain,
    c_Int_OBit1(X1) != c_Int_OPls,
    inference(split_conjunct,[status(thm)],[i_0_5959]) ).

cnf(i_0_9709,plain,
    c_Int_OPls != c_Int_OBit1(X1),
    inference(split_conjunct,[status(thm)],[i_0_5960]) ).

fof(i_0_9710,plain,
    ! [X30499,X30500] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X30500))),c_Enum_Osublists(X30500,X30499)) = 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(X30500)),X30499)),
    inference(variable_rename,[status(thm)],[fact_length__sublists]) ).

fof(i_0_9711,plain,
    ! [X25197] : 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)),X25197)) = X25197,
    inference(variable_rename,[status(thm)],[fact_transfer__int__nat__set__return__embed]) ).

fof(i_0_9712,plain,
    ! [X23907,X23908,X23909,X23910,X23911] :
      ( hAPP(c_Product__Type_Ofst(X23911,X23910),hAPP(hAPP(c_Product__Type_OPair(X23911,X23910),X23909),X23908)) != X23907
      | X23909 = X23907 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fst__eqD])]) ).

fof(i_0_9713,plain,
    ! [X23916,X23917,X23918,X23919,X23920] :
      ( hAPP(c_Product__Type_Osnd(X23920,X23919),hAPP(hAPP(c_Product__Type_OPair(X23920,X23919),X23918),X23917)) != X23916
      | X23917 = X23916 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snd__eqD])]) ).

cnf(i_0_9714,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_5941]) ).

cnf(i_0_9715,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_5942]) ).

fof(i_0_9716,plain,
    ! [X25524] :
      ( ~ c_Nat__Transfer_Onat__set(X25524)
      | 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),X25524)) = X25524 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__return__embed])]) ).

fof(i_0_9717,plain,
    ! [X20405,X20406] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X20406,X20406)),X20405))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20406),hAPP(c_Relation_OField(X20406),X20405))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Field])]) ).

fof(i_0_9718,plain,
    ! [X26251,X26252,X26253] :
      ( ~ class_Groups_Oordered__ab__group__add(X26253)
      | hAPP(c_Set_Oimage(X26253,X26253,c_Groups_Ouminus__class_Ouminus(X26253)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26253,X26252),X26251)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X26253,hAPP(c_Groups_Ouminus__class_Ouminus(X26253),X26251),hAPP(c_Groups_Ouminus__class_Ouminus(X26253),X26252)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastLessThan])]) ).

fof(i_0_9719,plain,
    ! [X18778,X18779,X18780,X18781] :
      ( ~ class_Orderings_Oorder(X18781)
      | ~ class_Orderings_Olinorder(X18780)
      | ~ c_Orderings_Oorder__class_Ostrict__mono(X18780,X18781,X18779)
      | c_Fun_Oinj__on(X18780,X18781,X18779,X18778) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_strict__mono__imp__inj__on])]) ).

fof(i_0_9720,plain,
    ! [X21638,X21639] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21639),X21638))
      | hAPP(c_Nat_OSuc,X21639) = X21638
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21639)),X21638)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).

fof(i_0_9721,plain,
    ! [X20837,X20839,X20840,X20841] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X20837))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X20839),X20837))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20839),esk78_1(X20837))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk79_2(X20840,X20841)),X20840))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X20840)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk79_2(X20840,X20841)),X20841))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X20840)) ) ),
    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_9722,plain,
    ! [X20822,X20824,X20825,X20826] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X20822))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X20824),X20822))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20824),esk76_1(X20822))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk77_2(X20825,X20826)),X20825))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X20825)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk77_2(X20825,X20826)),X20826))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X20825)) ) ),
    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_9723,plain,
    ! [X25280,X25281] :
      ( ( ~ 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),X25280)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25281),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25280)) = hAPP(c_Int_Onumber__class_Onumber__of(X25281),X25280)
        | ~ class_Int_Onumber__ring(X25281) )
      & ( 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),X25280)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25281),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25280)) = c_Groups_Ozero__class_Ozero(X25281)
        | ~ class_Int_Onumber__ring(X25281) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5961])])]) ).

fof(i_0_9724,plain,
    ! [X24076,X24077,X24078] :
      ( ~ class_Int_Onumber__ring(X24078)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24078),hAPP(c_Int_Onumber__class_Onumber__of(X24078),X24077)),hAPP(c_Int_Onumber__class_Onumber__of(X24078),X24076)) = hAPP(c_Int_Onumber__class_Onumber__of(X24078),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24077),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24076))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__number__of__eq])]) ).

fof(i_0_9725,plain,
    ! [X30541,X30542,X30543] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30543),X30542))
      | hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X30543)),c_Enum_On__lists(X30543,X30541,X30542))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__n__lists])]) ).

fof(i_0_9726,plain,
    ! [X25755,X25756,X25757,X25758,X25759] :
      ( ~ class_Orderings_Olinorder(X25759)
      | ~ class_Orderings_Olinorder(X25758)
      | ~ c_Orderings_Oorder__class_Omono(X25758,X25759,X25757)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25759),hAPP(X25757,X25756)),hAPP(X25757,X25755)) = hAPP(X25757,hAPP(hAPP(c_Orderings_Oord__class_Omax(X25758),X25756),X25755)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__of__mono])]) ).

fof(i_0_9727,plain,
    ! [X25308,X25309,X25310,X25311,X25312] :
      ( ~ class_Orderings_Olinorder(X25312)
      | ~ class_Orderings_Olinorder(X25311)
      | ~ c_Orderings_Oorder__class_Omono(X25311,X25312,X25310)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25312),hAPP(X25310,X25309)),hAPP(X25310,X25308)) = hAPP(X25310,hAPP(hAPP(c_Orderings_Oord__class_Omin(X25311),X25309),X25308)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__of__mono])]) ).

fof(i_0_9728,plain,
    ! [X21927,X21928,X21929] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21929),X21928))
      | hBOOL(hAPP(hAPP(c_member(X21929),X21927),X21928))
      | hAPP(c_Finite__Set_Ocard(X21929),hAPP(hAPP(c_Set_Oinsert(X21929),X21927),X21928)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X21929),X21928)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5962])]) ).

fof(i_0_9729,plain,
    ! [X24553] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X24553)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24553)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24553))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X24553))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__nat__eq])]) ).

fof(i_0_9730,plain,
    ! [X18533,X18534,X18535] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18535),X18534),X18533))
        | X18534 = X18533
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18535),X18534),X18533))
        | ~ class_Orderings_Olinorder(X18535) )
      & ( X18534 != X18533
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18535),X18534),X18533))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18535),X18534),X18533))
        | ~ class_Orderings_Olinorder(X18535) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5963])])]) ).

fof(i_0_9731,plain,
    ! [X32202,X32203,X32204] : c_List_Obutlast(X32204,hAPP(hAPP(c_List_Oappend(X32204),X32203),hAPP(hAPP(c_List_Olist_OCons(X32204),X32202),c_List_Olist_ONil(X32204)))) = X32203,
    inference(variable_rename,[status(thm)],[fact_butlast__snoc]) ).

fof(i_0_9732,plain,
    ! [X32127,X32128,X32129] : c_List_Olast(X32129,hAPP(hAPP(c_List_Oappend(X32129),X32128),hAPP(hAPP(c_List_Olist_OCons(X32129),X32127),c_List_Olist_ONil(X32129)))) = X32127,
    inference(variable_rename,[status(thm)],[fact_last__snoc]) ).

fof(i_0_9733,plain,
    ! [X28579,X28580] : hAPP(hAPP(c_Relation_Orel__comp(X28580,X28580,X28580),c_Transitive__Closure_Ortrancl(X28580,X28579)),c_Transitive__Closure_Ortrancl(X28580,X28579)) = c_Transitive__Closure_Ortrancl(X28580,X28579),
    inference(variable_rename,[status(thm)],[fact_rtrancl__idemp__self__comp]) ).

fof(i_0_9734,plain,
    ! [X23937,X23938,X23939] : hAPP(c_Product__Type_Ofst(X23939,X23938),X23937) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X23939,X23938,X23939),c_COMBK(X23939,X23938)),X23937),
    inference(variable_rename,[status(thm)],[fact_fst__def]) ).

fof(i_0_9735,plain,
    ! [X30169] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X30169)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X30169),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[i_0_5964]) ).

fof(i_0_9736,plain,
    ! [X28809,X28810] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28810,X28810)),X28809))
      | ~ c_Wellfounded_Oacyclic(X28810,X28809)
      | c_Wellfounded_Owf(X28810,hAPP(c_Relation_Oconverse(X28810,X28810),X28809)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__acyclic__wf__converse])]) ).

fof(i_0_9737,plain,
    ! [X17087,X17088,X17089] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17089),X17088),X17087))
        | X17088 != X17087
        | ~ class_Orderings_Oorder(X17089) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17089),X17087),X17088))
        | X17088 != X17087
        | ~ class_Orderings_Oorder(X17089) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17089),X17088),X17087))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17089),X17087),X17088))
        | X17088 = X17087
        | ~ class_Orderings_Oorder(X17089) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).

fof(i_0_9738,plain,
    ! [X17081,X17082,X17083] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17083),X17081),X17082))
        | X17081 = X17082
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17083),X17082),X17081))
        | ~ class_Orderings_Oorder(X17083) )
      & ( X17081 != X17082
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17083),X17081),X17082))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17083),X17082),X17081))
        | ~ class_Orderings_Oorder(X17083) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).

fof(i_0_9739,plain,
    ! [X17062,X17063,X17064] :
      ( ~ class_Orderings_Oorder(X17064)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17064),X17063),X17062))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17064),X17062),X17063))
      | X17063 = X17062 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).

fof(i_0_9740,plain,
    ! [X17055,X17056,X17057] :
      ( ~ class_Orderings_Oorder(X17057)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17057),X17056),X17055))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17057),X17055),X17056))
      | X17055 = X17056 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).

fof(i_0_9741,plain,
    ! [X23664,X23665] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23665),X23664))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23664,X23665) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23664),X23665),X23665) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__mod__geq])]) ).

fof(i_0_9742,plain,
    ! [X33356,X33357,X33358] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X33358),X33357),hAPP(c_List_Oset(X33358),X33356)))
        | c_List_Oinsert(X33358,X33357,X33356) = X33356 )
      & ( hBOOL(hAPP(hAPP(c_member(X33358),X33357),hAPP(c_List_Oset(X33358),X33356)))
        | c_List_Oinsert(X33358,X33357,X33356) = hAPP(hAPP(c_List_Olist_OCons(X33358),X33357),X33356) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5965])]) ).

fof(i_0_9743,plain,
    ! [X33340,X33341,X33342] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X33342),X33341),hAPP(c_List_Oset(X33342),X33340)))
      | c_List_Oinsert(X33342,X33341,X33340) = X33340 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__insert])]) ).

fof(i_0_9744,plain,
    ! [X21826,X21827] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21827),X21826))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21826)),X21827) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21826),X21827)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__le])]) ).

fof(i_0_9745,plain,
    ! [X18432,X18433,X18434] :
      ( ~ class_Orderings_Oorder(X18434)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18434),X18433),X18432))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18434),X18432),X18433)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5966])]) ).

fof(i_0_9746,plain,
    ! [X18402,X18403,X18404] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18404),X18403),X18402))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18404),X18402),X18403))
        | X18403 = X18402
        | ~ class_Orderings_Olinorder(X18404) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18404),X18402),X18403))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18404),X18403),X18402))
        | ~ class_Orderings_Olinorder(X18404) )
      & ( X18403 != X18402
        | ~ 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_5967])])]) ).

fof(i_0_9747,plain,
    ! [X18527,X18528,X18529] :
      ( ~ class_Orderings_Olinorder(X18529)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18529),X18528),X18527))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18529),X18527),X18528)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5968])]) ).

fof(i_0_9748,plain,
    ! [X18494,X18495,X18496] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18496),X18495),X18494))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18496),X18494),X18495))
        | ~ class_Orderings_Olinorder(X18496) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18496),X18494),X18495))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18496),X18495),X18494))
        | ~ class_Orderings_Olinorder(X18496) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5969])])]) ).

fof(i_0_9749,plain,
    ! [X18497,X18498,X18499] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18499),X18498),X18497))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18499),X18497),X18498))
        | ~ class_Orderings_Olinorder(X18499) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18499),X18497),X18498))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18499),X18498),X18497))
        | ~ class_Orderings_Olinorder(X18499) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5970])])]) ).

fof(i_0_9750,plain,
    ! [X18463,X18464,X18465] :
      ( ~ class_Orderings_Opreorder(X18465)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18465),X18464),X18463))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18465),X18463),X18464)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5971])]) ).

fof(i_0_9751,plain,
    ! [X18429,X18430,X18431] :
      ( ~ class_Orderings_Opreorder(X18431)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18431),X18430),X18429))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18431),X18429),X18430)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5972])]) ).

fof(i_0_9752,plain,
    ! [X18420,X18421,X18422] :
      ( ~ class_Orderings_Opreorder(X18422)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18422),X18421),X18420))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18422),X18420),X18421)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5973])]) ).

fof(i_0_9753,plain,
    ! [X18417,X18418,X18419] :
      ( ~ class_Orderings_Opreorder(X18419)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18419),X18418),X18417))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18419),X18417),X18418)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5974])]) ).

fof(i_0_9754,plain,
    ! [X27079,X27080] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27080)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27080),hAPP(c_Groups_Ouminus__class_Ouminus(X27080),X27079)),hAPP(c_Groups_Oabs__class_Oabs(X27080),X27079))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__minus__self])]) ).

fof(i_0_9755,plain,
    ! [X22140,X22141] :
      ( ~ class_Rings_Olinordered__ring(X22141)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22141),c_Groups_Ozero__class_Ozero(X22141)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22141),X22140),X22140))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__square])]) ).

fof(i_0_9756,plain,
    ! [X21784,X21785] :
      ( ~ class_Rings_Olinordered__semidom(X21785)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),X21784),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21785),X21784),c_Groups_Oone__class_Oone(X21785)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).

fof(i_0_9757,plain,
    ! [X27014,X27015] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27015),c_Groups_Ozero__class_Ozero(X27015)),hAPP(c_Groups_Oabs__class_Oabs(X27015),X27014)))
        | X27014 != c_Groups_Ozero__class_Ozero(X27015)
        | ~ class_Groups_Oordered__ab__group__add__abs(X27015) )
      & ( X27014 = c_Groups_Ozero__class_Ozero(X27015)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27015),c_Groups_Ozero__class_Ozero(X27015)),hAPP(c_Groups_Oabs__class_Oabs(X27015),X27014)))
        | ~ class_Groups_Oordered__ab__group__add__abs(X27015) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff])])]) ).

fof(i_0_9758,plain,
    ! [X23605,X23606,X23607,X23608] :
      ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X23608,X23607),X23606))
      | ~ hBOOL(hAPP(hAPP(X23607,X23605),X23606))
      | hBOOL(hAPP(c_Wellfounded_Oaccp(X23608,X23607),X23605)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__downward])]) ).

fof(i_0_9759,plain,
    ! [X24685,X24686] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24686),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24686)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24685)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24686),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24686)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24685)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24686),X24685)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5975])]) ).

fof(i_0_9760,plain,
    ! [X31901,X31902] :
      ( X31902 = c_List_Olist_ONil(X31901)
      | hBOOL(hAPP(hAPP(c_member(X31901),hAPP(c_List_Ohd(X31901),X31902)),hAPP(c_List_Oset(X31901),X31902))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__in__set])]) ).

fof(i_0_9761,plain,
    ! [X33772,X33773,X33774] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X33774)),c_Lazy__Sequence_Olazy__sequence_OInsert(X33774,X33773,X33772)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X33774)),X33772)),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_9762,plain,
    ! [X22589,X22590,X22591] :
      ( ~ class_Rings_Ocomm__semiring__1(X22591)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22591),hAPP(hAPP(c_Power_Opower__class_Opower(X22591),X22590),X22589)),X22590) = hAPP(hAPP(c_Power_Opower__class_Opower(X22591),X22590),hAPP(c_Nat_OSuc,X22589)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J])]) ).

fof(i_0_9763,plain,
    ! [X22691,X22692,X22693] :
      ( ~ class_Groups_Omonoid__mult(X22693)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22693),X22692),hAPP(c_Nat_OSuc,X22691)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22693),hAPP(hAPP(c_Power_Opower__class_Opower(X22693),X22692),X22691)),X22692) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc2])]) ).

fof(i_0_9764,plain,
    ! [X32632,X32633] :
      ( ~ class_Orderings_Olinorder(X32633)
      | c_List_Olinorder__class_Osorted__list__of__set(X32633,hAPP(c_List_Oset(X32633),X32632)) = c_List_Olinorder__class_Osort__key(X32633,X32633,c_COMBI(X32633),c_List_Oremdups(X32633,X32632)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__sort__remdups])]) ).

fof(i_0_9765,plain,
    ! [X19935,X19936,X19937,X19938,X19939] :
      ( hAPP(X19939,X19938) != hAPP(c_Option_Ooption_OSome(X19937),X19936)
      | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X19935,tc_Option_Ooption(X19937)),X19939),X19938),hAPP(c_Option_Ooption_OSome(X19937),X19936)) = X19939 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__upd__triv])]) ).

fof(i_0_9766,plain,
    ! [X30516,X30517,X30518] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30518)),hAPP(hAPP(c_List_Olist_OCons(X30518),X30517),X30516)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30518)),X30516)),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_9767,plain,
    ! [X30544,X30545,X30546] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X30546))),c_Enum_On__lists(X30546,X30545,X30544)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30546)),X30544)),X30545),
    inference(variable_rename,[status(thm)],[fact_length__n__lists]) ).

fof(i_0_9768,plain,
    ! [X25123,X25124,X25126,X25127] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25124))
        | ~ hBOOL(hAPP(X25123,X25124))
        | hBOOL(hAPP(X25123,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk152_1(X25123)))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk153_1(X25126)))
        | ~ hBOOL(hAPP(X25126,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25127))) )
      & ( hBOOL(hAPP(X25126,esk153_1(X25126)))
        | ~ hBOOL(hAPP(X25126,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25127))) ) ),
    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_9769,plain,
    ! [X21811,X21812] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21812),X21811))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21812)),X21811)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])]) ).

fof(i_0_9770,plain,
    ! [X25873,X25874,X25875] :
      ( ~ class_Orderings_Olinorder(X25875)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25875),X25874))
      | ~ hBOOL(hAPP(hAPP(c_member(X25875),X25873),X25874))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25875),X25873),c_Big__Operators_Olinorder__class_OMax(X25875,X25874)) = c_Big__Operators_Olinorder__class_OMax(X25875,X25874) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oin__idem])]) ).

fof(i_0_9771,plain,
    ! [X25426,X25427,X25428] :
      ( ~ class_Orderings_Olinorder(X25428)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25428),X25427))
      | ~ hBOOL(hAPP(hAPP(c_member(X25428),X25426),X25427))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25428),X25426),c_Big__Operators_Olinorder__class_OMin(X25428,X25427)) = c_Big__Operators_Olinorder__class_OMin(X25428,X25427) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oin__idem])]) ).

fof(i_0_9772,plain,
    ! [X20849,X20850,X20851] :
      ( ~ class_Lattices_Olattice(X20851)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20851),X20850))
      | ~ hBOOL(hAPP(hAPP(c_member(X20851),X20849),X20850))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20851),X20849),c_Big__Operators_Olattice__class_OInf__fin(X20851,X20850)) = c_Big__Operators_Olattice__class_OInf__fin(X20851,X20850) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oin__idem])]) ).

fof(i_0_9773,plain,
    ! [X20846,X20847,X20848] :
      ( ~ class_Lattices_Olattice(X20848)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20848),X20847))
      | ~ hBOOL(hAPP(hAPP(c_member(X20848),X20846),X20847))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20848),X20846),c_Big__Operators_Olattice__class_OSup__fin(X20848,X20847)) = c_Big__Operators_Olattice__class_OSup__fin(X20848,X20847) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oin__idem])]) ).

fof(i_0_9774,plain,
    ! [X29742,X29743,X29744] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29744)
      | ~ hBOOL(hAPP(hAPP(c_member(X29744),X29743),X29742))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29744),X29743),c_Complete__Lattice_OSup__class_OSup(X29744,X29742))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__upper])]) ).

cnf(i_0_9775,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_5976]) ).

fof(i_0_9776,plain,
    ! [X33500,X33501,X33502,X33503] :
      ( ( ~ c_List_Olist__ex(X33503,X33502,hAPP(hAPP(c_List_Olist_OCons(X33503),X33501),X33500))
        | hBOOL(hAPP(X33502,X33501))
        | c_List_Olist__ex(X33503,X33502,X33500) )
      & ( ~ hBOOL(hAPP(X33502,X33501))
        | c_List_Olist__ex(X33503,X33502,hAPP(hAPP(c_List_Olist_OCons(X33503),X33501),X33500)) )
      & ( ~ c_List_Olist__ex(X33503,X33502,X33500)
        | c_List_Olist__ex(X33503,X33502,hAPP(hAPP(c_List_Olist_OCons(X33503),X33501),X33500)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__simps_I1_J])])]) ).

fof(i_0_9777,plain,
    ! [X26417,X26418,X26419] :
      ( ~ class_Orderings_Oorder(X26419)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26419,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X26419),X26418)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26419,X26418),X26417)) = c_Orderings_Obot__class_Obot(tc_fun(X26419,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I2_J])]) ).

fof(i_0_9778,plain,
    ! [X22526,X22527] :
      ( ( X22526 != c_Orderings_Obot__class_Obot(tc_fun(X22527,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(X22527),X22526))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X22527),X22526))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X22527),X22526))) )
      & ( X22526 = c_Orderings_Obot__class_Obot(tc_fun(X22527,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22527),X22526))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X22527),X22526))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__gt__0__iff])])]) ).

fof(i_0_9779,plain,
    ! [X30952,X30953,X30954,X30955] : hAPP(hAPP(c_List_Onth(X30955),hAPP(hAPP(c_List_Olist_OCons(X30955),X30954),X30953)),hAPP(c_Nat_OSuc,X30952)) = hAPP(hAPP(c_List_Onth(X30955),X30953),X30952),
    inference(variable_rename,[status(thm)],[fact_nth__Cons__Suc]) ).

fof(i_0_9780,plain,
    ! [X31930,X31931,X31932,X31933] : hAPP(hAPP(c_List_Omap(X31933,X31932),X31931),hAPP(c_List_Otl(X31933),X31930)) = hAPP(c_List_Otl(X31932),hAPP(hAPP(c_List_Omap(X31933,X31932),X31931),X31930)),
    inference(variable_rename,[status(thm)],[fact_map__tl]) ).

fof(i_0_9781,plain,
    ! [X32915,X32916,X32917,X32918] : hAPP(c_List_Orev(X32918),hAPP(hAPP(c_List_Omap(X32917,X32918),X32916),X32915)) = hAPP(hAPP(c_List_Omap(X32917,X32918),X32916),hAPP(c_List_Orev(X32917),X32915)),
    inference(variable_rename,[status(thm)],[fact_rev__map]) ).

fof(i_0_9782,plain,
    ! [X17532,X17533] : ~ hBOOL(hAPP(hAPP(c_member(X17533),X17532),c_Orderings_Obot__class_Obot(tc_fun(X17533,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[i_0_5977]) ).

fof(i_0_9783,plain,
    ! [X17273,X17274] : ~ hBOOL(hAPP(hAPP(c_member(X17274),X17273),c_Orderings_Obot__class_Obot(tc_fun(X17274,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[i_0_5978]) ).

fof(i_0_9784,plain,
    ! [X24534,X24535,X24537,X24538] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk146_1(X24534)))
        | ~ hBOOL(hAPP(X24534,X24535)) )
      & ( hBOOL(hAPP(X24534,hAPP(c_Int_Onat,esk146_1(X24534))))
        | ~ hBOOL(hAPP(X24534,X24535)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24538))
        | ~ hBOOL(hAPP(X24537,hAPP(c_Int_Onat,X24538)))
        | hBOOL(hAPP(X24537,esk147_1(X24537))) ) ),
    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_9785,plain,
    ! [X22466,X22467] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X22467),X22466)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X22467),X22466)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__ge__0__finite])]) ).

cnf(i_0_9786,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_5917]) ).

fof(i_0_9787,plain,
    ! [X33595,X33596,X33597,X33598] :
      ( ( c_List_Olist__all(X33598,X33597,X33596)
        | ~ c_List_Olist__all(X33598,X33597,hAPP(hAPP(c_List_Oappend(X33598),X33596),X33595)) )
      & ( c_List_Olist__all(X33598,X33597,X33595)
        | ~ c_List_Olist__all(X33598,X33597,hAPP(hAPP(c_List_Oappend(X33598),X33596),X33595)) )
      & ( ~ c_List_Olist__all(X33598,X33597,X33596)
        | ~ c_List_Olist__all(X33598,X33597,X33595)
        | c_List_Olist__all(X33598,X33597,hAPP(hAPP(c_List_Oappend(X33598),X33596),X33595)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__append])])]) ).

fof(i_0_9788,plain,
    ! [X22468] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22468))
      | hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22468),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X22468 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__pred])]) ).

fof(i_0_9789,plain,
    ! [X17143,X17144,X17145] :
      ( hAPP(hAPP(c_Set_Oinsert(X17145),X17144),c_Orderings_Obot__class_Obot(tc_fun(X17145,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(X17145),X17143),c_Orderings_Obot__class_Obot(tc_fun(X17145,tc_HOL_Obool)))
      | X17144 = X17143 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__inject])]) ).

fof(i_0_9790,plain,
    ! [X31301] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X31301),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,X31301)) = X31301 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__inverse])]) ).

fof(i_0_9791,plain,
    ! [X24201,X24202,X24203,X24204] :
      ( ( X24202 = c_Groups_Ozero__class_Ozero(X24204)
        | X24203 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24204),hAPP(c_Int_Onumber__class_Onumber__of(X24204),X24201)),X24202)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24204),X24203),X24202) != hAPP(c_Int_Onumber__class_Onumber__of(X24204),X24201)
        | ~ class_Fields_Ofield__inverse__zero(X24204)
        | ~ class_Int_Onumber(X24204) )
      & ( X24202 != c_Groups_Ozero__class_Ozero(X24204)
        | hAPP(c_Int_Onumber__class_Onumber__of(X24204),X24201) = c_Groups_Ozero__class_Ozero(X24204)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24204),X24203),X24202) != hAPP(c_Int_Onumber__class_Onumber__of(X24204),X24201)
        | ~ class_Fields_Ofield__inverse__zero(X24204)
        | ~ class_Int_Onumber(X24204) )
      & ( X24202 = c_Groups_Ozero__class_Ozero(X24204)
        | X24202 != c_Groups_Ozero__class_Ozero(X24204)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24204),X24203),X24202) = hAPP(c_Int_Onumber__class_Onumber__of(X24204),X24201)
        | ~ class_Fields_Ofield__inverse__zero(X24204)
        | ~ class_Int_Onumber(X24204) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X24204),X24201) != c_Groups_Ozero__class_Ozero(X24204)
        | X24202 != c_Groups_Ozero__class_Ozero(X24204)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24204),X24203),X24202) = hAPP(c_Int_Onumber__class_Onumber__of(X24204),X24201)
        | ~ class_Fields_Ofield__inverse__zero(X24204)
        | ~ class_Int_Onumber(X24204) )
      & ( X24202 = c_Groups_Ozero__class_Ozero(X24204)
        | X24203 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24204),hAPP(c_Int_Onumber__class_Onumber__of(X24204),X24201)),X24202)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24204),X24203),X24202) = hAPP(c_Int_Onumber__class_Onumber__of(X24204),X24201)
        | ~ class_Fields_Ofield__inverse__zero(X24204)
        | ~ class_Int_Onumber(X24204) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X24204),X24201) != c_Groups_Ozero__class_Ozero(X24204)
        | X24203 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24204),hAPP(c_Int_Onumber__class_Onumber__of(X24204),X24201)),X24202)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24204),X24203),X24202) = hAPP(c_Int_Onumber__class_Onumber__of(X24204),X24201)
        | ~ class_Fields_Ofield__inverse__zero(X24204)
        | ~ class_Int_Onumber(X24204) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of])])]) ).

fof(i_0_9792,plain,
    ! [X24197,X24198,X24199,X24200] :
      ( ( X24197 = c_Groups_Ozero__class_Ozero(X24200)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24200),hAPP(c_Int_Onumber__class_Onumber__of(X24200),X24199)),X24197) = X24198
        | hAPP(c_Int_Onumber__class_Onumber__of(X24200),X24199) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24200),X24198),X24197)
        | ~ class_Fields_Ofield__inverse__zero(X24200)
        | ~ class_Int_Onumber(X24200) )
      & ( X24197 != c_Groups_Ozero__class_Ozero(X24200)
        | hAPP(c_Int_Onumber__class_Onumber__of(X24200),X24199) = c_Groups_Ozero__class_Ozero(X24200)
        | hAPP(c_Int_Onumber__class_Onumber__of(X24200),X24199) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24200),X24198),X24197)
        | ~ class_Fields_Ofield__inverse__zero(X24200)
        | ~ class_Int_Onumber(X24200) )
      & ( X24197 = c_Groups_Ozero__class_Ozero(X24200)
        | X24197 != c_Groups_Ozero__class_Ozero(X24200)
        | hAPP(c_Int_Onumber__class_Onumber__of(X24200),X24199) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24200),X24198),X24197)
        | ~ class_Fields_Ofield__inverse__zero(X24200)
        | ~ class_Int_Onumber(X24200) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X24200),X24199) != c_Groups_Ozero__class_Ozero(X24200)
        | X24197 != c_Groups_Ozero__class_Ozero(X24200)
        | hAPP(c_Int_Onumber__class_Onumber__of(X24200),X24199) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24200),X24198),X24197)
        | ~ class_Fields_Ofield__inverse__zero(X24200)
        | ~ class_Int_Onumber(X24200) )
      & ( X24197 = c_Groups_Ozero__class_Ozero(X24200)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24200),hAPP(c_Int_Onumber__class_Onumber__of(X24200),X24199)),X24197) != X24198
        | hAPP(c_Int_Onumber__class_Onumber__of(X24200),X24199) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24200),X24198),X24197)
        | ~ class_Fields_Ofield__inverse__zero(X24200)
        | ~ class_Int_Onumber(X24200) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X24200),X24199) != c_Groups_Ozero__class_Ozero(X24200)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24200),hAPP(c_Int_Onumber__class_Onumber__of(X24200),X24199)),X24197) != X24198
        | hAPP(c_Int_Onumber__class_Onumber__of(X24200),X24199) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24200),X24198),X24197)
        | ~ class_Fields_Ofield__inverse__zero(X24200)
        | ~ class_Int_Onumber(X24200) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of])])]) ).

fof(i_0_9793,plain,
    ! [X21657,X21658] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21658),hAPP(c_Nat_OSuc,X21657)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21658),X21657))
        | X21658 = hAPP(c_Nat_OSuc,X21657) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21658),X21657))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21658),hAPP(c_Nat_OSuc,X21657))) )
      & ( X21658 != hAPP(c_Nat_OSuc,X21657)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21658),hAPP(c_Nat_OSuc,X21657))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])]) ).

fof(i_0_9794,plain,
    ! [X21651,X21652] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21652),hAPP(c_Nat_OSuc,X21651)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21652),X21651))
      | X21652 = hAPP(c_Nat_OSuc,X21651) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5979])]) ).

fof(i_0_9795,plain,
    ! [X32216,X32217] :
      ( X32217 = c_List_Olist_ONil(X32216)
      | hAPP(hAPP(c_List_Oappend(X32216),c_List_Obutlast(X32216,X32217)),hAPP(hAPP(c_List_Olist_OCons(X32216),c_List_Olast(X32216,X32217)),c_List_Olist_ONil(X32216))) = X32217 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__butlast__last__id])]) ).

cnf(i_0_9796,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_5980]) ).

fof(i_0_9797,plain,
    ! [X23954,X23955,X23956] : hAPP(hAPP(c_Product__Type_OPair(X23956,X23955),hAPP(c_Product__Type_Ofst(X23956,X23955),X23954)),hAPP(c_Product__Type_Osnd(X23956,X23955),X23954)) = X23954,
    inference(variable_rename,[status(thm)],[fact_pair__collapse]) ).

fof(i_0_9798,plain,
    ! [X23957,X23958,X23959] : X23959 = hAPP(hAPP(c_Product__Type_OPair(X23958,X23957),hAPP(c_Product__Type_Ofst(X23958,X23957),X23959)),hAPP(c_Product__Type_Osnd(X23958,X23957),X23959)),
    inference(variable_rename,[status(thm)],[fact_surjective__pairing]) ).

fof(i_0_9799,plain,
    ! [X26261,X26262] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26262),X26261))
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26262),hAPP(c_Nat_OSuc,X26261)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X26261),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26262),X26261)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26262),X26261))
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26262),hAPP(c_Nat_OSuc,X26261)) = 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_5981])]) ).

fof(i_0_9800,plain,
    ! [X32636,X32637,X32638,X32639] :
      ( ~ class_Orderings_Olinorder(X32639)
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32638,X32639,X32637),X32636),c_List_Olist_ONil(X32638)) = hAPP(hAPP(c_List_Olist_OCons(X32638),X32636),c_List_Olist_ONil(X32638)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__key_Osimps_I1_J])]) ).

fof(i_0_9801,plain,
    ! [X18357,X18358,X18359,X18360,X18361] :
      ( ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18361,X18360),X18359),X18358),X18357) != X18359
        | hAPP(X18359,X18358) = X18357 )
      & ( hAPP(X18359,X18358) != X18357
        | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18361,X18360),X18359),X18358),X18357) = X18359 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__idem__iff])]) ).

fof(i_0_9802,plain,
    ! [X33320,X33321,X33322] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X33322),X33321))
      | hBOOL(hAPP(c_List_Odistinct(X33322),c_List_Oinsert(X33322,X33320,X33321))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__insert])]) ).

fof(i_0_9803,plain,
    ! [X33003,X33004,X33005] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X33005),X33004))
      | hBOOL(hAPP(c_List_Odistinct(X33005),c_List_OtakeWhile(X33005,X33003,X33004))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__takeWhile])]) ).

fof(i_0_9804,plain,
    ! [X32558,X32559,X32560] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X32560),X32559))
      | hBOOL(hAPP(c_List_Odistinct(X32560),c_List_Oremove1(X32560,X32558,X32559))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__remove1])]) ).

fof(i_0_9805,plain,
    ! [X30560,X30561,X30562] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30562),X30561))
      | hBOOL(hAPP(c_List_Odistinct(X30562),c_List_Osublist(X30562,X30561,X30560))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__sublistI])]) ).

fof(i_0_9806,plain,
    ! [X33824,X33825,X33826,X33827] : c_Lazy__Sequence_Oappend(X33827,c_Lazy__Sequence_Olazy__sequence_OInsert(X33827,X33826,X33825),X33824) = c_Lazy__Sequence_Olazy__sequence_OInsert(X33827,X33826,c_Lazy__Sequence_Oappend(X33827,X33825,X33824)),
    inference(variable_rename,[status(thm)],[fact__03]) ).

fof(i_0_9807,plain,
    ! [X32563,X32564,X32565,X32566] : c_List_Oremove1(X32566,X32565,c_List_Oremove1(X32566,X32564,X32563)) = c_List_Oremove1(X32566,X32564,c_List_Oremove1(X32566,X32565,X32563)),
    inference(variable_rename,[status(thm)],[fact_remove1__commute]) ).

fof(i_0_9808,plain,
    ! [X29160,X29161,X29162,X29163,X29164,X29165] :
      ( ~ c_Finite__Set_Ofun__left__comm(X29165,X29164,X29163)
      | hAPP(hAPP(X29163,X29162),hAPP(hAPP(X29163,X29161),X29160)) = hAPP(hAPP(X29163,X29161),hAPP(hAPP(X29163,X29162),X29160)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm])]) ).

fof(i_0_9809,plain,
    ! [X20852,X20853,X20854] :
      ( ~ class_Lattices_Olattice(X20854)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20854),X20853))
      | ~ hBOOL(hAPP(hAPP(c_member(X20854),X20852),X20853))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20854),X20852),c_Big__Operators_Olattice__class_OSup__fin(X20854,X20853)) = X20852 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Sup__absorb])]) ).

fof(i_0_9810,plain,
    ! [X20843,X20844,X20845] :
      ( ~ class_Lattices_Olattice(X20845)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20845),X20844))
      | ~ hBOOL(hAPP(hAPP(c_member(X20845),X20843),X20844))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20845),X20843),c_Big__Operators_Olattice__class_OInf__fin(X20845,X20844)) = X20843 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Inf__absorb])]) ).

fof(i_0_9811,plain,
    ! [X28179] : c_Wellfounded_OwfP(X28179,hAPP(c_COMBK(tc_fun(X28179,tc_HOL_Obool),X28179),hAPP(c_COMBK(tc_HOL_Obool,X28179),c_fFalse))),
    inference(variable_rename,[status(thm)],[fact_wfP__empty]) ).

fof(i_0_9812,plain,
    ! [X32294,X32295,X32296,X32297] :
      ( ( ~ hBOOL(hAPP(X32297,X32296))
        | hAPP(c_List_Ofilter(X32295,X32297),hAPP(hAPP(c_List_Olist_OCons(X32295),X32296),X32294)) = hAPP(hAPP(c_List_Olist_OCons(X32295),X32296),hAPP(c_List_Ofilter(X32295,X32297),X32294)) )
      & ( hBOOL(hAPP(X32297,X32296))
        | hAPP(c_List_Ofilter(X32295,X32297),hAPP(hAPP(c_List_Olist_OCons(X32295),X32296),X32294)) = hAPP(c_List_Ofilter(X32295,X32297),X32294) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5982])]) ).

fof(i_0_9813,plain,
    ! [X25824,X25825,X25826] :
      ( ~ class_Orderings_Olinorder(X25826)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25826),X25825),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25826),X25825),X25824))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__maxI1])]) ).

fof(i_0_9814,plain,
    ! [X25821,X25822,X25823] :
      ( ~ class_Orderings_Olinorder(X25823)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25823),X25822),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25823),X25821),X25822))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__maxI2])]) ).

fof(i_0_9815,plain,
    ! [X17708,X17709,X17710] :
      ( ~ class_Lattices_Olattice(X17710)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17710),X17709),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17710),X17709),X17708))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I3_J])]) ).

fof(i_0_9816,plain,
    ! [X17711,X17712,X17713] :
      ( ~ class_Lattices_Osemilattice__sup(X17713)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17713),X17712),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17713),X17712),X17711))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__ge1])]) ).

fof(i_0_9817,plain,
    ! [X17714,X17715,X17716] :
      ( ~ class_Lattices_Olattice(X17716)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17716),X17715),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17716),X17714),X17715))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I4_J])]) ).

fof(i_0_9818,plain,
    ! [X17717,X17718,X17719] :
      ( ~ class_Lattices_Osemilattice__sup(X17719)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17719),X17718),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17719),X17717),X17718))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__ge2])]) ).

fof(i_0_9819,plain,
    ! [X17592,X17593,X17594] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17594),X17593),hAPP(c_Set_OCollect(X17594),X17592)))
        | hBOOL(hAPP(X17592,X17593)) )
      & ( ~ hBOOL(hAPP(X17592,X17593))
        | hBOOL(hAPP(hAPP(c_member(X17594),X17593),hAPP(c_Set_OCollect(X17594),X17592))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__Collect__eq])]) ).

fof(i_0_9820,plain,
    ! [X17589,X17590,X17591] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17591),X17590),hAPP(c_Set_OCollect(X17591),X17589)))
      | hBOOL(hAPP(X17589,X17590)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_CollectD])]) ).

fof(i_0_9821,plain,
    ! [X17586,X17587,X17588] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17588),X17587),hAPP(c_Set_OCollect(X17588),X17586)))
      | hBOOL(hAPP(X17586,X17587)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_CollectE])]) ).

fof(i_0_9822,plain,
    ! [X24587] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24587))
      | hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X24587)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X24587)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__nat__eq__nat__zadd1])]) ).

cnf(i_0_9823,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_5897]) ).

fof(i_0_9824,plain,
    ! [X32551,X32552,X32553,X32554] :
      ( ( X32554 != X32553
        | c_List_Oremove1(X32552,X32554,hAPP(hAPP(c_List_Olist_OCons(X32552),X32553),X32551)) = X32551 )
      & ( X32554 = X32553
        | c_List_Oremove1(X32552,X32554,hAPP(hAPP(c_List_Olist_OCons(X32552),X32553),X32551)) = hAPP(hAPP(c_List_Olist_OCons(X32552),X32553),c_List_Oremove1(X32552,X32554,X32551)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remove1_Osimps_I2_J])]) ).

fof(i_0_9825,plain,
    ! [X21643,X21644] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21644),hAPP(c_Nat_OSuc,X21643)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21644),X21643))
      | X21644 = X21643 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5983])]) ).

fof(i_0_9826,plain,
    ! [X21634,X21635] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21635),X21634))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21635),hAPP(c_Nat_OSuc,X21634)))
      | X21634 = X21635 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5984])]) ).

fof(i_0_9827,plain,
    ! [X21632,X21633] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21633),hAPP(c_Nat_OSuc,X21632)))
        | X21633 = X21632
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21633),X21632)) )
      & ( X21633 != X21632
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21633),hAPP(c_Nat_OSuc,X21632)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21633),X21632)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5985])])]) ).

fof(i_0_9828,plain,
    ! [X21628,X21629] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21629),hAPP(c_Nat_OSuc,X21628)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21629),X21628))
        | X21629 = X21628 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21629),X21628))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21629),hAPP(c_Nat_OSuc,X21628))) )
      & ( X21629 != X21628
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21629),hAPP(c_Nat_OSuc,X21628))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).

cnf(i_0_9829,plain,
    hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),c_Divides_Odivmod__nat(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_5986]) ).

cnf(i_0_9830,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_5987]) ).

cnf(i_0_9831,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_5988]) ).

fof(i_0_9832,plain,
    ! [X20255,X20256,X20257] : hAPP(c_Relation_OImage(X20257,X20257,c_Relation_OId__on(X20257,X20256)),X20255) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20257,tc_HOL_Obool)),X20256),X20255),
    inference(variable_rename,[status(thm)],[fact_Image__Id__on]) ).

fof(i_0_9833,plain,
    ! [X25731,X25732,X25733,X25734] :
      ( ~ class_Orderings_Olinorder(X25734)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25734),X25733),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25734),X25732),X25731)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25734),X25732),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25734),X25733),X25731)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oleft__commute])]) ).

fof(i_0_9834,plain,
    ! [X25727,X25728,X25729,X25730] :
      ( ~ class_Orderings_Olinorder(X25730)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25730),X25729),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25730),X25728),X25727)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25730),X25728),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25730),X25729),X25727)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__left__commute])]) ).

fof(i_0_9835,plain,
    ! [X25342,X25343,X25344,X25345] :
      ( ~ class_Orderings_Olinorder(X25345)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25345),X25344),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25345),X25343),X25342)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25345),X25343),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25345),X25344),X25342)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__left__commute])]) ).

fof(i_0_9836,plain,
    ! [X25338,X25339,X25340,X25341] :
      ( ~ class_Orderings_Olinorder(X25341)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25341),X25340),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25341),X25339),X25338)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25341),X25339),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25341),X25340),X25338)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__commute])]) ).

fof(i_0_9837,plain,
    ! [X21474,X21475,X21476,X21477] :
      ( ~ class_Rings_Ocomm__semiring__1(X21477)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21477),X21476),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21477),X21475),X21474)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21477),X21475),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21477),X21476),X21474)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).

fof(i_0_9838,plain,
    ! [X21920,X21921,X21922,X21923] :
      ( ~ class_Rings_Ocomm__semiring__1(X21923)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21923),X21922),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21923),X21921),X21920)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21923),X21921),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21923),X21922),X21920)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])]) ).

fof(i_0_9839,plain,
    ! [X17842,X17843,X17844,X17845] :
      ( ~ class_Lattices_Osemilattice__inf(X17845)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17845),X17844),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17845),X17843),X17842)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17845),X17843),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17845),X17844),X17842)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__commute])]) ).

fof(i_0_9840,plain,
    ! [X17834,X17835,X17836,X17837] :
      ( ~ class_Lattices_Osemilattice__inf(X17837)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17837),X17836),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17837),X17835),X17834)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17837),X17835),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17837),X17836),X17834)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__commute])]) ).

fof(i_0_9841,plain,
    ! [X17838,X17839,X17840,X17841] :
      ( ~ class_Lattices_Olattice(X17841)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17841),X17840),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17841),X17839),X17838)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17841),X17839),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17841),X17840),X17838)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I3_J])]) ).

fof(i_0_9842,plain,
    ! [X17678,X17679,X17680,X17681] :
      ( ~ class_Lattices_Olattice(X17681)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17681),X17680),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17681),X17679),X17678)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17681),X17679),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17681),X17680),X17678)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I7_J])]) ).

fof(i_0_9843,plain,
    ! [X17682,X17683,X17684,X17685] :
      ( ~ class_Lattices_Osemilattice__sup(X17685)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17685),X17684),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17685),X17683),X17682)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17685),X17683),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17685),X17684),X17682)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oleft__commute])]) ).

fof(i_0_9844,plain,
    ! [X17674,X17675,X17676,X17677] :
      ( ~ class_Lattices_Osemilattice__sup(X17677)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17677),X17676),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17677),X17675),X17674)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17677),X17675),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17677),X17676),X17674)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__left__commute])]) ).

fof(i_0_9845,plain,
    ! [X21620,X21621,X21622] :
      ( ~ class_Groups_Ogroup__add(X21622)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21622),X21621),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21622),hAPP(c_Groups_Ouminus__class_Ouminus(X21622),X21621)),X21620)) = X21620 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__minus__cancel])]) ).

fof(i_0_9846,plain,
    ! [X22365,X22366,X22367] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22367),X22366) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22367),X22365)
        | X22366 = X22365
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22367)) )
      & ( X22366 != X22365
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22367),X22366) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22367),X22365)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22367)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1])])]) ).

fof(i_0_9847,plain,
    ! [X21817,X21818] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21818),hAPP(c_Nat_OSuc,X21817)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21818),X21817)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21818),X21817))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21818),hAPP(c_Nat_OSuc,X21817))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).

fof(i_0_9848,plain,
    ! [X24604] : 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),X24604)) = 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),X24604))),
    inference(variable_rename,[status(thm)],[fact_one__div__nat__number__of]) ).

fof(i_0_9849,plain,
    ! [X25254,X25255,X25256,X25257,X25258] :
      ( ( X25254 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25256)
        | hBOOL(hAPP(X25255,X25256))
        | ~ hBOOL(hAPP(X25255,hAPP(c_Int_Onat,X25254))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25254),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(X25255,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X25255,hAPP(c_Int_Onat,X25254))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25257),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X25257 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk156_2(X25257,X25258))
        | hBOOL(hAPP(X25258,hAPP(c_Int_Onat,X25257))) )
      & ( ~ hBOOL(hAPP(X25258,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | X25257 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk156_2(X25257,X25258))
        | hBOOL(hAPP(X25258,hAPP(c_Int_Onat,X25257))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25257),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X25258,esk156_2(X25257,X25258)))
        | hBOOL(hAPP(X25258,hAPP(c_Int_Onat,X25257))) )
      & ( ~ hBOOL(hAPP(X25258,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X25258,esk156_2(X25257,X25258)))
        | hBOOL(hAPP(X25258,hAPP(c_Int_Onat,X25257))) ) ),
    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_9850,plain,
    ! [X31777,X31778,X31779] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31779),X31778))
      | hBOOL(hAPP(c_List_Odistinct(X31779),hAPP(hAPP(c_List_Odrop(X31779),X31777),X31778))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__drop])]) ).

fof(i_0_9851,plain,
    ! [X31100,X31101,X31102] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31102),X31101))
      | hBOOL(hAPP(c_List_Odistinct(X31102),hAPP(hAPP(c_List_Otake(X31102),X31100),X31101))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__take])]) ).

fof(i_0_9852,plain,
    ! [X20326,X20327,X20328] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20328),X20327))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20328),hAPP(hAPP(c_Set_Oinsert(X20328),X20326),X20327))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite_OinsertI])]) ).

fof(i_0_9853,plain,
    ! [X26096,X26097] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26097,X26096)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X26097),hAPP(c_Nat_OSuc,X26096)),
    inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastAtMost]) ).

fof(i_0_9854,plain,
    ! [X29417,X29418,X29419] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29419,tc_fun(X29418,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X29419,tc_HOL_Obool))),X29417) = c_Orderings_Otop__class_Otop(tc_fun(X29418,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_INT__empty]) ).

fof(i_0_9855,plain,
    ! [X24079,X24080] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24080)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24079)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24080),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24079))),
    inference(variable_rename,[status(thm)],[fact_minus__numeral__code_I6_J]) ).

fof(i_0_9856,plain,
    ! [X20534,X20535] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20535,tc_HOL_Obool)),X20534) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20535,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X20535,tc_HOL_Obool))),X20534),
    inference(variable_rename,[status(thm)],[fact_Compl__eq__Diff__UNIV]) ).

fof(i_0_9857,plain,
    ! [X32185,X32186,X32187,X32188] : hAPP(hAPP(c_List_Omap(X32188,X32187),X32186),c_List_Obutlast(X32188,X32185)) = c_List_Obutlast(X32187,hAPP(hAPP(c_List_Omap(X32188,X32187),X32186),X32185)),
    inference(variable_rename,[status(thm)],[fact_map__butlast]) ).

fof(i_0_9858,plain,
    ! [X22512,X22513] :
      ( ~ class_Orderings_Olinorder(X22513)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22513),X22512))
      | X22512 = c_Orderings_Obot__class_Obot(tc_fun(X22513,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(X22513),c_Big__Operators_Olinorder__class_OMin(X22513,X22512)),X22512)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__in])]) ).

fof(i_0_9859,plain,
    ! [X22510,X22511] :
      ( ~ class_Orderings_Olinorder(X22511)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22511),X22510))
      | X22510 = c_Orderings_Obot__class_Obot(tc_fun(X22511,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(X22511),c_Big__Operators_Olinorder__class_OMax(X22511,X22510)),X22510)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__in])]) ).

fof(i_0_9860,plain,
    ! [X24528,X24530,X24531,X24533] :
      ( ( ~ hBOOL(hAPP(X24528,esk144_1(X24528)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24530))
        | hBOOL(hAPP(X24528,hAPP(c_Int_Onat,X24530))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk145_1(X24531)))
        | hBOOL(hAPP(X24531,X24533)) )
      & ( ~ hBOOL(hAPP(X24531,hAPP(c_Int_Onat,esk145_1(X24531))))
        | hBOOL(hAPP(X24531,X24533)) ) ),
    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_9861,plain,
    ! [X17561,X17562,X17563] : hBOOL(hAPP(hAPP(c_member(X17563),X17562),hAPP(hAPP(c_Set_Oinsert(X17563),X17562),X17561))),
    inference(variable_rename,[status(thm)],[fact_insertI1]) ).

fof(i_0_9862,plain,
    ! [X23640,X23641] :
      ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23641,X23640)) != X23640
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X23641),X23640) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23641,X23640)) = X23640
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X23641),X23640) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23641,X23640)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__Suc])]) ).

fof(i_0_9863,plain,
    ! [X27928] : c_Hilbert__Choice_Oinv__into(X27928,X27928,c_Orderings_Otop__class_Otop(tc_fun(X27928,tc_HOL_Obool)),c_Fun_Oid(X27928)) = c_Fun_Oid(X27928),
    inference(variable_rename,[status(thm)],[fact_inv__id]) ).

cnf(i_0_9864,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_5989]) ).

cnf(i_0_9865,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_5990]) ).

fof(i_0_9866,plain,
    ! [X17097,X17098,X17099,X17100] : hAPP(hAPP(c_Set_Oinsert(X17100),X17099),hAPP(hAPP(c_Set_Oinsert(X17100),X17098),X17097)) = hAPP(hAPP(c_Set_Oinsert(X17100),X17098),hAPP(hAPP(c_Set_Oinsert(X17100),X17099),X17097)),
    inference(variable_rename,[status(thm)],[fact_insert__commute]) ).

fof(i_0_9867,plain,
    ! [X20744,X20745,X20746,X20747] :
      ( ~ c_Finite__Set_Ofolding__one(X20747,X20746,X20745)
      | hAPP(X20745,hAPP(hAPP(c_Set_Oinsert(X20747),X20744),c_Orderings_Obot__class_Obot(tc_fun(X20747,tc_HOL_Obool)))) = X20744 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Osingleton])]) ).

fof(i_0_9868,plain,
    ! [X21992,X21993] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21993),hAPP(c_Nat_OSuc,X21992)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21993),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X21992),
    inference(variable_rename,[status(thm)],[fact_diff__Suc__eq__diff__pred]) ).

fof(i_0_9869,plain,
    ! [X29024,X29025,X29026,X29027] : hAPP(hAPP(c_Finite__Set_Ofold(X29027,X29026,X29025),X29024),c_Orderings_Obot__class_Obot(tc_fun(X29027,tc_HOL_Obool))) = X29024,
    inference(variable_rename,[status(thm)],[fact_fold__empty]) ).

fof(i_0_9870,plain,
    ! [X31772,X31773,X31774] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31774)),hAPP(hAPP(c_List_Odrop(X31774),X31773),X31772)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31774)),X31772)),X31773),
    inference(variable_rename,[status(thm)],[fact_length__drop]) ).

fof(i_0_9871,plain,
    ! [X31103,X31104,X31105] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31105)),hAPP(hAPP(c_List_Otake(X31105),X31104),X31103)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31105)),X31103)),X31104),
    inference(variable_rename,[status(thm)],[fact_length__take]) ).

cnf(i_0_9872,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_5991]) ).

fof(i_0_9873,plain,
    ! [X25215] :
      ( ~ class_Nat_Osemiring__char__0(X25215)
      | c_Fun_Oinj__on(tc_Nat_Onat,X25215,c_Nat_Osemiring__1__class_Oof__nat(X25215),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_9874,plain,
    ! [X18613,X18614,X18615] :
      ( ~ class_Orderings_Owellorder(X18615)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18615),X18614),c_Orderings_Oord__class_OLeast(X18615,X18613)))
      | ~ hBOOL(hAPP(X18613,X18614)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5992])]) ).

fof(i_0_9875,plain,
    ! [X31956,X31957,X31958] : hAPP(hAPP(c_List_Otake(X31958),X31957),hAPP(c_List_Otl(X31958),X31956)) = hAPP(c_List_Otl(X31958),hAPP(hAPP(c_List_Otake(X31958),hAPP(c_Nat_OSuc,X31957)),X31956)),
    inference(variable_rename,[status(thm)],[fact_take__tl]) ).

fof(i_0_9876,plain,
    ! [X30891,X30892] :
      ( ~ class_Enum_Oenum(X30892)
      | ~ class_Enum_Oenum(X30891)
      | c_Enum_Oenum__class_Oenum(tc_prod(X30892,X30891)) = c_Enum_Oproduct(X30892,X30891,c_Enum_Oenum__class_Oenum(X30892),c_Enum_Oenum__class_Oenum(X30891)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__prod__def])]) ).

fof(i_0_9877,plain,
    ! [X21418,X21419,X21421,X21422,X21423] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21419),X21418))
        | X21418 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21419),esk107_2(X21418,X21419))) )
      & ( X21421 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21422),X21423))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21422),X21421)) ) ),
    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_9878,plain,
    ! [X33991,X33992,X33993,X33994] : hAPP(hAPP(c_List_Odrop(X33994),X33993),c_List_Oreplicate(X33994,X33992,X33991)) = c_List_Oreplicate(X33994,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33992),X33993),X33991),
    inference(variable_rename,[status(thm)],[fact_drop__replicate]) ).

fof(i_0_9879,plain,
    ! [X33984,X33985,X33986,X33987] : hAPP(hAPP(c_List_Otake(X33987),X33986),c_List_Oreplicate(X33987,X33985,X33984)) = c_List_Oreplicate(X33987,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X33986),X33985),X33984),
    inference(variable_rename,[status(thm)],[fact_take__replicate]) ).

fof(i_0_9880,plain,
    ! [X26143,X26144,X26145] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X26145,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(X26145,X26144,X26143)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26145),X26144),X26143))
        | ~ class_Orderings_Oorder(X26145) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26145),X26144),X26143))
        | c_Orderings_Obot__class_Obot(tc_fun(X26145,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X26145,X26144,X26143)
        | ~ class_Orderings_Oorder(X26145) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5993])])]) ).

fof(i_0_9881,plain,
    ! [X25634,X25635,X25636] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X25636,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X25636,X25635,X25634)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25636),X25635),X25634))
        | ~ class_Orderings_Oorder(X25636) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25636),X25635),X25634))
        | c_Orderings_Obot__class_Obot(tc_fun(X25636,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X25636,X25635,X25634)
        | ~ class_Orderings_Oorder(X25636) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5994])])]) ).

fof(i_0_9882,plain,
    ! [X26140,X26141,X26142] :
      ( ( c_SetInterval_Oord__class_OatLeastAtMost(X26142,X26141,X26140) != c_Orderings_Obot__class_Obot(tc_fun(X26142,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26142),X26141),X26140))
        | ~ class_Orderings_Oorder(X26142) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26142),X26141),X26140))
        | c_SetInterval_Oord__class_OatLeastAtMost(X26142,X26141,X26140) = c_Orderings_Obot__class_Obot(tc_fun(X26142,tc_HOL_Obool))
        | ~ class_Orderings_Oorder(X26142) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5995])])]) ).

fof(i_0_9883,plain,
    ! [X25637,X25638,X25639] :
      ( ( c_SetInterval_Oord__class_OgreaterThanAtMost(X25639,X25638,X25637) != c_Orderings_Obot__class_Obot(tc_fun(X25639,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25639),X25638),X25637))
        | ~ class_Orderings_Oorder(X25639) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25639),X25638),X25637))
        | c_SetInterval_Oord__class_OgreaterThanAtMost(X25639,X25638,X25637) = c_Orderings_Obot__class_Obot(tc_fun(X25639,tc_HOL_Obool))
        | ~ class_Orderings_Oorder(X25639) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5996])])]) ).

fof(i_0_9884,plain,
    ! [X26842] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X26842) = 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),X26842))),
    inference(variable_rename,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I1_J]) ).

fof(i_0_9885,plain,
    ! [X33610,X33611,X33612,X33613] :
      ( ( hBOOL(hAPP(X33612,X33611))
        | ~ c_List_Olist__all(X33613,X33612,hAPP(hAPP(c_List_Olist_OCons(X33613),X33611),X33610)) )
      & ( c_List_Olist__all(X33613,X33612,X33610)
        | ~ c_List_Olist__all(X33613,X33612,hAPP(hAPP(c_List_Olist_OCons(X33613),X33611),X33610)) )
      & ( ~ hBOOL(hAPP(X33612,X33611))
        | ~ c_List_Olist__all(X33613,X33612,X33610)
        | c_List_Olist__all(X33613,X33612,hAPP(hAPP(c_List_Olist_OCons(X33613),X33611),X33610)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__simps_I1_J])])]) ).

fof(i_0_9886,plain,
    ! [X27093,X27094,X27095] :
      ( ~ class_Fields_Olinordered__field(X27095)
      | X27094 = c_Groups_Ozero__class_Ozero(X27095)
      | hAPP(c_Groups_Oabs__class_Oabs(X27095),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27095),X27093),X27094)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27095),hAPP(c_Groups_Oabs__class_Oabs(X27095),X27093)),hAPP(c_Groups_Oabs__class_Oabs(X27095),X27094)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__abs__divide])]) ).

fof(i_0_9887,plain,
    ! [X28360,X28361] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28361),esk316_2(X28360,X28361)),X28360))
        | hAPP(c_Finite__Set_Ocard(X28361),X28360) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28361),X28360)) )
      & ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Finite__Set_Ocard(X28361),X28360) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28361),X28360)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oneutral])])])]) ).

fof(i_0_9888,plain,
    ! [X20520,X20521] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20521,tc_HOL_Obool)),X20520),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20521,tc_HOL_Obool)),X20520)) = c_Orderings_Obot__class_Obot(tc_fun(X20521,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__disjoint]) ).

fof(i_0_9889,plain,
    ! [X20524,X20525] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20525,tc_HOL_Obool)),X20524),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20525,tc_HOL_Obool)),X20524)) = c_Orderings_Otop__class_Otop(tc_fun(X20525,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__partition]) ).

fof(i_0_9890,plain,
    ! [X18696,X18697,X18698] : c_Fun_Oinj__on(X18698,X18697,X18696,c_Orderings_Obot__class_Obot(tc_fun(X18698,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_inj__on__empty]) ).

fof(i_0_9891,plain,
    ! [X22931,X22932] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22932),X22931))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22931),X22932))
      | X22932 = X22931 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__antisym])]) ).

fof(i_0_9892,plain,
    ! [X21003,X21004] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21004),X21003))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21003),X21004))
      | X21004 = X21003 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).

cnf(i_0_9893,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_5753]) ).

fof(i_0_9894,plain,
    ! [X25074] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25074))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X25074) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25074),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__minus1])]) ).

fof(i_0_9895,plain,
    ! [X25470,X25471,X25472] :
      ( ~ class_Orderings_Olinorder(X25472)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25472),X25471))
      | X25471 = c_Orderings_Obot__class_Obot(tc_fun(X25472,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMin(X25472,hAPP(hAPP(c_Set_Oinsert(X25472),X25470),X25471)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25472),X25470),c_Big__Operators_Olinorder__class_OMin(X25472,X25471)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__insert])]) ).

fof(i_0_9896,plain,
    ! [X25894,X25895,X25896] :
      ( ~ class_Orderings_Olinorder(X25896)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25896),X25895))
      | X25895 = c_Orderings_Obot__class_Obot(tc_fun(X25896,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMax(X25896,hAPP(hAPP(c_Set_Oinsert(X25896),X25894),X25895)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25896),X25894),c_Big__Operators_Olinorder__class_OMax(X25896,X25895)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__insert])]) ).

fof(i_0_9897,plain,
    ! [X20855,X20856,X20857] :
      ( ~ class_Lattices_Olattice(X20857)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20857),X20856))
      | X20856 = c_Orderings_Obot__class_Obot(tc_fun(X20857,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OSup__fin(X20857,hAPP(hAPP(c_Set_Oinsert(X20857),X20855),X20856)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20857),X20855),c_Big__Operators_Olattice__class_OSup__fin(X20857,X20856)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__idem])]) ).

fof(i_0_9898,plain,
    ! [X20858,X20859,X20860] :
      ( ~ class_Lattices_Olattice(X20860)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20860),X20859))
      | X20859 = c_Orderings_Obot__class_Obot(tc_fun(X20860,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OInf__fin(X20860,hAPP(hAPP(c_Set_Oinsert(X20860),X20858),X20859)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20860),X20858),c_Big__Operators_Olattice__class_OInf__fin(X20860,X20859)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__idem])]) ).

fof(i_0_9899,plain,
    ! [X17484,X17485,X17486] :
      ( ( X17485 = c_Orderings_Obot__class_Obot(tc_fun(X17486,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17486,tc_HOL_Obool)),X17485),X17484) != c_Orderings_Obot__class_Obot(tc_fun(X17486,tc_HOL_Obool)) )
      & ( X17484 = c_Orderings_Obot__class_Obot(tc_fun(X17486,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17486,tc_HOL_Obool)),X17485),X17484) != c_Orderings_Obot__class_Obot(tc_fun(X17486,tc_HOL_Obool)) )
      & ( X17485 != c_Orderings_Obot__class_Obot(tc_fun(X17486,tc_HOL_Obool))
        | X17484 != c_Orderings_Obot__class_Obot(tc_fun(X17486,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17486,tc_HOL_Obool)),X17485),X17484) = c_Orderings_Obot__class_Obot(tc_fun(X17486,tc_HOL_Obool)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__empty])])]) ).

fof(i_0_9900,plain,
    ! [X31630,X31631,X31632] :
      ( ~ class_Groups_Omonoid__add(X31632)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X31632),hAPP(hAPP(c_List_Oappend(X31632),X31631),X31630)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31632),hAPP(c_List_Omonoid__add__class_Olistsum(X31632),X31631)),hAPP(c_List_Omonoid__add__class_Olistsum(X31632),X31630)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__append])]) ).

fof(i_0_9901,plain,
    ! [X27036,X27037,X27038] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X27038)
      | hAPP(c_Groups_Oabs__class_Oabs(X27038),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27038),X27037),X27036)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27038),hAPP(c_Groups_Oabs__class_Oabs(X27038),X27037)),hAPP(c_Groups_Oabs__class_Oabs(X27038),X27036)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__divide])]) ).

fof(i_0_9902,plain,
    ! [X27043,X27044,X27045] :
      ( ~ class_Rings_Olinordered__idom(X27045)
      | hAPP(c_Groups_Oabs__class_Oabs(X27045),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27045),X27044),X27043)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27045),hAPP(c_Groups_Oabs__class_Oabs(X27045),X27044)),hAPP(c_Groups_Oabs__class_Oabs(X27045),X27043)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult])]) ).

fof(i_0_9903,plain,
    ! [X25860,X25861,X25862] :
      ( ~ class_Groups_Olinordered__ab__group__add(X25862)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X25862),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25862),X25861),X25860)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25862),hAPP(c_Groups_Ouminus__class_Ouminus(X25862),X25861)),hAPP(c_Groups_Ouminus__class_Ouminus(X25862),X25860)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__max__eq__min])]) ).

fof(i_0_9904,plain,
    ! [X25863,X25864,X25865] :
      ( ~ class_Groups_Olinordered__ab__group__add(X25865)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X25865),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25865),X25864),X25863)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25865),hAPP(c_Groups_Ouminus__class_Ouminus(X25865),X25864)),hAPP(c_Groups_Ouminus__class_Ouminus(X25865),X25863)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__min__eq__max])]) ).

fof(i_0_9905,plain,
    ! [X21614,X21615,X21616] :
      ( ~ class_Groups_Oab__group__add(X21616)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X21616),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21616),X21615),X21614)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21616),hAPP(c_Groups_Ouminus__class_Ouminus(X21616),X21615)),hAPP(c_Groups_Ouminus__class_Ouminus(X21616),X21614)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__distrib])]) ).

fof(i_0_9906,plain,
    ! [X21617,X21618,X21619] :
      ( ~ class_Groups_Ogroup__add(X21619)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X21619),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21619),X21618),X21617)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21619),hAPP(c_Groups_Ouminus__class_Ouminus(X21619),X21617)),hAPP(c_Groups_Ouminus__class_Ouminus(X21619),X21618)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add])]) ).

fof(i_0_9907,plain,
    ! [X20509,X20510,X20511] :
      ( ~ class_Lattices_Oboolean__algebra(X20511)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X20511),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20511),X20510),X20509)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20511),hAPP(c_Groups_Ouminus__class_Ouminus(X20511),X20510)),hAPP(c_Groups_Ouminus__class_Ouminus(X20511),X20509)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__inf])]) ).

fof(i_0_9908,plain,
    ! [X20506,X20507,X20508] :
      ( ~ class_Lattices_Oboolean__algebra(X20508)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X20508),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20508),X20507),X20506)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20508),hAPP(c_Groups_Ouminus__class_Ouminus(X20508),X20507)),hAPP(c_Groups_Ouminus__class_Ouminus(X20508),X20506)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__sup])]) ).

cnf(i_0_9909,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_5553]) ).

cnf(i_0_9910,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_5997]) ).

fof(i_0_9911,plain,
    ! [X17928,X17929,X17930] : hAPP(c_Set_Oimage(X17929,tc_fun(X17929,tc_HOL_Obool),X17930),X17928) != hAPP(c_Set_OPow(X17929),X17928),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cantors__paradox])]) ).

fof(i_0_9912,plain,
    ! [X17104,X17105,X17106] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17104,tc_HOL_Obool)),X17106),X17105))
        | X17106 != X17105 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17104,tc_HOL_Obool)),X17105),X17106))
        | X17106 != X17105 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5998])])]) ).

fof(i_0_9913,plain,
    ! [X17114,X17115,X17116] :
      ( X17116 != X17115
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17114,tc_HOL_Obool)),X17116),X17115)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD1])]) ).

fof(i_0_9914,plain,
    ! [X17111,X17112,X17113] :
      ( X17113 != X17112
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17111,tc_HOL_Obool)),X17112),X17113)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD2])]) ).

fof(i_0_9915,plain,
    ! [X21661] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21661)),X21661)),
    inference(variable_rename,[status(thm)],[i_0_5999]) ).

fof(i_0_9916,plain,
    ! [X23247,X23248] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23248))
        | c_SMT_Oz3div(X23247,X23248) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23247),X23248) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23248))
        | c_SMT_Oz3div(X23247,X23248) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23247),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23248))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6000])]) ).

fof(i_0_9917,plain,
    ! [X32125,X32126] :
      ( X32126 = c_List_Olist_ONil(X32125)
      | hBOOL(hAPP(hAPP(c_member(X32125),c_List_Olast(X32125,X32126)),hAPP(c_List_Oset(X32125),X32126))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__in__set])]) ).

fof(i_0_9918,plain,
    ! [X21700,X21701,X21702] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21702)),X21701) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21702)),X21700)
        | X21701 = X21700 )
      & ( X21701 != X21700
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21702)),X21701) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21702)),X21700) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1])]) ).

fof(i_0_9919,plain,
    ! [X23868,X23869,X23870,X23871,X23872,X23873] :
      ( ( X23871 = X23869
        | hAPP(hAPP(c_Product__Type_OPair(X23873,X23872),X23871),X23870) != hAPP(hAPP(c_Product__Type_OPair(X23873,X23872),X23869),X23868) )
      & ( X23870 = X23868
        | hAPP(hAPP(c_Product__Type_OPair(X23873,X23872),X23871),X23870) != hAPP(hAPP(c_Product__Type_OPair(X23873,X23872),X23869),X23868) )
      & ( X23871 != X23869
        | X23870 != X23868
        | hAPP(hAPP(c_Product__Type_OPair(X23873,X23872),X23871),X23870) = hAPP(hAPP(c_Product__Type_OPair(X23873,X23872),X23869),X23868) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__eq])])]) ).

fof(i_0_9920,plain,
    ! [X23862,X23863,X23864,X23865,X23866,X23867] :
      ( ( X23865 = X23863
        | hAPP(hAPP(c_Product__Type_OPair(X23867,X23866),X23865),X23864) != hAPP(hAPP(c_Product__Type_OPair(X23867,X23866),X23863),X23862) )
      & ( X23864 = X23862
        | hAPP(hAPP(c_Product__Type_OPair(X23867,X23866),X23865),X23864) != hAPP(hAPP(c_Product__Type_OPair(X23867,X23866),X23863),X23862) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__inject])])]) ).

fof(i_0_9921,plain,
    ! [X23485,X23486] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X23486,X23485) != 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),X23486),X23485) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X23486,X23485) = 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),X23486),X23485) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23485),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23486,X23485)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus1__eq__if])]) ).

fof(i_0_9922,plain,
    ! [X23653,X23654] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23654),X23653))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23654,X23653) = X23654 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23654),X23653))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23654,X23653) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23654),X23653),X23653) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6001])]) ).

fof(i_0_9923,plain,
    ! [X23651,X23652] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23652),X23651))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23652,X23651) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23652),X23651),X23651) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6002])]) ).

fof(i_0_9924,plain,
    ! [X33306,X33307,X33308] :
      ( hBOOL(hAPP(hAPP(c_member(X33308),X33307),hAPP(c_List_Oset(X33308),X33306)))
      | c_List_Oinsert(X33308,X33307,X33306) = hAPP(hAPP(c_List_Olist_OCons(X33308),X33307),X33306) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6003])]) ).

fof(i_0_9925,plain,
    ! [X17120,X17121] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17121,tc_HOL_Obool)),X17120),X17120)),
    inference(variable_rename,[status(thm)],[fact_subset__refl]) ).

fof(i_0_9926,plain,
    ! [X26094,X26095] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26095),X26094)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X26095)),hAPP(c_Nat_OSuc,X26094)),
    inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastLessThan]) ).

fof(i_0_9927,plain,
    ! [X32876,X32877,X32878] : hAPP(c_List_Orev(X32878),hAPP(hAPP(c_List_Oappend(X32878),X32877),X32876)) = hAPP(hAPP(c_List_Oappend(X32878),hAPP(c_List_Orev(X32878),X32876)),hAPP(c_List_Orev(X32878),X32877)),
    inference(variable_rename,[status(thm)],[fact_rev__append]) ).

fof(i_0_9928,plain,
    ! [X31855,X31856,X31857,X31858] :
      ( hAPP(c_List_Orotate1(X31858),c_List_Olist_ONil(X31858)) = c_List_Olist_ONil(X31858)
      & hAPP(c_List_Orotate1(X31857),hAPP(hAPP(c_List_Olist_OCons(X31857),X31856),X31855)) = hAPP(hAPP(c_List_Oappend(X31857),X31855),hAPP(hAPP(c_List_Olist_OCons(X31857),X31856),c_List_Olist_ONil(X31857))) ),
    inference(variable_rename,[status(thm)],[fact_rotate__simps]) ).

fof(i_0_9929,plain,
    ! [X21636,X21637] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21637),X21636))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21637),hAPP(c_Nat_OSuc,X21636))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SucI])]) ).

fof(i_0_9930,plain,
    ! [X21813,X21814] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21814),X21813))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21814),hAPP(c_Nat_OSuc,X21813))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc])]) ).

fof(i_0_9931,plain,
    ! [X21653,X21654] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21654),X21653))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21654),hAPP(c_Nat_OSuc,X21653))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])]) ).

fof(i_0_9932,plain,
    ! [X30698,X30699] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X30699,X30698) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X30699),c_Groups_Oone__class_Oone(tc_Int_Oint)),X30698)),
    inference(variable_rename,[status(thm)],[fact_greaterThanAtMost__upto]) ).

fof(i_0_9933,plain,
    ! [X22904,X22905] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22905),X22904),X22904) != c_Groups_Ozero__class_Ozero(X22905)
        | X22904 = c_Groups_Ozero__class_Ozero(X22905)
        | ~ hBOOL(hAPP(hAPP(c_member(X22905),X22904),c_Int_Oring__1__class_OInts(X22905)))
        | ~ class_Int_Oring__char__0(X22905) )
      & ( X22904 != c_Groups_Ozero__class_Ozero(X22905)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22905),X22904),X22904) = c_Groups_Ozero__class_Ozero(X22905)
        | ~ hBOOL(hAPP(hAPP(c_member(X22905),X22904),c_Int_Oring__1__class_OInts(X22905)))
        | ~ class_Int_Oring__char__0(X22905) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__double__eq__0__iff])])]) ).

fof(i_0_9934,plain,
    ! [X25062] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25062))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),X25062) = 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_9935,plain,
    ! [X17916,X17917,X17918] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17918,tc_HOL_Obool)),X17917),X17916) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17918,tc_HOL_Obool)),X17916),X17917),
    inference(variable_rename,[status(thm)],[fact_Int__commute]) ).

fof(i_0_9936,plain,
    ! [X17410,X17411,X17412] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17412,tc_HOL_Obool)),X17411),X17410) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17412,tc_HOL_Obool)),X17410),X17411),
    inference(variable_rename,[status(thm)],[fact_Un__commute]) ).

fof(i_0_9937,plain,
    ! [X26070] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk189_1(X26070)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26070)) )
      & ( X26070 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk189_1(X26070))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26070)) ) ),
    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_9938,plain,
    ! [X24328,X24329,X24330,X24331,X24332] :
      ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24332),X24329),X24331) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24332),X24328),X24330)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24332),X24329),X24330) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24332),X24328),X24331)
        | X24330 = c_Groups_Ozero__class_Ozero(X24332)
        | X24331 = c_Groups_Ozero__class_Ozero(X24332)
        | ~ class_Fields_Ofield(X24332) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24332),X24329),X24330) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24332),X24328),X24331)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24332),X24329),X24331) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24332),X24328),X24330)
        | X24330 = c_Groups_Ozero__class_Ozero(X24332)
        | X24331 = c_Groups_Ozero__class_Ozero(X24332)
        | ~ class_Fields_Ofield(X24332) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__eq__eq])])]) ).

fof(i_0_9939,plain,
    ! [X23502,X23503] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23503),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23502),X23503)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23502),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23502,X23503)),
    inference(variable_rename,[status(thm)],[fact_zmult__div__cancel]) ).

fof(i_0_9940,plain,
    ! [X23668,X23669] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23669),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23668),X23669)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23668),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23668,X23669)),
    inference(variable_rename,[status(thm)],[fact_mult__div__cancel]) ).

fof(i_0_9941,plain,
    ! [X31304,X31305] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X31305),X31304) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X31305)),hAPP(c_Code__Numeral_Onat__of,X31304))),
    inference(variable_rename,[status(thm)],[fact_div__code__numeral__def]) ).

fof(i_0_9942,plain,
    ! [X31302,X31303] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X31303),X31302) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X31303)),hAPP(c_Code__Numeral_Onat__of,X31302))),
    inference(variable_rename,[status(thm)],[fact_plus__code__numeral__def]) ).

fof(i_0_9943,plain,
    ! [X31308,X31309] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X31309),X31308) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X31309)),hAPP(c_Code__Numeral_Onat__of,X31308))),
    inference(variable_rename,[status(thm)],[fact_times__code__numeral__def]) ).

fof(i_0_9944,plain,
    ! [X31299,X31300] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X31300),X31299) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X31300)),hAPP(c_Code__Numeral_Onat__of,X31299))),
    inference(variable_rename,[status(thm)],[fact_minus__code__numeral__def]) ).

fof(i_0_9945,plain,
    ! [X21845,X21846] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21846),X21845))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21846),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21845),X21846)) = X21845 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse])]) ).

fof(i_0_9946,plain,
    ! [X20992,X20993] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20993),X20992))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20992),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20992),X20993)) = X20993 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel])]) ).

fof(i_0_9947,plain,
    ! [X24741,X24742,X24743,X24744] : c_Nat_Onat_Onat__case(X24744,X24743,X24742,hAPP(c_Nat_OSuc,X24741)) = hAPP(X24742,X24741),
    inference(variable_rename,[status(thm)],[fact_nat__case__Suc]) ).

fof(i_0_9948,plain,
    ! [X30429,X30430,X30431] :
      ( ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X30429) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X30430),hAPP(c_List_Oset(tc_Nat_Onat),X30429)))
        | X30430 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk400_1(X30431)),hAPP(c_List_Oset(tc_Nat_Onat),X30431)))
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X30431) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( esk400_1(X30431) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X30431) = 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_9949,plain,
    ! [X18542,X18543,X18544] :
      ( ~ class_Orderings_Oorder(X18544)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18544),X18543),X18542))
      | X18542 = X18543
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18544),X18543),X18542)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).

fof(i_0_9950,plain,
    ! [X18539,X18540,X18541] :
      ( ~ class_Orderings_Oorder(X18541)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18541),X18540),X18539))
      | X18540 = X18539
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18541),X18540),X18539)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).

fof(i_0_9951,plain,
    ! [X18536,X18537,X18538] :
      ( ~ class_Orderings_Oorder(X18538)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18538),X18537),X18536))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18538),X18537),X18536))
      | X18537 = X18536 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).

fof(i_0_9952,plain,
    ! [X18521,X18522,X18523] :
      ( ~ class_Orderings_Oorder(X18523)
      | X18522 = X18521
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18523),X18522),X18521))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18523),X18522),X18521)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).

fof(i_0_9953,plain,
    ! [X18509,X18510,X18511] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18511),X18510),X18509))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18511),X18510),X18509))
        | X18510 = X18509
        | ~ class_Orderings_Oorder(X18511) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18511),X18510),X18509))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18511),X18510),X18509))
        | ~ class_Orderings_Oorder(X18511) )
      & ( X18510 != X18509
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18511),X18510),X18509))
        | ~ class_Orderings_Oorder(X18511) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).

fof(i_0_9954,plain,
    ! [X18503,X18504,X18505] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18505),X18504),X18503))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18505),X18504),X18503))
        | ~ class_Orderings_Oorder(X18505) )
      & ( X18504 != X18503
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18505),X18504),X18503))
        | ~ class_Orderings_Oorder(X18505) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18505),X18504),X18503))
        | X18504 = X18503
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18505),X18504),X18503))
        | ~ class_Orderings_Oorder(X18505) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).

fof(i_0_9955,plain,
    ! [X18518,X18519,X18520] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18520),X18519),X18518))
        | X18519 = X18518
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18520),X18519),X18518))
        | ~ class_Orderings_Olinorder(X18520) )
      & ( X18519 != X18518
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18520),X18519),X18518))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18520),X18519),X18518))
        | ~ class_Orderings_Olinorder(X18520) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6004])])]) ).

fof(i_0_9956,plain,
    ! [X18524,X18525,X18526] :
      ( ~ class_Orderings_Oorder(X18526)
      | X18525 = X18524
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18526),X18524),X18525))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18526),X18524),X18525)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).

fof(i_0_9957,plain,
    ! [X24044,X24045,X24046] :
      ( ~ class_Int_Onumber__ring(X24046)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24046),hAPP(c_Int_Onumber__class_Onumber__of(X24046),X24045)),hAPP(c_Int_Onumber__class_Onumber__of(X24046),X24044)) = hAPP(c_Int_Onumber__class_Onumber__of(X24046),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24045),X24044)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__eq])]) ).

fof(i_0_9958,plain,
    ! [X24054,X24055,X24056] :
      ( ~ class_Int_Onumber__ring(X24056)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24056),hAPP(c_Int_Onumber__class_Onumber__of(X24056),X24055)),hAPP(c_Int_Onumber__class_Onumber__of(X24056),X24054)) = hAPP(c_Int_Onumber__class_Onumber__of(X24056),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24055),X24054)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I32_J])]) ).

fof(i_0_9959,plain,
    ! [X25181,X25182,X25183] :
      ( ~ class_Rings_Osemiring__1(X25183)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25183),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25182),X25181)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25183),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25183),X25182)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25183),X25181)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__add])]) ).

fof(i_0_9960,plain,
    ! [X25184,X25185,X25186] :
      ( ~ class_Rings_Osemiring__1(X25186)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25186),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25185),X25184)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25186),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25186),X25185)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25186),X25184)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__mult])]) ).

fof(i_0_9961,plain,
    ! [X25021,X25022,X25023] :
      ( ~ class_Rings_Oring__1(X25023)
      | hAPP(c_Int_Oring__1__class_Oof__int(X25023),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25022),X25021)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25023),hAPP(c_Int_Oring__1__class_Oof__int(X25023),X25022)),hAPP(c_Int_Oring__1__class_Oof__int(X25023),X25021)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__add])]) ).

fof(i_0_9962,plain,
    ! [X25026,X25027,X25028] :
      ( ~ class_Rings_Oring__1(X25028)
      | hAPP(c_Int_Oring__1__class_Oof__int(X25028),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25027),X25026)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25028),hAPP(c_Int_Oring__1__class_Oof__int(X25028),X25027)),hAPP(c_Int_Oring__1__class_Oof__int(X25028),X25026)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__mult])]) ).

fof(i_0_9963,plain,
    ! [X25030,X25031,X25032] :
      ( ~ class_Rings_Oring__1(X25032)
      | hAPP(c_Int_Oring__1__class_Oof__int(X25032),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25031),X25030)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25032),hAPP(c_Int_Oring__1__class_Oof__int(X25032),X25031)),hAPP(c_Int_Oring__1__class_Oof__int(X25032),X25030)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__diff])]) ).

fof(i_0_9964,plain,
    ! [X24047,X24048,X24049] :
      ( ~ class_Int_Onumber__ring(X24049)
      | hAPP(c_Int_Onumber__class_Onumber__of(X24049),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24048),X24047)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24049),hAPP(c_Int_Onumber__class_Onumber__of(X24049),X24048)),hAPP(c_Int_Onumber__class_Onumber__of(X24049),X24047)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__add])]) ).

fof(i_0_9965,plain,
    ! [X24057,X24058,X24059] :
      ( ~ class_Int_Onumber__ring(X24059)
      | hAPP(c_Int_Onumber__class_Onumber__of(X24059),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24058),X24057)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24059),hAPP(c_Int_Onumber__class_Onumber__of(X24059),X24058)),hAPP(c_Int_Onumber__class_Onumber__of(X24059),X24057)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__mult])]) ).

fof(i_0_9966,plain,
    ! [X24060,X24061,X24062] :
      ( ~ class_Int_Onumber__ring(X24062)
      | hAPP(c_Int_Onumber__class_Onumber__of(X24062),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24061),X24060)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24062),hAPP(c_Int_Onumber__class_Onumber__of(X24062),X24061)),hAPP(c_Int_Onumber__class_Onumber__of(X24062),X24060)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__diff])]) ).

fof(i_0_9967,plain,
    ! [X31372,X31373,X31374] : c_Enum_Oproduct(X31374,X31373,c_List_Olist_ONil(X31374),X31372) = c_List_Olist_ONil(tc_prod(X31374,X31373)),
    inference(variable_rename,[status(thm)],[fact_product_Osimps_I1_J]) ).

fof(i_0_9968,plain,
    ! [X25060,X25061] :
      ( ~ class_Fields_Ofield__inverse__zero(X25061)
      | ~ class_Int_Onumber__ring(X25061)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25061),hAPP(c_Int_Onumber__class_Onumber__of(X25061),c_Int_OMin)),X25060) = hAPP(c_Groups_Ouminus__class_Ouminus(X25061),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25061),c_Groups_Oone__class_Oone(X25061)),X25060)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus1__divide])]) ).

fof(i_0_9969,plain,
    ! [X26437,X26438,X26439] :
      ( ~ class_Groups_Ocomm__monoid__add(X26439)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26438,X26439),hAPP(c_COMBK(X26439,X26438),c_Groups_Ozero__class_Ozero(X26439))),X26437) = c_Groups_Ozero__class_Ozero(X26439) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__0])]) ).

fof(i_0_9970,plain,
    ! [X23007,X23008,X23009] :
      ( ~ class_Groups_Ocomm__monoid__mult(X23009)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23008,X23009),hAPP(c_COMBK(X23009,X23008),c_Groups_Oone__class_Oone(X23009))),X23007) = c_Groups_Oone__class_Oone(X23009) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__1])]) ).

fof(i_0_9971,plain,
    ! [X26259,X26260] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26260),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26259) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X26260,X26259),
    inference(variable_rename,[status(thm)],[fact_atLeastPlusOneLessThan__greaterThanLessThan__int]) ).

fof(i_0_9972,plain,
    ! [X18530,X18531,X18532] :
      ( ~ class_Orderings_Opreorder(X18532)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18532),X18531),X18530))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18532),X18531),X18530)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).

fof(i_0_9973,plain,
    ! [X33945,X33946,X33947] :
      ( X33947 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(c_List_Otl(X33946),c_List_Oreplicate(X33946,X33947,X33945)) = c_List_Oreplicate(X33946,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33947),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X33945) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tl__replicate])]) ).

fof(i_0_9974,plain,
    ! [X23748,X23749] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X23749),X23748)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X23749),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23748)),
    inference(variable_rename,[status(thm)],[fact_negateSnd__eq]) ).

fof(i_0_9975,plain,
    ! [X27142,X27143] :
      ( ~ class_Int_Onumber__ring(X27143)
      | ~ class_Rings_Olinordered__idom(X27143)
      | hAPP(c_Groups_Oabs__class_Oabs(X27143),hAPP(hAPP(c_Power_Opower__class_Opower(X27143),hAPP(c_Int_Onumber__class_Onumber__of(X27143),c_Int_OMin)),X27142)) = c_Groups_Oone__class_Oone(X27143) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power__minus__one])]) ).

fof(i_0_9976,plain,
    ! [X26157,X26158,X26159] :
      ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26159,X26158),X26157) != c_Orderings_Obot__class_Obot(tc_fun(X26159,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26159),X26158),X26157))
        | ~ class_Orderings_Oorder(X26159) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26159),X26158),X26157))
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26159,X26158),X26157) = c_Orderings_Obot__class_Obot(tc_fun(X26159,tc_HOL_Obool))
        | ~ class_Orderings_Oorder(X26159) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6005])])]) ).

fof(i_0_9977,plain,
    ! [X26160,X26161,X26162] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X26162,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26162,X26161),X26160)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26162),X26161),X26160))
        | ~ class_Orderings_Oorder(X26162) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26162),X26161),X26160))
        | c_Orderings_Obot__class_Obot(tc_fun(X26162,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26162,X26161),X26160)
        | ~ class_Orderings_Oorder(X26162) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6006])])]) ).

cnf(i_0_9978,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_6007]) ).

fof(i_0_9979,plain,
    ! [X25508,X25509] :
      ( ~ c_Nat__Transfer_Onat__set(X25509)
      | ~ c_Nat__Transfer_Onat__set(X25508)
      | c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X25509),X25508)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J])]) ).

fof(i_0_9980,plain,
    ! [X25506,X25507] :
      ( ~ c_Nat__Transfer_Onat__set(X25507)
      | ~ c_Nat__Transfer_Onat__set(X25506)
      | c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X25507),X25506)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J])]) ).

fof(i_0_9981,plain,
    ! [X25146,X25147,X25149,X25150,X25151] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25147),X25146))
        | X25146 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25147),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk154_2(X25146,X25147))) )
      & ( X25149 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25150),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25151))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25150),X25149)) ) ),
    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_9982,plain,
    ! [X34024,X34025,X34026,X34027,X34028] : hAPP(hAPP(c_List_Omap(X34028,X34027),X34026),c_List_Oreplicate(X34028,X34025,X34024)) = c_List_Oreplicate(X34027,X34025,hAPP(X34026,X34024)),
    inference(variable_rename,[status(thm)],[fact_map__replicate]) ).

fof(i_0_9983,plain,
    ! [X32585,X32586,X32587,X32588] : hAPP(c_List_Ofilter(X32588,X32587),c_List_Oremove1(X32588,X32586,X32585)) = c_List_Oremove1(X32588,X32586,hAPP(c_List_Ofilter(X32588,X32587),X32585)),
    inference(variable_rename,[status(thm)],[fact_filter__remove1]) ).

fof(i_0_9984,plain,
    ! [X32218,X32219,X32220,X32221] :
      ( ( X32218 != c_List_Olist_ONil(X32221)
        | hAPP(hAPP(c_List_Oappend(X32221),X32220),hAPP(hAPP(c_List_Olist_OCons(X32221),X32219),c_List_Olist_ONil(X32221))) != X32218 )
      & ( c_List_Obutlast(X32221,X32218) = X32220
        | hAPP(hAPP(c_List_Oappend(X32221),X32220),hAPP(hAPP(c_List_Olist_OCons(X32221),X32219),c_List_Olist_ONil(X32221))) != X32218 )
      & ( c_List_Olast(X32221,X32218) = X32219
        | hAPP(hAPP(c_List_Oappend(X32221),X32220),hAPP(hAPP(c_List_Olist_OCons(X32221),X32219),c_List_Olist_ONil(X32221))) != X32218 )
      & ( X32218 = c_List_Olist_ONil(X32221)
        | c_List_Obutlast(X32221,X32218) != X32220
        | c_List_Olast(X32221,X32218) != X32219
        | hAPP(hAPP(c_List_Oappend(X32221),X32220),hAPP(hAPP(c_List_Olist_OCons(X32221),X32219),c_List_Olist_ONil(X32221))) = X32218 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__eq__iff__butlast])])]) ).

fof(i_0_9985,plain,
    ! [X26042] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26042),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | X26042 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk184_1(X26042)))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negD])])]) ).

fof(i_0_9986,plain,
    ! [X25665,X25666] :
      ( ~ class_Rings_Osemiring__1(X25666)
      | hBOOL(hAPP(hAPP(c_member(X25666),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25666),X25665)),c_Nat_Osemiring__1__class_ONats(X25666))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__in__Nats])]) ).

fof(i_0_9987,plain,
    ! [X25202,X25203] :
      ( ~ class_Rings_Oring__1(X25203)
      | hBOOL(hAPP(hAPP(c_member(X25203),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25203),X25202)),c_Int_Oring__1__class_OInts(X25203))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__of__nat])]) ).

fof(i_0_9988,plain,
    ! [X25036,X25037] :
      ( ~ class_Rings_Oring__1(X25037)
      | hBOOL(hAPP(hAPP(c_member(X25037),hAPP(c_Int_Oring__1__class_Oof__int(X25037),X25036)),c_Int_Oring__1__class_OInts(X25037))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__of__int])]) ).

fof(i_0_9989,plain,
    ! [X24067,X24068] :
      ( ~ class_Int_Onumber__ring(X24068)
      | hBOOL(hAPP(hAPP(c_member(X24068),hAPP(c_Int_Onumber__class_Onumber__of(X24068),X24067)),c_Int_Oring__1__class_OInts(X24068))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__number__of])]) ).

fof(i_0_9990,plain,
    ! [X22529] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22529))
      | hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22529),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X22529 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__1])]) ).

fof(i_0_9991,plain,
    ! [X22380] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22380))
      | X22380 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22380),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_9992,plain,
    ! [X31291] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X31291)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_nat__of]) ).

fof(i_0_9993,plain,
    ! [X23411,X23412,X23413] :
      ( ~ class_Divides_Osemiring__div(X23413)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23413),c_Divides_Odiv__class_Omod(X23413,X23412,X23411)),X23411) = c_Groups_Ozero__class_Ozero(X23413) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__trivial])]) ).

fof(i_0_9994,plain,
    ! [X25071] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X25071) = 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),X25071),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[fact_negDivAlg__minus1]) ).

fof(i_0_9995,plain,
    ! [X34062,X34063,X34064] : hAPP(c_List_Oset(X34064),c_List_Oreplicate(X34064,hAPP(c_Nat_OSuc,X34063),X34062)) = hAPP(hAPP(c_Set_Oinsert(X34064),X34062),c_Orderings_Obot__class_Obot(tc_fun(X34064,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_set__replicate__Suc]) ).

fof(i_0_9996,plain,
    ! [X26199,X26200] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26200))
      | c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X26200,X26199)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__function__closures])]) ).

fof(i_0_9997,plain,
    ! [X34166,X34167,X34168] : c_Lazy__Sequence_Ohb__map(X34168,X34167,X34166,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(X34168))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(X34167)),
    inference(variable_rename,[status(thm)],[fact_hb__map_Osimps_I1_J]) ).

fof(i_0_9998,plain,
    ! [X25941,X25942] :
      ( ~ class_Orderings_Olinorder(X25942)
      | c_Big__Operators_Olattice_OSup__fin(X25942,c_Orderings_Oord__class_Omax(X25942),hAPP(hAPP(c_Set_Oinsert(X25942),X25941),c_Orderings_Obot__class_Obot(tc_fun(X25942,tc_HOL_Obool)))) = X25941 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osingleton])]) ).

fof(i_0_9999,plain,
    ! [X25653,X25654] :
      ( ~ class_Orderings_Olinorder(X25654)
      | c_Big__Operators_Olattice_OInf__fin(X25654,c_Orderings_Oord__class_Omin(X25654),hAPP(hAPP(c_Set_Oinsert(X25654),X25653),c_Orderings_Obot__class_Obot(tc_fun(X25654,tc_HOL_Obool)))) = X25653 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osingleton])]) ).

fof(i_0_10000,plain,
    ! [X22847] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X22847))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22847)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22847))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X22847)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less])]) ).

fof(i_0_10001,plain,
    ! [X18074,X18075] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18075,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X18075,tc_HOL_Obool))),X18074) = c_Orderings_Obot__class_Obot(tc_fun(X18075,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Int__empty__left]) ).

fof(i_0_10002,plain,
    ! [X18060,X18061] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18061,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X18061,tc_HOL_Obool))),X18060) = c_Orderings_Obot__class_Obot(tc_fun(X18061,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_empty__Diff]) ).

fof(i_0_10003,plain,
    ! [X19117,X19118] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19118,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X19118,tc_HOL_Obool))),X19117) = c_Orderings_Otop__class_Otop(tc_fun(X19118,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Un__UNIV__left]) ).

fof(i_0_10004,plain,
    ! [X27670,X27671,X27672] : hAPP(hAPP(c_Product__Type_OSigma(X27672,X27671),c_Orderings_Obot__class_Obot(tc_fun(X27672,tc_HOL_Obool))),X27670) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27672,X27671),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Sigma__empty1]) ).

fof(i_0_10005,plain,
    ! [X21740,X21741] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21741),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21741),X21740))),
    inference(variable_rename,[status(thm)],[fact_le__add1]) ).

fof(i_0_10006,plain,
    ! [X21742,X21743] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21743),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21742),X21743))),
    inference(variable_rename,[status(thm)],[fact_le__add2]) ).

fof(i_0_10007,plain,
    ! [X21013] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21013),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21013),X21013))),
    inference(variable_rename,[status(thm)],[fact_le__square]) ).

fof(i_0_10008,plain,
    ! [X24205,X24206,X24207,X24208] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X24208),X24206) = c_Groups_Ozero__class_Ozero(X24208)
        | X24207 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24208),X24205),hAPP(c_Int_Onumber__class_Onumber__of(X24208),X24206))
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24208),X24207),hAPP(c_Int_Onumber__class_Onumber__of(X24208),X24206)) != X24205
        | ~ class_Fields_Ofield__inverse__zero(X24208)
        | ~ class_Int_Onumber(X24208) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X24208),X24206) != c_Groups_Ozero__class_Ozero(X24208)
        | X24205 = c_Groups_Ozero__class_Ozero(X24208)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24208),X24207),hAPP(c_Int_Onumber__class_Onumber__of(X24208),X24206)) != X24205
        | ~ class_Fields_Ofield__inverse__zero(X24208)
        | ~ class_Int_Onumber(X24208) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X24208),X24206) = c_Groups_Ozero__class_Ozero(X24208)
        | hAPP(c_Int_Onumber__class_Onumber__of(X24208),X24206) != c_Groups_Ozero__class_Ozero(X24208)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24208),X24207),hAPP(c_Int_Onumber__class_Onumber__of(X24208),X24206)) = X24205
        | ~ class_Fields_Ofield__inverse__zero(X24208)
        | ~ class_Int_Onumber(X24208) )
      & ( X24205 != c_Groups_Ozero__class_Ozero(X24208)
        | hAPP(c_Int_Onumber__class_Onumber__of(X24208),X24206) != c_Groups_Ozero__class_Ozero(X24208)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24208),X24207),hAPP(c_Int_Onumber__class_Onumber__of(X24208),X24206)) = X24205
        | ~ class_Fields_Ofield__inverse__zero(X24208)
        | ~ class_Int_Onumber(X24208) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X24208),X24206) = c_Groups_Ozero__class_Ozero(X24208)
        | X24207 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24208),X24205),hAPP(c_Int_Onumber__class_Onumber__of(X24208),X24206))
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24208),X24207),hAPP(c_Int_Onumber__class_Onumber__of(X24208),X24206)) = X24205
        | ~ class_Fields_Ofield__inverse__zero(X24208)
        | ~ class_Int_Onumber(X24208) )
      & ( X24205 != c_Groups_Ozero__class_Ozero(X24208)
        | X24207 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24208),X24205),hAPP(c_Int_Onumber__class_Onumber__of(X24208),X24206))
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24208),X24207),hAPP(c_Int_Onumber__class_Onumber__of(X24208),X24206)) = X24205
        | ~ class_Fields_Ofield__inverse__zero(X24208)
        | ~ class_Int_Onumber(X24208) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of1])])]) ).

fof(i_0_10009,plain,
    ! [X24193,X24194,X24195,X24196] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X24196),X24193) = c_Groups_Ozero__class_Ozero(X24196)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24196),X24195),hAPP(c_Int_Onumber__class_Onumber__of(X24196),X24193)) = X24194
        | X24195 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24196),X24194),hAPP(c_Int_Onumber__class_Onumber__of(X24196),X24193))
        | ~ class_Fields_Ofield__inverse__zero(X24196)
        | ~ class_Int_Onumber(X24196) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X24196),X24193) != c_Groups_Ozero__class_Ozero(X24196)
        | X24195 = c_Groups_Ozero__class_Ozero(X24196)
        | X24195 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24196),X24194),hAPP(c_Int_Onumber__class_Onumber__of(X24196),X24193))
        | ~ class_Fields_Ofield__inverse__zero(X24196)
        | ~ class_Int_Onumber(X24196) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X24196),X24193) = c_Groups_Ozero__class_Ozero(X24196)
        | hAPP(c_Int_Onumber__class_Onumber__of(X24196),X24193) != c_Groups_Ozero__class_Ozero(X24196)
        | X24195 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24196),X24194),hAPP(c_Int_Onumber__class_Onumber__of(X24196),X24193))
        | ~ class_Fields_Ofield__inverse__zero(X24196)
        | ~ class_Int_Onumber(X24196) )
      & ( X24195 != c_Groups_Ozero__class_Ozero(X24196)
        | hAPP(c_Int_Onumber__class_Onumber__of(X24196),X24193) != c_Groups_Ozero__class_Ozero(X24196)
        | X24195 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24196),X24194),hAPP(c_Int_Onumber__class_Onumber__of(X24196),X24193))
        | ~ class_Fields_Ofield__inverse__zero(X24196)
        | ~ class_Int_Onumber(X24196) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X24196),X24193) = c_Groups_Ozero__class_Ozero(X24196)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24196),X24195),hAPP(c_Int_Onumber__class_Onumber__of(X24196),X24193)) != X24194
        | X24195 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24196),X24194),hAPP(c_Int_Onumber__class_Onumber__of(X24196),X24193))
        | ~ class_Fields_Ofield__inverse__zero(X24196)
        | ~ class_Int_Onumber(X24196) )
      & ( X24195 != c_Groups_Ozero__class_Ozero(X24196)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24196),X24195),hAPP(c_Int_Onumber__class_Onumber__of(X24196),X24193)) != X24194
        | X24195 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24196),X24194),hAPP(c_Int_Onumber__class_Onumber__of(X24196),X24193))
        | ~ class_Fields_Ofield__inverse__zero(X24196)
        | ~ class_Int_Onumber(X24196) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of1])])]) ).

fof(i_0_10010,plain,
    ! [X20981,X20982,X20983] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20982),X20983))
        | hBOOL(hAPP(hAPP(X20981,X20982),X20983))
        | X20983 = X20982
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20983),X20982)) )
      & ( ~ hBOOL(hAPP(hAPP(X20981,X20982),X20983))
        | hBOOL(hAPP(hAPP(X20981,X20982),X20983))
        | X20983 = X20982
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20983),X20982)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20982),X20983))
        | hBOOL(hAPP(hAPP(X20981,X20982),X20983))
        | ~ hBOOL(hAPP(hAPP(X20981,X20982),X20983))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20983),X20982)) )
      & ( ~ hBOOL(hAPP(hAPP(X20981,X20982),X20983))
        | hBOOL(hAPP(hAPP(X20981,X20982),X20983))
        | ~ hBOOL(hAPP(hAPP(X20981,X20982),X20983))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20983),X20982)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20982),X20983))
        | hBOOL(hAPP(hAPP(X20981,X20982),X20983))
        | X20983 = X20982
        | ~ hBOOL(hAPP(hAPP(X20981,X20982),X20983)) )
      & ( ~ hBOOL(hAPP(hAPP(X20981,X20982),X20983))
        | hBOOL(hAPP(hAPP(X20981,X20982),X20983))
        | X20983 = X20982
        | ~ hBOOL(hAPP(hAPP(X20981,X20982),X20983)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20982),X20983))
        | hBOOL(hAPP(hAPP(X20981,X20982),X20983))
        | ~ hBOOL(hAPP(hAPP(X20981,X20982),X20983))
        | ~ hBOOL(hAPP(hAPP(X20981,X20982),X20983)) )
      & ( ~ hBOOL(hAPP(hAPP(X20981,X20982),X20983))
        | hBOOL(hAPP(hAPP(X20981,X20982),X20983))
        | ~ hBOOL(hAPP(hAPP(X20981,X20982),X20983))
        | ~ hBOOL(hAPP(hAPP(X20981,X20982),X20983)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).

fof(i_0_10011,plain,
    ! [X25108] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X25108) = 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)),X25108)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J]) ).

fof(i_0_10012,plain,
    ! [X31618,X31619,X31620,X31621,X31622,X31623] :
      ( hAPP(hAPP(c_List_Oappend(X31623),X31622),X31621) != X31620
      | X31619 != hAPP(hAPP(c_List_Oappend(X31623),X31621),X31618)
      | hAPP(hAPP(c_List_Oappend(X31623),X31622),X31619) = hAPP(hAPP(c_List_Oappend(X31623),X31620),X31618) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__appendI])]) ).

fof(i_0_10013,plain,
    ! [X31640,X31641,X31642,X31643,X31644,X31645] :
      ( hAPP(hAPP(c_List_Olist_OCons(X31645),X31644),X31643) != X31642
      | X31641 != hAPP(hAPP(c_List_Oappend(X31645),X31643),X31640)
      | hAPP(hAPP(c_List_Olist_OCons(X31645),X31644),X31641) = hAPP(hAPP(c_List_Oappend(X31645),X31642),X31640) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__eq__appendI])]) ).

fof(i_0_10014,plain,
    ! [X22863,X22864,X22865] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22865),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22864),X22863)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22864),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22865),X22863)),
    inference(variable_rename,[status(thm)],[fact_zadd__left__commute]) ).

fof(i_0_10015,plain,
    ! [X21437,X21438,X21439] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21439),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21438),X21437)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21438),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21439),X21437)),
    inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).

fof(i_0_10016,plain,
    ! [X30689,X30690] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X30690),X30689) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X30690,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X30689),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[fact_atLeastLessThan__upto]) ).

fof(i_0_10017,plain,
    ! [X25866,X25867] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25867),X25866)),X25866) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X25867),X25866),
    inference(variable_rename,[status(thm)],[fact_nat__minus__add__max]) ).

fof(i_0_10018,plain,
    ! [X25893] :
      ( ~ class_Orderings_Olinorder(X25893)
      | c_Orderings_Oord_Omin(X25893,hAPP(c_COMBC(X25893,X25893,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X25893))) = c_Orderings_Oord__class_Omax(X25893) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dual__min])]) ).

fof(i_0_10019,plain,
    ! [X25505] :
      ( ~ class_Orderings_Olinorder(X25505)
      | c_Orderings_Oord_Omax(X25505,hAPP(c_COMBC(X25505,X25505,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X25505))) = c_Orderings_Oord__class_Omin(X25505) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dual__max])]) ).

fof(i_0_10020,plain,
    ! [X32035] :
      ( ~ class_Groups_Omonoid__add(X32035)
      | c_List_Omonoid__add__class_Olistsum(X32035) = c_List_Ofoldl(X32035,X32035,c_Groups_Oplus__class_Oplus(X32035),c_Groups_Ozero__class_Ozero(X32035)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__foldl])]) ).

fof(i_0_10021,plain,
    ! [X20284,X20285,X20286] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20286),X20285),c_Option_Oset(X20286,X20284)))
        | X20284 = hAPP(c_Option_Ooption_OSome(X20286),X20285) )
      & ( X20284 != hAPP(c_Option_Ooption_OSome(X20286),X20285)
        | hBOOL(hAPP(hAPP(c_member(X20286),X20285),c_Option_Oset(X20286,X20284))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_elem__set])]) ).

fof(i_0_10022,plain,
    ! [X23077,X23078,X23079] :
      ( ~ class_Divides_Osemiring__div(X23079)
      | X23078 = c_Groups_Ozero__class_Ozero(X23079)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23079),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23079),X23078),X23077)),X23078) = X23077 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__id])]) ).

fof(i_0_10023,plain,
    ! [X23074,X23075,X23076] :
      ( ~ class_Divides_Osemiring__div(X23076)
      | X23075 = c_Groups_Ozero__class_Ozero(X23076)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23076),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23076),X23074),X23075)),X23075) = X23074 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2__is__id])]) ).

fof(i_0_10024,plain,
    ! [X21855,X21856,X21857] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21856),X21857) != X21855
        | X21856 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21855),X21857)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21857),X21856)) )
      & ( X21856 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21855),X21857)
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21856),X21857) = X21855
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21857),X21856)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add])])]) ).

fof(i_0_10025,plain,
    ! [X23386,X23387] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X23387,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23386)) = 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),X23387),X23386)),
    inference(variable_rename,[status(thm)],[fact_zmod__zminus2]) ).

fof(i_0_10026,plain,
    ! [X32555,X32556,X32557] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X32557),X32556))
      | c_List_Oremove1(X32557,X32555,c_List_Oremdups(X32557,X32556)) = c_List_Oremdups(X32557,c_List_Oremove1(X32557,X32555,X32556)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remove1__remdups])]) ).

fof(i_0_10027,plain,
    ! [X19990,X19991,X19992,X19993,X19994] :
      ( hAPP(X19994,X19993) != hAPP(c_Option_Ooption_OSome(X19992),X19991)
      | hAPP(hAPP(c_Set_Oinsert(X19990),X19993),c_Map_Odom(X19990,X19992,X19994)) = c_Map_Odom(X19990,X19992,X19994) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__dom])]) ).

fof(i_0_10028,plain,
    ! [X28214,X28215] :
      ( ( c_Wellfounded_Oacyclic(X28215,X28214)
        | ~ c_Nitpick_Owf_H(X28215,X28214) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28215,X28215)),X28214))
        | c_Nitpick_Ounknown(tc_HOL_Obool)
        | ~ c_Nitpick_Owf_H(X28215,X28214) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28215,X28215)),X28214))
        | ~ c_Wellfounded_Oacyclic(X28215,X28214)
        | c_Nitpick_Owf_H(X28215,X28214) )
      & ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
        | ~ c_Wellfounded_Oacyclic(X28215,X28214)
        | c_Nitpick_Owf_H(X28215,X28214) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Owf_H__def])])]) ).

fof(i_0_10029,plain,
    ! [X28210,X28211] :
      ( ( ~ c_Wellfounded_Owf(X28211,X28210)
        | c_Wellfounded_Oacyclic(X28211,X28210)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28211,X28211)),X28210)) )
      & ( ~ c_Wellfounded_Oacyclic(X28211,X28210)
        | c_Wellfounded_Owf(X28211,X28210)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28211,X28211)),X28210)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__iff__acyclic__if__finite])])]) ).

fof(i_0_10030,plain,
    ! [X28212,X28213] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28213,X28213)),X28212))
      | ~ c_Wellfounded_Oacyclic(X28213,X28212)
      | c_Wellfounded_Owf(X28213,X28212) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__acyclic__wf])]) ).

fof(i_0_10031,plain,
    ! [X32864,X32865] : c_Fun_Oinj__on(tc_List_Olist(X32865),tc_List_Olist(X32865),c_List_Orev(X32865),X32864),
    inference(variable_rename,[status(thm)],[fact_inj__on__rev]) ).

fof(i_0_10032,negated_conjecture,
    ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_5])]) ).

fof(i_0_10033,plain,
    ! [X17160,X17161,X17162] :
      ( ~ class_Orderings_Owellorder(X17162)
      | ~ hBOOL(hAPP(X17161,X17160))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17162),c_Orderings_Oord__class_OLeast(X17162,X17161)),X17160)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Least__le])]) ).

fof(i_0_10034,plain,
    ! [X32279,X32280,X32281] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X32281),X32280))
      | hBOOL(hAPP(c_List_Odistinct(X32281),hAPP(c_List_Ofilter(X32281,X32279),X32280))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__filter])]) ).

fof(i_0_10035,plain,
    ! [X20232,X20233,X20234,X20235,X20236,X20237,X20238,X20241] :
      ( ( ~ hBOOL(hAPP(hAPP(X20232,X20234),X20235))
        | hAPP(X20232,X20234) = hAPP(X20232,X20235)
        | ~ c_Equiv__Relations_Oequivp(X20233,X20232) )
      & ( hAPP(X20232,X20236) != hAPP(X20232,X20237)
        | hBOOL(hAPP(hAPP(X20232,X20236),X20237))
        | ~ c_Equiv__Relations_Oequivp(X20233,X20232) )
      & ( ~ hBOOL(hAPP(hAPP(X20238,esk72_1(X20238)),esk73_1(X20238)))
        | hAPP(X20238,esk72_1(X20238)) != hAPP(X20238,esk73_1(X20238))
        | c_Equiv__Relations_Oequivp(X20241,X20238) )
      & ( hBOOL(hAPP(hAPP(X20238,esk72_1(X20238)),esk73_1(X20238)))
        | hAPP(X20238,esk72_1(X20238)) = hAPP(X20238,esk73_1(X20238))
        | c_Equiv__Relations_Oequivp(X20241,X20238) ) ),
    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_10036,plain,
    ! [X21611,X21612,X21613] :
      ( ~ class_Groups_Ogroup__add(X21613)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21613),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21613),X21612),X21611)),X21611) = X21612 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])]) ).

fof(i_0_10037,plain,
    ! [X21608,X21609,X21610] :
      ( ~ class_Groups_Ogroup__add(X21610)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21610),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21610),X21609),X21608)),X21608) = X21609 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])]) ).

fof(i_0_10038,plain,
    ! [X32660,X32661,X32662] :
      ( ~ class_Orderings_Olinorder(X32662)
      | c_List_Olinorder__class_Osort__key(X32661,X32662,X32660,c_List_Olist_ONil(X32661)) = c_List_Olist_ONil(X32661) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sort__key__simps_I1_J])]) ).

fof(i_0_10039,plain,
    ! [X27613,X27614,X27615] : hAPP(c_Set_Oimage(tc_prod(X27615,X27614),X27615,c_Product__Type_Ofst(X27615,X27614)),X27613) = hAPP(c_Relation_ODomain(X27615,X27614),X27613),
    inference(variable_rename,[status(thm)],[fact_fst__eq__Domain]) ).

fof(i_0_10040,plain,
    ! [X27535,X27536,X27537] : hAPP(c_Set_Oimage(tc_prod(X27537,X27536),X27536,c_Product__Type_Osnd(X27537,X27536)),X27535) = hAPP(c_Relation_ORange(X27537,X27536),X27535),
    inference(variable_rename,[status(thm)],[fact_snd__eq__Range]) ).

fof(i_0_10041,plain,
    ! [X28741,X28742,X28743] :
      ( ( ~ c_Relation_Ototal__on(X28743,X28742,hAPP(c_Relation_Oconverse(X28743,X28743),X28741))
        | c_Relation_Ototal__on(X28743,X28742,X28741) )
      & ( ~ c_Relation_Ototal__on(X28743,X28742,X28741)
        | c_Relation_Ototal__on(X28743,X28742,hAPP(c_Relation_Oconverse(X28743,X28743),X28741)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__converse])]) ).

fof(i_0_10042,plain,
    ! [X28726,X28727,X28728] :
      ( ( ~ c_Relation_Orefl__on(X28728,X28727,hAPP(c_Relation_Oconverse(X28728,X28728),X28726))
        | c_Relation_Orefl__on(X28728,X28727,X28726) )
      & ( ~ c_Relation_Orefl__on(X28728,X28727,X28726)
        | c_Relation_Orefl__on(X28728,X28727,hAPP(c_Relation_Oconverse(X28728,X28728),X28726)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__converse])]) ).

fof(i_0_10043,plain,
    ! [X25526] :
      ( ~ c_Nat__Transfer_Onat__set(X25526)
      | hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X25526) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25526)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J])]) ).

fof(i_0_10044,plain,
    ! [X25521,X25522] :
      ( ~ c_Nat__Transfer_Onat__set(X25522)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25521),X25522))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25521)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J])]) ).

fof(i_0_10045,plain,
    ! [X25510,X25511,X25512] :
      ( ( ~ c_Nat__Transfer_Onat__set(X25510)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25511),X25510))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25511)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk163_1(X25512)),X25512))
        | c_Nat__Transfer_Onat__set(X25512) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk163_1(X25512)))
        | c_Nat__Transfer_Onat__set(X25512) ) ),
    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_10046,plain,
    ! [X28131] : c_Relation_Orefl__on(X28131,c_Orderings_Obot__class_Obot(tc_fun(X28131,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28131,X28131),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_refl__on__empty]) ).

fof(i_0_10047,plain,
    ! [X26717,X26718] : hAPP(c_Finite__Set_Ocard(X26718),X26717) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26718,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X26718),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X26717),
    inference(variable_rename,[status(thm)],[fact_card__eq__setsum]) ).

fof(i_0_10048,plain,
    ! [X23733,X23734,X23735,X23736] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23736,X23735),X23734))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X23736,X23735),X23733))
      | X23734 = X23733 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__unique])]) ).

fof(i_0_10049,plain,
    ! [X20339,X20340] :
      ( ~ class_Groups_Oordered__ab__group__add(X20340)
      | c_Fun_Oinj__on(X20340,X20340,c_Groups_Ouminus__class_Ouminus(X20340),X20339) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__uminus])]) ).

fof(i_0_10050,plain,
    ! [X31310,X31311] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X31311,X31310) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X31311),hAPP(c_Code__Numeral_Onat__of,X31310))),
    inference(variable_rename,[status(thm)],[fact_mod__code__numeral__def]) ).

fof(i_0_10051,plain,
    ! [X30956,X30957,X30958] : hAPP(hAPP(c_List_Onth(X30958),hAPP(hAPP(c_List_Olist_OCons(X30958),X30957),X30956)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X30957,
    inference(variable_rename,[status(thm)],[fact_nth__Cons__0]) ).

fof(i_0_10052,plain,
    ! [X17446,X17447,X17448,X17449] :
      ( ( hAPP(c_Set_Oimage(X17449,X17448,X17447),X17446) != c_Orderings_Obot__class_Obot(tc_fun(X17448,tc_HOL_Obool))
        | X17446 = c_Orderings_Obot__class_Obot(tc_fun(X17449,tc_HOL_Obool)) )
      & ( X17446 != c_Orderings_Obot__class_Obot(tc_fun(X17449,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(X17449,X17448,X17447),X17446) = c_Orderings_Obot__class_Obot(tc_fun(X17448,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__is__empty])]) ).

fof(i_0_10053,plain,
    ! [X17453,X17454,X17455,X17456] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X17456,tc_HOL_Obool)) != hAPP(c_Set_Oimage(X17455,X17456,X17454),X17453)
        | X17453 = c_Orderings_Obot__class_Obot(tc_fun(X17455,tc_HOL_Obool)) )
      & ( X17453 != c_Orderings_Obot__class_Obot(tc_fun(X17455,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(X17456,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X17455,X17456,X17454),X17453) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__is__image])]) ).

fof(i_0_10054,plain,
    ! [X20191,X20192] : c_Fun_Oinj__on(X20192,tc_Option_Ooption(X20192),c_Option_Ooption_OSome(X20192),X20191),
    inference(variable_rename,[status(thm)],[fact_inj__Some]) ).

fof(i_0_10055,plain,
    ! [X31379,X31380] : c_List_Olistrelp(X31380,X31379,c_List_Olist_ONil(X31380),c_List_Olist_ONil(X31380)),
    inference(variable_rename,[status(thm)],[fact_listrelp_ONil]) ).

fof(i_0_10056,plain,
    ! [X31377,X31378] : c_List_Olistrelp(X31378,X31377,c_List_Olist_ONil(X31378),c_List_Olist_ONil(X31378)),
    inference(variable_rename,[status(thm)],[fact_listrelp_Oequations_I1_J]) ).

fof(i_0_10057,plain,
    ! [X31891,X31892,X31893,X31894] :
      ( X31894 = c_List_Olist_ONil(X31893)
      | hAPP(c_List_Ohd(X31892),hAPP(hAPP(c_List_Omap(X31893,X31892),X31891),X31894)) = hAPP(X31891,hAPP(c_List_Ohd(X31893),X31894)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__map])]) ).

fof(i_0_10058,plain,
    ! [X25434,X25435,X25436] :
      ( ~ class_Rings_Osemiring__1(X25436)
      | c_Nat_Osemiring__1__class_Oof__nat__aux(X25436,X25435,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X25434) = X25434 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I1_J])]) ).

fof(i_0_10059,plain,
    ! [X26166,X26167,X26168,X26169] :
      ( ( X26168 = X26167
        | c_SetInterval_Oord__class_OatLeastAtMost(X26169,X26168,X26167) != hAPP(hAPP(c_Set_Oinsert(X26169),X26166),c_Orderings_Obot__class_Obot(tc_fun(X26169,tc_HOL_Obool)))
        | ~ class_Orderings_Oorder(X26169) )
      & ( X26167 = X26166
        | c_SetInterval_Oord__class_OatLeastAtMost(X26169,X26168,X26167) != hAPP(hAPP(c_Set_Oinsert(X26169),X26166),c_Orderings_Obot__class_Obot(tc_fun(X26169,tc_HOL_Obool)))
        | ~ class_Orderings_Oorder(X26169) )
      & ( X26168 != X26167
        | X26167 != X26166
        | c_SetInterval_Oord__class_OatLeastAtMost(X26169,X26168,X26167) = hAPP(hAPP(c_Set_Oinsert(X26169),X26166),c_Orderings_Obot__class_Obot(tc_fun(X26169,tc_HOL_Obool)))
        | ~ class_Orderings_Oorder(X26169) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton__iff])])]) ).

fof(i_0_10060,plain,
    ! [X33828,X33829,X33830,X33831,X33832] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X33832),X33831),X33830),X33829),X33828) = c_New__DSequence_Oneg__single(X33832,X33831),
    inference(variable_rename,[status(thm)],[fact_neg__single__def]) ).

fof(i_0_10061,plain,
    ! [X33791,X33792,X33793,X33794,X33795] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X33795),X33794),X33793),X33792),X33791) = c_New__DSequence_Opos__single(X33795,X33794),
    inference(variable_rename,[status(thm)],[fact_pos__single__def]) ).

fof(i_0_10062,plain,
    ! [X27051,X27052,X27053] :
      ( ~ class_Rings_Olinordered__idom(X27053)
      | hAPP(c_Groups_Oabs__class_Oabs(X27053),hAPP(hAPP(c_Power_Opower__class_Opower(X27053),X27052),X27051)) = hAPP(hAPP(c_Power_Opower__class_Opower(X27053),hAPP(c_Groups_Oabs__class_Oabs(X27053),X27052)),X27051) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__abs])]) ).

fof(i_0_10063,plain,
    ! [X24141,X24142,X24143] :
      ( ~ class_Rings_Odivision__ring(X24143)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X24143),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24143),X24142),X24141)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24143),hAPP(c_Groups_Ouminus__class_Ouminus(X24143),X24142)),X24141) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__left])]) ).

fof(i_0_10064,plain,
    ! [X20810,X20811,X20812] :
      ( ~ class_Rings_Oring(X20812)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X20812),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20812),X20811),X20810)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20812),hAPP(c_Groups_Ouminus__class_Ouminus(X20812),X20811)),X20810) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__left])]) ).

fof(i_0_10065,plain,
    ! [X22808,X22809,X22810,X22811] : hAPP(hAPP(c_Power_Opower_Opower(X22811,X22810,X22809),X22808),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X22810,
    inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__0]) ).

fof(i_0_10066,plain,
    ! [X33367,X33368,X33369] : c_List_Omaps(X33369,X33368,X33367,c_List_Olist_ONil(X33369)) = c_List_Olist_ONil(X33368),
    inference(variable_rename,[status(thm)],[fact_maps__simps_I2_J]) ).

fof(i_0_10067,plain,
    ! [X32337,X32338,X32339] : c_List_Omap__filter(X32339,X32338,X32337,c_List_Olist_ONil(X32339)) = c_List_Olist_ONil(X32338),
    inference(variable_rename,[status(thm)],[fact_map__filter__simps_I2_J]) ).

cnf(i_0_10068,plain,
    ( X1 = X2
    | c_Code__Numeral_OSuc__code__numeral(X1) != c_Code__Numeral_OSuc__code__numeral(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6008]) ).

fof(i_0_10069,plain,
    ! [X26146,X26147,X26148] :
      ( ~ class_Orderings_Oorder(X26148)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26148),X26147),X26146))
      | c_SetInterval_Oord__class_OatLeastAtMost(X26148,X26146,X26147) = c_Orderings_Obot__class_Obot(tc_fun(X26148,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty])]) ).

fof(i_0_10070,plain,
    ! [X25631,X25632,X25633] :
      ( ~ class_Orderings_Oorder(X25633)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25633),X25632),X25631))
      | c_SetInterval_Oord__class_OgreaterThanAtMost(X25633,X25631,X25632) = c_Orderings_Obot__class_Obot(tc_fun(X25633,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty])]) ).

fof(i_0_10071,plain,
    ! [X25568,X25569,X25570] :
      ( ~ class_Orderings_Oorder(X25570)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25570),X25569),X25568))
      | c_SetInterval_Oord__class_OgreaterThanLessThan(X25570,X25568,X25569) = c_Orderings_Obot__class_Obot(tc_fun(X25570,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThanLessThan__empty])]) ).

fof(i_0_10072,plain,
    ! [X31922,X31923,X31924] :
      ( X31924 = c_List_Olist_ONil(X31923)
      | hAPP(c_List_Otl(X31923),hAPP(hAPP(c_List_Oappend(X31923),X31924),X31922)) = hAPP(hAPP(c_List_Oappend(X31923),hAPP(c_List_Otl(X31923),X31924)),X31922) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tl__append2])]) ).

fof(i_0_10073,plain,
    ! [X23438,X23439] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23439,X23438)),X23438) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zmod__zdiv__trivial]) ).

fof(i_0_10074,plain,
    ! [X23929,X23930,X23931,X23932] :
      ( ( hAPP(c_Product__Type_Ofst(X23930,X23929),X23932) = hAPP(c_Product__Type_Ofst(X23930,X23929),X23931)
        | X23932 != X23931 )
      & ( hAPP(c_Product__Type_Osnd(X23930,X23929),X23932) = hAPP(c_Product__Type_Osnd(X23930,X23929),X23931)
        | X23932 != X23931 )
      & ( hAPP(c_Product__Type_Ofst(X23930,X23929),X23932) != hAPP(c_Product__Type_Ofst(X23930,X23929),X23931)
        | hAPP(c_Product__Type_Osnd(X23930,X23929),X23932) != hAPP(c_Product__Type_Osnd(X23930,X23929),X23931)
        | X23932 = X23931 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__fst__snd__eq])])]) ).

fof(i_0_10075,plain,
    ! [X23925,X23926,X23927,X23928] :
      ( hAPP(c_Product__Type_Ofst(X23928,X23927),X23926) != hAPP(c_Product__Type_Ofst(X23928,X23927),X23925)
      | hAPP(c_Product__Type_Osnd(X23928,X23927),X23926) != hAPP(c_Product__Type_Osnd(X23928,X23927),X23925)
      | X23926 = X23925 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_prod__eqI])]) ).

fof(i_0_10076,plain,
    ! [X27904,X27905] : c_Fun_Oinj__on(X27905,X27905,c_Fun_Oid(X27905),X27904),
    inference(variable_rename,[status(thm)],[fact_inj__on__id]) ).

fof(i_0_10077,plain,
    ! [X18699,X18700] : c_Fun_Oinj__on(X18700,X18700,c_COMBI(X18700),X18699),
    inference(variable_rename,[status(thm)],[fact_inj__on__id2]) ).

fof(i_0_10078,plain,
    ! [X26979,X26980,X26981] :
      ( ~ class_Rings_Olinordered__idom(X26981)
      | c_Groups_Osgn__class_Osgn(X26981,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26981),X26980),X26979)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26981),c_Groups_Osgn__class_Osgn(X26981,X26980)),c_Groups_Osgn__class_Osgn(X26981,X26979)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__times])]) ).

fof(i_0_10079,plain,
    ! [X32797,X32798,X32799] :
      ( ~ class_Orderings_Olinorder(X32799)
      | ~ c_List_Olinorder__class_Osorted(X32799,X32798)
      | ~ hBOOL(hAPP(c_List_Odistinct(X32799),X32798))
      | ~ c_List_Olinorder__class_Osorted(X32799,X32797)
      | ~ hBOOL(hAPP(c_List_Odistinct(X32799),X32797))
      | hAPP(c_List_Oset(X32799),X32798) != hAPP(c_List_Oset(X32799),X32797)
      | X32798 = X32797 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__distinct__set__unique])]) ).

fof(i_0_10080,plain,
    ! [X31813,X31814,X31815,X31816] : hAPP(hAPP(c_List_Odrop(X31816),hAPP(c_Nat_OSuc,X31815)),hAPP(hAPP(c_List_Olist_OCons(X31816),X31814),X31813)) = hAPP(hAPP(c_List_Odrop(X31816),X31815),X31813),
    inference(variable_rename,[status(thm)],[fact_drop__Suc__Cons]) ).

cnf(i_0_10081,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_10082,plain,
    ! [X27009,X27010,X27011] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27011)
      | hAPP(c_Groups_Oabs__class_Oabs(X27011),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27011),X27010),X27009)) = hAPP(c_Groups_Oabs__class_Oabs(X27011),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27011),X27009),X27010)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__commute])]) ).

cnf(i_0_10083,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_6009]) ).

fof(i_0_10084,plain,
    ! [X34206,X34207,X34208] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X34208,X34207,X34206,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X34207,
    inference(variable_rename,[status(thm)],[fact_code__numeral_Orecs_I1_J]) ).

fof(i_0_10085,plain,
    ! [X27150,X27151,X27152] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X27152,X27151,X27150,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X27151,
    inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I4_J]) ).

fof(i_0_10086,plain,
    ! [X24738,X24739,X24740] : c_Nat_Onat_Onat__case(X24740,X24739,X24738,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X24739,
    inference(variable_rename,[status(thm)],[fact_nat__case__0]) ).

fof(i_0_10087,plain,
    ! [X25194,X25195] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25195)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25194)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X25195),X25194)),
    inference(variable_rename,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I1_J]) ).

fof(i_0_10088,plain,
    ! [X25144,X25145] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25145)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25144)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25145),X25144)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J]) ).

fof(i_0_10089,plain,
    ! [X25139,X25140] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25140)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25139)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25140),X25139)),
    inference(variable_rename,[status(thm)],[fact_zadd__int]) ).

fof(i_0_10090,plain,
    ! [X24003,X24004] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24004)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24003)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24004),X24003)),
    inference(variable_rename,[status(thm)],[fact_plus__numeral__code_I9_J]) ).

fof(i_0_10091,plain,
    ! [X25166,X25167] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25167)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25166)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25167),X25166)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J]) ).

fof(i_0_10092,plain,
    ! [X25164,X25165] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25165)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25164)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25165),X25164)),
    inference(variable_rename,[status(thm)],[fact_zmult__int]) ).

fof(i_0_10093,plain,
    ! [X24012,X24013] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24013)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24012)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24013),X24012)),
    inference(variable_rename,[status(thm)],[fact_times__numeral__code_I5_J]) ).

fof(i_0_10094,plain,
    ! [X25192,X25193] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X25193),X25192)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25193)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25192)),
    inference(variable_rename,[status(thm)],[fact_zdiv__int]) ).

fof(i_0_10095,plain,
    ! [X25162,X25163] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25163),X25162)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25163)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25162)),
    inference(variable_rename,[status(thm)],[fact_int__mult]) ).

cnf(i_0_10096,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_6010]) ).

fof(i_0_10097,plain,
    ! [X22856,X22857] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22857),X22856)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22857)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22856)),
    inference(variable_rename,[status(thm)],[fact_zminus__zadd__distrib]) ).

fof(i_0_10098,plain,
    ! [X34039,X34040,X34041,X34042] :
      ( ( ~ hBOOL(hAPP(X34042,X34041))
        | hAPP(c_List_Ofilter(X34040,X34042),c_List_Oreplicate(X34040,X34039,X34041)) = c_List_Oreplicate(X34040,X34039,X34041) )
      & ( hBOOL(hAPP(X34042,X34041))
        | hAPP(c_List_Ofilter(X34040,X34042),c_List_Oreplicate(X34040,X34039,X34041)) = c_List_Olist_ONil(X34040) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6011])]) ).

fof(i_0_10099,plain,
    ! [X19121,X19122] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19122,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X19122,tc_HOL_Obool))),X19121) = X19121,
    inference(variable_rename,[status(thm)],[fact_Int__UNIV__left]) ).

fof(i_0_10100,plain,
    ! [X17489,X17490] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17490,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X17490,tc_HOL_Obool))),X17489) = X17489,
    inference(variable_rename,[status(thm)],[fact_Un__empty__left]) ).

fof(i_0_10101,plain,
    ! [X22803,X22804] :
      ( ( X22804 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22804),X22803) != 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)),X22804)) )
      & ( X22803 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22804),X22803) != 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)),X22804)) )
      & ( X22804 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X22803 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22804),X22803) = 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)),X22804)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff])])]) ).

cnf(i_0_10102,plain,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    inference(split_conjunct,[status(thm)],[fact_succ__Pls]) ).

fof(i_0_10103,plain,
    ! [X21199,X21200,X21201] : hAPP(c_Finite__Set_Ofold1(X21201,X21200),hAPP(hAPP(c_Set_Oinsert(X21201),X21199),c_Orderings_Obot__class_Obot(tc_fun(X21201,tc_HOL_Obool)))) = X21199,
    inference(variable_rename,[status(thm)],[fact_fold1__singleton]) ).

fof(i_0_10104,plain,
    ! [X31143,X31144,X31145,X31146] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31146)),hAPP(hAPP(c_List_Olist__update(X31146,X31145),X31144),X31143)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31146)),X31145),
    inference(variable_rename,[status(thm)],[fact_length__list__update]) ).

fof(i_0_10105,plain,
    ! [X30486,X30487,X30488,X30489] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30489)),hAPP(hAPP(c_List_Omap(X30488,X30489),X30487),X30486)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30488)),X30486),
    inference(variable_rename,[status(thm)],[fact_length__map]) ).

fof(i_0_10106,plain,
    ! [X25204,X25205,X25206] :
      ( ~ class_Rings_Osemiring__1(X25206)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25206),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X25205),X25204)) = hAPP(hAPP(c_Power_Opower__class_Opower(X25206),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25206),X25205)),X25204) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__power])]) ).

fof(i_0_10107,plain,
    ! [X25038,X25039,X25040] :
      ( ~ class_Rings_Oring__1(X25040)
      | hAPP(c_Int_Oring__1__class_Oof__int(X25040),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X25039),X25038)) = hAPP(hAPP(c_Power_Opower__class_Opower(X25040),hAPP(c_Int_Oring__1__class_Oof__int(X25040),X25039)),X25038) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__power])]) ).

fof(i_0_10108,plain,
    ! [X22854,X22855] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22855),X22854))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22855),X22854)) )
      & ( X22855 != X22854
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22855),X22854)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22855),X22854))
        | X22855 = X22854
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22855),X22854)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__le])])]) ).

fof(i_0_10109,plain,
    ! [X20949,X20950] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20950),X20949))
      | X20950 = X20949
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20950),X20949)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).

fof(i_0_10110,plain,
    ! [X20945,X20946] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20946),X20945))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20946),X20945))
        | X20946 = X20945 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20946),X20945))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20946),X20945)) )
      & ( X20946 != X20945
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20946),X20945)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).

fof(i_0_10111,plain,
    ! [X20943,X20944] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20944),X20943))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20944),X20943)) )
      & ( X20944 != X20943
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20944),X20943)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20944),X20943))
        | X20944 = X20943
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20944),X20943)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).

cnf(i_0_10112,plain,
    ( c_List_Oembed__list(c_List_Oreturn__list(X1)) = X1
    | ~ c_List_Onat__list(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6012]) ).

fof(i_0_10113,plain,
    ! [X21202,X21203,X21204,X21205] :
      ( X21205 != c_Finite__Set_Ofold1(X21204,X21203)
      | hAPP(X21205,hAPP(hAPP(c_Set_Oinsert(X21204),X21202),c_Orderings_Obot__class_Obot(tc_fun(X21204,tc_HOL_Obool)))) = X21202 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__singleton__def])]) ).

fof(i_0_10114,plain,
    ! [X31980,X31981] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31981)),hAPP(c_List_Otl(X31981),X31980)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31981)),X31980)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_length__tl]) ).

fof(i_0_10115,plain,
    ! [X18908,X18909,X18910,X18911,X18912] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X18912,X18911,X18910)
      | hAPP(hAPP(X18910,X18909),hAPP(hAPP(X18910,X18909),X18908)) = hAPP(hAPP(X18910,X18909),X18908) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__idem])]) ).

fof(i_0_10116,plain,
    ! [X25514] : 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)),X25514)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J]) ).

fof(i_0_10117,plain,
    ! [X26083,X26084] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X26084,X26083))),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastAtMost__int]) ).

fof(i_0_10118,plain,
    ! [X25629,X25630] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X25630,X25629))),
    inference(variable_rename,[status(thm)],[fact_finite__greaterThanAtMost__int]) ).

fof(i_0_10119,plain,
    ! [X25562,X25563] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X25563,X25562))),
    inference(variable_rename,[status(thm)],[fact_finite__greaterThanLessThan__int]) ).

fof(i_0_10120,plain,
    ! [X26081,X26082] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26082,X26081))),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastAtMost]) ).

fof(i_0_10121,plain,
    ! [X25627,X25628] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X25628,X25627))),
    inference(variable_rename,[status(thm)],[fact_finite__greaterThanAtMost]) ).

fof(i_0_10122,plain,
    ! [X25590,X25591] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X25591,X25590))),
    inference(variable_rename,[status(thm)],[fact_finite__greaterThanLessThan]) ).

fof(i_0_10123,plain,
    ! [X22328] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22328),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | X22328 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22328 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22328),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_10124,plain,
    ! [X21430] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X21430),
    inference(variable_rename,[status(thm)],[fact_inj__Suc]) ).

fof(i_0_10125,plain,
    ! [X20951,X20952] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20952),X20951))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20952),X20951)) )
      & ( X20952 != X20951
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20952),X20951)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).

fof(i_0_10126,plain,
    ! [X20947,X20948] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20948),X20947))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20948),X20947)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).

fof(i_0_10127,plain,
    ! [X20675,X20676] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20676),X20675))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20676),X20675)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).

fof(i_0_10128,plain,
    ! [X26154,X26155,X26156] :
      ( ~ class_Orderings_Oorder(X26156)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26156),X26155),X26154))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26156,X26154),X26155) = c_Orderings_Obot__class_Obot(tc_fun(X26156,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty])]) ).

fof(i_0_10129,plain,
    ! [X17316,X17317,X17318] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17318),X17317),hAPP(c_fequal,X17316)))
        | X17317 = X17316 )
      & ( X17317 != X17316
        | hBOOL(hAPP(hAPP(c_member(X17318),X17317),hAPP(c_fequal,X17316))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])]) ).

fof(i_0_10130,plain,
    ! [X32112,X32113,X32114,X32115] :
      ( X32115 = c_List_Olist_ONil(X32114)
      | c_List_Olast(X32113,hAPP(hAPP(c_List_Omap(X32114,X32113),X32112),X32115)) = hAPP(X32112,c_List_Olast(X32114,X32115)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__map])]) ).

cnf(i_0_10131,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_6013]) ).

fof(i_0_10132,plain,
    ! [X21623,X21624,X21625] :
      ( ~ class_Groups_Ogroup__add(X21625)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21625),hAPP(c_Groups_Ouminus__class_Ouminus(X21625),X21624)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21625),X21624),X21623)) = X21623 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__cancel])]) ).

fof(i_0_10133,plain,
    ! [X17534,X17535,X17536,X17537,X17538] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17535),X17536),X17534))
        | X17534 != c_Orderings_Obot__class_Obot(tc_fun(X17535,tc_HOL_Obool)) )
      & ( X17537 = c_Orderings_Obot__class_Obot(tc_fun(X17538,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(X17538),esk19_2(X17537,X17538)),X17537)) ) ),
    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_10134,plain,
    ! [X17540,X17541,X17543,X17544,X17545] :
      ( ( hBOOL(hAPP(hAPP(c_member(X17541),esk20_2(X17540,X17541)),X17540))
        | X17540 = c_Orderings_Obot__class_Obot(tc_fun(X17541,tc_HOL_Obool)) )
      & ( X17543 != c_Orderings_Obot__class_Obot(tc_fun(X17544,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(X17544),X17545),X17543)) ) ),
    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_6014])])])])]) ).

fof(i_0_10135,plain,
    ! [X32567,X32568,X32569] :
      ( hBOOL(hAPP(hAPP(c_member(X32569),X32568),hAPP(c_List_Oset(X32569),X32567)))
      | c_List_Oremove1(X32569,X32568,X32567) = X32567 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6015])]) ).

cnf(i_0_10136,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_6016]) ).

fof(i_0_10137,plain,
    ! [X25270,X25271] :
      ( ~ class_Rings_Oring__1(X25271)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25270))
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25271),hAPP(c_Int_Onat,X25270)) = hAPP(c_Int_Oring__1__class_Oof__int(X25271),X25270) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__nat])]) ).

fof(i_0_10138,plain,
    ! [X25189,X25190] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25190),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25189)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25190,X25189)),
    inference(variable_rename,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I2_J]) ).

fof(i_0_10139,plain,
    ! [X23388,X23389] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23389),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23388)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23389,X23388)),
    inference(variable_rename,[status(thm)],[fact_zmod__zminus__zminus]) ).

fof(i_0_10140,plain,
    ! [X25187,X25188] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25188,X25187)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25188),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25187)),
    inference(variable_rename,[status(thm)],[fact_zmod__int]) ).

fof(i_0_10141,plain,
    ! [X26968,X26969] :
      ( ( X26968 != c_Groups_Ozero__class_Ozero(X26969)
        | c_Groups_Osgn__class_Osgn(X26969,X26968) = c_Groups_Ozero__class_Ozero(X26969)
        | ~ class_Groups_Osgn__if(X26969) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26969),c_Groups_Ozero__class_Ozero(X26969)),X26968))
        | c_Groups_Osgn__class_Osgn(X26969,X26968) = c_Groups_Oone__class_Oone(X26969)
        | X26968 = c_Groups_Ozero__class_Ozero(X26969)
        | ~ class_Groups_Osgn__if(X26969) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26969),c_Groups_Ozero__class_Ozero(X26969)),X26968))
        | c_Groups_Osgn__class_Osgn(X26969,X26968) = hAPP(c_Groups_Ouminus__class_Ouminus(X26969),c_Groups_Oone__class_Oone(X26969))
        | X26968 = c_Groups_Ozero__class_Ozero(X26969)
        | ~ class_Groups_Osgn__if(X26969) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6017])])]) ).

fof(i_0_10142,plain,
    ! [X30444,X30445] :
      ( ~ class_Groups_Ocomm__monoid__add(X30445)
      | ~ hBOOL(hAPP(c_List_Odistinct(X30445),X30444))
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30445),X30444) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X30445,X30445),c_COMBI(X30445)),hAPP(c_List_Oset(X30445),X30444)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__listsum__conv__Setsum])]) ).

fof(i_0_10143,plain,
    ! [X22586,X22587,X22588] :
      ( ~ class_Rings_Ocomm__semiring__1(X22588)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22588),X22587),hAPP(hAPP(c_Power_Opower__class_Opower(X22588),X22587),X22586)) = hAPP(hAPP(c_Power_Opower__class_Opower(X22588),X22587),hAPP(c_Nat_OSuc,X22586)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J])]) ).

fof(i_0_10144,plain,
    ! [X22694,X22695,X22696] :
      ( ~ class_Power_Opower(X22696)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22696),X22695),hAPP(c_Nat_OSuc,X22694)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22696),X22695),hAPP(hAPP(c_Power_Opower__class_Opower(X22696),X22695),X22694)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc])]) ).

fof(i_0_10145,plain,
    ! [X22583,X22584,X22585] :
      ( ~ class_Rings_Ocomm__semiring__1(X22585)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22585),X22584),hAPP(c_Nat_OSuc,X22583)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22585),X22584),hAPP(hAPP(c_Power_Opower__class_Opower(X22585),X22584),X22583)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J])]) ).

fof(i_0_10146,plain,
    ! [X26945,X26946] :
      ( ~ class_Groups_Oordered__ab__group__add(X26946)
      | hAPP(c_Set_Oimage(X26946,X26946,c_Groups_Ouminus__class_Ouminus(X26946)),hAPP(c_SetInterval_Oord__class_OatLeast(X26946),X26945)) = hAPP(c_SetInterval_Oord__class_OatMost(X26946),hAPP(c_Groups_Ouminus__class_Ouminus(X26946),X26945)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeast])]) ).

fof(i_0_10147,plain,
    ! [X26894,X26895] :
      ( ~ class_Groups_Oordered__ab__group__add(X26895)
      | hAPP(c_Set_Oimage(X26895,X26895,c_Groups_Ouminus__class_Ouminus(X26895)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26895),X26894)) = hAPP(c_SetInterval_Oord__class_OlessThan(X26895),hAPP(c_Groups_Ouminus__class_Ouminus(X26895),X26894)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThan])]) ).

fof(i_0_10148,plain,
    ! [X26943,X26944] :
      ( ~ class_Groups_Oordered__ab__group__add(X26944)
      | hAPP(c_Set_Oimage(X26944,X26944,c_Groups_Ouminus__class_Ouminus(X26944)),hAPP(c_SetInterval_Oord__class_OatMost(X26944),X26943)) = hAPP(c_SetInterval_Oord__class_OatLeast(X26944),hAPP(c_Groups_Ouminus__class_Ouminus(X26944),X26943)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atMost])]) ).

fof(i_0_10149,plain,
    ! [X26892,X26893] :
      ( ~ class_Groups_Oordered__ab__group__add(X26893)
      | hAPP(c_Set_Oimage(X26893,X26893,c_Groups_Ouminus__class_Ouminus(X26893)),hAPP(c_SetInterval_Oord__class_OlessThan(X26893),X26892)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X26893),hAPP(c_Groups_Ouminus__class_Ouminus(X26893),X26892)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__lessThan])]) ).

fof(i_0_10150,plain,
    ! [X33963,X33964,X33965] : c_List_Oreplicate(X33965,hAPP(c_Nat_OSuc,X33964),X33963) = hAPP(hAPP(c_List_Olist_OCons(X33965),X33963),c_List_Oreplicate(X33965,X33964,X33963)),
    inference(variable_rename,[status(thm)],[fact_replicate__Suc]) ).

cnf(i_0_10151,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_6018]) ).

cnf(i_0_10152,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_6019]) ).

cnf(i_0_10153,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_6018]) ).

fof(i_0_10154,plain,
    ! [X23595,X23596] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23596))
        | c_SMT_Oz3mod(X23595,X23596) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X23595,X23596) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23596))
        | c_SMT_Oz3mod(X23595,X23596) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X23595,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23596)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6020])]) ).

fof(i_0_10155,plain,
    ! [X34059,X34060,X34061] :
      ( X34061 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(c_List_Oset(X34060),c_List_Oreplicate(X34060,X34061,X34059)) = hAPP(hAPP(c_Set_Oinsert(X34060),X34059),c_Orderings_Obot__class_Obot(tc_fun(X34060,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__replicate])]) ).

fof(i_0_10156,plain,
    ! [X34056,X34057,X34058] :
      ( ( X34058 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_List_Oset(X34057),c_List_Oreplicate(X34057,X34058,X34056)) = c_Orderings_Obot__class_Obot(tc_fun(X34057,tc_HOL_Obool)) )
      & ( X34058 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_List_Oset(X34057),c_List_Oreplicate(X34057,X34058,X34056)) = hAPP(hAPP(c_Set_Oinsert(X34057),X34056),c_Orderings_Obot__class_Obot(tc_fun(X34057,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__replicate__conv__if])]) ).

fof(i_0_10157,plain,
    ! [X27016,X27017] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27017)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27017),c_Groups_Ozero__class_Ozero(X27017)),X27016))
      | hAPP(c_Groups_Oabs__class_Oabs(X27017),X27016) = X27016 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__pos])]) ).

fof(i_0_10158,plain,
    ! [X27022,X27023] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27023)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27023),c_Groups_Ozero__class_Ozero(X27023)),X27022))
      | hAPP(c_Groups_Oabs__class_Oabs(X27023),X27022) = X27022 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg])]) ).

fof(i_0_10159,plain,
    ! [X27123,X27124] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27124),X27123),c_Groups_Ozero__class_Ozero(X27124)))
        | hAPP(c_Groups_Oabs__class_Oabs(X27124),X27123) = hAPP(c_Groups_Ouminus__class_Ouminus(X27124),X27123)
        | ~ class_Groups_Oabs__if(X27124) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27124),X27123),c_Groups_Ozero__class_Ozero(X27124)))
        | hAPP(c_Groups_Oabs__class_Oabs(X27124),X27123) = X27123
        | ~ class_Groups_Oabs__if(X27124) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6021])])]) ).

fof(i_0_10160,plain,
    ! [X27125,X27126] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27126)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27126),X27125),c_Groups_Ozero__class_Ozero(X27126)))
      | hAPP(c_Groups_Oabs__class_Oabs(X27126),X27125) = hAPP(c_Groups_Ouminus__class_Ouminus(X27126),X27125) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__neg])]) ).

fof(i_0_10161,plain,
    ! [X27121,X27122] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27122)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27122),X27121),c_Groups_Ozero__class_Ozero(X27122)))
      | hAPP(c_Groups_Oabs__class_Oabs(X27122),X27121) = hAPP(c_Groups_Ouminus__class_Ouminus(X27122),X27121) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonpos])]) ).

fof(i_0_10162,plain,
    ! [X26972,X26973] :
      ( ( c_Groups_Osgn__class_Osgn(X26973,X26972) != hAPP(c_Groups_Ouminus__class_Ouminus(X26973),c_Groups_Oone__class_Oone(X26973))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26973),X26972),c_Groups_Ozero__class_Ozero(X26973)))
        | ~ class_Rings_Olinordered__idom(X26973) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26973),X26972),c_Groups_Ozero__class_Ozero(X26973)))
        | c_Groups_Osgn__class_Osgn(X26973,X26972) = hAPP(c_Groups_Ouminus__class_Ouminus(X26973),c_Groups_Oone__class_Oone(X26973))
        | ~ class_Rings_Olinordered__idom(X26973) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__neg])])]) ).

fof(i_0_10163,plain,
    ! [X26970,X26971] :
      ( ~ class_Rings_Olinordered__idom(X26971)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26971),X26970),c_Groups_Ozero__class_Ozero(X26971)))
      | c_Groups_Osgn__class_Osgn(X26971,X26970) = hAPP(c_Groups_Ouminus__class_Ouminus(X26971),c_Groups_Oone__class_Oone(X26971)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__neg])]) ).

fof(i_0_10164,plain,
    ! [X20245,X20246,X20247,X20248] :
      ( ~ c_Equiv__Relations_Oequivp(X20248,X20247)
      | ~ hBOOL(hAPP(hAPP(X20247,X20246),X20245))
      | hBOOL(hAPP(hAPP(X20247,X20245),X20246)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__symp])]) ).

fof(i_0_10165,plain,
    ! [X33859,X33860,X33861,X33862] : hAPP(c_New__DSequence_Oneg__union(X33862,X33861,X33860),X33859) = c_Lazy__Sequence_Oappend(tc_Option_Ooption(X33862),hAPP(X33861,X33859),hAPP(X33860,X33859)),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Oneg__union__def]) ).

fof(i_0_10166,plain,
    ! [X32208,X32209] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32209)),c_List_Obutlast(X32209,X32208)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32209)),X32208)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_length__butlast]) ).

fof(i_0_10167,plain,
    ! [X22287] :
      ( ~ class_Rings_Olinordered__semidom(X22287)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22287),c_Groups_Oone__class_Oone(X22287)),c_Groups_Ozero__class_Ozero(X22287))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6022])]) ).

fof(i_0_10168,plain,
    ! [X22285] :
      ( ~ class_Rings_Olinordered__semidom(X22285)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22285),c_Groups_Oone__class_Oone(X22285)),c_Groups_Ozero__class_Ozero(X22285))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6023])]) ).

fof(i_0_10169,plain,
    ! [X21834,X21835] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21835),X21834))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21834),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21835),X21834)) = X21835 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6024])]) ).

fof(i_0_10170,plain,
    ! [X31321,X31322] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31322)),c_List_Olist_ONil(X31322)),c_List_Olists(X31322,X31321))),
    inference(variable_rename,[status(thm)],[fact_lists_ONil]) ).

fof(i_0_10171,plain,
    ! [X26988,X26989] :
      ( ( c_Groups_Osgn__class_Osgn(X26989,X26988) != c_Groups_Oone__class_Oone(X26989)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26989),c_Groups_Ozero__class_Ozero(X26989)),X26988))
        | ~ class_Rings_Olinordered__idom(X26989) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26989),c_Groups_Ozero__class_Ozero(X26989)),X26988))
        | c_Groups_Osgn__class_Osgn(X26989,X26988) = c_Groups_Oone__class_Oone(X26989)
        | ~ class_Rings_Olinordered__idom(X26989) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__pos])])]) ).

fof(i_0_10172,plain,
    ! [X26986,X26987] :
      ( ~ class_Rings_Olinordered__idom(X26987)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26987),c_Groups_Ozero__class_Ozero(X26987)),X26986))
      | c_Groups_Osgn__class_Osgn(X26987,X26986) = c_Groups_Oone__class_Oone(X26987) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__pos])]) ).

fof(i_0_10173,plain,
    ! [X24173,X24174,X24175] :
      ( ~ class_Rings_Odivision__ring(X24175)
      | X24174 = c_Groups_Ozero__class_Ozero(X24175)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24175),hAPP(c_Groups_Ouminus__class_Ouminus(X24175),X24173)),hAPP(c_Groups_Ouminus__class_Ouminus(X24175),X24174)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24175),X24173),X24174) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__divide])]) ).

fof(i_0_10174,plain,
    ! [X31473] : c_List_Olistset(X31473,c_List_Olist_ONil(tc_fun(X31473,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X31473)),c_List_Olist_ONil(X31473)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X31473),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_listset_Osimps_I1_J]) ).

fof(i_0_10175,plain,
    ! [X31448] : c_List_Olists(X31448,c_Orderings_Obot__class_Obot(tc_fun(X31448,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X31448)),c_List_Olist_ONil(X31448)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X31448),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_lists__empty]) ).

fof(i_0_10176,plain,
    ! [X17301,X17302,X17303] :
      ( ~ hBOOL(hAPP(X17303,X17302))
      | hBOOL(hAPP(hAPP(c_member(X17301),X17302),hAPP(c_Set_OCollect(X17301),X17303))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_CollectI])]) ).

fof(i_0_10177,plain,
    ! [X32885,X32886] :
      ( ( ~ hBOOL(hAPP(c_List_Odistinct(X32886),hAPP(c_List_Orev(X32886),X32885)))
        | hBOOL(hAPP(c_List_Odistinct(X32886),X32885)) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X32886),X32885))
        | hBOOL(hAPP(c_List_Odistinct(X32886),hAPP(c_List_Orev(X32886),X32885))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__rev])]) ).

fof(i_0_10178,plain,
    ! [X31775,X31776] :
      ( ( ~ hBOOL(hAPP(c_List_Odistinct(X31776),hAPP(c_List_Orotate1(X31776),X31775)))
        | hBOOL(hAPP(c_List_Odistinct(X31776),X31775)) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X31776),X31775))
        | hBOOL(hAPP(c_List_Odistinct(X31776),hAPP(c_List_Orotate1(X31776),X31775))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct1__rotate])]) ).

fof(i_0_10179,plain,
    ! [X18969,X18970] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X18970),c_Orderings_Obot__class_Obot(tc_fun(X18970,tc_HOL_Obool))),X18969) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X18970,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_quotient__empty]) ).

fof(i_0_10180,plain,
    ! [X27933,X27934] : hAPP(c_Product__Type_Oprod_Oprod__case(X27934,X27933,tc_prod(X27934,X27933)),c_Product__Type_OPair(X27934,X27933)) = c_Fun_Oid(tc_prod(X27934,X27933)),
    inference(variable_rename,[status(thm)],[fact_split__Pair]) ).

fof(i_0_10181,plain,
    ! [X25818,X25819,X25820] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25820),X25819),X25818))
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25820),X25819),X25818) = X25818
        | ~ class_Orderings_Olinorder(X25820) )
      & ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X25820),X25819),X25818) != X25818
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25820),X25819),X25818))
        | ~ class_Orderings_Olinorder(X25820) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__sup])])]) ).

fof(i_0_10182,plain,
    ! [X25803,X25804,X25805] :
      ( ~ class_Orderings_Olinorder(X25805)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25805),X25804),X25803))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25805),X25804),X25803) = X25803 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__absorb2])]) ).

fof(i_0_10183,plain,
    ! [X25800,X25801,X25802] :
      ( ~ class_Orderings_Olinorder(X25802)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25802),X25801),X25800))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25802),X25800),X25801) = X25800 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__absorb1])]) ).

fof(i_0_10184,plain,
    ! [X25411,X25412,X25413] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25413),X25412),X25411))
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25413),X25412),X25411) = X25412
        | ~ class_Orderings_Olinorder(X25413) )
      & ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X25413),X25412),X25411) != X25412
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25413),X25412),X25411))
        | ~ class_Orderings_Olinorder(X25413) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__inf])])]) ).

fof(i_0_10185,plain,
    ! [X25396,X25397,X25398] :
      ( ~ class_Orderings_Olinorder(X25398)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25398),X25397),X25396))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25398),X25397),X25396) = X25397 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__absorb1])]) ).

fof(i_0_10186,plain,
    ! [X25393,X25394,X25395] :
      ( ~ class_Orderings_Olinorder(X25395)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25395),X25394),X25393))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25395),X25393),X25394) = X25394 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__absorb2])]) ).

fof(i_0_10187,plain,
    ! [X17991,X17992,X17993] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17993),X17992),X17991))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17993),X17992),X17991) = X17992
        | ~ class_Lattices_Osemilattice__inf(X17993) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17993),X17992),X17991) != X17992
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17993),X17992),X17991))
        | ~ class_Lattices_Osemilattice__inf(X17993) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__inf])])]) ).

fof(i_0_10188,plain,
    ! [X17976,X17977,X17978] :
      ( ~ class_Lattices_Osemilattice__inf(X17978)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17978),X17977),X17976))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17978),X17977),X17976) = X17977 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb1])]) ).

fof(i_0_10189,plain,
    ! [X17973,X17974,X17975] :
      ( ~ class_Lattices_Osemilattice__inf(X17975)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17975),X17974),X17973))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17975),X17973),X17974) = X17974 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb2])]) ).

fof(i_0_10190,plain,
    ! [X17720,X17721,X17722] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17722),X17721),X17720))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17722),X17721),X17720) = X17720
        | ~ class_Lattices_Osemilattice__sup(X17722) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17722),X17721),X17720) != X17720
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17722),X17721),X17720))
        | ~ class_Lattices_Osemilattice__sup(X17722) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__sup])])]) ).

fof(i_0_10191,plain,
    ! [X17659,X17660,X17661] :
      ( ~ class_Lattices_Osemilattice__sup(X17661)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17661),X17660),X17659))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17661),X17660),X17659) = X17659 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__absorb2])]) ).

fof(i_0_10192,plain,
    ! [X17656,X17657,X17658] :
      ( ~ class_Lattices_Osemilattice__sup(X17658)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17658),X17657),X17656))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17658),X17656),X17657) = X17656 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__absorb1])]) ).

fof(i_0_10193,plain,
    ! [X29753,X29754] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29754)
      | c_Complete__Lattice_OSup__class_OSup(X29754,hAPP(hAPP(c_Set_Oinsert(X29754),X29753),c_Orderings_Obot__class_Obot(tc_fun(X29754,tc_HOL_Obool)))) = X29753 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__singleton])]) ).

fof(i_0_10194,plain,
    ! [X29764,X29765] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29765)
      | c_Complete__Lattice_OInf__class_OInf(X29765,hAPP(hAPP(c_Set_Oinsert(X29765),X29764),c_Orderings_Obot__class_Obot(tc_fun(X29765,tc_HOL_Obool)))) = X29764 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__singleton])]) ).

fof(i_0_10195,plain,
    ! [X22376,X22377] :
      ( ~ class_Orderings_Olinorder(X22377)
      | c_Big__Operators_Olinorder__class_OMin(X22377,hAPP(hAPP(c_Set_Oinsert(X22377),X22376),c_Orderings_Obot__class_Obot(tc_fun(X22377,tc_HOL_Obool)))) = X22376 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Osingleton])]) ).

fof(i_0_10196,plain,
    ! [X22374,X22375] :
      ( ~ class_Orderings_Olinorder(X22375)
      | c_Big__Operators_Olinorder__class_OMax(X22375,hAPP(hAPP(c_Set_Oinsert(X22375),X22374),c_Orderings_Obot__class_Obot(tc_fun(X22375,tc_HOL_Obool)))) = X22374 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Osingleton])]) ).

fof(i_0_10197,plain,
    ! [X20830,X20831] :
      ( ~ class_Lattices_Olattice(X20831)
      | c_Big__Operators_Olattice__class_OSup__fin(X20831,hAPP(hAPP(c_Set_Oinsert(X20831),X20830),c_Orderings_Obot__class_Obot(tc_fun(X20831,tc_HOL_Obool)))) = X20830 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osingleton])]) ).

fof(i_0_10198,plain,
    ! [X20832,X20833] :
      ( ~ class_Lattices_Olattice(X20833)
      | c_Big__Operators_Olattice__class_OInf__fin(X20833,hAPP(hAPP(c_Set_Oinsert(X20833),X20832),c_Orderings_Obot__class_Obot(tc_fun(X20833,tc_HOL_Obool)))) = X20832 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osingleton])]) ).

fof(i_0_10199,plain,
    ! [X21529,X21530] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21530)),X21529) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21529),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21530),X21529)),
    inference(variable_rename,[status(thm)],[fact_mult__Suc]) ).

fof(i_0_10200,plain,
    ! [X17003,X17004,X17005,X17006] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X17006,X17005,X17004)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(X17006,X17003,X17005)
      | c_Hoare__Mirabelle_Ohoare__derivs(X17006,X17003,X17004) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_cut])]) ).

cnf(i_0_10201,plain,
    ( c_Int_OBit1(X1) = c_Int_OMin
    | X1 != c_Int_OMin ),
    inference(split_conjunct,[status(thm)],[i_0_5958]) ).

cnf(i_0_10202,plain,
    ( c_Int_OMin = c_Int_OBit1(X1)
    | c_Int_OMin != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_5957]) ).

cnf(i_0_10203,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_5805]) ).

fof(i_0_10204,plain,
    ! [X21746,X21747] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21747),X21746)),X21747) = X21746,
    inference(variable_rename,[status(thm)],[fact_diff__add__inverse]) ).

fof(i_0_10205,plain,
    ! [X21744,X21745] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21745),X21744)),X21744) = X21745,
    inference(variable_rename,[status(thm)],[fact_diff__add__inverse2]) ).

fof(i_0_10206,plain,
    ! [X33833,X33834,X33835,X33836] : hAPP(c_New__DSequence_Opos__union(X33836,X33835,X33834),X33833) = c_Lazy__Sequence_Oappend(X33836,hAPP(X33835,X33833),hAPP(X33834,X33833)),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__union__def]) ).

fof(i_0_10207,plain,
    ! [X29711,X29712,X29713] :
      ( ~ c_Equiv__Relations_Oequiv(X29713,X29712,X29711)
      | c_Complete__Lattice_OSup__class_OSup(tc_fun(X29713,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X29713),X29712),X29711)) = X29712 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__quotient])]) ).

fof(i_0_10208,plain,
    ! [X24285,X24286,X24287] :
      ( ~ class_Fields_Ofield__inverse__zero(X24287)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24287),hAPP(c_Groups_Ouminus__class_Ouminus(X24287),X24286)),hAPP(c_Groups_Ouminus__class_Ouminus(X24287),X24285)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24287),X24286),X24285) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__divide])]) ).

fof(i_0_10209,plain,
    ! [X27046,X27047] :
      ( ~ class_Rings_Olinordered__idom(X27047)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27047),hAPP(c_Groups_Oabs__class_Oabs(X27047),X27046)),hAPP(c_Groups_Oabs__class_Oabs(X27047),X27046)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27047),X27046),X27046) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__self])]) ).

fof(i_0_10210,plain,
    ! [X20804,X20805,X20806] :
      ( ~ class_Rings_Oring(X20806)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20806),hAPP(c_Groups_Ouminus__class_Ouminus(X20806),X20805)),hAPP(c_Groups_Ouminus__class_Ouminus(X20806),X20804)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20806),X20805),X20804) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__minus])]) ).

fof(i_0_10211,plain,
    ! [X20807,X20808,X20809] :
      ( ~ class_Rings_Oring(X20809)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20809),hAPP(c_Groups_Ouminus__class_Ouminus(X20809),X20808)),X20807) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20809),X20808),hAPP(c_Groups_Ouminus__class_Ouminus(X20809),X20807)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__commute])]) ).

fof(i_0_10212,plain,
    ! [X28180,X28181,X28182,X28183,X28184] :
      ( ( ~ c_Wellfounded_OwfP(X28181,X28180)
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X28181,X28180),X28182)) )
      & ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X28184,X28183),esk289_2(X28183,X28184)))
        | c_Wellfounded_OwfP(X28184,X28183) ) ),
    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_10213,plain,
    ! [X24176,X24177,X24178] :
      ( ~ class_Rings_Odivision__ring(X24178)
      | X24177 = c_Groups_Ozero__class_Ozero(X24178)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X24178),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24178),X24176),X24177)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24178),X24176),hAPP(c_Groups_Ouminus__class_Ouminus(X24178),X24177)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__right])]) ).

cnf(i_0_10214,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_6025]) ).

fof(i_0_10215,plain,
    ! [X18971,X18972,X18973] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X18973,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(X18973),X18972),X18971)
        | X18972 = c_Orderings_Obot__class_Obot(tc_fun(X18973,tc_HOL_Obool)) )
      & ( X18972 != c_Orderings_Obot__class_Obot(tc_fun(X18973,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X18973,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X18973),X18972),X18971) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__is__empty2])]) ).

fof(i_0_10216,plain,
    ! [X18974,X18975,X18976] :
      ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X18976),X18975),X18974) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X18976,tc_HOL_Obool),tc_HOL_Obool))
        | X18975 = c_Orderings_Obot__class_Obot(tc_fun(X18976,tc_HOL_Obool)) )
      & ( X18975 != c_Orderings_Obot__class_Obot(tc_fun(X18976,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(X18976),X18975),X18974) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X18976,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__is__empty])]) ).

fof(i_0_10217,plain,
    ! [X25681,X25682] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X25682,X25681)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25681),X25682)),
    inference(variable_rename,[status(thm)],[fact_card__greaterThanAtMost__int]) ).

fof(i_0_10218,plain,
    ! [X18399,X18400,X18401] :
      ( ( X18400 = X18399
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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),X18400),X18399))
        | X18400 != X18399
        | ~ class_Orderings_Olinorder(X18401) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18401),X18399),X18400))
        | X18400 != X18399
        | ~ class_Orderings_Olinorder(X18401) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).

fof(i_0_10219,plain,
    ! [X20834,X20835,X20836] :
      ( ~ class_Rings_Olinordered__idom(X20836)
      | X20835 = X20834
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20836),X20835),X20834))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20836),X20834),X20835)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6026])]) ).

fof(i_0_10220,plain,
    ! [X18466,X18467,X18468] :
      ( ~ class_Orderings_Olinorder(X18468)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18468),X18467),X18466))
      | X18467 = X18466
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18468),X18466),X18467)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6027])]) ).

fof(i_0_10221,plain,
    ! [X18411,X18412,X18413] :
      ( ~ class_Orderings_Olinorder(X18413)
      | X18412 = X18411
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18413),X18412),X18411))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18413),X18411),X18412)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6028])]) ).

fof(i_0_10222,plain,
    ! [X18408,X18409,X18410] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18410),X18408),X18409))
        | X18408 = X18409
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18410),X18409),X18408))
        | ~ class_Orderings_Olinorder(X18410) )
      & ( X18408 != X18409
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18410),X18408),X18409))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18410),X18409),X18408))
        | ~ class_Orderings_Olinorder(X18410) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6029])])]) ).

fof(i_0_10223,plain,
    ! [X18405,X18406,X18407] :
      ( ~ class_Orderings_Olinorder(X18407)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18407),X18406),X18405))
      | X18406 = X18405
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18407),X18405),X18406)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).

fof(i_0_10224,plain,
    ! [X23336,X23337,X23338] :
      ( ~ class_Divides_Osemiring__div(X23338)
      | c_Divides_Odiv__class_Omod(X23338,c_Divides_Odiv__class_Omod(X23338,X23337,X23336),X23336) = c_Divides_Odiv__class_Omod(X23338,X23337,X23336) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mod__trivial])]) ).

fof(i_0_10225,plain,
    ! [X18072,X18073] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18073,tc_HOL_Obool)),X18072),c_Orderings_Obot__class_Obot(tc_fun(X18073,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X18073,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Int__empty__right]) ).

fof(i_0_10226,plain,
    ! [X19202,X19203] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19203,tc_HOL_Obool)),X19202),c_Orderings_Otop__class_Otop(tc_fun(X19203,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X19203,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Diff__UNIV]) ).

fof(i_0_10227,plain,
    ! [X19115,X19116] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X19116,tc_HOL_Obool)),X19115),c_Orderings_Otop__class_Otop(tc_fun(X19116,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X19116,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Un__UNIV__right]) ).

fof(i_0_10228,plain,
    ! [X27600,X27601] : hAPP(c_Relation_ODomain(X27601,X27600),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27601,X27600),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X27601,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Domain__empty]) ).

fof(i_0_10229,plain,
    ! [X27526,X27527] : hAPP(c_Relation_ORange(X27527,X27526),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27527,X27526),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X27526,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Range__empty]) ).

fof(i_0_10230,plain,
    ! [X18353,X18354,X18355,X18356] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18356,X18355),X18354),X18353),hAPP(X18354,X18353)) = X18354,
    inference(variable_rename,[status(thm)],[fact_fun__upd__triv]) ).

fof(i_0_10231,plain,
    ! [X23912,X23913,X23914,X23915] : hAPP(c_Product__Type_Ofst(X23915,X23914),hAPP(hAPP(c_Product__Type_OPair(X23915,X23914),X23913),X23912)) = X23913,
    inference(variable_rename,[status(thm)],[fact_fst__conv]) ).

fof(i_0_10232,plain,
    ! [X23921,X23922,X23923,X23924] : hAPP(c_Product__Type_Osnd(X23924,X23923),hAPP(hAPP(c_Product__Type_OPair(X23924,X23923),X23922),X23921)) = X23921,
    inference(variable_rename,[status(thm)],[fact_snd__conv]) ).

cnf(i_0_10233,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_10234,plain,
    ! [X21734,X21735,X21737,X21738,X21739] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21735),X21734))
        | X21734 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21735),esk109_2(X21734,X21735)) )
      & ( X21737 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21738),X21739)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21738),X21737)) ) ),
    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_10235,plain,
    ! [X17546,X17547,X17548] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17548),X17547),X17546))
      | hAPP(hAPP(c_Set_Oinsert(X17548),X17547),X17546) = X17546 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).

fof(i_0_10236,plain,
    ! [X17146,X17147] : c_Set_Othe__elem(X17147,hAPP(hAPP(c_Set_Oinsert(X17147),X17146),c_Orderings_Obot__class_Obot(tc_fun(X17147,tc_HOL_Obool)))) = X17146,
    inference(variable_rename,[status(thm)],[fact_the__elem__eq]) ).

fof(i_0_10237,plain,
    ! [X18515,X18516,X18517] :
      ( ~ class_Orderings_Olinorder(X18517)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18517),X18516),X18515))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18517),X18515),X18516)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6030])]) ).

fof(i_0_10238,plain,
    ! [X18500,X18501,X18502] :
      ( ~ class_Orderings_Olinorder(X18502)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18502),X18501),X18500))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18502),X18500),X18501)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).

fof(i_0_10239,plain,
    ! [X18512,X18513,X18514] :
      ( ~ class_Orderings_Olinorder(X18514)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18514),X18513),X18512))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18514),X18512),X18513)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6031])]) ).

fof(i_0_10240,plain,
    ! [X17090,X17091,X17092] :
      ( ~ class_Orderings_Olinorder(X17092)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17092),X17091),X17090))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17092),X17090),X17091)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).

fof(i_0_10241,plain,
    ! [X17048,X17049,X17050] :
      ( ~ class_Orderings_Olinorder(X17050)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17050),X17049),X17048))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17050),X17048),X17049)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6032])]) ).

fof(i_0_10242,plain,
    ! [X18392,X18393,X18394,X18395,X18396] :
      ( hAPP(X18396,X18395) != X18394
      | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X18393,X18392),X18396),X18395),X18394) = X18396 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__idem])]) ).

cnf(i_0_10243,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_6033]) ).

cnf(i_0_10244,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_6034]) ).

fof(i_0_10245,plain,
    ! [X30383,X30384,X30385] :
      ( ~ class_Groups_Omonoid__add(X30385)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30385),hAPP(hAPP(c_List_Olist_OCons(X30385),X30384),X30383)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X30385),X30384),hAPP(c_List_Omonoid__add__class_Olistsum(X30385),X30383)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__simps_I2_J])]) ).

fof(i_0_10246,plain,
    ! [X24282,X24283,X24284] :
      ( ~ class_Fields_Ofield__inverse__zero(X24284)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X24284),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24284),X24283),X24282)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24284),X24283),hAPP(c_Groups_Ouminus__class_Ouminus(X24284),X24282)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__right])]) ).

fof(i_0_10247,plain,
    ! [X20813,X20814,X20815] :
      ( ~ class_Rings_Oring(X20815)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X20815),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20815),X20814),X20813)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20815),X20814),hAPP(c_Groups_Ouminus__class_Ouminus(X20815),X20813)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__right])]) ).

fof(i_0_10248,plain,
    ! [X22562,X22563,X22564] : c_Option_Ooption_Ooption__size(X22564,X22563,hAPP(c_Option_Ooption_OSome(X22564),X22562)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X22563,X22562)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_option_Osize_I2_J]) ).

fof(i_0_10249,plain,
    ! [X32620,X32621] : c_List_Opartition(X32621,X32620,c_List_Olist_ONil(X32621)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32621),tc_List_Olist(X32621)),c_List_Olist_ONil(X32621)),c_List_Olist_ONil(X32621)),
    inference(variable_rename,[status(thm)],[fact_partition_Osimps_I1_J]) ).

cnf(i_0_10250,plain,
    c_Int_Osucc(c_Int_Opred(X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_6035]) ).

fof(i_0_10251,plain,
    ! [X31419,X31420,X31421] : hAPP(hAPP(c_List_Otake(X31421),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X31421),X31420),X31419)) = hAPP(hAPP(c_List_Olist_OCons(X31421),X31420),c_List_Olist_ONil(X31421)),
    inference(variable_rename,[status(thm)],[fact_take__1__Cons]) ).

fof(i_0_10252,plain,
    ! [X27385,X27386,X27387,X27388] :
      ( ~ c_Wellfounded_Owf(X27388,X27387)
      | c_Wellfounded_Owf(X27386,hAPP(hAPP(c_Relation_Oinv__image(X27388,X27386),X27387),X27385)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__inv__image])]) ).

fof(i_0_10253,plain,
    ! [X24592,X24593,X24594,X24595] :
      ( ~ c_FunDef_Oreduction__pair(X24595,X24594)
      | c_FunDef_Oreduction__pair(X24593,hAPP(hAPP(c_FunDef_Orp__inv__image(X24595,X24593),X24594),X24592)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rp__inv__image__rp])]) ).

fof(i_0_10254,plain,
    ! [X23294,X23295,X23296] :
      ( ~ class_Divides_Osemiring__div(X23296)
      | c_Divides_Odiv__class_Omod(X23296,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23296),X23295),X23294),X23295) = c_Divides_Odiv__class_Omod(X23296,X23294,X23295) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self1])]) ).

fof(i_0_10255,plain,
    ! [X23297,X23298,X23299] :
      ( ~ class_Divides_Osemiring__div(X23299)
      | c_Divides_Odiv__class_Omod(X23299,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23299),X23298),X23297),X23297) = c_Divides_Odiv__class_Omod(X23299,X23298,X23297) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self2])]) ).

fof(i_0_10256,plain,
    ! [X31805,X31806,X31807,X31808,X31809] :
      ( hAPP(hAPP(c_List_Odrop(X31809),X31808),X31807) != hAPP(hAPP(c_List_Olist_OCons(X31809),X31806),X31805)
      | hAPP(hAPP(c_List_Onth(X31809),X31807),X31808) = X31806 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__via__drop])]) ).

fof(i_0_10257,plain,
    ! [X25749,X25750] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25750)),hAPP(c_Nat_OSuc,X25749)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X25750),X25749)),
    inference(variable_rename,[status(thm)],[fact_max__Suc__Suc]) ).

fof(i_0_10258,plain,
    ! [X25322,X25323] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25323)),hAPP(c_Nat_OSuc,X25322)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X25323),X25322)),
    inference(variable_rename,[status(thm)],[fact_min__Suc__Suc]) ).

fof(i_0_10259,plain,
    ! [X31117,X31118] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X31118)),hAPP(c_Code__Numeral_Oof__nat,X31117)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31118),X31117)),
    inference(variable_rename,[status(thm)],[fact_plus__code__numeral__code]) ).

fof(i_0_10260,plain,
    ! [X31092,X31093] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X31093)),hAPP(c_Code__Numeral_Oof__nat,X31092)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31093),X31092)),
    inference(variable_rename,[status(thm)],[fact_times__code__numeral__code]) ).

fof(i_0_10261,plain,
    ! [X25211,X25212] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25212)),X25211) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X25212),X25211)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J]) ).

fof(i_0_10262,plain,
    ! [X25207,X25208] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25208)),X25207) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X25208),X25207)),
    inference(variable_rename,[status(thm)],[fact_zpower__int]) ).

fof(i_0_10263,plain,
    ! [X22788,X22789] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22789)),X22788) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22789),X22788)),
    inference(variable_rename,[status(thm)],[fact_zmult__zminus]) ).

fof(i_0_10264,plain,
    ! [X25209,X25210] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X25210),X25209)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25210)),X25209),
    inference(variable_rename,[status(thm)],[fact_int__power]) ).

fof(i_0_10265,plain,
    ! [X33343,X33344,X33345] : hAPP(c_List_Oset(X33345),c_List_Oinsert(X33345,X33344,X33343)) = hAPP(hAPP(c_Set_Oinsert(X33345),X33344),hAPP(c_List_Oset(X33345),X33343)),
    inference(variable_rename,[status(thm)],[fact_List_Oset__insert]) ).

cnf(i_0_10266,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_6036]) ).

fof(i_0_10267,plain,
    ! [X33942,X33943,X33944] : c_List_Osplice(X33944,hAPP(hAPP(c_List_Olist_OCons(X33944),X33943),X33942),c_List_Olist_ONil(X33944)) = hAPP(hAPP(c_List_Olist_OCons(X33944),X33943),X33942),
    inference(variable_rename,[status(thm)],[fact_splice_Osimps_I2_J]) ).

fof(i_0_10268,plain,
    ! [X27018,X27019] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27019)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27019),c_Groups_Ozero__class_Ozero(X27019)),hAPP(c_Groups_Oabs__class_Oabs(X27019),X27018))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__zero])]) ).

fof(i_0_10269,plain,
    ! [X25154,X25155] :
      ( ~ class_Rings_Olinordered__semidom(X25155)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25155),c_Groups_Ozero__class_Ozero(X25155)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25155),X25154))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__imp__of__nat])]) ).

fof(i_0_10270,plain,
    ! [X25152,X25153] :
      ( ~ class_Rings_Olinordered__semidom(X25153)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25153),c_Groups_Ozero__class_Ozero(X25153)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25153),X25152))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0__le__iff])]) ).

fof(i_0_10271,plain,
    ! [X30895,X30896] :
      ( ~ class_Enum_Oenum(X30896)
      | hBOOL(hAPP(hAPP(c_member(X30896),X30895),hAPP(c_List_Oset(X30896),c_Enum_Oenum__class_Oenum(X30896)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__enum])]) ).

fof(i_0_10272,plain,
    ! [X25738,X25739,X25740] :
      ( ~ class_Orderings_Olinorder(X25740)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25740),X25739),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25740),X25739),X25738)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25740),X25739),X25738) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oleft__idem])]) ).

fof(i_0_10273,plain,
    ! [X25735,X25736,X25737] :
      ( ~ class_Orderings_Olinorder(X25737)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25737),X25736),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25737),X25736),X25735)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25737),X25736),X25735) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__left__idem])]) ).

fof(i_0_10274,plain,
    ! [X25335,X25336,X25337] :
      ( ~ class_Orderings_Olinorder(X25337)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25337),X25336),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25337),X25336),X25335)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25337),X25336),X25335) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__left__idem])]) ).

fof(i_0_10275,plain,
    ! [X25332,X25333,X25334] :
      ( ~ class_Orderings_Olinorder(X25334)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25334),X25333),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25334),X25333),X25332)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25334),X25333),X25332) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__idem])]) ).

fof(i_0_10276,plain,
    ! [X20373,X20374,X20375] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X20375)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20375),X20374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20375),X20374),X20373)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20375),X20374),X20373) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__idem])]) ).

fof(i_0_10277,plain,
    ! [X17852,X17853,X17854] :
      ( ~ class_Lattices_Osemilattice__inf(X17854)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17854),X17853),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17854),X17853),X17852)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17854),X17853),X17852) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__idem])]) ).

fof(i_0_10278,plain,
    ! [X17846,X17847,X17848] :
      ( ~ class_Lattices_Osemilattice__inf(X17848)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17848),X17847),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17848),X17847),X17846)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17848),X17847),X17846) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__idem])]) ).

fof(i_0_10279,plain,
    ! [X17849,X17850,X17851] :
      ( ~ class_Lattices_Olattice(X17851)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17851),X17850),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17851),X17850),X17849)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17851),X17850),X17849) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I4_J])]) ).

fof(i_0_10280,plain,
    ! [X17689,X17690,X17691] :
      ( ~ class_Lattices_Olattice(X17691)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17691),X17690),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17691),X17690),X17689)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17691),X17690),X17689) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I8_J])]) ).

fof(i_0_10281,plain,
    ! [X17692,X17693,X17694] :
      ( ~ class_Lattices_Osemilattice__sup(X17694)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17694),X17693),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17694),X17693),X17692)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17694),X17693),X17692) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oleft__idem])]) ).

fof(i_0_10282,plain,
    ! [X17686,X17687,X17688] :
      ( ~ class_Lattices_Osemilattice__sup(X17688)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17688),X17687),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17688),X17687),X17686)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17688),X17687),X17686) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__left__idem])]) ).

fof(i_0_10283,plain,
    ! [X33436,X33437,X33439] :
      ( ( hAPP(c_List_Oset(X33437),esk482_2(X33436,X33437)) = X33436
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33437),X33436))
        | ~ class_Orderings_Olinorder(X33437) )
      & ( c_List_Olinorder__class_Osorted(X33437,esk482_2(X33436,X33437))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33437),X33436))
        | ~ class_Orderings_Olinorder(X33437) )
      & ( hBOOL(hAPP(c_List_Odistinct(X33437),esk482_2(X33436,X33437)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33437),X33436))
        | ~ class_Orderings_Olinorder(X33437) )
      & ( hAPP(c_List_Oset(X33437),X33439) != X33436
        | ~ c_List_Olinorder__class_Osorted(X33437,X33439)
        | ~ hBOOL(hAPP(c_List_Odistinct(X33437),X33439))
        | X33439 = esk482_2(X33436,X33437)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33437),X33436))
        | ~ class_Orderings_Olinorder(X33437) ) ),
    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_10284,plain,
    ! [X31913,X31914,X31915] : hAPP(hAPP(c_List_Odrop(X31915),X31914),hAPP(c_List_Otl(X31915),X31913)) = hAPP(c_List_Otl(X31915),hAPP(hAPP(c_List_Odrop(X31915),X31914),X31913)),
    inference(variable_rename,[status(thm)],[fact_drop__tl]) ).

fof(i_0_10285,plain,
    ! [X31910,X31911,X31912] : hAPP(c_List_Otl(X31912),hAPP(hAPP(c_List_Odrop(X31912),X31911),X31910)) = hAPP(hAPP(c_List_Odrop(X31912),X31911),hAPP(c_List_Otl(X31912),X31910)),
    inference(variable_rename,[status(thm)],[fact_tl__drop]) ).

fof(i_0_10286,plain,
    ! [X30294,X30295,X30296] : hAPP(c_List_Oset(X30296),hAPP(hAPP(c_List_Olist_OCons(X30296),X30295),X30294)) = hAPP(hAPP(c_Set_Oinsert(X30296),X30295),hAPP(c_List_Oset(X30296),X30294)),
    inference(variable_rename,[status(thm)],[fact_List_Oset_Osimps_I2_J]) ).

fof(i_0_10287,plain,
    ! [X26201,X26202] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26202,X26201)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26201)),X26202),
    inference(variable_rename,[status(thm)],[fact_card__atLeastAtMost]) ).

fof(i_0_10288,plain,
    ! [X17529,X17530,X17531] :
      ( X17531 != c_Orderings_Obot__class_Obot(tc_fun(X17530,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X17530),X17529),X17531)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6037])]) ).

fof(i_0_10289,plain,
    ! [X27927] : hAPP(c_Set_Oimage(X27927,X27927,c_Fun_Oid(X27927)),c_Orderings_Otop__class_Otop(tc_fun(X27927,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X27927,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_surj__id]) ).

fof(i_0_10290,plain,
    ! [X31396,X31397,X31398] : hAPP(hAPP(c_Map_Omap__of(X31398,X31397),c_List_Olist_ONil(tc_prod(X31398,X31397))),X31396) = c_Option_Ooption_ONone(X31397),
    inference(variable_rename,[status(thm)],[fact_map__of_Osimps_I1_J]) ).

fof(i_0_10291,plain,
    ! [X31369,X31370,X31371] : hAPP(hAPP(c_Map_Omap__of(X31371,X31370),c_List_Olist_ONil(tc_prod(X31371,X31370))),X31369) = c_Option_Ooption_ONone(X31370),
    inference(variable_rename,[status(thm)],[fact_map__of__Cons__code_I1_J]) ).

fof(i_0_10292,plain,
    ! [X28298,X28299,X28301,X28302,X28303] :
      ( ( ~ hBOOL(hAPP(X28299,c_Hilbert__Choice_OEps(X28298,X28299)))
        | hBOOL(hAPP(X28299,esk309_2(X28298,X28299))) )
      & ( ~ hBOOL(hAPP(X28302,X28303))
        | hBOOL(hAPP(X28302,c_Hilbert__Choice_OEps(X28301,X28302))) ) ),
    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_10293,plain,
    ! [X32607,X32608,X32609] : hAPP(c_Product__Type_Ofst(tc_List_Olist(X32609),tc_List_Olist(X32609)),c_List_Opartition(X32609,X32608,X32607)) = hAPP(c_List_Ofilter(X32609,X32608),X32607),
    inference(variable_rename,[status(thm)],[fact_partition__filter1]) ).

fof(i_0_10294,plain,
    ! [X24510] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X24510))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24510)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24510))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X24510)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6038])]) ).

fof(i_0_10295,plain,
    ! [X19090,X19091] : hBOOL(hAPP(hAPP(c_member(X19091),X19090),c_Orderings_Otop__class_Otop(tc_fun(X19091,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_iso__tuple__UNIV__I]) ).

fof(i_0_10296,plain,
    ! [X19055,X19056] : hBOOL(hAPP(hAPP(c_member(X19056),X19055),c_Orderings_Otop__class_Otop(tc_fun(X19056,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).

fof(i_0_10297,plain,
    ! [X25250,X25251] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25251))
        | X25251 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25250)
        | hAPP(c_Int_Onat,X25251) != X25250 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25251))
        | X25250 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Int_Onat,X25251) != X25250 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25251))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25251))
        | hAPP(c_Int_Onat,X25251) = X25250 )
      & ( X25250 != 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)),X25251))
        | hAPP(c_Int_Onat,X25251) = X25250 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25251))
        | X25251 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25250)
        | hAPP(c_Int_Onat,X25251) = X25250 )
      & ( X25250 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X25251 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25250)
        | hAPP(c_Int_Onat,X25251) = X25250 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6039])])]) ).

fof(i_0_10298,plain,
    ! [X25252,X25253] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25252))
        | X25252 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25253)
        | X25253 != hAPP(c_Int_Onat,X25252) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25252))
        | X25253 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X25253 != hAPP(c_Int_Onat,X25252) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25252))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25252))
        | X25253 = hAPP(c_Int_Onat,X25252) )
      & ( X25253 != 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)),X25252))
        | X25253 = hAPP(c_Int_Onat,X25252) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25252))
        | X25252 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25253)
        | X25253 = hAPP(c_Int_Onat,X25252) )
      & ( X25253 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X25252 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25253)
        | X25253 = hAPP(c_Int_Onat,X25252) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6040])])]) ).

fof(i_0_10299,plain,
    ! [X20390,X20391,X20392] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20392,tc_HOL_Obool)),X20391) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20392,tc_HOL_Obool)),X20390)
        | X20391 = X20390 )
      & ( X20391 != X20390
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20392,tc_HOL_Obool)),X20391) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20392,tc_HOL_Obool)),X20390) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__eq__Compl__iff])]) ).

fof(i_0_10300,plain,
    ! [X20386,X20387,X20388,X20389] :
      ( ~ class_Groups_Ouminus(X20389)
      | hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20388,X20389)),X20387),X20386) = hAPP(c_Groups_Ouminus__class_Ouminus(X20389),hAPP(X20387,X20386)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__Compl__def])]) ).

fof(i_0_10301,plain,
    ! [X20376,X20377,X20378,X20379] :
      ( ~ class_Groups_Ouminus(X20379)
      | hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20378,X20379)),X20377),X20376) = hAPP(c_Groups_Ouminus__class_Ouminus(X20379),hAPP(X20377,X20376)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__apply])]) ).

fof(i_0_10302,plain,
    ! [X25229] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25229))
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X25229)) = X25229 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__le])]) ).

fof(i_0_10303,plain,
    ! [X25226] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25226))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X25226)) = X25226 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25226))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X25226)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6041])]) ).

fof(i_0_10304,plain,
    ! [X23232,X23233] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23233),X23232))
      | c_Nat__Transfer_Otsub(X23232,X23233) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23232),X23233) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tsub__eq])]) ).

fof(i_0_10305,plain,
    ! [X22963,X22964] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22964),X22963))
        | c_Nat__Transfer_Otsub(X22963,X22964) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X22963),X22964) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22964),X22963))
        | c_Nat__Transfer_Otsub(X22963,X22964) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6042])]) ).

fof(i_0_10306,plain,
    ! [X31280,X31281] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,X31281)),hAPP(c_Code__Numeral_Oof__nat,X31280)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31281),X31280)),
    inference(variable_rename,[status(thm)],[fact_subtract__code__numeral__code]) ).

fof(i_0_10307,plain,
    ! [X30050,X30051] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,X30051,X30050) = c_Smallcheck_Ofull__small_H(X30051,hAPP(c_Code__Numeral_Oint__of,X30050),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X30050))),
    inference(variable_rename,[status(thm)],[fact_full__small__int__def]) ).

fof(i_0_10308,plain,
    ! [X25227,X25228] :
      ( ( X25228 = hAPP(c_Int_Onat,X25227)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25228) != X25227 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25227))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25228) != X25227 )
      & ( X25228 != hAPP(c_Int_Onat,X25227)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25227))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25228) = X25227 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__eq__iff])])]) ).

fof(i_0_10309,plain,
    ! [X21321,X21322,X21323,X21324] :
      ( ~ c_Big__Operators_Osemilattice__big(X21324,X21323,X21322)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21324),X21321))
      | hAPP(X21322,X21321) = hAPP(c_Finite__Set_Ofold1(X21324,X21323),X21321) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semilattice__big_OF__eq])]) ).

fof(i_0_10310,plain,
    ! [X21220,X21221,X21222,X21223] :
      ( ~ c_Finite__Set_Ofolding__one(X21223,X21222,X21221)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21223),X21220))
      | hAPP(X21221,X21220) = hAPP(c_Finite__Set_Ofold1(X21223,X21222),X21220) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oeq__fold])]) ).

fof(i_0_10311,plain,
    ! [X25278,X25279] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25278)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25279),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25278)) = c_Groups_Ozero__class_Ozero(X25279)
        | ~ class_Int_Onumber__ring(X25279) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25278)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25279),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25278)) = hAPP(c_Int_Onumber__class_Onumber__of(X25279),X25278)
        | ~ class_Int_Onumber__ring(X25279) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6043])])]) ).

fof(i_0_10312,plain,
    ! [X29727] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X29727,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X29727,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X29727,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Union__UNIV]) ).

fof(i_0_10313,plain,
    ! [X29707] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X29707,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X29707,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X29707,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Union__empty]) ).

fof(i_0_10314,plain,
    ! [X29745] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X29745,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X29745,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X29745,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Inter__UNIV]) ).

fof(i_0_10315,plain,
    ! [X29724] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X29724,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X29724,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X29724,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Inter__empty]) ).

cnf(i_0_10316,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_5753]) ).

fof(i_0_10317,plain,
    ! [X17101,X17102,X17103] : hAPP(hAPP(c_Set_Oinsert(X17103),X17102),hAPP(hAPP(c_Set_Oinsert(X17103),X17102),X17101)) = hAPP(hAPP(c_Set_Oinsert(X17103),X17102),X17101),
    inference(variable_rename,[status(thm)],[fact_insert__absorb2]) ).

cnf(i_0_10318,plain,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    inference(split_conjunct,[status(thm)],[fact_Bit1__Min]) ).

fof(i_0_10319,plain,
    ! [X29403,X29404,X29405,X29406] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29406)
      | X29405 = c_Orderings_Obot__class_Obot(tc_fun(X29404,tc_HOL_Obool))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29404,X29406),X29405),hAPP(c_COMBK(X29406,X29404),X29403)) = X29403 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__const])]) ).

fof(i_0_10320,plain,
    ! [X19654,X19655,X19656,X19657] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X19657)
      | X19656 = c_Orderings_Obot__class_Obot(tc_fun(X19655,tc_HOL_Obool))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19655,X19657),X19656),hAPP(c_COMBK(X19657,X19655),X19654)) = X19654 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__const])]) ).

cnf(i_0_10321,plain,
    ~ hBOOL(hAPP(hAPP(c_List_Omember(X1),c_List_Olist_ONil(X1)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_6044]) ).

fof(i_0_10322,plain,
    ! [X20600,X20601,X20602] :
      ( ~ class_Lattices_Oboolean__algebra(X20602)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20602),X20601),X20600) != c_Orderings_Obot__class_Obot(X20602)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20602),X20601),X20600) != c_Orderings_Otop__class_Otop(X20602)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X20602),X20601) = X20600 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__unique])]) ).

fof(i_0_10323,plain,
    ! [X21527,X21528] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21528),hAPP(c_Nat_OSuc,X21527)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21528),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21528),X21527)),
    inference(variable_rename,[status(thm)],[fact_mult__Suc__right]) ).

cnf(i_0_10324,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_6045]) ).

fof(i_0_10325,plain,
    ! [X26198] : 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)),X26198))),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastZeroLessThan__int]) ).

fof(i_0_10326,plain,
    ! [X32230,X32231] : c_List_Otranspose(X32231,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X32231)),c_List_Olist_ONil(X32231)),X32230)) = c_List_Otranspose(X32231,X32230),
    inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I2_J]) ).

fof(i_0_10327,plain,
    ! [X32581,X32582,X32583,X32584] :
      ( hBOOL(hAPP(X32584,X32583))
      | c_List_Oremove1(X32582,X32583,hAPP(c_List_Ofilter(X32582,X32584),X32581)) = hAPP(c_List_Ofilter(X32582,X32584),X32581) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6046])]) ).

fof(i_0_10328,plain,
    ! [X20258] : hAPP(c_Relation_OField(X20258),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X20258,X20258),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X20258,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Field__empty]) ).

fof(i_0_10329,plain,
    ! [X23627,X23628] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23628),X23627))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23628,X23627) = X23628 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__less])]) ).

fof(i_0_10330,plain,
    ! [X26206,X26207] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26207),c_Groups_Oone__class_Oone(tc_Int_Oint)),X26206) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X26207,X26206),
    inference(variable_rename,[status(thm)],[fact_atLeastPlusOneAtMost__greaterThanAtMost__int]) ).

fof(i_0_10331,plain,
    ! [X29755,X29756,X29757] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29757)
      | c_Complete__Lattice_OSup__class_OSup(X29757,hAPP(hAPP(c_Set_Oinsert(X29757),X29756),X29755)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X29757),X29756),c_Complete__Lattice_OSup__class_OSup(X29757,X29755)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__insert])]) ).

fof(i_0_10332,plain,
    ! [X29768,X29769,X29770] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29770)
      | c_Complete__Lattice_OInf__class_OInf(X29770,hAPP(hAPP(c_Set_Oinsert(X29770),X29769),X29768)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X29770),X29769),c_Complete__Lattice_OInf__class_OInf(X29770,X29768)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__insert])]) ).

fof(i_0_10333,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_10334,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_10335,plain,
    ! [X30058,X30059] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),X30059),X30058) = c_Smallcheck_Osmall_H(X30059,hAPP(c_Code__Numeral_Oint__of,X30058),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X30058))),
    inference(variable_rename,[status(thm)],[fact_small__int__def]) ).

fof(i_0_10336,plain,
    ! [X33326,X33327,X33328] : c_List_Oinsert(X33328,X33327,c_List_Oremdups(X33328,X33326)) = c_List_Oremdups(X33328,c_List_Oinsert(X33328,X33327,X33326)),
    inference(variable_rename,[status(thm)],[fact_insert__remdups]) ).

fof(i_0_10337,plain,
    ! [X33599,X33600,X33601] :
      ( ( ~ c_List_Olist__all(X33601,X33600,hAPP(c_List_Orev(X33601),X33599))
        | c_List_Olist__all(X33601,X33600,X33599) )
      & ( ~ c_List_Olist__all(X33601,X33600,X33599)
        | c_List_Olist__all(X33601,X33600,hAPP(c_List_Orev(X33601),X33599)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__rev])]) ).

fof(i_0_10338,plain,
    ! [X33504,X33505,X33506] :
      ( ( ~ c_List_Olist__ex(X33506,X33505,hAPP(c_List_Orev(X33506),X33504))
        | c_List_Olist__ex(X33506,X33505,X33504) )
      & ( ~ c_List_Olist__ex(X33506,X33505,X33504)
        | c_List_Olist__ex(X33506,X33505,hAPP(c_List_Orev(X33506),X33504)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__rev])]) ).

fof(i_0_10339,plain,
    ! [X32182,X32183,X32184] :
      ( ( X32184 != c_List_Olist_ONil(X32183)
        | c_List_Obutlast(X32183,hAPP(hAPP(c_List_Oappend(X32183),X32182),X32184)) = c_List_Obutlast(X32183,X32182) )
      & ( X32184 = c_List_Olist_ONil(X32183)
        | c_List_Obutlast(X32183,hAPP(hAPP(c_List_Oappend(X32183),X32182),X32184)) = hAPP(hAPP(c_List_Oappend(X32183),X32182),c_List_Obutlast(X32183,X32184)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__append])]) ).

fof(i_0_10340,plain,
    ! [X32195,X32196,X32197] :
      ( ( X32197 != c_List_Olist_ONil(X32196)
        | c_List_Obutlast(X32196,hAPP(hAPP(c_List_Olist_OCons(X32196),X32195),X32197)) = c_List_Olist_ONil(X32196) )
      & ( X32197 = c_List_Olist_ONil(X32196)
        | c_List_Obutlast(X32196,hAPP(hAPP(c_List_Olist_OCons(X32196),X32195),X32197)) = hAPP(hAPP(c_List_Olist_OCons(X32196),X32195),c_List_Obutlast(X32196,X32197)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast_Osimps_I2_J])]) ).

fof(i_0_10341,plain,
    ! [X19442,X19443,X19444] : hAPP(c_Set_Ovimage(X19444,X19443,X19442),c_Orderings_Otop__class_Otop(tc_fun(X19443,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X19444,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_vimage__UNIV]) ).

fof(i_0_10342,plain,
    ! [X19434,X19435,X19436] : hAPP(c_Set_Ovimage(X19436,X19435,X19434),c_Orderings_Obot__class_Obot(tc_fun(X19435,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X19436,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_vimage__empty]) ).

fof(i_0_10343,plain,
    ! [X19360,X19361,X19362] : hAPP(c_Relation_OImage(X19362,X19361,X19360),c_Orderings_Obot__class_Obot(tc_fun(X19362,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X19361,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Image__empty]) ).

fof(i_0_10344,plain,
    ! [X17450,X17451,X17452] : hAPP(c_Set_Oimage(X17452,X17451,X17450),c_Orderings_Obot__class_Obot(tc_fun(X17452,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X17451,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_image__empty]) ).

fof(i_0_10345,plain,
    ! [X30990,X30991,X30992] :
      ( ~ c_Relation_Orefl__on(X30992,X30991,X30990)
      | c_Relation_Orefl__on(tc_List_Olist(X30992),c_List_Olists(X30992,X30991),c_List_Olistrel(X30992,X30990)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__refl__on])]) ).

fof(i_0_10346,plain,
    ! [X30987,X30988,X30989] :
      ( ~ c_Equiv__Relations_Oequiv(X30989,X30988,X30987)
      | c_Equiv__Relations_Oequiv(tc_List_Olist(X30989),c_List_Olists(X30989,X30988),c_List_Olistrel(X30989,X30987)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__listrel])]) ).

fof(i_0_10347,plain,
    ! [X17413,X17414,X17415] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17415),X17414),X17413))
        | hBOOL(hAPP(X17413,X17414)) )
      & ( ~ hBOOL(hAPP(X17413,X17414))
        | hBOOL(hAPP(hAPP(c_member(X17415),X17414),X17413)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).

cnf(i_0_10348,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_6047]) ).

fof(i_0_10349,plain,
    ! [X23415,X23416] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23416),X23415))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23416),X23415) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less])]) ).

fof(i_0_10350,plain,
    ! [X33697,X33698] :
      ( ( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X33698),X33697))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X33698),X33697) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X33698),X33697) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X33698),X33697)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__int__def])]) ).

fof(i_0_10351,plain,
    ! [X22372,X22373] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22373),X22372))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22373),X22372) = 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_10352,plain,
    ! [X22370,X22371] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22371),X22370) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22371),X22370)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22371),X22370))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22371),X22370) = 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_10353,plain,
    ! [X19119,X19120] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19120,tc_HOL_Obool)),X19119),c_Orderings_Otop__class_Otop(tc_fun(X19120,tc_HOL_Obool))) = X19119,
    inference(variable_rename,[status(thm)],[fact_Int__UNIV__right]) ).

fof(i_0_10354,plain,
    ! [X18058,X18059] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18059,tc_HOL_Obool)),X18058),c_Orderings_Obot__class_Obot(tc_fun(X18059,tc_HOL_Obool))) = X18058,
    inference(variable_rename,[status(thm)],[fact_Diff__empty]) ).

fof(i_0_10355,plain,
    ! [X17487,X17488] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17488,tc_HOL_Obool)),X17487),c_Orderings_Obot__class_Obot(tc_fun(X17488,tc_HOL_Obool))) = X17487,
    inference(variable_rename,[status(thm)],[fact_Un__empty__right]) ).

fof(i_0_10356,plain,
    ! [X20393,X20394] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20394,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20394,tc_HOL_Obool)),X20393)) = X20393,
    inference(variable_rename,[status(thm)],[fact_double__complement]) ).

fof(i_0_10357,plain,
    ! [X28862,X28863] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28863,X28863),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X28862) = X28862,
    inference(variable_rename,[status(thm)],[fact_rel__pow__1]) ).

fof(i_0_10358,plain,
    ! [X20201,X20202] : c_Map_Oran(X20202,X20201,hAPP(c_COMBK(tc_Option_Ooption(X20201),X20202),c_Option_Ooption_ONone(X20201))) = c_Orderings_Obot__class_Obot(tc_fun(X20201,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_ran__empty]) ).

fof(i_0_10359,plain,
    ! [X19262,X19263] : c_Map_Odom(X19263,X19262,hAPP(c_COMBK(tc_Option_Ooption(X19262),X19263),c_Option_Ooption_ONone(X19262))) = c_Orderings_Obot__class_Obot(tc_fun(X19263,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_dom__empty]) ).

fof(i_0_10360,plain,
    ! [X25269] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25269)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25269)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25269)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25269)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25269) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6048])]) ).

fof(i_0_10361,plain,
    ! [X31129,X31130,X31131] : hAPP(hAPP(c_List_Olist__update(X31131,X31130),X31129),hAPP(hAPP(c_List_Onth(X31131),X31130),X31129)) = X31130,
    inference(variable_rename,[status(thm)],[fact_list__update__id]) ).

fof(i_0_10362,plain,
    ! [X20801,X20802,X20803] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20803),X20802),X20802) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20803),X20801),X20801)
        | X20802 = X20801
        | X20802 = hAPP(c_Groups_Ouminus__class_Ouminus(X20803),X20801)
        | ~ class_Rings_Oidom(X20803) )
      & ( X20802 != X20801
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20803),X20802),X20802) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20803),X20801),X20801)
        | ~ class_Rings_Oidom(X20803) )
      & ( X20802 != hAPP(c_Groups_Ouminus__class_Ouminus(X20803),X20801)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20803),X20802),X20802) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20803),X20801),X20801)
        | ~ class_Rings_Oidom(X20803) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__iff])])]) ).

fof(i_0_10363,plain,
    ! [X21440,X21441] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21441)),X21440) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21441),X21440)),
    inference(variable_rename,[status(thm)],[fact_add__Suc]) ).

fof(i_0_10364,plain,
    ! [X32179,X32180,X32181] : hAPP(hAPP(c_List_Odrop(X32181),X32180),c_List_Obutlast(X32181,X32179)) = c_List_Obutlast(X32181,hAPP(hAPP(c_List_Odrop(X32181),X32180),X32179)),
    inference(variable_rename,[status(thm)],[fact_drop__butlast]) ).

fof(i_0_10365,plain,
    ! [X32176,X32177,X32178] : c_List_Obutlast(X32178,hAPP(hAPP(c_List_Odrop(X32178),X32177),X32176)) = hAPP(hAPP(c_List_Odrop(X32178),X32177),c_List_Obutlast(X32178,X32176)),
    inference(variable_rename,[status(thm)],[fact_butlast__drop]) ).

fof(i_0_10366,plain,
    ! [X31121] :
      ( ( X31121 = 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)),X31121)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X31121))
        | X31121 != 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_10367,plain,
    ! [X27597,X27598,X27599] :
      ( ( hAPP(c_Relation_ODomain(X27599,X27598),X27597) != c_Orderings_Obot__class_Obot(tc_fun(X27599,tc_HOL_Obool))
        | X27597 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27599,X27598),tc_HOL_Obool)) )
      & ( X27597 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27599,X27598),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(X27599,X27598),X27597) = c_Orderings_Obot__class_Obot(tc_fun(X27599,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__empty__iff])]) ).

fof(i_0_10368,plain,
    ! [X27523,X27524,X27525] :
      ( ( hAPP(c_Relation_ORange(X27525,X27524),X27523) != c_Orderings_Obot__class_Obot(tc_fun(X27524,tc_HOL_Obool))
        | X27523 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27525,X27524),tc_HOL_Obool)) )
      & ( X27523 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27525,X27524),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(X27525,X27524),X27523) = c_Orderings_Obot__class_Obot(tc_fun(X27524,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Range__empty__iff])]) ).

fof(i_0_10369,plain,
    ! [X27135] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X27135),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X27135) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X27135) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X27135),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X27135) = X27135 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6049])]) ).

fof(i_0_10370,plain,
    ! [X27099,X27100] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X27100),X27099)) != c_Groups_Oone__class_Oone(tc_Int_Oint)
      | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X27100) = 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_10371,plain,
    ! [X22851,X22852] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22852),X22851))
      | X22852 = X22851
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22851),X22852)) ),
    inference(variable_rename,[status(thm)],[fact_zless__linear]) ).

fof(i_0_10372,plain,
    ! [X20974,X20975] :
      ( X20975 = X20974
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20975),X20974))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20974),X20975)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6050])]) ).

fof(i_0_10373,plain,
    ! [X20972,X20973] :
      ( ( X20973 = X20972
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20973),X20972))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20972),X20973)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20973),X20972))
        | X20973 != X20972 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20972),X20973))
        | X20973 != X20972 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).

fof(i_0_10374,plain,
    ! [X26257,X26258] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X26258),X26257)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26257),X26258)),
    inference(variable_rename,[status(thm)],[fact_card__atLeastLessThan__int]) ).

cnf(i_0_10375,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_6051]) ).

fof(i_0_10376,plain,
    ! [X27060,X27061] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27061)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27061),X27060),hAPP(c_Groups_Oabs__class_Oabs(X27061),X27060))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__self])]) ).

fof(i_0_10377,plain,
    ! [X25592,X25593] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X25593,X25592)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25592),hAPP(c_Nat_OSuc,X25593)),
    inference(variable_rename,[status(thm)],[fact_card__greaterThanLessThan]) ).

fof(i_0_10378,plain,
    ! [X22936,X22937] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22937),X22936))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22936),X22937)) ),
    inference(variable_rename,[status(thm)],[fact_zle__linear]) ).

fof(i_0_10379,plain,
    ! [X21010,X21011] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21011),X21010))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21010),X21011)) ),
    inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).

fof(i_0_10380,plain,
    ! [X22992,X22993] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22993)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22992)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22993),X22992),
    inference(variable_rename,[status(thm)],[fact_zdiv__zminus__zminus]) ).

fof(i_0_10381,plain,
    ! [X22994,X22995] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22995),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22994)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22995)),X22994),
    inference(variable_rename,[status(thm)],[fact_zdiv__zminus2]) ).

fof(i_0_10382,plain,
    ! [X31919,X31920,X31921] : hAPP(hAPP(c_List_Odrop(X31921),hAPP(c_Nat_OSuc,X31920)),X31919) = hAPP(hAPP(c_List_Odrop(X31921),X31920),hAPP(c_List_Otl(X31921),X31919)),
    inference(variable_rename,[status(thm)],[fact_drop__Suc]) ).

fof(i_0_10383,plain,
    ! [X19259,X19260,X19261] :
      ( ( c_Map_Odom(X19261,X19260,X19259) != c_Orderings_Obot__class_Obot(tc_fun(X19261,tc_HOL_Obool))
        | X19259 = hAPP(c_COMBK(tc_Option_Ooption(X19260),X19261),c_Option_Ooption_ONone(X19260)) )
      & ( X19259 != hAPP(c_COMBK(tc_Option_Ooption(X19260),X19261),c_Option_Ooption_ONone(X19260))
        | c_Map_Odom(X19261,X19260,X19259) = c_Orderings_Obot__class_Obot(tc_fun(X19261,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dom__eq__empty__conv])]) ).

fof(i_0_10384,plain,
    ! [X22329,X22331,X22332] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22329))
        | X22329 = hAPP(c_Nat_OSuc,esk111_1(X22329)) )
      & ( X22331 != hAPP(c_Nat_OSuc,X22332)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22331)) ) ),
    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_10385,plain,
    ! [X25943,X25944] :
      ( ~ class_Orderings_Olinorder(X25944)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25944),X25943))
      | c_Big__Operators_Olattice_OSup__fin(X25944,c_Orderings_Oord__class_Omax(X25944),X25943) = hAPP(c_Finite__Set_Ofold1(X25944,c_Orderings_Oord__class_Omax(X25944)),X25943) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_OF__eq])]) ).

fof(i_0_10386,plain,
    ! [X25655,X25656] :
      ( ~ class_Orderings_Olinorder(X25656)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25656),X25655))
      | c_Big__Operators_Olattice_OInf__fin(X25656,c_Orderings_Oord__class_Omin(X25656),X25655) = hAPP(c_Finite__Set_Ofold1(X25656,c_Orderings_Oord__class_Omin(X25656)),X25655) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_OF__eq])]) ).

fof(i_0_10387,plain,
    ! [X32682] :
      ( ~ class_Orderings_Olinorder(X32682)
      | c_Finite__Set_Ofun__left__comm(X32682,tc_List_Olist(X32682),c_List_Olinorder__class_Oinsort__key(X32682,X32682,c_COMBI(X32682))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__insort])]) ).

fof(i_0_10388,plain,
    ! [X26990] :
      ( ( X26990 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Groups_Osgn__class_Osgn(tc_Int_Oint,X26990) = 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)),X26990))
        | c_Groups_Osgn__class_Osgn(tc_Int_Oint,X26990) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X26990 = 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)),X26990))
        | c_Groups_Osgn__class_Osgn(tc_Int_Oint,X26990) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | X26990 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6052])])]) ).

fof(i_0_10389,plain,
    ! [X31944,X31945] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31945),X31944))
      | hBOOL(hAPP(c_List_Odistinct(X31945),hAPP(c_List_Otl(X31945),X31944))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__tl])]) ).

fof(i_0_10390,plain,
    ! [X26092,X26093] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X26093),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26092),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X26093,X26092),
    inference(variable_rename,[status(thm)],[fact_atLeastLessThanPlusOne__atLeastAtMost__int]) ).

fof(i_0_10391,plain,
    ! [X24511] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X24511))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24511),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24511),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,X24511)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__def])]) ).

fof(i_0_10392,plain,
    ! [X30508,X30509] :
      ( hAPP(c_Finite__Set_Ocard(X30509),hAPP(c_List_Oset(X30509),X30508)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30509)),X30508)
      | hBOOL(hAPP(c_List_Odistinct(X30509),X30508)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__distinct])]) ).

fof(i_0_10393,plain,
    ! [X25213,X25214] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25214),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25213)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25214),X25213)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J]) ).

fof(i_0_10394,plain,
    ! [X32879,X32880,X32881] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(X32881),X32880),c_List_Olist_ONil(X32881)) != hAPP(c_List_Orev(X32881),X32879)
        | X32879 = hAPP(hAPP(c_List_Olist_OCons(X32881),X32880),c_List_Olist_ONil(X32881)) )
      & ( X32879 != hAPP(hAPP(c_List_Olist_OCons(X32881),X32880),c_List_Olist_ONil(X32881))
        | hAPP(hAPP(c_List_Olist_OCons(X32881),X32880),c_List_Olist_ONil(X32881)) = hAPP(c_List_Orev(X32881),X32879) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__rev__conv])]) ).

fof(i_0_10395,plain,
    ! [X32882,X32883,X32884] :
      ( ( hAPP(c_List_Orev(X32884),X32883) != hAPP(hAPP(c_List_Olist_OCons(X32884),X32882),c_List_Olist_ONil(X32884))
        | X32883 = hAPP(hAPP(c_List_Olist_OCons(X32884),X32882),c_List_Olist_ONil(X32884)) )
      & ( X32883 != hAPP(hAPP(c_List_Olist_OCons(X32884),X32882),c_List_Olist_ONil(X32884))
        | hAPP(c_List_Orev(X32884),X32883) = hAPP(hAPP(c_List_Olist_OCons(X32884),X32882),c_List_Olist_ONil(X32884)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__singleton__conv])]) ).

fof(i_0_10396,plain,
    ! [X30600,X30601] : c_List_Olistrel1(X30601,hAPP(c_Relation_Oconverse(X30601,X30601),X30600)) = hAPP(c_Relation_Oconverse(tc_List_Olist(X30601),tc_List_Olist(X30601)),c_List_Olistrel1(X30601,X30600)),
    inference(variable_rename,[status(thm)],[fact_listrel1__converse]) ).

fof(i_0_10397,plain,
    ! [X20443,X20444,X20445] :
      ( ~ class_Groups_Oab__group__add(X20445)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X20445),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20445),X20444),X20443)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20445),X20443),X20444) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__diff__eq])]) ).

cnf(i_0_10398,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_5848]) ).

fof(i_0_10399,plain,
    ! [X33970,X33971,X33972] : hAPP(c_List_Orev(X33972),c_List_Oreplicate(X33972,X33971,X33970)) = c_List_Oreplicate(X33972,X33971,X33970),
    inference(variable_rename,[status(thm)],[fact_rev__replicate]) ).

fof(i_0_10400,plain,
    ! [X27452,X27453,X27454] :
      ( ~ c_Wellfounded_Owf(X27454,X27453)
      | hBOOL(hAPP(hAPP(c_member(X27454),X27452),c_Wellfounded_Oacc(X27454,X27453))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__wfD])]) ).

fof(i_0_10401,plain,
    ! [X21394,X21395] :
      ( ~ class_Rings_Ocomm__ring__1(X21395)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X21395),X21394) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21395),hAPP(c_Groups_Ouminus__class_Ouminus(X21395),c_Groups_Oone__class_Oone(X21395))),X21394) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J])]) ).

fof(i_0_10402,plain,
    ! [X26085,X26086] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X26086),X26085))),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan__int]) ).

fof(i_0_10403,plain,
    ! [X26079,X26080] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26080),X26079))),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan]) ).

fof(i_0_10404,plain,
    ! [X34184,X34185,X34186] :
      ( ( ~ c_List_Olist__all(tc_Int_Oint,X34186,c_List_Oupto(X34185,X34184))
        | c_List_Oall__interval__int(X34186,X34185,X34184) )
      & ( ~ c_List_Oall__interval__int(X34186,X34185,X34184)
        | c_List_Olist__all(tc_Int_Oint,X34186,c_List_Oupto(X34185,X34184)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__iff__all__interval__int])]) ).

fof(i_0_10405,plain,
    ! [X17191,X17192,X17193] :
      ( ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X17192),X17191))
        | hBOOL(hAPP(X17191,X17193))
        | ~ class_Enum_Oenum(X17192) )
      & ( ~ hBOOL(hAPP(X17191,esk5_2(X17191,X17192)))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X17192),X17191))
        | ~ class_Enum_Oenum(X17192) ) ),
    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_10406,plain,
    ! [X17187,X17188,X17190] :
      ( ( ~ hBOOL(hAPP(X17187,esk4_2(X17187,X17188)))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X17188),X17187))
        | ~ class_Enum_Oenum(X17188) )
      & ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X17188),X17187))
        | hBOOL(hAPP(X17187,X17190))
        | ~ class_Enum_Oenum(X17188) ) ),
    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_10407,plain,
    ! [X22822] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22822)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X22822)),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_10408,plain,
    c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_6053]) ).

fof(i_0_10409,plain,
    ! [X18426,X18427,X18428] :
      ( ~ class_Orderings_Oorder(X18428)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18428),X18427),X18426))
      | X18426 != X18427 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).

fof(i_0_10410,plain,
    ! [X18423,X18424,X18425] :
      ( ~ class_Orderings_Oorder(X18425)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18425),X18424),X18423))
      | X18424 != X18423 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).

fof(i_0_10411,plain,
    ! [X18414,X18415,X18416] :
      ( ~ class_Orderings_Oorder(X18416)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18416),X18415),X18414))
      | X18415 != X18414 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).

cnf(i_0_10412,plain,
    c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_6054]) ).

fof(i_0_10413,plain,
    ! [X33999,X34000,X34001,X34002,X34003] :
      ( ( X34002 = X34000
        | c_List_Oreplicate(X34003,X34002,X34001) != c_List_Oreplicate(X34003,X34000,X33999) )
      & ( X34002 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X34001 = X33999
        | c_List_Oreplicate(X34003,X34002,X34001) != c_List_Oreplicate(X34003,X34000,X33999) )
      & ( X34002 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X34002 != X34000
        | c_List_Oreplicate(X34003,X34002,X34001) = c_List_Oreplicate(X34003,X34000,X33999) )
      & ( X34001 != X33999
        | X34002 != X34000
        | c_List_Oreplicate(X34003,X34002,X34001) = c_List_Oreplicate(X34003,X34000,X33999) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_replicate__eq__replicate])])]) ).

fof(i_0_10414,plain,
    ! [X18625,X18626,X18627,X18628,X18629] :
      ( ( X18628 != X18627
        | X18626 = X18625
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18629),X18628),X18627) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18629),X18626),X18625)
        | ~ class_Groups_Oab__group__add(X18629) )
      & ( X18626 != X18625
        | X18628 = X18627
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18629),X18628),X18627) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18629),X18626),X18625)
        | ~ class_Groups_Oab__group__add(X18629) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq])])]) ).

fof(i_0_10415,plain,
    ! [X33680,X33681,X33682] :
      ( ( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X33682),X33681),X33680))
        | X33681 = X33680
        | ~ class_HOL_Oequal(X33682) )
      & ( X33681 != X33680
        | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X33682),X33681),X33680))
        | ~ class_HOL_Oequal(X33682) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__eq])])]) ).

fof(i_0_10416,plain,
    ! [X30158,X30159,X30160,X30161] : hAPP(hAPP(c_Option_Omap(X30161,X30160),X30159),hAPP(c_Option_Ooption_OSome(X30161),X30158)) = hAPP(c_Option_Ooption_OSome(X30160),hAPP(X30159,X30158)),
    inference(variable_rename,[status(thm)],[fact_option__map__Some]) ).

fof(i_0_10417,plain,
    ! [X32910,X32911,X32912] : hAPP(c_List_Orev(X32912),hAPP(c_List_Ofilter(X32912,X32911),X32910)) = hAPP(c_List_Ofilter(X32912,X32911),hAPP(c_List_Orev(X32912),X32910)),
    inference(variable_rename,[status(thm)],[fact_rev__filter]) ).

fof(i_0_10418,plain,
    ! [X23434,X23435] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23435),X23434) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23435,X23434) != 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_10419,plain,
    ! [X23436,X23437] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X23437,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23436)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23437,X23436) != 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_10420,plain,
    ! [X18397,X18398] :
      ( ~ class_Orderings_Opreorder(X18398)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18398),X18397),X18397)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6055])]) ).

fof(i_0_10421,plain,
    ! [X22071] :
      ( ( X22071 = 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)),X22071)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22071))
        | X22071 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).

fof(i_0_10422,plain,
    ! [X31338,X31339] :
      ( ( X31339 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Enum_On__lists(X31338,X31339,c_List_Olist_ONil(X31338)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31338)),c_List_Olist_ONil(X31338)),c_List_Olist_ONil(tc_List_Olist(X31338))) )
      & ( X31339 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Enum_On__lists(X31338,X31339,c_List_Olist_ONil(X31338)) = c_List_Olist_ONil(tc_List_Olist(X31338)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__lists__Nil])]) ).

fof(i_0_10423,plain,
    ! [X21501,X21502,X21503,X21504] :
      ( ~ class_Groups_Ocancel__semigroup__add(X21504)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21504),X21503),X21502) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21504),X21501),X21502)
      | X21503 = X21501 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).

fof(i_0_10424,plain,
    ! [X21489,X21490,X21491,X21492] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21492),X21491),X21490) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21492),X21489),X21490)
        | X21491 = X21489
        | ~ class_Groups_Ocancel__semigroup__add(X21492) )
      & ( X21491 != X21489
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21492),X21491),X21490) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21492),X21489),X21490)
        | ~ class_Groups_Ocancel__semigroup__add(X21492) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).

fof(i_0_10425,plain,
    ! [X21497,X21498,X21499,X21500] :
      ( ~ class_Groups_Ocancel__ab__semigroup__add(X21500)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21500),X21499),X21498) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21500),X21499),X21497)
      | X21498 = X21497 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).

fof(i_0_10426,plain,
    ! [X21493,X21494,X21495,X21496] :
      ( ~ class_Groups_Ocancel__semigroup__add(X21496)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21496),X21495),X21494) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21496),X21495),X21493)
      | X21494 = X21493 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).

fof(i_0_10427,plain,
    ! [X21485,X21486,X21487,X21488] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21488),X21487),X21486) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21488),X21487),X21485)
        | X21486 = X21485
        | ~ class_Groups_Ocancel__semigroup__add(X21488) )
      & ( X21486 != X21485
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21488),X21487),X21486) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21488),X21487),X21485)
        | ~ class_Groups_Ocancel__semigroup__add(X21488) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).

fof(i_0_10428,plain,
    ! [X33764,X33765,X33766,X33767,X33768] :
      ( ( X33767 = X33765
        | c_Lazy__Sequence_Olazy__sequence_OInsert(X33768,X33767,X33766) != c_Lazy__Sequence_Olazy__sequence_OInsert(X33768,X33765,X33764) )
      & ( X33766 = X33764
        | c_Lazy__Sequence_Olazy__sequence_OInsert(X33768,X33767,X33766) != c_Lazy__Sequence_Olazy__sequence_OInsert(X33768,X33765,X33764) )
      & ( X33767 != X33765
        | X33766 != X33764
        | c_Lazy__Sequence_Olazy__sequence_OInsert(X33768,X33767,X33766) = c_Lazy__Sequence_Olazy__sequence_OInsert(X33768,X33765,X33764) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Oinject])])]) ).

fof(i_0_10429,plain,
    ! [X24544] :
      ( ( hAPP(c_Int_Onat,X24544) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24544),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24544),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onat,X24544) = 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_10430,plain,
    ! [X24543] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24543),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(c_Int_Onat,X24543) = 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_10431,plain,
    ! [X25550] :
      ( ( ~ c_Nat__Transfer_Ois__nat(X25550)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25550)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25550))
        | c_Nat__Transfer_Ois__nat(X25550) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_is__nat__def])]) ).

fof(i_0_10432,plain,
    ! [X21435,X21436] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21436),hAPP(c_Nat_OSuc,X21435)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21436),X21435)),
    inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).

fof(i_0_10433,plain,
    ! [X27501,X27502] : hAPP(c_List_Olexn(X27502,X27501),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X27502),tc_List_Olist(X27502)),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_lexn_Osimps_I1_J]) ).

fof(i_0_10434,plain,
    ! [X25129] : 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),X25129))),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J]) ).

fof(i_0_10435,plain,
    ! [X25116] : 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),X25116))),
    inference(variable_rename,[status(thm)],[fact_zero__zle__int]) ).

fof(i_0_10436,plain,
    ! [X18056,X18057] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18057,tc_HOL_Obool)),X18056),X18056) = c_Orderings_Obot__class_Obot(tc_fun(X18057,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Diff__cancel]) ).

fof(i_0_10437,plain,
    ! [X27384] : c_Wellfounded_Owf(X27384,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27384,X27384),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_wf__empty]) ).

fof(i_0_10438,plain,
    ! [X26163,X26164,X26165] :
      ( ~ class_Orderings_Oorder(X26165)
      | X26164 != X26163
      | c_SetInterval_Oord__class_OatLeastAtMost(X26165,X26164,X26163) = hAPP(hAPP(c_Set_Oinsert(X26165),X26164),c_Orderings_Obot__class_Obot(tc_fun(X26165,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton_H])]) ).

fof(i_0_10439,plain,
    ! [X32829,X32830] :
      ( ( hAPP(c_List_Oset(X32830),c_List_Olinorder__class_Osorted__list__of__set(X32830,X32829)) = X32829
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32830),X32829))
        | ~ class_Orderings_Olinorder(X32830) )
      & ( c_List_Olinorder__class_Osorted(X32830,c_List_Olinorder__class_Osorted__list__of__set(X32830,X32829))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32830),X32829))
        | ~ class_Orderings_Olinorder(X32830) )
      & ( hBOOL(hAPP(c_List_Odistinct(X32830),c_List_Olinorder__class_Osorted__list__of__set(X32830,X32829)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32830),X32829))
        | ~ class_Orderings_Olinorder(X32830) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set])])]) ).

fof(i_0_10440,plain,
    ! [X23395,X23396,X23397] :
      ( ~ class_Divides_Osemiring__div(X23397)
      | c_Divides_Odiv__class_Omod(X23397,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23397),X23396),X23395),X23396) = c_Groups_Ozero__class_Ozero(X23397) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1__is__0])]) ).

fof(i_0_10441,plain,
    ! [X23398,X23399,X23400] :
      ( ~ class_Divides_Osemiring__div(X23400)
      | c_Divides_Odiv__class_Omod(X23400,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23400),X23399),X23398),X23398) = c_Groups_Ozero__class_Ozero(X23400) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2__is__0])]) ).

fof(i_0_10442,plain,
    ! [X32190,X32191] :
      ( X32191 = c_List_Olist_ONil(X32190)
      | ~ hBOOL(hAPP(c_List_Odistinct(X32190),X32191))
      | hBOOL(hAPP(c_List_Odistinct(X32190),c_List_Obutlast(X32190,X32191))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__butlast])]) ).

fof(i_0_10443,plain,
    ! [X25648,X25649] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X25649,X25648)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25648),X25649),
    inference(variable_rename,[status(thm)],[fact_card__greaterThanAtMost]) ).

fof(i_0_10444,plain,
    ! [X30297,X30298,X30299,X30300,X30301] :
      ( ( X30300 = X30298
        | hAPP(hAPP(c_List_Olist_OCons(X30301),X30300),X30299) != hAPP(hAPP(c_List_Olist_OCons(X30301),X30298),X30297) )
      & ( X30299 = X30297
        | hAPP(hAPP(c_List_Olist_OCons(X30301),X30300),X30299) != hAPP(hAPP(c_List_Olist_OCons(X30301),X30298),X30297) )
      & ( X30300 != X30298
        | X30299 != X30297
        | hAPP(hAPP(c_List_Olist_OCons(X30301),X30300),X30299) = hAPP(hAPP(c_List_Olist_OCons(X30301),X30298),X30297) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list_Oinject])])]) ).

fof(i_0_10445,plain,
    ! [X31614,X31615,X31616,X31617] :
      ( ( hAPP(hAPP(c_List_Oappend(X31617),X31616),X31615) != hAPP(hAPP(c_List_Oappend(X31617),X31614),X31615)
        | X31616 = X31614 )
      & ( X31616 != X31614
        | hAPP(hAPP(c_List_Oappend(X31617),X31616),X31615) = hAPP(hAPP(c_List_Oappend(X31617),X31614),X31615) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__same__eq])]) ).

fof(i_0_10446,plain,
    ! [X31610,X31611,X31612,X31613] :
      ( ( hAPP(hAPP(c_List_Oappend(X31613),X31612),X31611) != hAPP(hAPP(c_List_Oappend(X31613),X31612),X31610)
        | X31611 = X31610 )
      & ( X31611 != X31610
        | hAPP(hAPP(c_List_Oappend(X31613),X31612),X31611) = hAPP(hAPP(c_List_Oappend(X31613),X31612),X31610) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__append__eq])]) ).

fof(i_0_10447,plain,
    ! [X26170,X26171] :
      ( ~ class_Orderings_Oorder(X26171)
      | c_SetInterval_Oord__class_OatLeastAtMost(X26171,X26170,X26170) = hAPP(hAPP(c_Set_Oinsert(X26171),X26170),c_Orderings_Obot__class_Obot(tc_fun(X26171,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton])]) ).

fof(i_0_10448,plain,
    ! [X31355,X31356] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X31356),X31355))
      | c_List_Oupto(X31355,X31356) = c_List_Olist_ONil(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upto__empty])]) ).

fof(i_0_10449,plain,
    ! [X31336,X31337] : c_Enum_On__lists(X31337,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31336) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31337)),c_List_Olist_ONil(X31337)),c_List_Olist_ONil(tc_List_Olist(X31337))),
    inference(variable_rename,[status(thm)],[fact_n__lists_Osimps_I1_J]) ).

fof(i_0_10450,plain,
    ! [X26803] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26803)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26803)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X26803)),
    inference(variable_rename,[status(thm)],[fact_atMost__Suc]) ).

fof(i_0_10451,plain,
    ! [X24644] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24644) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24644),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24644),c_Int_OPls))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24644) = 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_10452,plain,
    ! [X24513] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24513)))
      | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24513) = 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_10453,plain,
    ! [X24643] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24643)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24643),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24643),c_Int_OPls))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24643) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__0__number__of])]) ).

cnf(i_0_10454,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_6056]) ).

fof(i_0_10455,plain,
    ! [X25846,X25847,X25848] :
      ( ~ class_Orderings_Olinorder(X25848)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25848),X25847),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25848),X25847),X25846)) = X25847 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__absorb])]) ).

fof(i_0_10456,plain,
    ! [X25843,X25844,X25845] :
      ( ~ class_Orderings_Olinorder(X25845)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25845),X25844),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25845),X25844),X25843)) = X25844 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__absorb])]) ).

fof(i_0_10457,plain,
    ! [X18010,X18011,X18012] :
      ( ~ class_Lattices_Olattice(X18012)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18012),X18011),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18012),X18011),X18010)) = X18011 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__absorb])]) ).

fof(i_0_10458,plain,
    ! [X18013,X18014,X18015] :
      ( ~ class_Lattices_Olattice(X18015)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18015),X18014),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18015),X18014),X18013)) = X18014 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__absorb])]) ).

fof(i_0_10459,plain,
    ! [X33920,X33921,X33922] : c_Predicate_Oconversep(X33922,X33921,c_Predicate_Oconversep(X33921,X33922,X33920)) = X33920,
    inference(variable_rename,[status(thm)],[fact_conversep__conversep]) ).

fof(i_0_10460,plain,
    ! [X22082] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22082),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | X22082 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22082 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22082),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_10461,plain,
    ! [X31810,X31811,X31812] : hAPP(hAPP(c_List_Odrop(X31812),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X31812),X31811),X31810)) = X31810,
    inference(variable_rename,[status(thm)],[fact_drop__1__Cons]) ).

fof(i_0_10462,plain,
    ! [X21695,X21696] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21696)),hAPP(c_Nat_OSuc,X21695)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21696),X21695),
    inference(variable_rename,[status(thm)],[fact_diff__Suc__Suc]) ).

fof(i_0_10463,plain,
    ! [X21442,X21443] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21443)),X21442) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21443),hAPP(c_Nat_OSuc,X21442)),
    inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).

fof(i_0_10464,plain,
    ! [X21255,X21256,X21257] : hAPP(c_Finite__Set_Ofold1(X21257,X21256),X21255) = c_HOL_OThe(X21257,c_Finite__Set_Ofold1Set(X21257,X21256,X21255)),
    inference(variable_rename,[status(thm)],[fact_fold1__def]) ).

fof(i_0_10465,plain,
    ! [X23428,X23429,X23431,X23432,X23433] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X23429,X23428) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X23429 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23428),esk123_2(X23428,X23429)) )
      & ( X23432 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23431),X23433)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23432,X23431) = 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_10466,plain,
    ! [X23645,X23646,X23648,X23649,X23650] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23646,X23645) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X23646 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23645),esk133_2(X23645,X23646)) )
      & ( X23649 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23648),X23650)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23649,X23648) = 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_10467,plain,
    ! [X25551,X25552] :
      ( ~ c_Nat__Transfer_Onat__set(X25552)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25551),X25552))
      | c_Nat__Transfer_Ois__nat(X25551) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J])]) ).

fof(i_0_10468,plain,
    ! [X28764,X28765] :
      ( ( ~ c_Wellfounded_Oacyclic(X28765,hAPP(c_Relation_Oconverse(X28765,X28765),X28764))
        | c_Wellfounded_Oacyclic(X28765,X28764) )
      & ( ~ c_Wellfounded_Oacyclic(X28765,X28764)
        | c_Wellfounded_Oacyclic(X28765,hAPP(c_Relation_Oconverse(X28765,X28765),X28764)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__converse])]) ).

fof(i_0_10469,plain,
    ! [X22072] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22072),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[i_0_6057]) ).

fof(i_0_10470,plain,
    ! [X22070] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22070),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[i_0_6058]) ).

fof(i_0_10471,plain,
    ! [X22004] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22004),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[i_0_6059]) ).

fof(i_0_10472,plain,
    ! [X30506,X30507] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30507),X30506))
      | hAPP(c_Finite__Set_Ocard(X30507),hAPP(c_List_Oset(X30507),X30506)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30507)),X30506) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__card])]) ).

fof(i_0_10473,plain,
    ! [X32515,X32516] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32516)),c_List_Oremdups(X32516,X32515)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32516)),X32515)
        | c_List_Oremdups(X32516,X32515) = X32515 )
      & ( c_List_Oremdups(X32516,X32515) != X32515
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32516)),c_List_Oremdups(X32516,X32515)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32516)),X32515) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__remdups__eq])]) ).

fof(i_0_10474,plain,
    ! [X28774,X28775,X28776] : hAPP(c_Relation_ODomain(X28776,X28775),hAPP(c_Relation_Oconverse(X28775,X28776),X28774)) = hAPP(c_Relation_ORange(X28775,X28776),X28774),
    inference(variable_rename,[status(thm)],[fact_Domain__converse]) ).

fof(i_0_10475,plain,
    ! [X28771,X28772,X28773] : hAPP(c_Relation_ORange(X28773,X28772),hAPP(c_Relation_Oconverse(X28772,X28773),X28771)) = hAPP(c_Relation_ODomain(X28772,X28773),X28771),
    inference(variable_rename,[status(thm)],[fact_Range__converse]) ).

fof(i_0_10476,plain,
    ! [X32500,X32501,X32502] : c_List_Oremdups(X32502,hAPP(c_List_Ofilter(X32502,X32501),X32500)) = hAPP(c_List_Ofilter(X32502,X32501),c_List_Oremdups(X32502,X32500)),
    inference(variable_rename,[status(thm)],[fact_remdups__filter]) ).

fof(i_0_10477,plain,
    ! [X28707,X28708] : c_Transitive__Closure_Ortrancl(X28708,hAPP(c_Relation_Oconverse(X28708,X28708),X28707)) = hAPP(c_Relation_Oconverse(X28708,X28708),c_Transitive__Closure_Ortrancl(X28708,X28707)),
    inference(variable_rename,[status(thm)],[fact_rtrancl__converse]) ).

fof(i_0_10478,plain,
    ! [X28777,X28778,X28779] : hAPP(c_Relation_ORange(X28779,X28778),X28777) = hAPP(c_Relation_ODomain(X28778,X28779),hAPP(c_Relation_Oconverse(X28779,X28778),X28777)),
    inference(variable_rename,[status(thm)],[fact_Range__def]) ).

fof(i_0_10479,plain,
    ! [X18728,X18729,X18730] :
      ( ( ~ hBOOL(hAPP(X18728,X18730))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X18729),X18728))
        | ~ class_Enum_Oenum(X18729) )
      & ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X18729),X18728))
        | hBOOL(hAPP(X18728,esk35_2(X18728,X18729)))
        | ~ class_Enum_Oenum(X18729) ) ),
    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_10480,plain,
    ! [X18724,X18725,X18727] :
      ( ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X18725),X18724))
        | hBOOL(hAPP(X18724,esk34_2(X18724,X18725)))
        | ~ class_Enum_Oenum(X18725) )
      & ( ~ hBOOL(hAPP(X18724,X18727))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X18725),X18724))
        | ~ class_Enum_Oenum(X18725) ) ),
    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_10481,plain,
    ! [X31413,X31414,X31415,X31416] :
      ( ( hAPP(hAPP(c_List_Olist__update(X31416,X31415),X31414),X31413) != c_List_Olist_ONil(X31416)
        | X31415 = c_List_Olist_ONil(X31416) )
      & ( X31415 != c_List_Olist_ONil(X31416)
        | hAPP(hAPP(c_List_Olist__update(X31416,X31415),X31414),X31413) = c_List_Olist_ONil(X31416) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__nonempty])]) ).

fof(i_0_10482,plain,
    ! [X31385,X31386,X31387,X31388] :
      ( ( hAPP(hAPP(c_List_Omap(X31388,X31387),X31386),X31385) != c_List_Olist_ONil(X31387)
        | X31385 = c_List_Olist_ONil(X31388) )
      & ( X31385 != c_List_Olist_ONil(X31388)
        | hAPP(hAPP(c_List_Omap(X31388,X31387),X31386),X31385) = c_List_Olist_ONil(X31387) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__is__Nil__conv])]) ).

fof(i_0_10483,plain,
    ! [X30162,X30163,X30164,X30165] :
      ( ( hAPP(hAPP(c_Option_Omap(X30165,X30164),X30163),X30162) != c_Option_Ooption_ONone(X30164)
        | X30162 = c_Option_Ooption_ONone(X30165) )
      & ( X30162 != c_Option_Ooption_ONone(X30165)
        | hAPP(hAPP(c_Option_Omap(X30165,X30164),X30163),X30162) = c_Option_Ooption_ONone(X30164) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_option__map__is__None])]) ).

fof(i_0_10484,plain,
    ! [X31392,X31393,X31394,X31395] :
      ( ( c_List_Olist_ONil(X31395) != hAPP(hAPP(c_List_Omap(X31394,X31395),X31393),X31392)
        | X31392 = c_List_Olist_ONil(X31394) )
      & ( X31392 != c_List_Olist_ONil(X31394)
        | c_List_Olist_ONil(X31395) = hAPP(hAPP(c_List_Omap(X31394,X31395),X31393),X31392) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__map__conv])]) ).

fof(i_0_10485,plain,
    ! [X20203,X20204] : c_Option_Oset(X20204,hAPP(c_Option_Ooption_OSome(X20204),X20203)) = hAPP(hAPP(c_Set_Oinsert(X20204),X20203),c_Orderings_Obot__class_Obot(tc_fun(X20204,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_Option_Oset_Osimps_I2_J]) ).

fof(i_0_10486,plain,
    ! [X22087,X22088] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22088),X22087) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22087),X22088) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | X22088 = X22087 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diffs0__imp__equal])]) ).

fof(i_0_10487,plain,
    ! [X17258,X17259,X17260] :
      ( ~ class_Orderings_Oorder(X17260)
      | ~ class_Orderings_Oorder(X17259)
      | ~ c_Orderings_Oorder__class_Ostrict__mono(X17259,X17260,X17258)
      | c_Orderings_Oorder__class_Omono(X17259,X17260,X17258) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_strict__mono__mono])]) ).

fof(i_0_10488,plain,
    ! [X26489,X26490,X26491] :
      ( ~ class_Groups_Ocomm__monoid__add(X26491)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26490,X26491),X26489),c_Orderings_Obot__class_Obot(tc_fun(X26490,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X26491) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__empty])]) ).

fof(i_0_10489,plain,
    ! [X26486,X26487,X26488] :
      ( ~ class_Groups_Ocomm__monoid__add(X26488)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26487,X26488),X26486),c_Orderings_Obot__class_Obot(tc_fun(X26487,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X26488) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oempty])]) ).

fof(i_0_10490,plain,
    ! [X23040,X23041,X23042] :
      ( ~ class_Groups_Ocomm__monoid__mult(X23042)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23041,X23042),X23040),c_Orderings_Obot__class_Obot(tc_fun(X23041,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X23042) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oempty])]) ).

fof(i_0_10491,plain,
    ! [X23037,X23038,X23039] :
      ( ~ class_Groups_Ocomm__monoid__mult(X23039)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23038,X23039),X23037),c_Orderings_Obot__class_Obot(tc_fun(X23038,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X23039) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__empty])]) ).

fof(i_0_10492,plain,
    ! [X22073,X22074] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22074),X22073))
      | X22073 != 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_10493,plain,
    ! [X20468] :
      ( ~ class_Finite__Set_Ofinite(X20468)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20468),c_Orderings_Otop__class_Otop(tc_fun(X20468,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV])]) ).

fof(i_0_10494,plain,
    ! [X24341,X24342,X24343,X24344] :
      ( ( X24342 = c_Groups_Ozero__class_Ozero(X24344)
        | X24343 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24344),X24341),X24342)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24344),X24343),X24342) != X24341
        | ~ class_Fields_Ofield__inverse__zero(X24344) )
      & ( X24342 != c_Groups_Ozero__class_Ozero(X24344)
        | X24341 = c_Groups_Ozero__class_Ozero(X24344)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24344),X24343),X24342) != X24341
        | ~ class_Fields_Ofield__inverse__zero(X24344) )
      & ( X24342 = c_Groups_Ozero__class_Ozero(X24344)
        | X24342 != c_Groups_Ozero__class_Ozero(X24344)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24344),X24343),X24342) = X24341
        | ~ class_Fields_Ofield__inverse__zero(X24344) )
      & ( X24341 != c_Groups_Ozero__class_Ozero(X24344)
        | X24342 != c_Groups_Ozero__class_Ozero(X24344)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24344),X24343),X24342) = X24341
        | ~ class_Fields_Ofield__inverse__zero(X24344) )
      & ( X24342 = c_Groups_Ozero__class_Ozero(X24344)
        | X24343 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24344),X24341),X24342)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24344),X24343),X24342) = X24341
        | ~ class_Fields_Ofield__inverse__zero(X24344) )
      & ( X24341 != c_Groups_Ozero__class_Ozero(X24344)
        | X24343 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24344),X24341),X24342)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24344),X24343),X24342) = X24341
        | ~ class_Fields_Ofield__inverse__zero(X24344) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq])])]) ).

fof(i_0_10495,plain,
    ! [X24345,X24346,X24347,X24348] :
      ( ( X24345 = c_Groups_Ozero__class_Ozero(X24348)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24348),X24347),X24345) = X24346
        | X24347 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24348),X24346),X24345)
        | ~ class_Fields_Ofield__inverse__zero(X24348) )
      & ( X24345 != c_Groups_Ozero__class_Ozero(X24348)
        | X24347 = c_Groups_Ozero__class_Ozero(X24348)
        | X24347 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24348),X24346),X24345)
        | ~ class_Fields_Ofield__inverse__zero(X24348) )
      & ( X24345 = c_Groups_Ozero__class_Ozero(X24348)
        | X24345 != c_Groups_Ozero__class_Ozero(X24348)
        | X24347 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24348),X24346),X24345)
        | ~ class_Fields_Ofield__inverse__zero(X24348) )
      & ( X24347 != c_Groups_Ozero__class_Ozero(X24348)
        | X24345 != c_Groups_Ozero__class_Ozero(X24348)
        | X24347 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24348),X24346),X24345)
        | ~ class_Fields_Ofield__inverse__zero(X24348) )
      & ( X24345 = c_Groups_Ozero__class_Ozero(X24348)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24348),X24347),X24345) != X24346
        | X24347 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24348),X24346),X24345)
        | ~ class_Fields_Ofield__inverse__zero(X24348) )
      & ( X24347 != c_Groups_Ozero__class_Ozero(X24348)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24348),X24347),X24345) != X24346
        | X24347 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24348),X24346),X24345)
        | ~ class_Fields_Ofield__inverse__zero(X24348) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq])])]) ).

fof(i_0_10496,plain,
    ! [X25243,X25244] :
      ( ~ class_Rings_Osemiring__1(X25244)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25244),hAPP(c_Nat_OSuc,X25243)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25244),c_Groups_Oone__class_Oone(X25244)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25244),X25243)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__Suc])]) ).

fof(i_0_10497,plain,
    ! [X22006] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X22006))),
    inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).

fof(i_0_10498,plain,
    ! [X20979,X20980] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20980),X20979))
      | X20980 != X20979 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).

fof(i_0_10499,plain,
    ! [X20977,X20978] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20978),X20977))
      | X20977 != X20978 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).

cnf(i_0_10500,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_6060]) ).

fof(i_0_10501,plain,
    ! [X26205] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26205),hAPP(c_Nat_OSuc,X26205)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X26205),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_atLeastLessThan__singleton]) ).

cnf(i_0_10502,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_5553]) ).

fof(i_0_10503,plain,
    ! [X32968,X32969,X32970] :
      ( ~ class_Orderings_Olinorder(X32970)
      | ~ c_List_Olinorder__class_Osorted(X32970,X32969)
      | c_List_Olinorder__class_Osorted(X32970,c_List_OtakeWhile(X32970,X32968,X32969)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__takeWhile])]) ).

fof(i_0_10504,plain,
    ! [X32758,X32759,X32760] :
      ( ~ class_Orderings_Olinorder(X32760)
      | ~ c_List_Olinorder__class_Osorted(X32760,X32759)
      | c_List_Olinorder__class_Osorted(X32760,c_List_Oremove1(X32760,X32758,X32759)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__remove1])]) ).

fof(i_0_10505,plain,
    ! [X22089,X22090,X22091] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22091),X22090) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22089),X22090)
        | X22091 = X22089
        | X22090 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22091 != X22089
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22091),X22090) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22089),X22090) )
      & ( X22090 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22091),X22090) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22089),X22090) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel2])])]) ).

fof(i_0_10506,plain,
    ! [X22099,X22100,X22101] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22101),X22100) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22101),X22099)
        | X22101 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22100 = X22099 )
      & ( X22101 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22101),X22100) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22101),X22099) )
      & ( X22100 != X22099
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22101),X22100) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22101),X22099) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj])])]) ).

fof(i_0_10507,plain,
    ! [X22092,X22093,X22094] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22094),X22093) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22094),X22092)
        | X22093 = X22092
        | X22094 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22093 != X22092
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22094),X22093) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22094),X22092) )
      & ( X22094 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22094),X22093) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22094),X22092) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel1])])]) ).

fof(i_0_10508,plain,
    ! [X31895,X31896,X31897] :
      ( ( X31897 != c_List_Olist_ONil(X31896)
        | hAPP(c_List_Ohd(X31896),hAPP(hAPP(c_List_Oappend(X31896),X31897),X31895)) = hAPP(c_List_Ohd(X31896),X31895) )
      & ( X31897 = c_List_Olist_ONil(X31896)
        | hAPP(c_List_Ohd(X31896),hAPP(hAPP(c_List_Oappend(X31896),X31897),X31895)) = hAPP(c_List_Ohd(X31896),X31897) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__append])]) ).

fof(i_0_10509,plain,
    ! [X27103,X27104] :
      ( ~ class_Rings_Olinordered__idom(X27104)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27104),c_Groups_Osgn__class_Osgn(X27104,X27103)),hAPP(c_Groups_Oabs__class_Oabs(X27104),X27103)) = X27103 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__sgn__abs])]) ).

fof(i_0_10510,plain,
    ! [X22286] :
      ( ~ class_Rings_Olinordered__semidom(X22286)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22286),c_Groups_Ozero__class_Ozero(X22286)),c_Groups_Oone__class_Oone(X22286))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).

fof(i_0_10511,plain,
    ! [X25657] :
      ( ~ class_Rings_Osemiring__1(X25657)
      | hBOOL(hAPP(hAPP(c_member(X25657),c_Groups_Ozero__class_Ozero(X25657)),c_Nat_Osemiring__1__class_ONats(X25657))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__0])]) ).

fof(i_0_10512,plain,
    ! [X22888] :
      ( ~ class_Rings_Oring__1(X22888)
      | hBOOL(hAPP(hAPP(c_member(X22888),c_Groups_Ozero__class_Ozero(X22888)),c_Int_Oring__1__class_OInts(X22888))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__0])]) ).

fof(i_0_10513,plain,
    ! [X25664] :
      ( ~ class_Rings_Osemiring__1(X25664)
      | hBOOL(hAPP(hAPP(c_member(X25664),c_Groups_Oone__class_Oone(X25664)),c_Nat_Osemiring__1__class_ONats(X25664))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__1])]) ).

fof(i_0_10514,plain,
    ! [X22898] :
      ( ~ class_Rings_Oring__1(X22898)
      | hBOOL(hAPP(hAPP(c_member(X22898),c_Groups_Oone__class_Oone(X22898)),c_Int_Oring__1__class_OInts(X22898))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__1])]) ).

fof(i_0_10515,plain,
    ! [X22284] :
      ( ~ class_Rings_Olinordered__semidom(X22284)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22284),c_Groups_Ozero__class_Ozero(X22284)),c_Groups_Oone__class_Oone(X22284))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).

fof(i_0_10516,plain,
    ! [X24154,X24155,X24156,X24157] :
      ( ~ class_Rings_Odivision__ring(X24157)
      | X24156 = c_Groups_Ozero__class_Ozero(X24157)
      | X24155 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24157),X24154),X24156)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24157),X24155),X24156) = X24154 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__imp])]) ).

fof(i_0_10517,plain,
    ! [X24158,X24159,X24160,X24161] :
      ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24161),X24159),X24160) != X24158
        | X24159 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24161),X24158),X24160)
        | X24160 = c_Groups_Ozero__class_Ozero(X24161)
        | ~ class_Rings_Odivision__ring(X24161) )
      & ( X24159 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24161),X24158),X24160)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24161),X24159),X24160) = X24158
        | X24160 = c_Groups_Ozero__class_Ozero(X24161)
        | ~ class_Rings_Odivision__ring(X24161) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__divide__eq__eq])])]) ).

fof(i_0_10518,plain,
    ! [X24162,X24163,X24164,X24165] :
      ( ( X24163 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24165),X24162),X24164)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24165),X24163),X24164) = X24162
        | X24164 = c_Groups_Ozero__class_Ozero(X24165)
        | ~ class_Rings_Odivision__ring(X24165) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24165),X24163),X24164) != X24162
        | X24163 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24165),X24162),X24164)
        | X24164 = c_Groups_Ozero__class_Ozero(X24165)
        | ~ class_Rings_Odivision__ring(X24165) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__eq__divide__eq])])]) ).

fof(i_0_10519,plain,
    ! [X24150,X24151,X24152,X24153] :
      ( ~ class_Rings_Odivision__ring(X24153)
      | X24152 = c_Groups_Ozero__class_Ozero(X24153)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24153),X24151),X24152) != X24150
      | X24151 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24153),X24150),X24152) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__imp])]) ).

fof(i_0_10520,plain,
    ! [X21804,X21805,X21806] :
      ( ~ class_Groups_Ogroup__add(X21806)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21806),X21805),hAPP(c_Groups_Ouminus__class_Ouminus(X21806),X21804)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21806),X21805),X21804) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add])]) ).

fof(i_0_10521,plain,
    ! [X21771,X21772,X21773] :
      ( ~ class_Rings_Ocomm__ring__1(X21773)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21773),X21772),X21771) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21773),X21772),hAPP(c_Groups_Ouminus__class_Ouminus(X21773),X21771)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J])]) ).

fof(i_0_10522,plain,
    ! [X21798,X21799,X21800] :
      ( ~ class_Groups_Ogroup__add(X21800)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21800),X21799),X21798) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21800),X21799),hAPP(c_Groups_Ouminus__class_Ouminus(X21800),X21798)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__def])]) ).

fof(i_0_10523,plain,
    ! [X21801,X21802,X21803] :
      ( ~ class_Groups_Oab__group__add(X21803)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21803),X21802),X21801) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21803),X21802),hAPP(c_Groups_Ouminus__class_Ouminus(X21803),X21801)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__diff__minus])]) ).

fof(i_0_10524,plain,
    ! [X20501,X20502,X20503] :
      ( ~ class_Lattices_Oboolean__algebra(X20503)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20503),X20502),X20501) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20503),X20502),hAPP(c_Groups_Ouminus__class_Ouminus(X20503),X20501)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq])]) ).

fof(i_0_10525,plain,
    ! [X25041,X25042] :
      ( ~ class_Int_Onumber__ring(X25042)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25042),hAPP(c_Int_Onumber__class_Onumber__of(X25042),c_Int_OMin)),X25041) = hAPP(c_Groups_Ouminus__class_Ouminus(X25042),X25041) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__minus1])]) ).

fof(i_0_10526,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_10527,plain,
    ! [X20976] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20976),X20976)),
    inference(variable_rename,[status(thm)],[i_0_6061]) ).

fof(i_0_10528,plain,
    ! [X20971] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20971),X20971)),
    inference(variable_rename,[status(thm)],[i_0_6062]) ).

fof(i_0_10529,plain,
    ! [X31898,X31899,X31900] :
      ( X31900 = c_List_Olist_ONil(X31899)
      | hAPP(c_List_Ohd(X31899),hAPP(hAPP(c_List_Oappend(X31899),X31900),X31898)) = hAPP(c_List_Ohd(X31899),X31900) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__append2])]) ).

fof(i_0_10530,plain,
    ! [X18619,X18620] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X18620)
      | ~ c_Orderings_Oorder__class_Omono(X18620,X18620,X18619)
      | c_Inductive_Ocomplete__lattice__class_Olfp(X18620,X18619) = hAPP(X18619,c_Inductive_Ocomplete__lattice__class_Olfp(X18620,X18619)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lfp__unfold])]) ).

fof(i_0_10531,plain,
    ! [X17951,X17952] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X17952)
      | ~ c_Orderings_Oorder__class_Omono(X17952,X17952,X17951)
      | c_Inductive_Ocomplete__lattice__class_Ogfp(X17952,X17951) = hAPP(X17951,c_Inductive_Ocomplete__lattice__class_Ogfp(X17952,X17951)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gfp__unfold])]) ).

fof(i_0_10532,plain,
    ! [X17198,X17199,X17200,X17201,X17202] :
      ( ( hAPP(X17200,X17199) != hAPP(X17200,X17198)
        | X17199 = X17198
        | ~ c_Orderings_Oorder__class_Ostrict__mono(X17201,X17202,X17200)
        | ~ class_Orderings_Oorder(X17202)
        | ~ class_Orderings_Olinorder(X17201) )
      & ( X17199 != X17198
        | hAPP(X17200,X17199) = hAPP(X17200,X17198)
        | ~ c_Orderings_Oorder__class_Ostrict__mono(X17201,X17202,X17200)
        | ~ class_Orderings_Oorder(X17202)
        | ~ class_Orderings_Olinorder(X17201) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_strict__mono__eq])])]) ).

cnf(i_0_10533,plain,
    ( X1 = X2
    | c_Int_OBit0(X1) != c_Int_OBit0(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6063]) ).

fof(i_0_10534,plain,
    ! [X21452,X21453,X21454] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21454),X21453) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21452),X21453)
        | X21454 = X21452 )
      & ( X21454 != X21452
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21454),X21453) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21452),X21453) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).

fof(i_0_10535,plain,
    ! [X21449,X21450,X21451] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21451),X21450) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21451),X21449)
        | X21450 = X21449 )
      & ( X21450 != X21449
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21451),X21450) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21451),X21449) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).

fof(i_0_10536,plain,
    ! [X17183,X17184] : hAPP(c_Set_OCollect(X17184),hAPP(c_fequal,X17183)) = hAPP(hAPP(c_Set_Oinsert(X17184),X17183),c_Orderings_Obot__class_Obot(tc_fun(X17184,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_singleton__conv2]) ).

fof(i_0_10537,plain,
    ! [X32773,X32774,X32775] :
      ( ~ class_Orderings_Olinorder(X32775)
      | ~ c_List_Olinorder__class_Osorted(X32775,X32774)
      | c_List_Olinorder__class_Osorted(X32775,hAPP(hAPP(c_List_Odrop(X32775),X32773),X32774)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__drop])]) ).

fof(i_0_10538,plain,
    ! [X32784,X32785,X32786] :
      ( ~ class_Orderings_Olinorder(X32786)
      | ~ c_List_Olinorder__class_Osorted(X32786,X32785)
      | c_List_Olinorder__class_Osorted(X32786,hAPP(hAPP(c_List_Otake(X32786),X32784),X32785)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__take])]) ).

fof(i_0_10539,plain,
    ! [X20452] : hBOOL(hAPP(c_Finite__Set_Ofinite(X20452),c_Orderings_Obot__class_Obot(tc_fun(X20452,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_finite_Oequations_I1_J]) ).

fof(i_0_10540,plain,
    ! [X20325] : hBOOL(hAPP(c_Finite__Set_Ofinite(X20325),c_Orderings_Obot__class_Obot(tc_fun(X20325,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_finite_OemptyI]) ).

fof(i_0_10541,plain,
    ! [X17924,X17925] : hAPP(c_Set_OPow(X17925),X17924) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X17925,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Pow__not__empty]) ).

fof(i_0_10542,plain,
    ! [X26496,X26497,X26498,X26499] :
      ( ~ class_Groups_Ocomm__monoid__add(X26499)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X26498),X26497))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26498,X26499),X26496),X26497) = c_Groups_Ozero__class_Ozero(X26499) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6064])]) ).

fof(i_0_10543,plain,
    ! [X26492,X26493,X26494,X26495] :
      ( ~ class_Groups_Ocomm__monoid__add(X26495)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X26494),X26493))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26494,X26495),X26492),X26493) = c_Groups_Ozero__class_Ozero(X26495) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6065])]) ).

fof(i_0_10544,plain,
    ! [X23047,X23048,X23049,X23050] :
      ( ~ class_Groups_Ocomm__monoid__mult(X23050)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X23049),X23048))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23049,X23050),X23047),X23048) = c_Groups_Oone__class_Oone(X23050) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6066])]) ).

fof(i_0_10545,plain,
    ! [X23043,X23044,X23045,X23046] :
      ( ~ class_Groups_Ocomm__monoid__mult(X23046)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X23045),X23044))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23045,X23046),X23043),X23044) = c_Groups_Oone__class_Oone(X23046) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6067])]) ).

fof(i_0_10546,plain,
    ! [X20518] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20518,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X20518,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X20518,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq]) ).

fof(i_0_10547,plain,
    ! [X20519] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20519,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X20519,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X20519,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).

fof(i_0_10548,plain,
    ! [X19092] : hAPP(c_Set_OPow(X19092),c_Orderings_Otop__class_Otop(tc_fun(X19092,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X19092,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Pow__UNIV]) ).

fof(i_0_10549,plain,
    ! [X20254] : c_Relation_OId__on(X20254,c_Orderings_Obot__class_Obot(tc_fun(X20254,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X20254,X20254),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Id__on__empty]) ).

fof(i_0_10550,plain,
    ! [X17919,X17920] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17920,tc_HOL_Obool)),X17919),X17919) = X17919,
    inference(variable_rename,[status(thm)],[fact_Int__absorb]) ).

fof(i_0_10551,plain,
    ! [X17416,X17417] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17417,tc_HOL_Obool)),X17416),X17416) = X17416,
    inference(variable_rename,[status(thm)],[fact_Un__absorb]) ).

fof(i_0_10552,plain,
    ! [X28192,X28193] :
      ( ~ c_Wellfounded_Owf(X28193,X28192)
      | c_Wellfounded_OwfP(X28193,c_FunDef_Oin__rel(X28193,X28193,X28192)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__in__rel])]) ).

fof(i_0_10553,plain,
    ! [X27398,X27399,X27400] :
      ( ~ c_Wellfounded_Owf(X27400,X27399)
      | c_Wellfounded_Owf(X27400,c_Wellfounded_Omlex__prod(X27400,X27398,X27399)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__mlex])]) ).

fof(i_0_10554,plain,
    ! [X25102] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25102))),
    inference(variable_rename,[status(thm)],[i_0_6068]) ).

fof(i_0_10555,plain,
    ! [X25441,X25442] :
      ( ~ class_Orderings_Olinorder(X25442)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25442),X25441))
      | c_Big__Operators_Olinorder__class_OMin(X25442,X25441) = hAPP(c_Finite__Set_Ofold1(X25442,c_Orderings_Oord__class_Omin(X25442)),X25441) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_OF__eq])]) ).

fof(i_0_10556,plain,
    ! [X25891,X25892] :
      ( ~ class_Orderings_Olinorder(X25892)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25892),X25891))
      | c_Big__Operators_Olinorder__class_OMax(X25892,X25891) = hAPP(c_Finite__Set_Ofold1(X25892,c_Orderings_Oord__class_Omax(X25892)),X25891) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_OF__eq])]) ).

fof(i_0_10557,plain,
    ! [X21258,X21259] :
      ( ~ class_Lattices_Olattice(X21259)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21259),X21258))
      | c_Big__Operators_Olattice__class_OSup__fin(X21259,X21258) = hAPP(c_Finite__Set_Ofold1(X21259,c_Lattices_Osemilattice__sup__class_Osup(X21259)),X21258) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_OF__eq])]) ).

fof(i_0_10558,plain,
    ! [X21260,X21261] :
      ( ~ class_Lattices_Olattice(X21261)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21261),X21260))
      | c_Big__Operators_Olattice__class_OInf__fin(X21261,X21260) = hAPP(c_Finite__Set_Ofold1(X21261,c_Lattices_Osemilattice__inf__class_Oinf(X21261)),X21260) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_OF__eq])]) ).

fof(i_0_10559,plain,
    ! [X21415] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21415),hAPP(c_Nat_OSuc,X21415))),
    inference(variable_rename,[status(thm)],[fact_lessI]) ).

fof(i_0_10560,plain,
    ! [X33960,X33961,X33962] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33962)),c_List_Oreplicate(X33962,X33961,X33960)) = X33961,
    inference(variable_rename,[status(thm)],[fact_length__replicate]) ).

fof(i_0_10561,plain,
    ! [X22313,X22314] :
      ( ~ class_Groups_Ogroup__add(X22314)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22314),hAPP(c_Groups_Ouminus__class_Ouminus(X22314),X22313)),X22313) = c_Groups_Ozero__class_Ozero(X22314) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__minus])]) ).

fof(i_0_10562,plain,
    ! [X22315,X22316] :
      ( ~ class_Groups_Oab__group__add(X22316)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22316),hAPP(c_Groups_Ouminus__class_Ouminus(X22316),X22315)),X22315) = c_Groups_Ozero__class_Ozero(X22316) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__left__minus])]) ).

fof(i_0_10563,plain,
    ! [X20497,X20498] :
      ( ~ class_Lattices_Oboolean__algebra(X20498)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20498),hAPP(c_Groups_Ouminus__class_Ouminus(X20498),X20497)),X20497) = c_Orderings_Obot__class_Obot(X20498) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__inf__bot])]) ).

fof(i_0_10564,plain,
    ! [X20512,X20513] :
      ( ~ class_Lattices_Oboolean__algebra(X20513)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20513),hAPP(c_Groups_Ouminus__class_Ouminus(X20513),X20512)),X20512) = c_Orderings_Otop__class_Otop(X20513) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__sup__top])]) ).

fof(i_0_10565,plain,
    ! [X32109,X32110,X32111] :
      ( ( X32111 != c_List_Olist_ONil(X32110)
        | c_List_Olast(X32110,hAPP(hAPP(c_List_Oappend(X32110),X32109),X32111)) = c_List_Olast(X32110,X32109) )
      & ( X32111 = c_List_Olist_ONil(X32110)
        | c_List_Olast(X32110,hAPP(hAPP(c_List_Oappend(X32110),X32109),X32111)) = c_List_Olast(X32110,X32111) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__append])]) ).

fof(i_0_10566,plain,
    ! [X32103,X32104,X32105] :
      ( X32105 != c_List_Olist_ONil(X32104)
      | c_List_Olast(X32104,hAPP(hAPP(c_List_Oappend(X32104),X32103),X32105)) = c_List_Olast(X32104,X32103) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__appendL])]) ).

fof(i_0_10567,plain,
    ! [X22368,X22369] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22369),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22369),X22368)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_diff__add__0]) ).

fof(i_0_10568,plain,
    ! [X31089,X31090,X31091] : c_List_Osublist(X31091,X31090,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X31089)) = hAPP(hAPP(c_List_Otake(X31091),X31089),X31090),
    inference(variable_rename,[status(thm)],[fact_sublist__upt__eq__take]) ).

fof(i_0_10569,plain,
    ! [X17122,X17123] :
      ( ~ class_Orderings_Obot(X17123)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17123),c_Orderings_Obot__class_Obot(X17123)),X17122)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__least])]) ).

fof(i_0_10570,plain,
    ! [X23699,X23700] :
      ( X23700 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X23699,X23700),c_Divides_Odivmod__int(X23699,X23700))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__correct])]) ).

fof(i_0_10571,plain,
    ! [X27192,X27193] :
      ( ( X27193 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Opdivmod(X27192,X27193) = 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),X27192)) )
      & ( X27193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Opdivmod(X27192,X27193) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X27192),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X27193)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pdivmod__posDivAlg])]) ).

fof(i_0_10572,plain,
    ! [X17215,X17216,X17217] :
      ( ~ class_Orderings_Owellorder(X17217)
      | ~ hBOOL(hAPP(X17216,X17215))
      | hBOOL(hAPP(X17216,c_Orderings_Oord__class_OLeast(X17217,X17216))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_LeastI])]) ).

fof(i_0_10573,plain,
    ! [X17195,X17196,X17197] :
      ( ~ class_Orderings_Owellorder(X17196)
      | ~ hBOOL(hAPP(X17195,X17197))
      | hBOOL(hAPP(X17195,c_Orderings_Oord__class_OLeast(X17196,X17195))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_LeastI__ex])])]) ).

fof(i_0_10574,plain,
    ! [X32722,X32723] :
      ( ~ class_Orderings_Olinorder(X32723)
      | c_List_Olinorder__class_Osorted(X32723,hAPP(hAPP(c_List_Olist_OCons(X32723),X32722),c_List_Olist_ONil(X32723))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__single])]) ).

fof(i_0_10575,plain,
    ! [X32106,X32107,X32108] :
      ( X32108 = c_List_Olist_ONil(X32107)
      | c_List_Olast(X32107,hAPP(hAPP(c_List_Oappend(X32107),X32106),X32108)) = c_List_Olast(X32107,X32108) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__appendR])]) ).

fof(i_0_10576,plain,
    ! [X32119,X32120,X32121] :
      ( X32121 = c_List_Olist_ONil(X32120)
      | c_List_Olast(X32120,hAPP(hAPP(c_List_Olist_OCons(X32120),X32119),X32121)) = c_List_Olast(X32120,X32121) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__ConsR])]) ).

fof(i_0_10577,plain,
    ! [X32116,X32117,X32118] :
      ( ( X32118 != c_List_Olist_ONil(X32117)
        | c_List_Olast(X32117,hAPP(hAPP(c_List_Olist_OCons(X32117),X32116),X32118)) = X32116 )
      & ( X32118 = c_List_Olist_ONil(X32117)
        | c_List_Olast(X32117,hAPP(hAPP(c_List_Olist_OCons(X32117),X32116),X32118)) = c_List_Olast(X32117,X32118) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last_Osimps])]) ).

fof(i_0_10578,plain,
    ! [X27188,X27189] :
      ( ( X27189 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nitpick_Onat__gcd(X27188,X27189) = X27188 )
      & ( X27189 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nitpick_Onat__gcd(X27188,X27189) = c_Nitpick_Onat__gcd(X27189,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X27188,X27189)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__gcd_Osimps])]) ).

fof(i_0_10579,plain,
    ! [X26194,X26195] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X26195)),X26194) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X26195,X26194),
    inference(variable_rename,[status(thm)],[fact_atLeastSucLessThan__greaterThanLessThan]) ).

fof(i_0_10580,plain,
    ! [X26132,X26133] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26133),X26132)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26132),X26133),
    inference(variable_rename,[status(thm)],[fact_card__atLeastLessThan]) ).

fof(i_0_10581,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    inference(fof_simplification,[status(thm)],[fact_eq__int__code_I5_J]) ).

fof(i_0_10582,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(fof_simplification,[status(thm)],[fact_eq__int__code_I2_J]) ).

fof(i_0_10583,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_10584,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_10585,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_10586,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_10587,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_10588,plain,
    ! [X31347,X31348,X31349] : hAPP(hAPP(c_List_Ozip(X31349,X31348),c_List_Olist_ONil(X31349)),X31347) = c_List_Olist_ONil(tc_prod(X31349,X31348)),
    inference(variable_rename,[status(thm)],[fact_zip__Nil]) ).

fof(i_0_10589,plain,
    ! [X19053,X19054] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X19054,tc_HOL_Obool)),X19053)),
    inference(variable_rename,[status(thm)],[fact_top1I]) ).

fof(i_0_10590,plain,
    ! [X27906,X27907] : hAPP(c_Set_Ovimage(X27907,X27907,c_Fun_Oid(X27907)),X27906) = X27906,
    inference(variable_rename,[status(thm)],[fact_vimage__id]) ).

fof(i_0_10591,plain,
    ! [X19405,X19406] : hAPP(c_Set_Ovimage(X19406,X19406,c_COMBI(X19406)),X19405) = X19405,
    inference(variable_rename,[status(thm)],[fact_vimage__ident]) ).

fof(i_0_10592,plain,
    ! [X27900,X27901] : hAPP(c_Set_Oimage(X27901,X27901,c_Fun_Oid(X27901)),X27900) = X27900,
    inference(variable_rename,[status(thm)],[fact_image__id]) ).

fof(i_0_10593,plain,
    ! [X17740,X17741] : hAPP(c_Set_Oimage(X17741,X17741,c_COMBI(X17741)),X17740) = X17740,
    inference(variable_rename,[status(thm)],[fact_image__ident]) ).

fof(i_0_10594,plain,
    ! [X18616,X18617,X18618] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X18618)
      | X18617 != c_Inductive_Ocomplete__lattice__class_Olfp(X18618,X18616)
      | ~ c_Orderings_Oorder__class_Omono(X18618,X18618,X18616)
      | X18617 = hAPP(X18616,X18617) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_def__lfp__unfold])]) ).

fof(i_0_10595,plain,
    ! [X17953,X17954,X17955] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X17955)
      | X17954 != c_Inductive_Ocomplete__lattice__class_Ogfp(X17955,X17953)
      | ~ c_Orderings_Oorder__class_Omono(X17955,X17955,X17953)
      | X17954 = hAPP(X17953,X17954) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_def__gfp__unfold])]) ).

fof(i_0_10596,plain,
    ! [X28573,X28574] : c_Relation_Orefl__on(X28574,c_Orderings_Otop__class_Otop(tc_fun(X28574,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X28574,X28573)),
    inference(variable_rename,[status(thm)],[fact_refl__rtrancl]) ).

fof(i_0_10597,plain,
    ! [X33988,X33989,X33990] :
      ( X33990 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(c_List_Ohd(X33989),c_List_Oreplicate(X33989,X33990,X33988)) = X33988 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__replicate])]) ).

cnf(i_0_10598,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_6069]) ).

cnf(i_0_10599,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_6070]) ).

fof(i_0_10600,plain,
    ! [X34358,X34359] :
      ( ~ hBOOL(hAPP(hAPP(c_fimplies,X34359),X34358))
      | ~ hBOOL(X34359)
      | hBOOL(X34358) ),
    inference(variable_rename,[status(thm)],[i_0_6071]) ).

fof(i_0_10601,plain,
    ! [X26923,X26924] :
      ( ~ class_Orderings_Olinorder(X26924)
      | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26924,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X26924),X26923)) = hAPP(c_SetInterval_Oord__class_OlessThan(X26924),X26923) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__atLeast])]) ).

fof(i_0_10602,plain,
    ! [X26884,X26885] :
      ( ~ class_Orderings_Olinorder(X26885)
      | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26885,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26885),X26884)) = hAPP(c_SetInterval_Oord__class_OatMost(X26885),X26884) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__greaterThan])]) ).

fof(i_0_10603,plain,
    ! [X26882,X26883] :
      ( ~ class_Orderings_Olinorder(X26883)
      | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26883,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X26883),X26882)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X26883),X26882) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__atMost])]) ).

fof(i_0_10604,plain,
    ! [X26921,X26922] :
      ( ~ class_Orderings_Olinorder(X26922)
      | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26922,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X26922),X26921)) = hAPP(c_SetInterval_Oord__class_OatLeast(X26922),X26921) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__lessThan])]) ).

fof(i_0_10605,plain,
    ! [X22464,X22465] :
      ( ( hAPP(c_Finite__Set_Ocard(X22465),X22464) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22464 = c_Orderings_Obot__class_Obot(tc_fun(X22465,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22465),X22464)) )
      & ( X22464 != c_Orderings_Obot__class_Obot(tc_fun(X22465,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(X22465),X22464) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X22465),X22464))
        | hAPP(c_Finite__Set_Ocard(X22465),X22464) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6072])])]) ).

fof(i_0_10606,plain,
    ! [X16994,X16995] : c_Hoare__Mirabelle_Ohoare__derivs(X16995,X16994,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X16995),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_hoare__derivs_Oequations_I1_J]) ).

fof(i_0_10607,plain,
    ! [X16992,X16993] : c_Hoare__Mirabelle_Ohoare__derivs(X16993,X16992,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X16993),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_empty]) ).

fof(i_0_10608,plain,
    ! [X29797,X29798] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29798)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29798),X29797))
      | X29797 = c_Orderings_Obot__class_Obot(tc_fun(X29798,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OSup__fin(X29798,X29797) = c_Complete__Lattice_OSup__class_OSup(X29798,X29797) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin__Sup])]) ).

fof(i_0_10609,plain,
    ! [X29802,X29803] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29803)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29803),X29802))
      | X29802 = c_Orderings_Obot__class_Obot(tc_fun(X29803,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OInf__fin(X29803,X29802) = c_Complete__Lattice_OInf__class_OInf(X29803,X29802) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin__Inf])]) ).

fof(i_0_10610,plain,
    ! [X24622,X24623] :
      ( ~ class_Int_Onumber__ring(X24623)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24623),hAPP(c_Int_Onumber__class_Onumber__of(X24623),c_Int_OPls)),X24622) = X24622 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0])]) ).

fof(i_0_10611,plain,
    ! [X22335,X22336] :
      ( ( X22336 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22336 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22336),X22335) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22335 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X22336 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22336),X22335) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22336 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22335 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22336),X22335) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22335 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X22335 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22336),X22335) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22336 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X22335 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22336),X22335) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22336 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22335 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22336),X22335) = 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_10612,plain,
    ! [X22333,X22334] :
      ( ( X22334 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22334 = 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),X22334),X22333) )
      & ( X22333 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X22334 = 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),X22334),X22333) )
      & ( X22334 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22333 = 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),X22334),X22333) )
      & ( X22333 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X22333 = 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),X22334),X22333) )
      & ( X22334 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X22333 != 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),X22334),X22333) )
      & ( X22334 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22333 != 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),X22334),X22333) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).

fof(i_0_10613,plain,
    ! [X28310,X28311,X28312] :
      ( ~ hBOOL(hAPP(X28311,X28312))
      | hBOOL(hAPP(X28311,c_Hilbert__Choice_OEps(X28310,X28311))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tfl__some])])]) ).

fof(i_0_10614,plain,
    ! [X28307,X28308,X28309] :
      ( ~ hBOOL(hAPP(X28309,X28308))
      | hBOOL(hAPP(X28309,c_Hilbert__Choice_OEps(X28307,X28309))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_someI])]) ).

fof(i_0_10615,plain,
    ! [X28304,X28305,X28306] :
      ( ~ hBOOL(hAPP(X28305,X28306))
      | hBOOL(hAPP(X28305,c_Hilbert__Choice_OEps(X28304,X28305))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_someI__ex])])]) ).

fof(i_0_10616,plain,
    ! [X34352,X34353] :
      ( ~ hBOOL(hAPP(hAPP(c_fdisj,X34353),X34352))
      | hBOOL(X34353)
      | hBOOL(X34352) ),
    inference(variable_rename,[status(thm)],[i_0_6073]) ).

fof(i_0_10617,plain,
    ! [X26196,X26197] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X26197),X26196) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X26197,X26196),
    inference(variable_rename,[status(thm)],[fact_atLeastSucAtMost__greaterThanAtMost]) ).

fof(i_0_10618,plain,
    ! [X21370,X21371] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21371),X21370),X21370) != c_Groups_Oone__class_Oone(X21371)
        | X21370 = c_Groups_Oone__class_Oone(X21371)
        | X21370 = hAPP(c_Groups_Ouminus__class_Ouminus(X21371),c_Groups_Oone__class_Oone(X21371))
        | ~ class_Rings_Oring__1__no__zero__divisors(X21371) )
      & ( X21370 != c_Groups_Oone__class_Oone(X21371)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21371),X21370),X21370) = c_Groups_Oone__class_Oone(X21371)
        | ~ class_Rings_Oring__1__no__zero__divisors(X21371) )
      & ( X21370 != hAPP(c_Groups_Ouminus__class_Ouminus(X21371),c_Groups_Oone__class_Oone(X21371))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21371),X21370),X21370) = c_Groups_Oone__class_Oone(X21371)
        | ~ class_Rings_Oring__1__no__zero__divisors(X21371) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff])])]) ).

fof(i_0_10619,plain,
    ! [X16989,X16990] :
      ( hAPP(X16990,esk1_2(X16989,X16990)) != hAPP(X16989,esk1_2(X16989,X16990))
      | X16990 = X16989 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).

fof(i_0_10620,plain,
    ! [X31350,X31351,X31352] : hAPP(hAPP(c_List_Ozip(X31352,X31351),X31350),c_List_Olist_ONil(X31351)) = c_List_Olist_ONil(tc_prod(X31352,X31351)),
    inference(variable_rename,[status(thm)],[fact_zip_Osimps_I1_J]) ).

fof(i_0_10621,plain,
    ! [X21146,X21147,X21148,X21149] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X21149,X21148,X21147)
      | hAPP(hAPP(X21148,X21146),X21146) = X21146 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oidem])]) ).

fof(i_0_10622,plain,
    ! [X31340] : c_Enum_Osublists(X31340,c_List_Olist_ONil(X31340)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31340)),c_List_Olist_ONil(X31340)),c_List_Olist_ONil(tc_List_Olist(X31340))),
    inference(variable_rename,[status(thm)],[fact_sublists_Osimps_I1_J]) ).

fof(i_0_10623,plain,
    ! [X19160,X19161] :
      ( ~ class_Orderings_Otop(X19161)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19161),X19160),c_Orderings_Otop__class_Otop(X19161))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__greatest])]) ).

fof(i_0_10624,plain,
    ! [X32122,X32123,X32124] :
      ( X32124 != c_List_Olist_ONil(X32123)
      | c_List_Olast(X32123,hAPP(hAPP(c_List_Olist_OCons(X32123),X32122),X32124)) = X32122 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__ConsL])]) ).

fof(i_0_10625,plain,
    ! [X33981,X33982,X33983] :
      ( X33983 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | c_List_Olast(X33982,c_List_Oreplicate(X33982,X33983,X33981)) = X33981 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__replicate])]) ).

fof(i_0_10626,plain,
    ! [X24731,X24732,X24733] : hAPP(c_Nat_Onat_Onat__rec(X24733,X24732,X24731),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X24732,
    inference(variable_rename,[status(thm)],[fact_nat__rec__0]) ).

fof(i_0_10627,plain,
    ! [X17040,X17041,X17042] : hAPP(hAPP(c_Set_Oinsert(X17042),X17041),X17040) != c_Orderings_Obot__class_Obot(tc_fun(X17042,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_insert__not__empty]) ).

fof(i_0_10628,plain,
    ! [X17037,X17038,X17039] : c_Orderings_Obot__class_Obot(tc_fun(X17039,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X17039),X17038),X17037),
    inference(variable_rename,[status(thm)],[fact_empty__not__insert]) ).

fof(i_0_10629,plain,
    ! [X34344,X34345] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X34345),X34344))
      | hBOOL(X34345) ),
    inference(variable_rename,[status(thm)],[i_0_6074]) ).

fof(i_0_10630,plain,
    ! [X34346,X34347] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X34347),X34346))
      | hBOOL(X34346) ),
    inference(variable_rename,[status(thm)],[i_0_6075]) ).

fof(i_0_10631,plain,
    ! [X25234] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X25234)) = 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),X25234)),
    inference(variable_rename,[status(thm)],[fact_int__Suc]) ).

fof(i_0_10632,plain,
    ! [X22878,X22879] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22879),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22878)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X22879),X22878),
    inference(variable_rename,[status(thm)],[fact_diff__int__def__symmetric]) ).

fof(i_0_10633,plain,
    ! [X22876,X22877] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X22877),X22876) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22877),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22876)),
    inference(variable_rename,[status(thm)],[fact_diff__int__def]) ).

fof(i_0_10634,plain,
    ! [X31953,X31954,X31955] : hAPP(c_List_Otl(X31955),hAPP(hAPP(c_List_Olist_OCons(X31955),X31954),X31953)) = X31953,
    inference(variable_rename,[status(thm)],[fact_tl_Osimps_I2_J]) ).

fof(i_0_10635,plain,
    ! [X31888,X31889,X31890] : hAPP(c_List_Ohd(X31890),hAPP(hAPP(c_List_Olist_OCons(X31890),X31889),X31888)) = X31889,
    inference(variable_rename,[status(thm)],[fact_hd_Osimps]) ).

fof(i_0_10636,plain,
    ! [X22679,X22680,X22681] :
      ( ( X22680 = c_Groups_Ozero__class_Ozero(X22681)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X22681),X22680),X22679) != c_Groups_Ozero__class_Ozero(X22681)
        | ~ class_Power_Opower(X22681)
        | ~ class_Rings_Omult__zero(X22681)
        | ~ class_Rings_Ono__zero__divisors(X22681)
        | ~ class_Rings_Ozero__neq__one(X22681) )
      & ( X22679 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X22681),X22680),X22679) != c_Groups_Ozero__class_Ozero(X22681)
        | ~ class_Power_Opower(X22681)
        | ~ class_Rings_Omult__zero(X22681)
        | ~ class_Rings_Ono__zero__divisors(X22681)
        | ~ class_Rings_Ozero__neq__one(X22681) )
      & ( X22680 != c_Groups_Ozero__class_Ozero(X22681)
        | X22679 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X22681),X22680),X22679) = c_Groups_Ozero__class_Ozero(X22681)
        | ~ class_Power_Opower(X22681)
        | ~ class_Rings_Omult__zero(X22681)
        | ~ class_Rings_Ono__zero__divisors(X22681)
        | ~ class_Rings_Ozero__neq__one(X22681) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff])])]) ).

fof(i_0_10637,plain,
    ! [X25542,X25543] :
      ( ~ c_Nat__Transfer_Ois__nat(X25543)
      | ~ c_Nat__Transfer_Ois__nat(X25542)
      | c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X25543,X25542)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I2_J])]) ).

fof(i_0_10638,plain,
    ! [X17203,X17204,X17205,X17206,X17208] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X17204,tc_HOL_Obool)) != hAPP(c_Set_OCollect(X17204),X17203)
        | ~ hBOOL(hAPP(X17203,X17205)) )
      & ( hBOOL(hAPP(X17206,esk6_1(X17206)))
        | c_Orderings_Obot__class_Obot(tc_fun(X17208,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X17208),X17206) ) ),
    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_6076])])])])]) ).

fof(i_0_10639,plain,
    ! [X17209,X17210,X17211,X17212,X17214] :
      ( ( hAPP(c_Set_OCollect(X17210),X17209) != c_Orderings_Obot__class_Obot(tc_fun(X17210,tc_HOL_Obool))
        | ~ hBOOL(hAPP(X17209,X17211)) )
      & ( hBOOL(hAPP(X17212,esk7_1(X17212)))
        | hAPP(c_Set_OCollect(X17214),X17212) = c_Orderings_Obot__class_Obot(tc_fun(X17214,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_6077])])])])]) ).

fof(i_0_10640,plain,
    ! [X34336,X34337] :
      ( ~ hBOOL(hAPP(hAPP(c_fequal,X34337),X34336))
      | X34337 = X34336 ),
    inference(variable_rename,[status(thm)],[i_0_6078]) ).

fof(i_0_10641,plain,
    ! [X25047,X25048] :
      ( ~ class_Fields_Ofield__inverse__zero(X25048)
      | ~ class_Int_Onumber__ring(X25048)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25048),X25047),hAPP(c_Int_Onumber__class_Onumber__of(X25048),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X25048),X25047) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__minus1])]) ).

fof(i_0_10642,plain,
    ! [X27496,X27497,X27498] :
      ( ~ c_Wellfounded_Owf(X27498,X27497)
      | c_Wellfounded_Owf(tc_List_Olist(X27498),hAPP(c_List_Olexn(X27498,X27497),X27496)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lexn])]) ).

fof(i_0_10643,plain,
    ! [X31410,X31411,X31412] : hAPP(hAPP(c_List_Olist__update(X31412,c_List_Olist_ONil(X31412)),X31411),X31410) = c_List_Olist_ONil(X31412),
    inference(variable_rename,[status(thm)],[fact_list__update_Osimps_I1_J]) ).

fof(i_0_10644,plain,
    ! [X31407,X31408,X31409] : hAPP(hAPP(c_List_Olist__update(X31409,c_List_Olist_ONil(X31409)),X31408),X31407) = c_List_Olist_ONil(X31409),
    inference(variable_rename,[status(thm)],[fact_list__update__code_I1_J]) ).

fof(i_0_10645,plain,
    ! [X22703] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22703) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_power__Suc__0]) ).

fof(i_0_10646,plain,
    ! [X33346,X33347] : c_List_Oinsert(X33347,X33346,c_List_Olist_ONil(X33347)) = hAPP(hAPP(c_List_Olist_OCons(X33347),X33346),c_List_Olist_ONil(X33347)),
    inference(variable_rename,[status(thm)],[fact_insert__Nil]) ).

fof(i_0_10647,plain,
    ! [X30265,X30266] : hBOOL(hAPP(c_Finite__Set_Ofinite(X30266),hAPP(c_List_Oset(X30266),X30265))),
    inference(variable_rename,[status(thm)],[fact_finite__set]) ).

fof(i_0_10648,plain,
    ! [X28744,X28745,X28746] : hAPP(c_Relation_Oconverse(X28746,X28745),hAPP(c_Relation_Oconverse(X28745,X28746),X28744)) = X28744,
    inference(variable_rename,[status(thm)],[fact_converse__converse]) ).

fof(i_0_10649,plain,
    ! [X26399] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26399)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X26399),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26399)),
    inference(variable_rename,[status(thm)],[fact_lessThan__Suc]) ).

fof(i_0_10650,plain,
    ! [X28747,X28748] : hAPP(c_Relation_OField(X28748),hAPP(c_Relation_Oconverse(X28748,X28748),X28747)) = hAPP(c_Relation_OField(X28748),X28747),
    inference(variable_rename,[status(thm)],[fact_Field__converse]) ).

fof(i_0_10651,plain,
    ! [X25034,X25035] :
      ( ~ class_Rings_Oring__1(X25035)
      | hAPP(c_Int_Oring__1__class_Oof__int(X25035),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25034)) = hAPP(c_Groups_Ouminus__class_Ouminus(X25035),hAPP(c_Int_Oring__1__class_Oof__int(X25035),X25034)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__minus])]) ).

fof(i_0_10652,plain,
    ! [X24063,X24064] :
      ( ~ class_Int_Onumber__ring(X24064)
      | hAPP(c_Int_Onumber__class_Onumber__of(X24064),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24063)) = hAPP(c_Groups_Ouminus__class_Ouminus(X24064),hAPP(c_Int_Onumber__class_Onumber__of(X24064),X24063)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__minus])]) ).

fof(i_0_10653,plain,
    ! [X24065,X24066] :
      ( ~ class_Int_Onumber__ring(X24066)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X24066),hAPP(c_Int_Onumber__class_Onumber__of(X24066),X24065)) = hAPP(c_Int_Onumber__class_Onumber__of(X24066),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24065)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I30_J])]) ).

fof(i_0_10654,plain,
    ! [X22704,X22705] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22705),X22704) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X22704 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22705 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22704 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22705),X22704) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22705 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22705),X22704) = 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_10655,plain,
    ! [X17084,X17085,X17086] :
      ( ~ class_Orderings_Opreorder(X17086)
      | X17085 != X17084
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17086),X17085),X17084)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).

fof(i_0_10656,plain,
    ! [X22317,X22318,X22319] :
      ( ~ class_Groups_Ogroup__add(X22319)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22319),X22318),X22317) != c_Groups_Ozero__class_Ozero(X22319)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X22319),X22318) = X22317 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__unique])]) ).

fof(i_0_10657,plain,
    ! [X22310,X22311,X22312] :
      ( ( X22311 != hAPP(c_Groups_Ouminus__class_Ouminus(X22312),X22310)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22312),X22311),X22310) = c_Groups_Ozero__class_Ozero(X22312)
        | ~ class_Groups_Ogroup__add(X22312) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22312),X22311),X22310) != c_Groups_Ozero__class_Ozero(X22312)
        | X22311 = hAPP(c_Groups_Ouminus__class_Ouminus(X22312),X22310)
        | ~ class_Groups_Ogroup__add(X22312) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0])])]) ).

fof(i_0_10658,plain,
    ! [X32525,X32526] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32526)),c_List_Oremdups(X32526,X32525)) = hAPP(c_Finite__Set_Ocard(X32526),hAPP(c_List_Oset(X32526),X32525)),
    inference(variable_rename,[status(thm)],[fact_length__remdups__card__conv]) ).

fof(i_0_10659,plain,
    ! [X19146] : c_Orderings_Otop__class_Otop(tc_fun(X19146,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X19146),hAPP(c_COMBK(tc_HOL_Obool,X19146),c_fTrue)),
    inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).

fof(i_0_10660,plain,
    ! [X17218] : c_Orderings_Obot__class_Obot(tc_fun(X17218,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X17218),hAPP(c_COMBK(tc_HOL_Obool,X17218),c_fFalse)),
    inference(variable_rename,[status(thm)],[fact_empty__def]) ).

fof(i_0_10661,plain,
    ! [X34177] : c_Lazy__Sequence_Ohb__flat(X34177,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X34177))))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(X34177)),
    inference(variable_rename,[status(thm)],[fact_hb__flat_Osimps_I1_J]) ).

fof(i_0_10662,plain,
    ! [X26134,X26135] :
      ( ~ c_Nat__Transfer_Ois__nat(X26135)
      | c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X26135,X26134)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__function__closures])]) ).

fof(i_0_10663,plain,
    ! [X25043,X25044] :
      ( ~ class_Int_Onumber__ring(X25044)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25044),X25043),hAPP(c_Int_Onumber__class_Onumber__of(X25044),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X25044),X25043) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__minus1__right])]) ).

fof(i_0_10664,plain,
    ! [X22342,X22343] :
      ( ( X22343 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22343),X22342) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22342 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22343),X22342) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22343 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X22342 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22343),X22342) = 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_10665,plain,
    ! [X22767] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X22767)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X22767)),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_10666,plain,
    ! [X33683,X33684] :
      ( ~ class_HOL_Oequal(X33684)
      | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X33684),X33683),X33683)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__refl])]) ).

fof(i_0_10667,plain,
    ! [X17019,X17020] :
      ( ~ class_Orderings_Opreorder(X17020)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17020),X17019),X17019)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).

fof(i_0_10668,plain,
    ! [X26256] : 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)),X26256)) = hAPP(c_Int_Onat,X26256),
    inference(variable_rename,[status(thm)],[fact_card__atLeastZeroLessThan__int]) ).

fof(i_0_10669,plain,
    ! [X22844] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22844)),X22844) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zadd__zminus__inverse2]) ).

fof(i_0_10670,plain,
    ! [X26101,X26102] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26102),hAPP(c_Nat_OSuc,X26101)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26102,X26101),
    inference(variable_rename,[status(thm)],[fact_atLeastLessThanSuc__atLeastAtMost]) ).

fof(i_0_10671,plain,
    ! [X23772,X23773] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X23773,X23772) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X23773,X23772)),
    inference(variable_rename,[status(thm)],[fact_mod__int__def]) ).

fof(i_0_10672,plain,
    ! [X25744,X25745,X25746] :
      ( ~ class_Orderings_Olinorder(X25746)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25746),X25745),X25744) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25746),X25744),X25745) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Ocommute])]) ).

fof(i_0_10673,plain,
    ! [X25741,X25742,X25743] :
      ( ~ class_Orderings_Olinorder(X25743)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25743),X25742),X25741) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25743),X25741),X25742) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__commute])]) ).

fof(i_0_10674,plain,
    ! [X25329,X25330,X25331] :
      ( ~ class_Orderings_Olinorder(X25331)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25331),X25330),X25329) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25331),X25329),X25330) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__commute])]) ).

fof(i_0_10675,plain,
    ! [X25326,X25327,X25328] :
      ( ~ class_Orderings_Olinorder(X25328)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25328),X25327),X25326) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25328),X25326),X25327) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Ocommute])]) ).

fof(i_0_10676,plain,
    ! [X21478,X21479,X21480] :
      ( ~ class_Rings_Ocomm__semiring__1(X21480)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21480),X21479),X21478) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21480),X21478),X21479) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).

fof(i_0_10677,plain,
    ! [X21924,X21925,X21926] :
      ( ~ class_Rings_Ocomm__semiring__1(X21926)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21926),X21925),X21924) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21926),X21924),X21925) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).

fof(i_0_10678,plain,
    ! [X17861,X17862,X17863] :
      ( ~ class_Lattices_Osemilattice__inf(X17863)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17863),X17862),X17861) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17863),X17861),X17862) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Ocommute])]) ).

fof(i_0_10679,plain,
    ! [X17855,X17856,X17857] :
      ( ~ class_Lattices_Osemilattice__inf(X17857)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17857),X17856),X17855) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17857),X17855),X17856) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__commute])]) ).

fof(i_0_10680,plain,
    ! [X17858,X17859,X17860] :
      ( ~ class_Lattices_Olattice(X17860)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17860),X17859),X17858) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17860),X17858),X17859) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I1_J])]) ).

fof(i_0_10681,plain,
    ! [X17698,X17699,X17700] :
      ( ~ class_Lattices_Olattice(X17700)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17700),X17699),X17698) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17700),X17698),X17699) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I5_J])]) ).

fof(i_0_10682,plain,
    ! [X17701,X17702,X17703] :
      ( ~ class_Lattices_Osemilattice__sup(X17703)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17703),X17702),X17701) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17703),X17701),X17702) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Ocommute])]) ).

fof(i_0_10683,plain,
    ! [X17695,X17696,X17697] :
      ( ~ class_Lattices_Osemilattice__sup(X17697)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17697),X17696),X17695) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17697),X17695),X17696) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__commute])]) ).

fof(i_0_10684,plain,
    ! [X25236] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25236))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_nat__zminus__int]) ).

fof(i_0_10685,plain,
    ! [X22075] :
      ( X22075 = 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)),X22075)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).

fof(i_0_10686,plain,
    ! [X25544,X25545] :
      ( ~ c_Nat__Transfer_Ois__nat(X25545)
      | ~ c_Nat__Transfer_Ois__nat(X25544)
      | c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25545),X25544)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I1_J])]) ).

fof(i_0_10687,plain,
    ! [X25537,X25538] :
      ( ~ c_Nat__Transfer_Ois__nat(X25538)
      | ~ c_Nat__Transfer_Ois__nat(X25537)
      | c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25538),X25537)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J])]) ).

fof(i_0_10688,plain,
    ! [X25540,X25541] :
      ( ~ c_Nat__Transfer_Ois__nat(X25541)
      | ~ c_Nat__Transfer_Ois__nat(X25540)
      | c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25541),X25540)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J])]) ).

fof(i_0_10689,plain,
    ! [X25156,X25157] :
      ( ( X25157 = 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),X25157)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25156) )
      & ( X25156 = 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),X25157)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25156) )
      & ( X25157 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X25156 != 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),X25157)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25156) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negative__eq__positive])])]) ).

cnf(i_0_10690,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_6079]) ).

fof(i_0_10691,plain,
    ! [X22083] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22083)),
    inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).

fof(i_0_10692,plain,
    ! [X22005] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22005)),
    inference(variable_rename,[status(thm)],[fact_le0]) ).

fof(i_0_10693,plain,
    ! [X28780,X28781] : c_Relation_Ototal__on(X28781,c_Orderings_Obot__class_Obot(tc_fun(X28781,tc_HOL_Obool)),X28780),
    inference(variable_rename,[status(thm)],[fact_total__on__empty]) ).

fof(i_0_10694,plain,
    ! [X22040,X22041,X22042] :
      ( ~ class_Rings_Ono__zero__divisors(X22042)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22042),X22041),X22040) != c_Groups_Ozero__class_Ozero(X22042)
      | X22041 = c_Groups_Ozero__class_Ozero(X22042)
      | X22040 = c_Groups_Ozero__class_Ozero(X22042) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divisors__zero])]) ).

fof(i_0_10695,plain,
    ! [X22037,X22038,X22039] :
      ( ~ class_Rings_Ono__zero__divisors(X22039)
      | X22038 = c_Groups_Ozero__class_Ozero(X22039)
      | X22037 = c_Groups_Ozero__class_Ozero(X22039)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22039),X22038),X22037) != c_Groups_Ozero__class_Ozero(X22039) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_no__zero__divisors])]) ).

fof(i_0_10696,plain,
    ! [X22034,X22035,X22036] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22036),X22035),X22034) != c_Groups_Ozero__class_Ozero(X22036)
        | X22035 = c_Groups_Ozero__class_Ozero(X22036)
        | X22034 = c_Groups_Ozero__class_Ozero(X22036)
        | ~ class_Rings_Oring__no__zero__divisors(X22036) )
      & ( X22035 != c_Groups_Ozero__class_Ozero(X22036)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22036),X22035),X22034) = c_Groups_Ozero__class_Ozero(X22036)
        | ~ class_Rings_Oring__no__zero__divisors(X22036) )
      & ( X22034 != c_Groups_Ozero__class_Ozero(X22036)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22036),X22035),X22034) = c_Groups_Ozero__class_Ozero(X22036)
        | ~ class_Rings_Oring__no__zero__divisors(X22036) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff])])]) ).

fof(i_0_10697,plain,
    ! [X23677] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23677) = 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_10698,plain,
    ! [X23770,X23771] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23771),X23770) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X23771,X23770)),
    inference(variable_rename,[status(thm)],[fact_div__int__def]) ).

fof(i_0_10699,plain,
    ! [X22685,X22686] :
      ( ~ class_Power_Opower(X22686)
      | ~ class_Rings_Osemiring__0(X22686)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22686),c_Groups_Ozero__class_Ozero(X22686)),hAPP(c_Nat_OSuc,X22685)) = c_Groups_Ozero__class_Ozero(X22686) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__Suc])]) ).

fof(i_0_10700,plain,
    ! [X24639,X24640] :
      ( ~ class_Fields_Ofield__inverse__zero(X24640)
      | ~ class_Int_Onumber__ring(X24640)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24640),X24639),hAPP(c_Int_Onumber__class_Onumber__of(X24640),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(X24640) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__Numeral0])]) ).

fof(i_0_10701,plain,
    ! [X27101,X27102] :
      ( ~ class_Rings_Olinordered__idom(X27102)
      | hAPP(c_Groups_Oabs__class_Oabs(X27102),X27101) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27102),X27101),c_Groups_Osgn__class_Osgn(X27102,X27101)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__sgn])]) ).

fof(i_0_10702,plain,
    ! [X30986] : c_List_Olists(X30986,c_Orderings_Otop__class_Otop(tc_fun(X30986,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X30986),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_lists__UNIV]) ).

fof(i_0_10703,plain,
    ! [X30112,X30113] : hAPP(hAPP(c_List_Omap(X30113,X30113),c_COMBI(X30113)),X30112) = X30112,
    inference(variable_rename,[status(thm)],[fact_map__ident]) ).

fof(i_0_10704,plain,
    ! [X28186,X28187,X28188] :
      ( ~ c_Wellfounded_OwfP(X28188,X28187)
      | hBOOL(hAPP(c_Wellfounded_Oaccp(X28188,X28187),X28186)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__wfPD])]) ).

fof(i_0_10705,plain,
    ! [X28167,X28168,X28169] :
      ( ~ c_Predicate_Oreflp(X28169,X28168)
      | hBOOL(hAPP(hAPP(X28168,X28167),X28167)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflpE])]) ).

fof(i_0_10706,plain,
    ! [X20242,X20243,X20244] :
      ( ~ c_Equiv__Relations_Oequivp(X20244,X20243)
      | hBOOL(hAPP(hAPP(X20243,X20242),X20242)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__reflp])]) ).

fof(i_0_10707,plain,
    ! [X31353,X31354] : c_List_Osublist(X31354,X31353,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(X31354),
    inference(variable_rename,[status(thm)],[fact_sublist__empty]) ).

fof(i_0_10708,plain,
    ! [X24166,X24167,X24168] :
      ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24168),X24166),X24167) != c_Groups_Oone__class_Oone(X24168)
        | X24166 = X24167
        | X24167 = c_Groups_Ozero__class_Ozero(X24168)
        | ~ class_Rings_Odivision__ring(X24168) )
      & ( X24166 != X24167
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24168),X24166),X24167) = c_Groups_Oone__class_Oone(X24168)
        | X24167 = c_Groups_Ozero__class_Ozero(X24168)
        | ~ class_Rings_Odivision__ring(X24168) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__inverse__eq])])]) ).

fof(i_0_10709,plain,
    ! [X32892,X32893] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32893)),hAPP(c_List_Orev(X32893),X32892)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32893)),X32892),
    inference(variable_rename,[status(thm)],[fact_length__rev]) ).

fof(i_0_10710,plain,
    ! [X31770,X31771] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31771)),hAPP(c_List_Orotate1(X31771),X31770)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31771)),X31770),
    inference(variable_rename,[status(thm)],[fact_length__rotate1]) ).

fof(i_0_10711,plain,
    ! [X28313,X28314,X28315,X28316] :
      ( ~ hBOOL(hAPP(X28315,X28316))
      | X28314 != c_Hilbert__Choice_OEps(X28313,X28315)
      | hBOOL(hAPP(X28315,X28314)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exE__some])])]) ).

fof(i_0_10712,plain,
    ! [X28935,X28936] : hAPP(hAPP(c_Nat_Ocompow(X28936,X28936),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28935) = c_Fun_Oid(X28936),
    inference(variable_rename,[status(thm)],[fact_funpow_Osimps_I1_J]) ).

fof(i_0_10713,plain,
    ! [X30166,X30167,X30168] : hAPP(hAPP(c_Option_Omap(X30168,X30167),X30166),c_Option_Ooption_ONone(X30168)) = c_Option_Ooption_ONone(X30167),
    inference(variable_rename,[status(thm)],[fact_option__map__None]) ).

fof(i_0_10714,plain,
    ! [X31389,X31390,X31391] : hAPP(hAPP(c_List_Omap(X31391,X31390),X31389),c_List_Olist_ONil(X31391)) = c_List_Olist_ONil(X31390),
    inference(variable_rename,[status(thm)],[fact_map_Osimps_I1_J]) ).

fof(i_0_10715,plain,
    ! [X22308,X22309] :
      ( ~ class_Groups_Ogroup__add(X22309)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22309),X22308),hAPP(c_Groups_Ouminus__class_Ouminus(X22309),X22308)) = c_Groups_Ozero__class_Ozero(X22309) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus])]) ).

fof(i_0_10716,plain,
    ! [X20499,X20500] :
      ( ~ class_Lattices_Oboolean__algebra(X20500)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20500),X20499),hAPP(c_Groups_Ouminus__class_Ouminus(X20500),X20499)) = c_Orderings_Obot__class_Obot(X20500) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__compl__bot])]) ).

fof(i_0_10717,plain,
    ! [X20514,X20515] :
      ( ~ class_Lattices_Oboolean__algebra(X20515)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20515),X20514),hAPP(c_Groups_Ouminus__class_Ouminus(X20515),X20514)) = c_Orderings_Otop__class_Otop(X20515) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__compl__top])]) ).

fof(i_0_10718,plain,
    ! [X25546,X25547] :
      ( ~ c_Nat__Transfer_Ois__nat(X25547)
      | c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X25547),X25546)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J])]) ).

fof(i_0_10719,plain,
    ! [X25053,X25054] :
      ( ( X25054 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | X25054 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25054),X25053) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X25053 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | X25054 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25054),X25053) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X25054 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | X25053 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25054),X25053) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X25053 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | X25053 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25054),X25053) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X25054 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X25053 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25054),X25053) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X25054 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | X25053 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25054),X25053) = 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_10720,plain,
    ! [X19170,X19171,X19172] :
      ( ( X19171 = c_Orderings_Otop__class_Otop(X19172)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X19172),X19171),X19170) != c_Orderings_Otop__class_Otop(X19172)
        | ~ class_Lattices_Obounded__lattice__top(X19172) )
      & ( X19170 = c_Orderings_Otop__class_Otop(X19172)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X19172),X19171),X19170) != c_Orderings_Otop__class_Otop(X19172)
        | ~ class_Lattices_Obounded__lattice__top(X19172) )
      & ( X19171 != c_Orderings_Otop__class_Otop(X19172)
        | X19170 != c_Orderings_Otop__class_Otop(X19172)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X19172),X19171),X19170) = c_Orderings_Otop__class_Otop(X19172)
        | ~ class_Lattices_Obounded__lattice__top(X19172) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__eq__top__iff])])]) ).

fof(i_0_10721,plain,
    ! [X17632,X17633,X17634] :
      ( ( X17633 = c_Orderings_Obot__class_Obot(X17634)
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17634),X17633),X17632) != c_Orderings_Obot__class_Obot(X17634)
        | ~ class_Lattices_Obounded__lattice__bot(X17634) )
      & ( X17632 = c_Orderings_Obot__class_Obot(X17634)
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17634),X17633),X17632) != c_Orderings_Obot__class_Obot(X17634)
        | ~ class_Lattices_Obounded__lattice__bot(X17634) )
      & ( X17633 != c_Orderings_Obot__class_Obot(X17634)
        | X17632 != c_Orderings_Obot__class_Obot(X17634)
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17634),X17633),X17632) = c_Orderings_Obot__class_Obot(X17634)
        | ~ class_Lattices_Obounded__lattice__bot(X17634) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__eq__bot__iff])])]) ).

fof(i_0_10722,plain,
    ! [X22651,X22652,X22653] :
      ( ~ class_Rings_Oring__1__no__zero__divisors(X22653)
      | X22652 = c_Groups_Ozero__class_Ozero(X22653)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22653),X22652),X22651) != c_Groups_Ozero__class_Ozero(X22653) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__power__not__zero])]) ).

fof(i_0_10723,plain,
    ! [X22567,X22568] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22568),X22567),X22567) != c_Groups_Ozero__class_Ozero(X22568)
        | X22567 = c_Groups_Ozero__class_Ozero(X22568)
        | ~ class_Groups_Olinordered__ab__group__add(X22568) )
      & ( X22567 != c_Groups_Ozero__class_Ozero(X22568)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22568),X22567),X22567) = c_Groups_Ozero__class_Ozero(X22568)
        | ~ class_Groups_Olinordered__ab__group__add(X22568) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).

fof(i_0_10724,plain,
    ! [X22020,X22021] :
      ( ( c_Groups_Ozero__class_Ozero(X22021) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22021),X22020),X22020)
        | X22020 = c_Groups_Ozero__class_Ozero(X22021)
        | ~ class_Groups_Olinordered__ab__group__add(X22021) )
      & ( X22020 != c_Groups_Ozero__class_Ozero(X22021)
        | c_Groups_Ozero__class_Ozero(X22021) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22021),X22020),X22020)
        | ~ class_Groups_Olinordered__ab__group__add(X22021) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).

fof(i_0_10725,plain,
    ! [X26796] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X26796))),
    inference(variable_rename,[status(thm)],[fact_finite__atMost]) ).

fof(i_0_10726,plain,
    ! [X26393] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26393))),
    inference(variable_rename,[status(thm)],[fact_finite__lessThan]) ).

fof(i_0_10727,plain,
    ! [X18480,X18481] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X18481)
      | c_Inductive_Ocomplete__lattice__class_Olfp(X18481,hAPP(c_COMBK(X18481,X18481),X18480)) = X18480 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lfp__const])]) ).

cnf(i_0_10728,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_5863]) ).

fof(i_0_10729,plain,
    ! [X24014] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24014)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24014)),
    inference(variable_rename,[status(thm)],[fact_minus__numeral__code_I5_J]) ).

fof(i_0_10730,plain,
    ! [X22043,X22044,X22045] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22045),X22044),X22043) != c_Groups_Ozero__class_Ozero(X22045)
        | X22044 = X22043
        | ~ class_Groups_Ogroup__add(X22045) )
      & ( X22044 != X22043
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22045),X22044),X22043) = c_Groups_Ozero__class_Ozero(X22045)
        | ~ class_Groups_Ogroup__add(X22045) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus__eq])])]) ).

fof(i_0_10731,plain,
    ! [X22046,X22047,X22048] :
      ( ( X22047 != X22046
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22048),X22047),X22046) = c_Groups_Ozero__class_Ozero(X22048)
        | ~ class_Groups_Oab__group__add(X22048) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22048),X22047),X22046) != c_Groups_Ozero__class_Ozero(X22048)
        | X22047 = X22046
        | ~ class_Groups_Oab__group__add(X22048) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0])])]) ).

fof(i_0_10732,plain,
    ! [X21008,X21009] :
      ( X21009 != X21008
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21009),X21008)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).

fof(i_0_10733,plain,
    ! [X31329,X31330,X31331] :
      ( ( hAPP(hAPP(c_List_Otake(X31331),X31330),X31329) != c_List_Olist_ONil(X31331)
        | X31330 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X31329 = c_List_Olist_ONil(X31331) )
      & ( X31330 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(X31331),X31330),X31329) = c_List_Olist_ONil(X31331) )
      & ( X31329 != c_List_Olist_ONil(X31331)
        | hAPP(hAPP(c_List_Otake(X31331),X31330),X31329) = c_List_Olist_ONil(X31331) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__eq__Nil])])]) ).

fof(i_0_10734,plain,
    ! [X25055,X25056] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25056),X25055) != c_Groups_Oone__class_Oone(tc_Int_Oint)
      | X25056 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | X25056 = 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_10735,plain,
    ! [X22009,X22010,X22011] :
      ( ( X22010 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22011),X22010),X22009)
        | X22009 = c_Groups_Ozero__class_Ozero(X22011)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X22011) )
      & ( X22009 != c_Groups_Ozero__class_Ozero(X22011)
        | X22010 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22011),X22010),X22009)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X22011) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).

fof(i_0_10736,plain,
    ! [X34029,X34030,X34031] :
      ( ( c_List_Oreplicate(X34031,X34030,X34029) != c_List_Olist_ONil(X34031)
        | X34030 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X34030 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oreplicate(X34031,X34030,X34029) = c_List_Olist_ONil(X34031) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_replicate__empty])]) ).

fof(i_0_10737,plain,
    ! [X34032,X34033,X34034] :
      ( ( c_List_Olist_ONil(X34034) != c_List_Oreplicate(X34034,X34033,X34032)
        | X34033 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X34033 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Olist_ONil(X34034) = c_List_Oreplicate(X34034,X34033,X34032) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__replicate])]) ).

fof(i_0_10738,plain,
    ! [X21867] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21867)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X21867,
    inference(variable_rename,[status(thm)],[fact_diff__Suc__1]) ).

fof(i_0_10739,plain,
    ! [X30662,X30663] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X30663,X30662)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X30663,X30662),
    inference(variable_rename,[status(thm)],[fact_set__upto]) ).

fof(i_0_10740,plain,
    ! [X30664,X30665] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X30665,X30664) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X30665,X30664)),
    inference(variable_rename,[status(thm)],[fact_atLeastAtMost__upto]) ).

fof(i_0_10741,plain,
    ! [X33635,X33636] : ~ c_List_Olist__ex1(X33636,X33635,c_List_Olist_ONil(X33636)),
    inference(variable_rename,[status(thm)],[i_0_6080]) ).

fof(i_0_10742,plain,
    ! [X33519,X33520] : ~ c_List_Olist__ex(X33520,X33519,c_List_Olist_ONil(X33520)),
    inference(variable_rename,[status(thm)],[i_0_6081]) ).

fof(i_0_10743,plain,
    ! [X24624,X24625] :
      ( ~ class_Int_Onumber__ring(X24625)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24625),X24624),hAPP(c_Int_Onumber__class_Onumber__of(X24625),c_Int_OPls)) = X24624 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0__right])]) ).

fof(i_0_10744,plain,
    ! [X33726] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X33726),X33726)),
    inference(variable_rename,[status(thm)],[fact_eq__int__refl]) ).

fof(i_0_10745,plain,
    ! [X22938] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22938),X22938)),
    inference(variable_rename,[status(thm)],[fact_zle__refl]) ).

fof(i_0_10746,plain,
    ! [X21012] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21012),X21012)),
    inference(variable_rename,[status(thm)],[fact_le__refl]) ).

fof(i_0_10747,plain,
    ! [X33127,X33128] : hBOOL(hAPP(c_List_Olistsp(X33128,X33127),c_List_Olist_ONil(X33128))),
    inference(variable_rename,[status(thm)],[fact_listsp_Oequations_I1_J]) ).

fof(i_0_10748,plain,
    ! [X33117,X33118] : hBOOL(hAPP(c_List_Olistsp(X33118,X33117),c_List_Olist_ONil(X33118))),
    inference(variable_rename,[status(thm)],[fact_listsp_ONil]) ).

fof(i_0_10749,plain,
    ! [X32496,X32497] : hBOOL(hAPP(c_List_Odistinct(X32497),c_List_Oremdups(X32497,X32496))),
    inference(variable_rename,[status(thm)],[fact_distinct__remdups]) ).

fof(i_0_10750,plain,
    ! [X31546,X31547,X31548] :
      ( ( X31547 = c_List_Olist_ONil(X31548)
        | hAPP(hAPP(c_List_Oappend(X31548),X31547),X31546) != c_List_Olist_ONil(X31548) )
      & ( X31546 = c_List_Olist_ONil(X31548)
        | hAPP(hAPP(c_List_Oappend(X31548),X31547),X31546) != c_List_Olist_ONil(X31548) )
      & ( X31547 != c_List_Olist_ONil(X31548)
        | X31546 != c_List_Olist_ONil(X31548)
        | hAPP(hAPP(c_List_Oappend(X31548),X31547),X31546) = c_List_Olist_ONil(X31548) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__is__Nil__conv])])]) ).

fof(i_0_10751,plain,
    ! [X31557,X31558,X31559] :
      ( ( X31558 = c_List_Olist_ONil(X31559)
        | c_List_Olist_ONil(X31559) != hAPP(hAPP(c_List_Oappend(X31559),X31558),X31557) )
      & ( X31557 = c_List_Olist_ONil(X31559)
        | c_List_Olist_ONil(X31559) != hAPP(hAPP(c_List_Oappend(X31559),X31558),X31557) )
      & ( X31558 != c_List_Olist_ONil(X31559)
        | X31557 != c_List_Olist_ONil(X31559)
        | c_List_Olist_ONil(X31559) = hAPP(hAPP(c_List_Oappend(X31559),X31558),X31557) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__append__conv])])]) ).

cnf(i_0_10752,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_6082]) ).

cnf(i_0_10753,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_6083]) ).

cnf(i_0_10754,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_6084]) ).

fof(i_0_10755,plain,
    ! [X28614,X28615] : hAPP(c_Relation_ODomain(X28615,X28615),c_Transitive__Closure_Ortrancl(X28615,X28614)) = c_Orderings_Otop__class_Otop(tc_fun(X28615,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Domain__rtrancl]) ).

fof(i_0_10756,plain,
    ! [X28611,X28612] : hAPP(c_Relation_ORange(X28612,X28612),c_Transitive__Closure_Ortrancl(X28612,X28611)) = c_Orderings_Otop__class_Otop(tc_fun(X28612,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Range__rtrancl]) ).

fof(i_0_10757,plain,
    ! [X34314,X34315,X34316,X34317] : hAPP(hAPP(c_COMBK(X34317,X34316),X34315),X34314) = X34315,
    inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).

cnf(i_0_10758,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_6018]) ).

fof(i_0_10759,plain,
    ! [X34172,X34173,X34174] : c_Lazy__Sequence_Olazy__sequence_OInsert(X34174,X34173,X34172) != c_Lazy__Sequence_Olazy__sequence_OEmpty(X34174),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I3_J]) ).

fof(i_0_10760,plain,
    ! [X34169,X34170,X34171] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X34171) != c_Lazy__Sequence_Olazy__sequence_OInsert(X34171,X34170,X34169),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I2_J]) ).

fof(i_0_10761,plain,
    ! [X25059] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25059),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25059),
    inference(variable_rename,[status(thm)],[fact_zdiv__minus1__right]) ).

fof(i_0_10762,plain,
    ! [X22861,X22862] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22862),X22861) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22861),X22862),
    inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).

fof(i_0_10763,plain,
    ! [X21433,X21434] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21434),X21433) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21433),X21434),
    inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).

fof(i_0_10764,plain,
    ! [X22793,X22794] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22794),X22793) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22793),X22794),
    inference(variable_rename,[status(thm)],[fact_zmult__commute]) ).

fof(i_0_10765,plain,
    ! [X21067,X21068] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21068),X21067) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21067),X21068),
    inference(variable_rename,[status(thm)],[fact_nat__mult__commute]) ).

fof(i_0_10766,plain,
    ! [X27579,X27580,X27581] : hAPP(hAPP(c_Nitpick_Ofrac(X27581),X27580),X27579) = c_Nitpick_OAbs__Frac(X27581,c_Nitpick_Onorm__frac(X27580,X27579)),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Ofrac__def]) ).

fof(i_0_10767,plain,
    ! [X22320,X22321] :
      ( ~ class_Groups_Ogroup__add(X22321)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22321),c_Groups_Ozero__class_Ozero(X22321)),X22320) = hAPP(c_Groups_Ouminus__class_Ouminus(X22321),X22320) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0])]) ).

fof(i_0_10768,plain,
    ! [X34342,X34343] :
      ( ~ hBOOL(X34343)
      | ~ hBOOL(X34342)
      | hBOOL(hAPP(hAPP(c_fconj,X34343),X34342)) ),
    inference(variable_rename,[status(thm)],[i_0_6085]) ).

fof(i_0_10769,plain,
    ! [X31540,X31541,X31542] :
      ( ( hAPP(hAPP(c_List_Oappend(X31542),X31541),X31540) != X31540
        | X31541 = c_List_Olist_ONil(X31542) )
      & ( X31541 != c_List_Olist_ONil(X31542)
        | hAPP(hAPP(c_List_Oappend(X31542),X31541),X31540) = X31540 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__self__conv2])]) ).

fof(i_0_10770,plain,
    ! [X31543,X31544,X31545] :
      ( ( hAPP(hAPP(c_List_Oappend(X31545),X31544),X31543) != X31544
        | X31543 = c_List_Olist_ONil(X31545) )
      & ( X31543 != c_List_Olist_ONil(X31545)
        | hAPP(hAPP(c_List_Oappend(X31545),X31544),X31543) = X31544 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__self__conv])]) ).

fof(i_0_10771,plain,
    ! [X31552,X31553,X31554] :
      ( ( X31554 != hAPP(hAPP(c_List_Oappend(X31553),X31554),X31552)
        | X31552 = c_List_Olist_ONil(X31553) )
      & ( X31552 != c_List_Olist_ONil(X31553)
        | X31554 = hAPP(hAPP(c_List_Oappend(X31553),X31554),X31552) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv])]) ).

fof(i_0_10772,plain,
    ! [X31549,X31550,X31551] :
      ( ( X31551 != hAPP(hAPP(c_List_Oappend(X31550),X31549),X31551)
        | X31549 = c_List_Olist_ONil(X31550) )
      & ( X31549 != c_List_Olist_ONil(X31550)
        | X31551 = hAPP(hAPP(c_List_Oappend(X31550),X31549),X31551) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv2])]) ).

fof(i_0_10773,plain,
    ! [X22729,X22730] :
      ( ( X22729 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X22730),c_Groups_Ozero__class_Ozero(X22730)),X22729) = c_Groups_Oone__class_Oone(X22730)
        | ~ class_Power_Opower(X22730)
        | ~ class_Rings_Osemiring__0(X22730) )
      & ( X22729 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X22730),c_Groups_Ozero__class_Ozero(X22730)),X22729) = c_Groups_Ozero__class_Ozero(X22730)
        | ~ class_Power_Opower(X22730)
        | ~ class_Rings_Osemiring__0(X22730) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__left])])]) ).

fof(i_0_10774,plain,
    ! [X31341,X31342,X31343] : hAPP(hAPP(c_List_Olist_OCons(X31343),X31342),X31341) != c_List_Olist_ONil(X31343),
    inference(variable_rename,[status(thm)],[fact_list_Osimps_I3_J]) ).

fof(i_0_10775,plain,
    ! [X31344,X31345,X31346] : c_List_Olist_ONil(X31346) != hAPP(hAPP(c_List_Olist_OCons(X31346),X31345),X31344),
    inference(variable_rename,[status(thm)],[fact_list_Osimps_I2_J]) ).

fof(i_0_10776,plain,
    ! [X30666,X30667] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X30667,X30666))),
    inference(variable_rename,[status(thm)],[fact_distinct__upto]) ).

cnf(i_0_10777,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_6086]) ).

fof(i_0_10778,plain,
    ! [X30687,X30688] : c_List_Olistrel(X30688,c_Transitive__Closure_Ortrancl(X30688,X30687)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(X30688),c_List_Olistrel1(X30688,X30687)),
    inference(variable_rename,[status(thm)],[fact_listrel__rtrancl__eq__rtrancl__listrel1]) ).

fof(i_0_10779,plain,
    ! [X27410,X27411] :
      ( ~ c_Wellfounded_Owf(X27411,X27410)
      | c_Wellfounded_Owf(tc_fun(X27411,tc_HOL_Obool),c_Wellfounded_Omin__ext(X27411,X27410)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ext__wf])]) ).

fof(i_0_10780,plain,
    ! [X27428,X27429] :
      ( ~ c_Wellfounded_Owf(X27429,X27428)
      | c_Wellfounded_Owf(tc_fun(X27429,tc_HOL_Obool),c_Wellfounded_Omax__ext(X27429,X27428)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__wf])]) ).

fof(i_0_10781,plain,
    ! [X32902,X32903] :
      ( ~ class_Groups_Ocomm__monoid__add(X32903)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X32903),hAPP(c_List_Orev(X32903),X32902)) = hAPP(c_List_Omonoid__add__class_Olistsum(X32903),X32902) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__rev])]) ).

fof(i_0_10782,plain,
    ! [X27041,X27042] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27042)
      | hAPP(c_Groups_Oabs__class_Oabs(X27042),hAPP(c_Groups_Oabs__class_Oabs(X27042),X27041)) = hAPP(c_Groups_Oabs__class_Oabs(X27042),X27041) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__idempotent])]) ).

fof(i_0_10783,plain,
    ! [X27028,X27029] :
      ( ~ class_Rings_Olinordered__idom(X27029)
      | hAPP(c_Groups_Oabs__class_Oabs(X27029),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27029),X27028)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27029),X27028) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nat])]) ).

fof(i_0_10784,plain,
    ! [X27039,X27040] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27040)
      | hAPP(c_Groups_Oabs__class_Oabs(X27040),hAPP(c_Groups_Ouminus__class_Ouminus(X27040),X27039)) = hAPP(c_Groups_Oabs__class_Oabs(X27040),X27039) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__cancel])]) ).

fof(i_0_10785,plain,
    ! [X25020] :
      ( ~ class_Int_Onumber__ring(X25020)
      | ~ c_Int_Oiszero(X25020,hAPP(c_Int_Onumber__class_Onumber__of(X25020),c_Int_OMin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6087])]) ).

fof(i_0_10786,plain,
    ! [X19112] : c_Orderings_Otop__class_Otop(tc_fun(X19112,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X19112,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_UNIV__not__empty]) ).

fof(i_0_10787,plain,
    ! [X25051] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X25051,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_10788,plain,
    ! [X23642] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23642,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_10789,plain,
    ! [X22095,X22096] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22096),X22095) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22096 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22095 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22096 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22096),X22095) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22095 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22096),X22095) = 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_10790,plain,
    ! [X30302,X30303,X30304] : hAPP(hAPP(c_List_Olist_OCons(X30304),X30303),X30302) != X30302,
    inference(variable_rename,[status(thm)],[fact_not__Cons__self2]) ).

fof(i_0_10791,plain,
    ! [X30305,X30306,X30307] : X30307 != hAPP(hAPP(c_List_Olist_OCons(X30306),X30305),X30307),
    inference(variable_rename,[status(thm)],[fact_not__Cons__self]) ).

fof(i_0_10792,plain,
    ! [X18947] : c_Finite__Set_Ofun__left__comm__idem(X18947,tc_fun(X18947,tc_HOL_Obool),c_Set_Oinsert(X18947)),
    inference(variable_rename,[status(thm)],[fact_fun__left__comm__idem__insert]) ).

fof(i_0_10793,plain,
    ! [X34348,X34349] :
      ( ~ hBOOL(X34349)
      | hBOOL(hAPP(hAPP(c_fdisj,X34349),X34348)) ),
    inference(variable_rename,[status(thm)],[i_0_6088]) ).

fof(i_0_10794,plain,
    ! [X34350,X34351] :
      ( ~ hBOOL(X34351)
      | hBOOL(hAPP(hAPP(c_fdisj,X34350),X34351)) ),
    inference(variable_rename,[status(thm)],[i_0_6089]) ).

fof(i_0_10795,plain,
    ! [X34356,X34357] :
      ( ~ hBOOL(X34357)
      | hBOOL(hAPP(hAPP(c_fimplies,X34356),X34357)) ),
    inference(variable_rename,[status(thm)],[i_0_6090]) ).

fof(i_0_10796,plain,
    ! [X19078,X19079,X19080] :
      ( ~ class_Orderings_Otop(X19080)
      | hAPP(c_Orderings_Otop__class_Otop(tc_fun(X19079,X19080)),X19078) = c_Orderings_Otop__class_Otop(X19080) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__apply])]) ).

fof(i_0_10797,plain,
    ! [X17140,X17141,X17142] :
      ( ~ class_Orderings_Obot(X17142)
      | hAPP(c_Orderings_Obot__class_Obot(tc_fun(X17141,X17142)),X17140) = c_Orderings_Obot__class_Obot(X17142) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__apply])]) ).

fof(i_0_10798,plain,
    ! [X17021,X17022,X17023] :
      ( ~ class_Orderings_Obot(X17023)
      | hAPP(c_Orderings_Obot__class_Obot(tc_fun(X17022,X17023)),X17021) = c_Orderings_Obot__class_Obot(X17023) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__fun__def])]) ).

fof(i_0_10799,plain,
    ! [X31306,X31307] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X31307),X31306) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,X31307),X31306),
    inference(variable_rename,[status(thm)],[fact_minus__code__numeral__code]) ).

fof(i_0_10800,plain,
    ! [X32766,X32767] :
      ( ~ class_Orderings_Olinorder(X32767)
      | ~ c_List_Olinorder__class_Osorted(X32767,X32766)
      | c_List_Olinorder__class_Osorted(X32767,hAPP(c_List_Otl(X32767),X32766)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__tl])]) ).

fof(i_0_10801,plain,
    ! [X32513,X32514] :
      ( ( c_List_Oremdups(X32514,X32513) != X32513
        | hBOOL(hAPP(c_List_Odistinct(X32514),X32513)) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X32514),X32513))
        | c_List_Oremdups(X32514,X32513) = X32513 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remdups__id__iff__distinct])]) ).

fof(i_0_10802,plain,
    ! [X32511,X32512] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X32512),X32511))
      | c_List_Oremdups(X32512,X32511) = X32511 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__remdups__id])]) ).

cnf(i_0_10803,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_10804,plain,
    ! [X22378,X22379] :
      ( X22379 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22379),X22378)
      | X22378 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | X22379 = 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_10805,plain,
    ! [X31903,X31904] :
      ( X31904 = c_List_Olist_ONil(X31903)
      | hAPP(c_List_Ohd(X31903),X31904) = hAPP(hAPP(c_List_Onth(X31903),X31904),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_10806,plain,
    ! [X34354,X34355] :
      ( hBOOL(X34355)
      | hBOOL(hAPP(hAPP(c_fimplies,X34355),X34354)) ),
    inference(variable_rename,[status(thm)],[help_c__fimplies__1]) ).

fof(i_0_10807,plain,
    ! [X28880,X28881] : c_Relation_Osingle__valued(X28881,X28881,c_Relation_OId__on(X28881,X28880)),
    inference(variable_rename,[status(thm)],[fact_single__valued__Id__on]) ).

fof(i_0_10808,plain,
    ! [X28129,X28130] : c_Relation_Orefl__on(X28130,X28129,c_Relation_OId__on(X28130,X28129)),
    inference(variable_rename,[status(thm)],[fact_refl__on__Id__on]) ).

fof(i_0_10809,plain,
    ! [X22078,X22079] :
      ( ( X22079 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22079),X22078) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22078 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22079),X22078) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22079 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22078 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22079),X22078) = 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_10810,plain,
    ! [X21365,X21366] :
      ( ( X21366 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21366),X21365) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X21365 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21366),X21365) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X21366 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X21365 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21366),X21365) = 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_10811,plain,
    ! [X21362,X21363] :
      ( ( X21363 = 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),X21363),X21362) )
      & ( X21362 = 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),X21363),X21362) )
      & ( X21363 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X21362 != 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),X21363),X21362) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff])])]) ).

fof(i_0_10812,plain,
    ! [X24009,X24010,X24011] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X24011),X24010) != hAPP(c_Int_Onumber__class_Onumber__of(X24011),X24009)
        | X24010 = X24009
        | ~ class_Int_Onumber__ring(X24011)
        | ~ class_Int_Oring__char__0(X24011) )
      & ( X24010 != X24009
        | hAPP(c_Int_Onumber__class_Onumber__of(X24011),X24010) = hAPP(c_Int_Onumber__class_Onumber__of(X24011),X24009)
        | ~ class_Int_Onumber__ring(X24011)
        | ~ class_Int_Oring__char__0(X24011) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of])])]) ).

fof(i_0_10813,plain,
    ! [X28749,X28750] : hAPP(c_Relation_Oconverse(X28750,X28750),c_Relation_OId__on(X28750,X28749)) = c_Relation_OId__on(X28750,X28749),
    inference(variable_rename,[status(thm)],[fact_converse__Id__on]) ).

fof(i_0_10814,plain,
    ! [X34338,X34339] :
      ( X34339 != X34338
      | hBOOL(hAPP(hAPP(c_fequal,X34339),X34338)) ),
    inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).

fof(i_0_10815,plain,
    ! [X25097,X25098] :
      ( ~ class_Rings_Oring__1(X25098)
      | hAPP(c_Int_Oring__1__class_Oof__int(X25098),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25097)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25098),X25097) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__of__nat__eq])]) ).

fof(i_0_10816,plain,
    ! [X25024,X25025] :
      ( ~ class_Int_Onumber__ring(X25025)
      | hAPP(c_Int_Oring__1__class_Oof__int(X25025),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25024)) = hAPP(c_Int_Onumber__class_Onumber__of(X25025),X25024) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__number__of__eq])]) ).

fof(i_0_10817,plain,
    ! [X31359,X31360] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X31360,tc_HOL_Obool)) != hAPP(c_List_Oset(X31360),X31359)
        | X31359 = c_List_Olist_ONil(X31360) )
      & ( X31359 != c_List_Olist_ONil(X31360)
        | c_Orderings_Obot__class_Obot(tc_fun(X31360,tc_HOL_Obool)) = hAPP(c_List_Oset(X31360),X31359) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__empty2])]) ).

fof(i_0_10818,plain,
    ! [X31357,X31358] :
      ( ( hAPP(c_List_Oset(X31358),X31357) != c_Orderings_Obot__class_Obot(tc_fun(X31358,tc_HOL_Obool))
        | X31357 = c_List_Olist_ONil(X31358) )
      & ( X31357 != c_List_Olist_ONil(X31358)
        | hAPP(c_List_Oset(X31358),X31357) = c_Orderings_Obot__class_Obot(tc_fun(X31358,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__empty])]) ).

fof(i_0_10819,plain,
    ! [X32904,X32905] : hAPP(c_List_Oset(X32905),hAPP(c_List_Orev(X32905),X32904)) = hAPP(c_List_Oset(X32905),X32904),
    inference(variable_rename,[status(thm)],[fact_set__rev]) ).

fof(i_0_10820,plain,
    ! [X31786,X31787] : hAPP(c_List_Oset(X31787),hAPP(c_List_Orotate1(X31787),X31786)) = hAPP(c_List_Oset(X31787),X31786),
    inference(variable_rename,[status(thm)],[fact_set__rotate1]) ).

fof(i_0_10821,plain,
    ! [X22776] :
      ( ~ class_Power_Opower(X22776)
      | c_Power_Opower__class_Opower(X22776) = c_Power_Opower_Opower(X22776,c_Groups_Oone__class_Oone(X22776),c_Groups_Otimes__class_Otimes(X22776)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__power__power])]) ).

fof(i_0_10822,plain,
    ! [X22080,X22081] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22081),X22080) != X22081
      | X22080 = 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_10823,plain,
    ! [X32926,X32927] :
      ( X32927 = c_List_Olist_ONil(X32926)
      | hAPP(c_List_Ohd(X32926),hAPP(c_List_Orev(X32926),X32927)) = c_List_Olast(X32926,X32927) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__rev])]) ).

fof(i_0_10824,plain,
    ! [X32928,X32929] :
      ( X32929 = c_List_Olist_ONil(X32928)
      | c_List_Olast(X32928,hAPP(c_List_Orev(X32928),X32929)) = hAPP(c_List_Ohd(X32928),X32929) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__rev])]) ).

fof(i_0_10825,plain,
    ! [X32610] :
      ( ~ class_Orderings_Olinorder(X32610)
      | c_List_Olinorder__class_Osorted__list__of__set(X32610,c_Orderings_Obot__class_Obot(tc_fun(X32610,tc_HOL_Obool))) = c_List_Olist_ONil(X32610) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__empty])]) ).

fof(i_0_10826,plain,
    ! [X29763] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29763)
      | c_Complete__Lattice_OSup__class_OSup(X29763,c_Orderings_Otop__class_Otop(tc_fun(X29763,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X29763) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__UNIV])]) ).

fof(i_0_10827,plain,
    ! [X29752] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29752)
      | c_Complete__Lattice_OSup__class_OSup(X29752,c_Orderings_Obot__class_Obot(tc_fun(X29752,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X29752) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__empty])]) ).

fof(i_0_10828,plain,
    ! [X29767] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29767)
      | c_Complete__Lattice_OInf__class_OInf(X29767,c_Orderings_Otop__class_Otop(tc_fun(X29767,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X29767) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__UNIV])]) ).

fof(i_0_10829,plain,
    ! [X29766] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29766)
      | c_Complete__Lattice_OInf__class_OInf(X29766,c_Orderings_Obot__class_Obot(tc_fun(X29766,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X29766) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__empty])]) ).

fof(i_0_10830,plain,
    ! [X23414] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X23414),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X23414,
    inference(variable_rename,[status(thm)],[fact_div__1]) ).

fof(i_0_10831,plain,
    ! [X29658,X29659] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X29659,tc_HOL_Obool),hAPP(c_Set_OPow(X29659),X29658)) = X29658,
    inference(variable_rename,[status(thm)],[fact_Union__Pow__eq]) ).

fof(i_0_10832,plain,
    ! [X24123,X24124] :
      ( ~ class_Rings_Odivision__ring(X24124)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24124),c_Groups_Ozero__class_Ozero(X24124)),X24123) = c_Groups_Ozero__class_Ozero(X24124) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero__left])]) ).

fof(i_0_10833,plain,
    ! [X22998,X22999] :
      ( ~ class_Divides_Osemiring__div(X22999)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X22999),c_Groups_Ozero__class_Ozero(X22999)),X22998) = c_Groups_Ozero__class_Ozero(X22999) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__0])]) ).

fof(i_0_10834,plain,
    ! [X22661,X22662] :
      ( ~ class_Groups_Omonoid__mult(X22662)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22662),c_Groups_Oone__class_Oone(X22662)),X22661) = c_Groups_Oone__class_Oone(X22662) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])]) ).

fof(i_0_10835,plain,
    ! [X22030,X22031] :
      ( ~ class_Rings_Omult__zero(X22031)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22031),c_Groups_Ozero__class_Ozero(X22031)),X22030) = c_Groups_Ozero__class_Ozero(X22031) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__left])]) ).

fof(i_0_10836,plain,
    ! [X22028,X22029] :
      ( ~ class_Rings_Ocomm__semiring__1(X22029)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22029),c_Groups_Ozero__class_Ozero(X22029)),X22028) = c_Groups_Ozero__class_Ozero(X22029) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])]) ).

fof(i_0_10837,plain,
    ! [X18008,X18009] :
      ( ~ class_Lattices_Obounded__lattice__bot(X18009)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18009),c_Orderings_Obot__class_Obot(X18009)),X18008) = c_Orderings_Obot__class_Obot(X18009) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__bot__left])]) ).

fof(i_0_10838,plain,
    ! [X19166,X19167] :
      ( ~ class_Lattices_Obounded__lattice__top(X19167)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19167),c_Orderings_Otop__class_Otop(X19167)),X19166) = c_Orderings_Otop__class_Otop(X19167) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__top__left])]) ).

fof(i_0_10839,plain,
    ! [X32795,X32796] :
      ( ~ class_Orderings_Olinorder(X32796)
      | X32795 = c_List_Olist_ONil(X32796)
      | ~ c_List_Olinorder__class_Osorted(X32796,X32795)
      | c_List_Olinorder__class_Osorted(X32796,c_List_Obutlast(X32796,X32795)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__butlast])]) ).

fof(i_0_10840,plain,
    ! [X24985] :
      ( ~ class_Int_Onumber__ring(X24985)
      | hAPP(c_Int_Oring__1__class_Oof__int(X24985),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(X24985),c_Int_OMin) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__m1])]) ).

fof(i_0_10841,plain,
    ! [X22339] : hAPP(c_Finite__Set_Ocard(X22339),c_Orderings_Obot__class_Obot(tc_fun(X22339,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_card_Oempty]) ).

cnf(i_0_10842,plain,
    ( c_Int_OPls = X1
    | c_Int_OPls != c_Int_OBit0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6091]) ).

cnf(i_0_10843,plain,
    ( X1 = c_Int_OPls
    | c_Int_OBit0(X1) != c_Int_OPls ),
    inference(split_conjunct,[status(thm)],[i_0_6092]) ).

fof(i_0_10844,plain,
    ! [X27133] :
      ( ~ class_Int_Onumber__ring(X27133)
      | ~ class_Rings_Olinordered__idom(X27133)
      | hAPP(c_Groups_Oabs__class_Oabs(X27133),hAPP(c_Int_Onumber__class_Onumber__of(X27133),c_Int_OMin)) = c_Groups_Oone__class_Oone(X27133) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__one])]) ).

fof(i_0_10845,plain,
    ! [X22823,X22824] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X22824)),hAPP(c_Option_Ooption_OSome(X22824),X22823)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_option_Osize_I4_J]) ).

fof(i_0_10846,plain,
    ! [X26800] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26800) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X26800),
    inference(variable_rename,[status(thm)],[fact_atLeast0AtMost]) ).

cnf(i_0_10847,plain,
    c_Int_OBit0(X1) != c_Int_OMin,
    inference(split_conjunct,[status(thm)],[i_0_6093]) ).

cnf(i_0_10848,plain,
    c_Int_OMin != c_Int_OBit0(X1),
    inference(split_conjunct,[status(thm)],[i_0_6094]) ).

fof(i_0_10849,plain,
    ! [X26912,X26913,X26914] :
      ( ( hAPP(c_SetInterval_Oord__class_OatLeast(X26914),X26913) != hAPP(c_SetInterval_Oord__class_OatLeast(X26914),X26912)
        | X26913 = X26912
        | ~ class_Orderings_Olinorder(X26914) )
      & ( X26913 != X26912
        | hAPP(c_SetInterval_Oord__class_OatLeast(X26914),X26913) = hAPP(c_SetInterval_Oord__class_OatLeast(X26914),X26912)
        | ~ class_Orderings_Olinorder(X26914) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeast__eq__iff])])]) ).

fof(i_0_10850,plain,
    ! [X26873,X26874,X26875] :
      ( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(X26875),X26874) != hAPP(c_SetInterval_Oord__class_OgreaterThan(X26875),X26873)
        | X26874 = X26873
        | ~ class_Orderings_Olinorder(X26875) )
      & ( X26874 != X26873
        | hAPP(c_SetInterval_Oord__class_OgreaterThan(X26875),X26874) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X26875),X26873)
        | ~ class_Orderings_Olinorder(X26875) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__eq__iff])])]) ).

fof(i_0_10851,plain,
    ! [X26797,X26798,X26799] :
      ( ( hAPP(c_SetInterval_Oord__class_OatMost(X26799),X26798) != hAPP(c_SetInterval_Oord__class_OatMost(X26799),X26797)
        | X26798 = X26797
        | ~ class_Orderings_Olinorder(X26799) )
      & ( X26798 != X26797
        | hAPP(c_SetInterval_Oord__class_OatMost(X26799),X26798) = hAPP(c_SetInterval_Oord__class_OatMost(X26799),X26797)
        | ~ class_Orderings_Olinorder(X26799) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__eq__iff])])]) ).

fof(i_0_10852,plain,
    ! [X26394,X26395,X26396] :
      ( ( hAPP(c_SetInterval_Oord__class_OlessThan(X26396),X26395) != hAPP(c_SetInterval_Oord__class_OlessThan(X26396),X26394)
        | X26395 = X26394
        | ~ class_Orderings_Olinorder(X26396) )
      & ( X26395 != X26394
        | hAPP(c_SetInterval_Oord__class_OlessThan(X26396),X26395) = hAPP(c_SetInterval_Oord__class_OlessThan(X26396),X26394)
        | ~ class_Orderings_Olinorder(X26396) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__eq__iff])])]) ).

fof(i_0_10853,plain,
    ! [X25103,X25104,X25105] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25105),X25104) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25105),X25103)
        | X25104 = X25103
        | ~ class_Nat_Osemiring__char__0(X25105) )
      & ( X25104 != X25103
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25105),X25104) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25105),X25103)
        | ~ class_Nat_Osemiring__char__0(X25105) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__eq__iff])])]) ).

fof(i_0_10854,plain,
    ! [X24988,X24989,X24990] :
      ( ( hAPP(c_Int_Oring__1__class_Oof__int(X24990),X24989) != hAPP(c_Int_Oring__1__class_Oof__int(X24990),X24988)
        | X24989 = X24988
        | ~ class_Int_Oring__char__0(X24990) )
      & ( X24989 != X24988
        | hAPP(c_Int_Oring__1__class_Oof__int(X24990),X24989) = hAPP(c_Int_Oring__1__class_Oof__int(X24990),X24988)
        | ~ class_Int_Oring__char__0(X24990) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__eq__iff])])]) ).

fof(i_0_10855,plain,
    ! [X20370,X20371,X20372] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X20372),X20371) != hAPP(c_Groups_Ouminus__class_Ouminus(X20372),X20370)
        | X20371 = X20370
        | ~ class_Lattices_Oboolean__algebra(X20372) )
      & ( X20371 != X20370
        | hAPP(c_Groups_Ouminus__class_Ouminus(X20372),X20371) = hAPP(c_Groups_Ouminus__class_Ouminus(X20372),X20370)
        | ~ class_Lattices_Oboolean__algebra(X20372) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff])])]) ).

fof(i_0_10856,plain,
    ! [X20359,X20360,X20361] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X20361),X20360) != hAPP(c_Groups_Ouminus__class_Ouminus(X20361),X20359)
        | X20360 = X20359
        | ~ class_Groups_Ogroup__add(X20361) )
      & ( X20360 != X20359
        | hAPP(c_Groups_Ouminus__class_Ouminus(X20361),X20360) = hAPP(c_Groups_Ouminus__class_Ouminus(X20361),X20359)
        | ~ class_Groups_Ogroup__add(X20361) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal])])]) ).

fof(i_0_10857,plain,
    ! [X22018,X22019] :
      ( ~ class_Groups_Ocomm__monoid__add(X22019)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22019),c_Groups_Ozero__class_Ozero(X22019)),X22018) = X22018 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).

fof(i_0_10858,plain,
    ! [X22016,X22017] :
      ( ~ class_Groups_Omonoid__add(X22017)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22017),c_Groups_Ozero__class_Ozero(X22017)),X22016) = X22016 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).

fof(i_0_10859,plain,
    ! [X22014,X22015] :
      ( ~ class_Rings_Ocomm__semiring__1(X22015)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22015),c_Groups_Ozero__class_Ozero(X22015)),X22014) = X22014 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).

fof(i_0_10860,plain,
    ! [X21405,X21406] :
      ( ~ class_Rings_Ocomm__semiring__1(X21406)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21406),c_Groups_Oone__class_Oone(X21406)),X21405) = X21405 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])]) ).

fof(i_0_10861,plain,
    ! [X21359,X21360] :
      ( ~ class_Groups_Omonoid__mult(X21360)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21360),c_Groups_Oone__class_Oone(X21360)),X21359) = X21359 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__left])]) ).

fof(i_0_10862,plain,
    ! [X21357,X21358] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21358)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21358),c_Groups_Oone__class_Oone(X21358)),X21357) = X21357 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1])]) ).

fof(i_0_10863,plain,
    ! [X19175,X19176] :
      ( ~ class_Lattices_Obounded__lattice__top(X19176)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X19176),c_Orderings_Otop__class_Otop(X19176)),X19175) = X19175 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__top__left])]) ).

fof(i_0_10864,plain,
    ! [X17637,X17638] :
      ( ~ class_Lattices_Obounded__lattice__bot(X17638)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17638),c_Orderings_Obot__class_Obot(X17638)),X17637) = X17637 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__bot__left])]) ).

fof(i_0_10865,plain,
    ! [X24171,X24172] :
      ( ( X24171 != c_Groups_Ozero__class_Ozero(X24172)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24172),X24171),X24171) = c_Groups_Ozero__class_Ozero(X24172)
        | ~ class_Rings_Odivision__ring__inverse__zero(X24172) )
      & ( X24171 = c_Groups_Ozero__class_Ozero(X24172)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24172),X24171),X24171) = c_Groups_Oone__class_Oone(X24172)
        | ~ class_Rings_Odivision__ring__inverse__zero(X24172) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self__if])])]) ).

fof(i_0_10866,plain,
    ! [X23334,X23335] :
      ( ~ class_Divides_Osemiring__div(X23335)
      | c_Divides_Odiv__class_Omod(X23335,c_Groups_Ozero__class_Ozero(X23335),X23334) = c_Groups_Ozero__class_Ozero(X23335) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__0])]) ).

fof(i_0_10867,plain,
    ! [X23409,X23410] :
      ( ~ class_Divides_Osemiring__div(X23410)
      | c_Divides_Odiv__class_Omod(X23410,X23409,c_Groups_Oone__class_Oone(X23410)) = c_Groups_Ozero__class_Ozero(X23410) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__1])]) ).

fof(i_0_10868,plain,
    ! [X32782,X32783] :
      ( ~ class_Orderings_Olinorder(X32783)
      | ~ c_List_Olinorder__class_Osorted(X32783,X32782)
      | c_List_Olinorder__class_Osorted(X32783,c_List_Oremdups(X32783,X32782)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__remdups])]) ).

fof(i_0_10869,plain,
    ! [X20228,X20229] :
      ( ( c_Option_Oset(X20229,X20228) != c_Orderings_Obot__class_Obot(tc_fun(X20229,tc_HOL_Obool))
        | X20228 = c_Option_Ooption_ONone(X20229) )
      & ( X20228 != c_Option_Ooption_ONone(X20229)
        | c_Option_Oset(X20229,X20228) = c_Orderings_Obot__class_Obot(tc_fun(X20229,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__empty__eq])]) ).

fof(i_0_10870,plain,
    ! [X24125,X24126] :
      ( ~ class_Rings_Odivision__ring__inverse__zero(X24126)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24126),X24125),c_Groups_Ozero__class_Ozero(X24126)) = c_Groups_Ozero__class_Ozero(X24126) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero])]) ).

fof(i_0_10871,plain,
    ! [X22996,X22997] :
      ( ~ class_Divides_Osemiring__div(X22997)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X22997),X22996),c_Groups_Ozero__class_Ozero(X22997)) = c_Groups_Ozero__class_Ozero(X22997) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__0])]) ).

fof(i_0_10872,plain,
    ! [X22032,X22033] :
      ( ~ class_Rings_Omult__zero(X22033)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22033),X22032),c_Groups_Ozero__class_Ozero(X22033)) = c_Groups_Ozero__class_Ozero(X22033) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__right])]) ).

fof(i_0_10873,plain,
    ! [X22026,X22027] :
      ( ~ class_Rings_Ocomm__semiring__1(X22027)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22027),X22026),c_Groups_Ozero__class_Ozero(X22027)) = c_Groups_Ozero__class_Ozero(X22027) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])]) ).

fof(i_0_10874,plain,
    ! [X18006,X18007] :
      ( ~ class_Lattices_Obounded__lattice__bot(X18007)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18007),X18006),c_Orderings_Obot__class_Obot(X18007)) = c_Orderings_Obot__class_Obot(X18007) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__bot__right])]) ).

fof(i_0_10875,plain,
    ! [X19168,X19169] :
      ( ~ class_Lattices_Obounded__lattice__top(X19169)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X19169),X19168),c_Orderings_Otop__class_Otop(X19169)) = c_Orderings_Otop__class_Otop(X19169) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__top__right])]) ).

fof(i_0_10876,plain,
    ! [X27494,X27495] :
      ( ~ c_Wellfounded_Owf(X27495,X27494)
      | c_Wellfounded_Owf(tc_List_Olist(X27495),c_List_Olex(X27495,X27494)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lex])]) ).

fof(i_0_10877,plain,
    ! [X27481,X27482] :
      ( ~ c_Wellfounded_Owf(X27482,X27481)
      | c_Wellfounded_Owf(tc_List_Olist(X27482),c_List_Olenlex(X27482,X27481)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lenlex])]) ).

fof(i_0_10878,plain,
    ! [X31537,X31538,X31539] :
      ( X31539 != X31538
      | X31539 = hAPP(hAPP(c_List_Oappend(X31537),c_List_Olist_ONil(X31537)),X31538) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__Nil__appendI])]) ).

fof(i_0_10879,plain,
    ! [X24169,X24170] :
      ( ~ class_Rings_Odivision__ring(X24170)
      | X24169 = c_Groups_Ozero__class_Ozero(X24170)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24170),X24169),X24169) = c_Groups_Oone__class_Oone(X24170) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self])]) ).

fof(i_0_10880,plain,
    ! [X23088,X23089] :
      ( ~ class_Divides_Osemiring__div(X23089)
      | X23088 = c_Groups_Ozero__class_Ozero(X23089)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23089),X23088),X23088) = c_Groups_Oone__class_Oone(X23089) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__self])]) ).

fof(i_0_10881,plain,
    ! [X23332,X23333] :
      ( ~ class_Divides_Osemiring__div(X23333)
      | c_Divides_Odiv__class_Omod(X23333,X23332,c_Groups_Ozero__class_Ozero(X23333)) = X23332 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__0])]) ).

fof(i_0_10882,plain,
    ! [X25191] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X25191))
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X25191)) = X25191 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6095])]) ).

fof(i_0_10883,plain,
    ! [X34182] : hAPP(c_Lazy__Sequence_Oyield(X34182),c_Lazy__Sequence_Olazy__sequence_OEmpty(X34182)) = c_Option_Ooption_ONone(tc_prod(X34182,tc_Lazy__Sequence_Olazy__sequence(X34182))),
    inference(variable_rename,[status(thm)],[fact__05]) ).

fof(i_0_10884,plain,
    ! [X29171] :
      ( ~ class_Groups_Oab__semigroup__mult(X29171)
      | c_Finite__Set_Ofun__left__comm(X29171,X29171,c_Groups_Otimes__class_Otimes(X29171)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm])]) ).

fof(i_0_10885,plain,
    ! [X25760] :
      ( ~ class_Orderings_Olinorder(X25760)
      | c_Finite__Set_Ofun__left__comm__idem(X25760,X25760,c_Orderings_Oord__class_Omax(X25760)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__sup])]) ).

fof(i_0_10886,plain,
    ! [X25307] :
      ( ~ class_Orderings_Olinorder(X25307)
      | c_Finite__Set_Ofun__left__comm__idem(X25307,X25307,c_Orderings_Oord__class_Omin(X25307)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__inf])]) ).

fof(i_0_10887,plain,
    ! [X20490] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X20490)
      | c_Finite__Set_Ofun__left__comm__idem(X20490,X20490,c_Groups_Otimes__class_Otimes(X20490)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem])]) ).

fof(i_0_10888,plain,
    ! [X18949] :
      ( ~ class_Lattices_Osemilattice__inf(X18949)
      | c_Finite__Set_Ofun__left__comm__idem(X18949,X18949,c_Lattices_Osemilattice__inf__class_Oinf(X18949)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__inf])]) ).

fof(i_0_10889,plain,
    ! [X18948] :
      ( ~ class_Lattices_Osemilattice__sup(X18948)
      | c_Finite__Set_Ofun__left__comm__idem(X18948,X18948,c_Lattices_Osemilattice__sup__class_Osup(X18948)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__sup])]) ).

fof(i_0_10890,plain,
    ! [X27595,X27596] : hAPP(c_Relation_ODomain(X27596,X27596),c_Relation_OId__on(X27596,X27595)) = X27595,
    inference(variable_rename,[status(thm)],[fact_Domain__Id__on]) ).

fof(i_0_10891,plain,
    ! [X27517,X27518] : hAPP(c_Relation_ORange(X27518,X27518),c_Relation_OId__on(X27518,X27517)) = X27517,
    inference(variable_rename,[status(thm)],[fact_Range__Id__on]) ).

fof(i_0_10892,plain,
    ! [X22697,X22698] :
      ( ~ class_Power_Opower(X22698)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22698),X22697),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X22698) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0])]) ).

fof(i_0_10893,plain,
    ! [X22592,X22593] :
      ( ~ class_Rings_Ocomm__semiring__1(X22593)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22593),X22592),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X22593) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J])]) ).

fof(i_0_10894,plain,
    ! [X24144,X24145] :
      ( ~ class_Rings_Odivision__ring(X24145)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24145),X24144),c_Groups_Oone__class_Oone(X24145)) = X24144 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__1])]) ).

fof(i_0_10895,plain,
    ! [X23000,X23001] :
      ( ~ class_Divides_Osemiring__div(X23001)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23001),X23000),c_Groups_Oone__class_Oone(X23001)) = X23000 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__1])]) ).

fof(i_0_10896,plain,
    ! [X22024,X22025] :
      ( ~ class_Groups_Ocomm__monoid__add(X22025)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22025),X22024),c_Groups_Ozero__class_Ozero(X22025)) = X22024 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).

fof(i_0_10897,plain,
    ! [X22022,X22023] :
      ( ~ class_Groups_Omonoid__add(X22023)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22023),X22022),c_Groups_Ozero__class_Ozero(X22023)) = X22022 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).

fof(i_0_10898,plain,
    ! [X22012,X22013] :
      ( ~ class_Rings_Ocomm__semiring__1(X22013)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22013),X22012),c_Groups_Ozero__class_Ozero(X22013)) = X22012 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).

fof(i_0_10899,plain,
    ! [X21407,X21408] :
      ( ~ class_Rings_Ocomm__semiring__1(X21408)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21408),X21407),c_Groups_Oone__class_Oone(X21408)) = X21407 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])]) ).

fof(i_0_10900,plain,
    ! [X21355,X21356] :
      ( ~ class_Groups_Omonoid__mult(X21356)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21356),X21355),c_Groups_Oone__class_Oone(X21356)) = X21355 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__right])]) ).

fof(i_0_10901,plain,
    ! [X21353,X21354] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21354)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21354),X21353),c_Groups_Oone__class_Oone(X21354)) = X21353 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral])]) ).

fof(i_0_10902,plain,
    ! [X19173,X19174] :
      ( ~ class_Lattices_Obounded__lattice__top(X19174)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X19174),X19173),c_Orderings_Otop__class_Otop(X19174)) = X19173 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__top__right])]) ).

fof(i_0_10903,plain,
    ! [X22051,X22052] :
      ( ~ class_Groups_Ogroup__add(X22052)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22052),X22051),c_Groups_Ozero__class_Ozero(X22052)) = X22051 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0__right])]) ).

fof(i_0_10904,plain,
    ! [X17635,X17636] :
      ( ~ class_Lattices_Obounded__lattice__bot(X17636)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17636),X17635),c_Orderings_Obot__class_Obot(X17636)) = X17635 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__bot__right])]) ).

fof(i_0_10905,plain,
    ! [X20384,X20385] :
      ( ~ class_Lattices_Oboolean__algebra(X20385)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X20385),hAPP(c_Groups_Ouminus__class_Ouminus(X20385),X20384)) = X20384 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__compl])]) ).

fof(i_0_10906,plain,
    ! [X20368,X20369] :
      ( ~ class_Groups_Ogroup__add(X20369)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X20369),hAPP(c_Groups_Ouminus__class_Ouminus(X20369),X20368)) = X20368 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])]) ).

fof(i_0_10907,plain,
    ! [X27030] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X27030)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X27030),
    inference(variable_rename,[status(thm)],[fact_abs__int__eq]) ).

fof(i_0_10908,plain,
    ! [X25099] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25099)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25099),
    inference(variable_rename,[status(thm)],[fact_of__int__int__eq]) ).

fof(i_0_10909,plain,
    ! [X32507,X32508] : hAPP(c_List_Oset(X32508),c_List_Oremdups(X32508,X32507)) = hAPP(c_List_Oset(X32508),X32507),
    inference(variable_rename,[status(thm)],[fact_set__remdups]) ).

fof(i_0_10910,plain,
    ! [X23330,X23331] :
      ( ~ class_Divides_Osemiring__div(X23331)
      | c_Divides_Odiv__class_Omod(X23331,X23330,X23330) = c_Groups_Ozero__class_Ozero(X23331) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__self])]) ).

fof(i_0_10911,plain,
    ! [X32899,X32900,X32901] :
      ( ( hAPP(c_List_Orev(X32901),X32900) != hAPP(c_List_Orev(X32901),X32899)
        | X32900 = X32899 )
      & ( X32900 != X32899
        | hAPP(c_List_Orev(X32901),X32900) = hAPP(c_List_Orev(X32901),X32899) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__is__rev__conv])]) ).

fof(i_0_10912,plain,
    ! [X20193,X20194,X20195] :
      ( ( hAPP(c_Option_Ooption_OSome(X20195),X20194) != hAPP(c_Option_Ooption_OSome(X20195),X20193)
        | X20194 = X20193 )
      & ( X20194 != X20193
        | hAPP(c_Option_Ooption_OSome(X20195),X20194) = hAPP(c_Option_Ooption_OSome(X20195),X20193) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_option_Oinject])]) ).

fof(i_0_10913,plain,
    ! [X22340,X22341] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X22341),X22340))
      | hAPP(c_Finite__Set_Ocard(X22341),X22340) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6096])]) ).

fof(i_0_10914,plain,
    ! [X28523,X28524] :
      ( ( X28524 != X28523
        | c_Random_Oinc__shift(X28524,X28523) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
      & ( X28524 = X28523
        | c_Random_Oinc__shift(X28524,X28523) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X28523),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_10915,plain,
    ! [X31560,X31561] : hAPP(hAPP(c_List_Oappend(X31561),c_List_Olist_ONil(X31561)),X31560) = X31560,
    inference(variable_rename,[status(thm)],[fact_append__Nil]) ).

fof(i_0_10916,plain,
    ! [X21995] : hAPP(c_Nat_OSuc,X21995) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X21995),
    inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).

fof(i_0_10917,plain,
    ! [X31362,X31363] : c_List_Osublist(X31363,c_List_Olist_ONil(X31363),X31362) = c_List_Olist_ONil(X31363),
    inference(variable_rename,[status(thm)],[fact_sublist__nil]) ).

fof(i_0_10918,plain,
    ! [X33001,X33002] : c_List_OtakeWhile(X33002,X33001,c_List_Olist_ONil(X33002)) = c_List_Olist_ONil(X33002),
    inference(variable_rename,[status(thm)],[fact_takeWhile_Osimps_I1_J]) ).

fof(i_0_10919,plain,
    ! [X32561,X32562] : c_List_Oremove1(X32562,X32561,c_List_Olist_ONil(X32562)) = c_List_Olist_ONil(X32562),
    inference(variable_rename,[status(thm)],[fact_remove1_Osimps_I1_J]) ).

fof(i_0_10920,plain,
    ! [X26128] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26128),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_10921,plain,
    ! [X22581,X22582] :
      ( ~ class_Rings_Ocomm__semiring__1(X22582)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22582),X22581),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X22581 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J])]) ).

fof(i_0_10922,plain,
    ! [X22667,X22668] :
      ( ~ class_Groups_Omonoid__mult(X22668)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22668),X22667),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X22667 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__right])]) ).

fof(i_0_10923,plain,
    ! [X22049,X22050] :
      ( ~ class_Groups_Ogroup__add(X22050)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22050),X22049),X22049) = c_Groups_Ozero__class_Ozero(X22050) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__self])]) ).

fof(i_0_10924,plain,
    ! [X31375,X31376] : c_List_Olist_Olist__size(X31376,X31375,c_List_Olist_ONil(X31376)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_list_Osize_I1_J]) ).

fof(i_0_10925,plain,
    ! [X22598,X22599] : c_Option_Ooption_Ooption__size(X22599,X22598,c_Option_Ooption_ONone(X22599)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_option_Osize_I1_J]) ).

fof(i_0_10926,plain,
    ! [X31332,X31333] : hAPP(hAPP(c_List_Otake(X31333),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31332) = c_List_Olist_ONil(X31333),
    inference(variable_rename,[status(thm)],[fact_take__0]) ).

fof(i_0_10927,plain,
    ! [X31765,X31766] : hAPP(hAPP(c_List_Odrop(X31766),X31765),c_List_Olist_ONil(X31766)) = c_List_Olist_ONil(X31766),
    inference(variable_rename,[status(thm)],[fact_drop__Nil]) ).

fof(i_0_10928,plain,
    ! [X31334,X31335] : hAPP(hAPP(c_List_Otake(X31335),X31334),c_List_Olist_ONil(X31335)) = c_List_Olist_ONil(X31335),
    inference(variable_rename,[status(thm)],[fact_take__Nil]) ).

fof(i_0_10929,plain,
    ! [X20362,X20363,X20364] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X20364),X20363) != X20362
        | hAPP(c_Groups_Ouminus__class_Ouminus(X20364),X20362) = X20363
        | ~ class_Groups_Ogroup__add(X20364) )
      & ( hAPP(c_Groups_Ouminus__class_Ouminus(X20364),X20362) != X20363
        | hAPP(c_Groups_Ouminus__class_Ouminus(X20364),X20363) = X20362
        | ~ class_Groups_Ogroup__add(X20364) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__equation__iff])])]) ).

fof(i_0_10930,plain,
    ! [X20365,X20366,X20367] :
      ( ( X20366 != hAPP(c_Groups_Ouminus__class_Ouminus(X20367),X20365)
        | X20365 = hAPP(c_Groups_Ouminus__class_Ouminus(X20367),X20366)
        | ~ class_Groups_Ogroup__add(X20367) )
      & ( X20365 != hAPP(c_Groups_Ouminus__class_Ouminus(X20367),X20366)
        | X20366 = hAPP(c_Groups_Ouminus__class_Ouminus(X20367),X20365)
        | ~ class_Groups_Ogroup__add(X20367) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equation__minus__iff])])]) ).

fof(i_0_10931,plain,
    ! [X30893] :
      ( ~ class_Enum_Oenum(X30893)
      | hBOOL(hAPP(c_List_Odistinct(X30893),c_Enum_Oenum__class_Oenum(X30893))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__distinct])]) ).

fof(i_0_10932,plain,
    ! [X30710] :
      ( ( ~ c_List_Onat__list(X30710)
        | c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X30710)) )
      & ( ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X30710))
        | c_List_Onat__list(X30710) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__list__def])]) ).

fof(i_0_10933,plain,
    ! [X26802] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X26802)) = hAPP(c_Nat_OSuc,X26802),
    inference(variable_rename,[status(thm)],[fact_card__atMost]) ).

fof(i_0_10934,plain,
    ! [X31292] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X31292)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31292),
    inference(variable_rename,[status(thm)],[fact_nat__of__number]) ).

fof(i_0_10935,plain,
    ! [X24541] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24541)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24541),
    inference(variable_rename,[status(thm)],[fact_nat__number__of]) ).

fof(i_0_10936,plain,
    ! [X24540] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24540) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24540)),
    inference(variable_rename,[status(thm)],[fact_nat__number__of__def]) ).

fof(i_0_10937,plain,
    ! [X21994] : hAPP(c_Nat_OSuc,X21994) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21994),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).

fof(i_0_10938,plain,
    ! [X34035,X34036] : c_List_Oreplicate(X34036,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X34035) = c_List_Olist_ONil(X34036),
    inference(variable_rename,[status(thm)],[fact_replicate__0]) ).

fof(i_0_10939,plain,
    ! [X33888,X33889] : c_List_Osplice(X33889,c_List_Olist_ONil(X33889),X33888) = X33888,
    inference(variable_rename,[status(thm)],[fact_splice_Osimps_I1_J]) ).

fof(i_0_10940,plain,
    ! [X34175,X34176] : c_Lazy__Sequence_Oappend(X34176,c_Lazy__Sequence_Olazy__sequence_OEmpty(X34176),X34175) = X34175,
    inference(variable_rename,[status(thm)],[fact__04]) ).

fof(i_0_10941,plain,
    ! [X33890,X33891] : c_List_Osplice(X33891,X33890,c_List_Olist_ONil(X33891)) = X33890,
    inference(variable_rename,[status(thm)],[fact_splice__Nil2]) ).

fof(i_0_10942,plain,
    ! [X26977,X26978] :
      ( ~ class_Rings_Olinordered__idom(X26978)
      | c_Groups_Osgn__class_Osgn(X26978,c_Groups_Osgn__class_Osgn(X26978,X26977)) = c_Groups_Osgn__class_Osgn(X26978,X26977) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__sgn])]) ).

fof(i_0_10943,plain,
    ! [X33585,X33586] : c_List_Olist__all(X33586,X33585,c_List_Olist_ONil(X33586)),
    inference(variable_rename,[status(thm)],[fact_list__all__simps_I2_J]) ).

fof(i_0_10944,plain,
    ! [X30898] :
      ( ~ class_Enum_Oenum(X30898)
      | hAPP(c_List_Oset(X30898),c_Enum_Oenum__class_Oenum(X30898)) = c_Orderings_Otop__class_Otop(tc_fun(X30898,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__UNIV])]) ).

fof(i_0_10945,plain,
    ! [X30897] :
      ( ~ class_Enum_Oenum(X30897)
      | c_Orderings_Otop__class_Otop(tc_fun(X30897,tc_HOL_Obool)) = hAPP(c_List_Oset(X30897),c_Enum_Oenum__class_Oenum(X30897)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UNIV__enum])]) ).

fof(i_0_10946,plain,
    ! [X25747,X25748] :
      ( ~ class_Orderings_Olinorder(X25748)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25748),X25747),X25747) = X25747 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oidem])]) ).

fof(i_0_10947,plain,
    ! [X25717,X25718] :
      ( ~ class_Orderings_Olinorder(X25718)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25718),X25717),X25717) = X25717 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oidem])]) ).

fof(i_0_10948,plain,
    ! [X25354,X25355] :
      ( ~ class_Orderings_Olinorder(X25355)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25355),X25354),X25354) = X25354 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oidem])]) ).

fof(i_0_10949,plain,
    ! [X25324,X25325] :
      ( ~ class_Orderings_Olinorder(X25325)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25325),X25324),X25324) = X25324 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oidem])]) ).

fof(i_0_10950,plain,
    ! [X20382,X20383] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X20383)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20383),X20382),X20382) = X20382 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times_Oidem])]) ).

fof(i_0_10951,plain,
    ! [X20380,X20381] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X20381)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20381),X20380),X20380) = X20380 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__idem])]) ).

fof(i_0_10952,plain,
    ! [X17876,X17877] :
      ( ~ class_Lattices_Osemilattice__inf(X17877)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17877),X17876),X17876) = X17876 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oidem])]) ).

fof(i_0_10953,plain,
    ! [X17874,X17875] :
      ( ~ class_Lattices_Osemilattice__inf(X17875)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17875),X17874),X17874) = X17874 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__idem])]) ).

fof(i_0_10954,plain,
    ! [X18857,X18858] :
      ( ~ class_Lattices_Olattice(X18858)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X18858),X18857),X18857) = X18857 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oidem])]) ).

fof(i_0_10955,plain,
    ! [X18859,X18860] :
      ( ~ class_Lattices_Olattice(X18860)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X18860),X18859),X18859) = X18859 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oidem])]) ).

fof(i_0_10956,plain,
    ! [X17706,X17707] :
      ( ~ class_Lattices_Osemilattice__sup(X17707)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17707),X17706),X17706) = X17706 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oidem])]) ).

fof(i_0_10957,plain,
    ! [X17704,X17705] :
      ( ~ class_Lattices_Osemilattice__sup(X17705)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17705),X17704),X17704) = X17704 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__idem])]) ).

fof(i_0_10958,plain,
    ! [X31383,X31384] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31384)),X31383) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X31383 = c_List_Olist_ONil(X31384) )
      & ( X31383 != c_List_Olist_ONil(X31384)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31384)),X31383) = 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_10959,plain,
    ! [X25006] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X25006) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25006),
    inference(variable_rename,[status(thm)],[fact_mult__Min]) ).

fof(i_0_10960,plain,
    ! [X26398] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26398) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26398),
    inference(variable_rename,[status(thm)],[fact_atLeast0LessThan]) ).

fof(i_0_10961,plain,
    ! [X33796,X33797,X33798] : hAPP(c_New__DSequence_Opos__single(X33798,X33797),X33796) = hAPP(c_Lazy__Sequence_Osingle(X33798),X33797),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__single__def]) ).

fof(i_0_10962,plain,
    ! [X31784,X31785] : hAPP(hAPP(c_List_Odrop(X31785),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31784) = X31784,
    inference(variable_rename,[status(thm)],[fact_drop__0]) ).

fof(i_0_10963,plain,
    ! [X31555,X31556] : hAPP(hAPP(c_List_Oappend(X31556),X31555),c_List_Olist_ONil(X31556)) = X31555,
    inference(variable_rename,[status(thm)],[fact_append__Nil2]) ).

fof(i_0_10964,plain,
    ! [X32894,X32895] : hAPP(c_List_Orev(X32895),hAPP(c_List_Orev(X32895),X32894)) = X32894,
    inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).

fof(i_0_10965,plain,
    ! [X30369,X30370] : hAPP(c_Option_Othe(X30370),hAPP(c_Option_Ooption_OSome(X30370),X30369)) = X30369,
    inference(variable_rename,[status(thm)],[fact_the_Osimps]) ).

fof(i_0_10966,plain,
    ! [X33850] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X33850) = c_Lazy__Sequence_Osmall__lazy_H(X33850,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X33850)),
    inference(variable_rename,[status(thm)],[fact_small__lazy__int__def]) ).

fof(i_0_10967,plain,
    ! [X23372] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23372) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zmod__zero]) ).

fof(i_0_10968,plain,
    ! [X24542] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X24542))
      | hAPP(c_Int_Onat,X24542) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__nat])]) ).

fof(i_0_10969,plain,
    ! [X26925] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26925)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X26925),
    inference(variable_rename,[status(thm)],[fact_atLeast__Suc__greaterThan]) ).

fof(i_0_10970,plain,
    ! [X26801] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26801)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X26801),
    inference(variable_rename,[status(thm)],[fact_lessThan__Suc__atMost]) ).

fof(i_0_10971,plain,
    ! [X21868] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21868) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21868)),
    inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).

fof(i_0_10972,plain,
    ! [X23440] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23440),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      & c_Divides_Odiv__class_Omod(tc_Int_Oint,X23440,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X23440 ),
    inference(variable_rename,[status(thm)],[fact_DIVISION__BY__ZERO]) ).

fof(i_0_10973,plain,
    ! [X24842] :
      ( ~ class_Int_Onumber__ring(X24842)
      | c_Int_Oiszero(X24842,hAPP(c_Int_Onumber__class_Onumber__of(X24842),c_Int_OPls)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__Numeral0])]) ).

fof(i_0_10974,plain,
    ! [X30175] : hAPP(c_Option_Omap(X30175,X30175),c_Fun_Oid(X30175)) = c_Fun_Oid(tc_Option_Ooption(X30175)),
    inference(variable_rename,[status(thm)],[fact_Option_Omap_Oid]) ).

fof(i_0_10975,plain,
    ! [X30176] : hAPP(c_Option_Omap(X30176,X30176),c_COMBI(X30176)) = c_Fun_Oid(tc_Option_Ooption(X30176)),
    inference(variable_rename,[status(thm)],[fact_Option_Omap_Oidentity]) ).

fof(i_0_10976,plain,
    ! [X30110] : hAPP(c_List_Omap(X30110,X30110),c_Fun_Oid(X30110)) = c_Fun_Oid(tc_List_Olist(X30110)),
    inference(variable_rename,[status(thm)],[fact_List_Omap_Oid]) ).

fof(i_0_10977,plain,
    ! [X30111] : hAPP(c_List_Omap(X30111,X30111),c_COMBI(X30111)) = c_Fun_Oid(tc_List_Olist(X30111)),
    inference(variable_rename,[status(thm)],[fact_List_Omap_Oidentity]) ).

fof(i_0_10978,plain,
    ! [X25303,X25304] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25304) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25303)
        | X25304 = X25303 )
      & ( X25304 != X25303
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25304) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25303) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__int__eq])]) ).

fof(i_0_10979,plain,
    ! [X25301,X25302] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25302) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25301)
        | X25302 = X25301 )
      & ( X25302 != X25301
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25302) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25301) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I1_J])]) ).

fof(i_0_10980,plain,
    ! [X23373] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X23373,X23373) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zmod__self]) ).

fof(i_0_10981,plain,
    ! [X32896,X32897,X32898] :
      ( ( hAPP(c_List_Orev(X32898),X32897) != X32896
        | X32897 = hAPP(c_List_Orev(X32898),X32896) )
      & ( X32897 != hAPP(c_List_Orev(X32898),X32896)
        | hAPP(c_List_Orev(X32898),X32897) = X32896 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__swap])]) ).

fof(i_0_10982,plain,
    ! [X25305] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25305) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_min__0L]) ).

fof(i_0_10983,plain,
    ! [X22991] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22991) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zdiv__zero]) ).

fof(i_0_10984,plain,
    ! [X22098] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22098) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_mult__0]) ).

fof(i_0_10985,plain,
    ! [X22084] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22084) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_diff__0__eq__0]) ).

fof(i_0_10986,plain,
    ! [X31381] : hBOOL(hAPP(c_List_Odistinct(X31381),c_List_Olist_ONil(X31381))),
    inference(variable_rename,[status(thm)],[fact_distinct_Osimps_I1_J]) ).

fof(i_0_10987,plain,
    ! [X33837,X33838,X33839] : hAPP(c_New__DSequence_Oneg__single(X33839,X33838),X33837) = c_Lazy__Sequence_Ohb__single(X33839,X33838),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Oneg__single__def]) ).

fof(i_0_10988,plain,
    ! [X32509,X32510] : c_List_Oremdups(X32510,c_List_Oremdups(X32510,X32509)) = c_List_Oremdups(X32510,X32509),
    inference(variable_rename,[status(thm)],[fact_remdups__remdups]) ).

fof(i_0_10989,plain,
    ! [X28594,X28595] : c_Transitive__Closure_Ortrancl(X28595,c_Transitive__Closure_Ortrancl(X28595,X28594)) = c_Transitive__Closure_Ortrancl(X28595,X28594),
    inference(variable_rename,[status(thm)],[fact_rtrancl__idemp]) ).

fof(i_0_10990,plain,
    ! [X31361] : hAPP(c_List_Oset(X31361),c_List_Olist_ONil(X31361)) = c_Orderings_Obot__class_Obot(tc_fun(X31361,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_List_Oset_Osimps_I1_J]) ).

fof(i_0_10991,plain,
    ! [X25762] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25762) = X25762,
    inference(variable_rename,[status(thm)],[fact_max__0L]) ).

fof(i_0_10992,plain,
    ! [X22843] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22843) = X22843,
    inference(variable_rename,[status(thm)],[fact_zadd__0]) ).

fof(i_0_10993,plain,
    ! [X22076] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22076) = X22076,
    inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).

fof(i_0_10994,plain,
    ! [X22802] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X22802) = X22802,
    inference(variable_rename,[status(thm)],[fact_zmult__1]) ).

fof(i_0_10995,plain,
    ! [X21361] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X21361) = X21361,
    inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).

fof(i_0_10996,plain,
    ! [X33923] : c_Predicate_Oconversep(X33923,X33923,c_fequal) = c_fequal,
    inference(variable_rename,[status(thm)],[fact_conversep__eq]) ).

fof(i_0_10997,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_10998,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_10999,plain,
    ! [X23064] :
      ( X23064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23064),X23064) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__self])]) ).

fof(i_0_11000,plain,
    ! [X20105,X20106,X20108,X20109,X20110] :
      ( ( X20106 = c_Option_Ooption_ONone(X20105)
        | X20106 = hAPP(c_Option_Ooption_OSome(X20105),esk68_2(X20105,X20106)) )
      & ( X20109 != hAPP(c_Option_Ooption_OSome(X20108),X20110)
        | X20109 != c_Option_Ooption_ONone(X20108) ) ),
    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_not__None__eq])])])])]) ).

fof(i_0_11001,plain,
    ! [X20099,X20100,X20102,X20103,X20104] :
      ( ( X20100 = hAPP(c_Option_Ooption_OSome(X20099),esk67_2(X20099,X20100))
        | X20100 = c_Option_Ooption_ONone(X20099) )
      & ( X20103 != c_Option_Ooption_ONone(X20102)
        | X20103 != hAPP(c_Option_Ooption_OSome(X20102),X20104) ) ),
    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_not__Some__eq])])])])]) ).

fof(i_0_11002,plain,
    ! [X25046] :
      ( ~ class_Int_Onumber__ring(X25046)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X25046),c_Groups_Oone__class_Oone(X25046)) = hAPP(c_Int_Onumber__class_Onumber__of(X25046),c_Int_OMin) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I31_J])]) ).

fof(i_0_11003,plain,
    ! [X25045] :
      ( ~ class_Int_Onumber__ring(X25045)
      | hAPP(c_Int_Onumber__class_Onumber__of(X25045),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(X25045),c_Groups_Oone__class_Oone(X25045)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Min])]) ).

fof(i_0_11004,plain,
    ! [X25306] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X25306),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_11005,plain,
    ! [X22097] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22097),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_11006,plain,
    ! [X22056,X22057] :
      ( ( c_Groups_Ozero__class_Ozero(X22057) != hAPP(c_Groups_Ouminus__class_Ouminus(X22057),X22056)
        | c_Groups_Ozero__class_Ozero(X22057) = X22056
        | ~ class_Groups_Ogroup__add(X22057) )
      & ( c_Groups_Ozero__class_Ozero(X22057) != X22056
        | c_Groups_Ozero__class_Ozero(X22057) = hAPP(c_Groups_Ouminus__class_Ouminus(X22057),X22056)
        | ~ class_Groups_Ogroup__add(X22057) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal])])]) ).

fof(i_0_11007,plain,
    ! [X27054,X27055] :
      ( ( hAPP(c_Groups_Oabs__class_Oabs(X27055),X27054) != c_Groups_Ozero__class_Ozero(X27055)
        | X27054 = c_Groups_Ozero__class_Ozero(X27055)
        | ~ class_Groups_Oordered__ab__group__add__abs(X27055) )
      & ( X27054 != c_Groups_Ozero__class_Ozero(X27055)
        | hAPP(c_Groups_Oabs__class_Oabs(X27055),X27054) = c_Groups_Ozero__class_Ozero(X27055)
        | ~ class_Groups_Oordered__ab__group__add__abs(X27055) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__0])])]) ).

fof(i_0_11008,plain,
    ! [X22060,X22061] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X22061),X22060) != c_Groups_Ozero__class_Ozero(X22061)
        | X22060 = c_Groups_Ozero__class_Ozero(X22061)
        | ~ class_Groups_Ogroup__add(X22061) )
      & ( X22060 != c_Groups_Ozero__class_Ozero(X22061)
        | hAPP(c_Groups_Ouminus__class_Ouminus(X22061),X22060) = c_Groups_Ozero__class_Ozero(X22061)
        | ~ class_Groups_Ogroup__add(X22061) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal])])]) ).

fof(i_0_11009,plain,
    ! [X34340] :
      ( ~ hBOOL(hAPP(c_fNot,X34340))
      | ~ hBOOL(X34340) ),
    inference(variable_rename,[status(thm)],[i_0_6097]) ).

fof(i_0_11010,plain,
    ! [X25761] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X25761),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X25761,
    inference(variable_rename,[status(thm)],[fact_max__0R]) ).

fof(i_0_11011,plain,
    ! [X22842] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22842),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X22842,
    inference(variable_rename,[status(thm)],[fact_zadd__0__right]) ).

fof(i_0_11012,plain,
    ! [X22077] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22077),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X22077,
    inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).

fof(i_0_11013,plain,
    ! [X22801] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22801),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X22801,
    inference(variable_rename,[status(thm)],[fact_zmult__1__right]) ).

fof(i_0_11014,plain,
    ! [X21364] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21364),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X21364,
    inference(variable_rename,[status(thm)],[fact_nat__mult__1__right]) ).

fof(i_0_11015,plain,
    ! [X22085] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22085),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X22085,
    inference(variable_rename,[status(thm)],[fact_minus__nat_Odiff__0]) ).

fof(i_0_11016,plain,
    ! [X26397] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26397)) = X26397,
    inference(variable_rename,[status(thm)],[fact_card__lessThan]) ).

fof(i_0_11017,plain,
    ! [X22850] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22850)) = X22850,
    inference(variable_rename,[status(thm)],[fact_zminus__zminus]) ).

fof(i_0_11018,plain,
    ! [X32268,X32269] : hAPP(c_List_Ofilter(X32269,X32268),c_List_Olist_ONil(X32269)) = c_List_Olist_ONil(X32269),
    inference(variable_rename,[status(thm)],[fact_filter_Osimps_I1_J]) ).

fof(i_0_11019,plain,
    ! [X20353,X20354] :
      ( ~ class_Finite__Set_Ofinite(X20354)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20354),X20353)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite])]) ).

fof(i_0_11020,plain,
    ! [X20351,X20352] :
      ( ~ class_Finite__Set_Ofinite(X20352)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X20352),X20351)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__code])]) ).

fof(i_0_11021,plain,
    ! [X25012,X25013] :
      ( ( hAPP(c_Int_Oring__1__class_Oof__int(X25013),X25012) != c_Groups_Ozero__class_Ozero(X25013)
        | X25012 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ class_Int_Oring__char__0(X25013) )
      & ( X25012 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(c_Int_Oring__1__class_Oof__int(X25013),X25012) = c_Groups_Ozero__class_Ozero(X25013)
        | ~ class_Int_Oring__char__0(X25013) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__eq__0__iff])])]) ).

fof(i_0_11022,plain,
    ! [X25010,X25011] :
      ( ( c_Groups_Ozero__class_Ozero(X25011) != hAPP(c_Int_Oring__1__class_Oof__int(X25011),X25010)
        | X25010 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ class_Int_Oring__char__0(X25011) )
      & ( X25010 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Groups_Ozero__class_Ozero(X25011) = hAPP(c_Int_Oring__1__class_Oof__int(X25011),X25010)
        | ~ class_Int_Oring__char__0(X25011) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0__eq__iff])])]) ).

cnf(i_0_11023,plain,
    ( c_Int_OBit0(X1) = c_Int_OPls
    | X1 != c_Int_OPls ),
    inference(split_conjunct,[status(thm)],[i_0_6092]) ).

cnf(i_0_11024,plain,
    ( c_Int_OPls = c_Int_OBit0(X1)
    | c_Int_OPls != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_6091]) ).

fof(i_0_11025,plain,
    ! [X22086] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22086),X22086) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_diff__self__eq__0]) ).

fof(i_0_11026,plain,
    ! [X34164,X34165] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X34165,X34164),c_Lazy__Sequence_Olazy__sequence_OEmpty(X34165)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osize_I1_J]) ).

fof(i_0_11027,plain,
    ! [X24992,X24993] :
      ( ~ class_Int_Onumber__ring(X24993)
      | hAPP(c_Int_Onumber__class_Onumber__of(X24993),X24992) = hAPP(c_Int_Oring__1__class_Oof__int(X24993),X24992) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__eq])]) ).

fof(i_0_11028,plain,
    ! [X20230] : c_Option_Oset(X20230,c_Option_Ooption_ONone(X20230)) = c_Orderings_Obot__class_Obot(tc_fun(X20230,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Option_Oset_Osimps_I1_J]) ).

fof(i_0_11029,plain,
    ! [X22062,X22063] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X22063),X22062) != X22062
        | X22062 = c_Groups_Ozero__class_Ozero(X22063)
        | ~ class_Groups_Olinordered__ab__group__add(X22063) )
      & ( X22062 != c_Groups_Ozero__class_Ozero(X22063)
        | hAPP(c_Groups_Ouminus__class_Ouminus(X22063),X22062) = X22062
        | ~ class_Groups_Olinordered__ab__group__add(X22063) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__zero])])]) ).

fof(i_0_11030,plain,
    ! [X22058,X22059] :
      ( ( X22058 != hAPP(c_Groups_Ouminus__class_Ouminus(X22059),X22058)
        | X22058 = c_Groups_Ozero__class_Ozero(X22059)
        | ~ class_Groups_Olinordered__ab__group__add(X22059) )
      & ( X22058 != c_Groups_Ozero__class_Ozero(X22059)
        | X22058 = hAPP(c_Groups_Ouminus__class_Ouminus(X22059),X22058)
        | ~ class_Groups_Olinordered__ab__group__add(X22059) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__neg__zero])])]) ).

fof(i_0_11031,plain,
    ! [X24615] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24615),c_Int_OPls) = X24615,
    inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).

fof(i_0_11032,plain,
    ! [X24613] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24613),c_Int_OPls) = X24613,
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I1_J]) ).

fof(i_0_11033,plain,
    ! [X25106] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25106)) = X25106,
    inference(variable_rename,[status(thm)],[fact_nat__int]) ).

fof(i_0_11034,plain,
    ! [X34296,X34297] :
      ( ~ class_Lazy__Sequence_Osmall__lazy(X34297)
      | ~ class_Lazy__Sequence_Osmall__lazy(X34296)
      | class_Lazy__Sequence_Osmall__lazy(tc_prod(X34297,X34296)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Lazy__Sequence_Osmall__lazy])]) ).

fof(i_0_11035,plain,
    ! [X34273,X34274] :
      ( ~ class_Enum_Oenum(X34274)
      | ~ class_HOL_Oequal(X34273)
      | class_HOL_Oequal(tc_fun(X34274,X34273)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__HOL_Oequal])]) ).

fof(i_0_11036,plain,
    ! [X34300,X34301] :
      ( ~ class_Smallcheck_Osmall(X34301)
      | ~ class_Smallcheck_Osmall(X34300)
      | class_Smallcheck_Osmall(tc_prod(X34301,X34300)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Smallcheck_Osmall])]) ).

fof(i_0_11037,plain,
    ! [X25548,X25549] :
      ( ~ c_Nat__Transfer_Ois__nat(X25549)
      | ~ c_Nat__Transfer_Ois__nat(X25548)
      | c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X25549,X25548)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J])]) ).

fof(i_0_11038,plain,
    ! [X34280,X34281] :
      ( ~ class_Finite__Set_Ofinite(X34281)
      | ~ class_Finite__Set_Ofinite(X34280)
      | class_Finite__Set_Ofinite(tc_sum(X34281,X34280)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum__Finite__Set_Ofinite])]) ).

fof(i_0_11039,plain,
    ! [X34298,X34299] :
      ( ~ class_Finite__Set_Ofinite(X34299)
      | ~ class_Finite__Set_Ofinite(X34298)
      | class_Finite__Set_Ofinite(tc_prod(X34299,X34298)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Finite__Set_Ofinite])]) ).

fof(i_0_11040,plain,
    ! [X34257,X34258] :
      ( ~ class_Finite__Set_Ofinite(X34258)
      | ~ class_Finite__Set_Ofinite(X34257)
      | class_Finite__Set_Ofinite(tc_fun(X34258,X34257)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Finite__Set_Ofinite])]) ).

fof(i_0_11041,plain,
    ! [X34284,X34285] :
      ( ~ class_Enum_Oenum(X34285)
      | ~ class_Enum_Oenum(X34284)
      | class_Enum_Oenum(tc_sum(X34285,X34284)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum__Enum_Oenum])]) ).

fof(i_0_11042,plain,
    ! [X34304,X34305] :
      ( ~ class_Enum_Oenum(X34305)
      | ~ class_Enum_Oenum(X34304)
      | class_Enum_Oenum(tc_prod(X34305,X34304)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Enum_Oenum])]) ).

fof(i_0_11043,plain,
    ! [X34275,X34276] :
      ( ~ class_Enum_Oenum(X34276)
      | ~ class_Enum_Oenum(X34275)
      | class_Enum_Oenum(tc_fun(X34276,X34275)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Enum_Oenum])]) ).

fof(i_0_11044,plain,
    ! [X24616] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X24616) = X24616,
    inference(variable_rename,[status(thm)],[fact_add__Pls]) ).

fof(i_0_11045,plain,
    ! [X32890,X32891] :
      ( ( hAPP(c_List_Orev(X32891),X32890) != c_List_Olist_ONil(X32891)
        | X32890 = c_List_Olist_ONil(X32891) )
      & ( X32890 != c_List_Olist_ONil(X32891)
        | hAPP(c_List_Orev(X32891),X32890) = c_List_Olist_ONil(X32891) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__is__Nil__conv])]) ).

fof(i_0_11046,plain,
    ! [X31763,X31764] :
      ( ( hAPP(c_List_Orotate1(X31764),X31763) != c_List_Olist_ONil(X31764)
        | X31763 = c_List_Olist_ONil(X31764) )
      & ( X31763 != c_List_Olist_ONil(X31764)
        | hAPP(c_List_Orotate1(X31764),X31763) = c_List_Olist_ONil(X31764) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__is__Nil__conv])]) ).

fof(i_0_11047,plain,
    ! [X32888,X32889] :
      ( ( c_List_Olist_ONil(X32889) != hAPP(c_List_Orev(X32889),X32888)
        | X32888 = c_List_Olist_ONil(X32889) )
      & ( X32888 != c_List_Olist_ONil(X32889)
        | c_List_Olist_ONil(X32889) = hAPP(c_List_Orev(X32889),X32888) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__rev__conv])]) ).

fof(i_0_11048,plain,
    ! [X24614] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X24614) = c_Int_OPls,
    inference(variable_rename,[status(thm)],[fact_mult__Pls]) ).

fof(i_0_11049,plain,
    ! [X27397] : c_Wellfounded_Owf(tc_fun(X27397,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X27397)),
    inference(variable_rename,[status(thm)],[fact_wf__finite__psubset]) ).

fof(i_0_11050,plain,
    ! [X32229] : c_List_Otranspose(X32229,c_List_Olist_ONil(tc_List_Olist(X32229))) = c_List_Olist_ONil(tc_List_Olist(X32229)),
    inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I1_J]) ).

cnf(i_0_11051,plain,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    inference(split_conjunct,[status(thm)],[fact_pred__Pls]) ).

cnf(i_0_11052,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(split_conjunct,[status(thm)],[fact_Bit0__Pls]) ).

cnf(i_0_11053,plain,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    inference(split_conjunct,[status(thm)],[fact_succ__Min]) ).

fof(i_0_11054,plain,
    ! [X31287,X31288] :
      ( ( hAPP(c_Code__Numeral_Onat__of,X31288) != hAPP(c_Code__Numeral_Onat__of,X31287)
        | X31288 = X31287 )
      & ( X31288 != X31287
        | hAPP(c_Code__Numeral_Onat__of,X31288) = hAPP(c_Code__Numeral_Onat__of,X31287) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral_Onat__of__inject])]) ).

fof(i_0_11055,plain,
    ! [X31285,X31286] :
      ( ( hAPP(c_Code__Numeral_Onat__of,X31286) != hAPP(c_Code__Numeral_Onat__of,X31285)
        | X31286 = X31285 )
      & ( X31286 != X31285
        | hAPP(c_Code__Numeral_Onat__of,X31286) = hAPP(c_Code__Numeral_Onat__of,X31285) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Onat__of__inject])]) ).

fof(i_0_11056,plain,
    ! [X31094,X31095] :
      ( ( hAPP(c_Code__Numeral_Oof__nat,X31095) != hAPP(c_Code__Numeral_Oof__nat,X31094)
        | X31095 = X31094 )
      & ( X31095 != X31094
        | hAPP(c_Code__Numeral_Oof__nat,X31095) = hAPP(c_Code__Numeral_Oof__nat,X31094) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Oof__nat__inject])]) ).

fof(i_0_11057,plain,
    ! [X25613,X25614] :
      ( ( hAPP(c_Int_ORep__Integ,X25614) != hAPP(c_Int_ORep__Integ,X25613)
        | X25614 = X25613 )
      & ( X25614 != X25613
        | hAPP(c_Int_ORep__Integ,X25614) = hAPP(c_Int_ORep__Integ,X25613) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__inject])]) ).

fof(i_0_11058,plain,
    ! [X21455,X21456] :
      ( hAPP(c_Nat_OSuc,X21456) != hAPP(c_Nat_OSuc,X21455)
      | X21456 = X21455 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).

fof(i_0_11059,plain,
    ! [X21444,X21445] :
      ( ( hAPP(c_Nat_OSuc,X21445) != hAPP(c_Nat_OSuc,X21444)
        | X21445 = X21444 )
      & ( X21445 != X21444
        | hAPP(c_Nat_OSuc,X21445) = hAPP(c_Nat_OSuc,X21444) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).

fof(i_0_11060,plain,
    ! [X26975,X26976] :
      ( ( c_Groups_Osgn__class_Osgn(X26976,X26975) != c_Groups_Ozero__class_Ozero(X26976)
        | X26975 = c_Groups_Ozero__class_Ozero(X26976)
        | ~ class_Rings_Olinordered__idom(X26976) )
      & ( X26975 != c_Groups_Ozero__class_Ozero(X26976)
        | c_Groups_Osgn__class_Osgn(X26976,X26975) = c_Groups_Ozero__class_Ozero(X26976)
        | ~ class_Rings_Olinordered__idom(X26976) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__0__0])])]) ).

fof(i_0_11061,plain,
    ! [X34183] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X34183)),c_Lazy__Sequence_Olazy__sequence_OEmpty(X34183)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osize_I3_J]) ).

fof(i_0_11062,plain,
    ! [X31382] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31382)),c_List_Olist_ONil(X31382)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_list_Osize_I3_J]) ).

fof(i_0_11063,plain,
    ! [X22825] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X22825)),c_Option_Ooption_ONone(X22825)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_option_Osize_I3_J]) ).

fof(i_0_11064,plain,
    ! [X33385,X33386] : c_Wellfounded_Owf(X33386,c_List_Omeasures(X33386,X33385)),
    inference(variable_rename,[status(thm)],[fact_wf__measures]) ).

fof(i_0_11065,plain,
    ! [X24790] :
      ( ~ class_Rings_Osemiring__1(X24790)
      | ~ c_Int_Oiszero(X24790,c_Groups_Oone__class_Oone(X24790)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6098])]) ).

fof(i_0_11066,plain,
    ! [X32768,X32769] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X32769,X32768)),
    inference(variable_rename,[status(thm)],[fact_sorted__upto]) ).

fof(i_0_11067,plain,
    ! [X20097,X20098] : hAPP(c_Option_Ooption_OSome(X20098),X20097) != c_Option_Ooption_ONone(X20098),
    inference(variable_rename,[status(thm)],[fact_option_Osimps_I3_J]) ).

fof(i_0_11068,plain,
    ! [X20095,X20096] : c_Option_Ooption_ONone(X20096) != hAPP(c_Option_Ooption_OSome(X20096),X20095),
    inference(variable_rename,[status(thm)],[fact_option_Osimps_I2_J]) ).

fof(i_0_11069,plain,
    ! [X28294,X28295] : c_Hilbert__Choice_OEps(X28295,hAPP(c_fequal,X28294)) = X28294,
    inference(variable_rename,[status(thm)],[fact_some__sym__eq__trivial]) ).

fof(i_0_11070,plain,
    ! [X17226,X17227] : c_HOL_OThe(X17227,hAPP(c_fequal,X17226)) = X17226,
    inference(variable_rename,[status(thm)],[fact_the__sym__eq__trivial]) ).

fof(i_0_11071,plain,
    ! [X31364] :
      ( ~ class_Groups_Omonoid__add(X31364)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X31364),c_List_Olist_ONil(X31364)) = c_Groups_Ozero__class_Ozero(X31364) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__simps_I1_J])]) ).

fof(i_0_11072,plain,
    ! [X27056] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X27056)
      | hAPP(c_Groups_Oabs__class_Oabs(X27056),c_Groups_Ozero__class_Ozero(X27056)) = c_Groups_Ozero__class_Ozero(X27056) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zero])]) ).

fof(i_0_11073,plain,
    ! [X27035] :
      ( ~ class_Rings_Olinordered__idom(X27035)
      | hAPP(c_Groups_Oabs__class_Oabs(X27035),c_Groups_Oone__class_Oone(X27035)) = c_Groups_Oone__class_Oone(X27035) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__one])]) ).

fof(i_0_11074,plain,
    ! [X22055] :
      ( ~ class_Groups_Ogroup__add(X22055)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X22055),c_Groups_Ozero__class_Ozero(X22055)) = c_Groups_Ozero__class_Ozero(X22055) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__zero])]) ).

fof(i_0_11075,plain,
    ! [X20504] :
      ( ~ class_Lattices_Oboolean__algebra(X20504)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X20504),c_Orderings_Otop__class_Otop(X20504)) = c_Orderings_Obot__class_Obot(X20504) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__top__eq])]) ).

fof(i_0_11076,plain,
    ! [X20505] :
      ( ~ class_Lattices_Oboolean__algebra(X20505)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X20505),c_Orderings_Obot__class_Obot(X20505)) = c_Orderings_Otop__class_Otop(X20505) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__bot__eq])]) ).

fof(i_0_11077,plain,
    ! [X34239,X34240] :
      ( ~ class_Lattices_Obounded__lattice(X34240)
      | class_Lattices_Obounded__lattice(tc_fun(X34239,X34240)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice])]) ).

fof(i_0_11078,plain,
    ! [X34269,X34270] :
      ( ~ class_Groups_Ouminus(X34270)
      | class_Groups_Ouminus(tc_fun(X34269,X34270)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ouminus])]) ).

fof(i_0_11079,plain,
    ! [X34253,X34254] :
      ( ~ class_Lattices_Oboolean__algebra(X34254)
      | class_Lattices_Oboolean__algebra(tc_fun(X34253,X34254)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Oboolean__algebra])]) ).

fof(i_0_11080,plain,
    ! [X34243,X34244] :
      ( ~ class_Lattices_Obounded__lattice(X34244)
      | class_Lattices_Obounded__lattice__top(tc_fun(X34243,X34244)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__top])]) ).

fof(i_0_11081,plain,
    ! [X34263,X34264] :
      ( ~ class_Orderings_Otop(X34264)
      | class_Orderings_Otop(tc_fun(X34263,X34264)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Otop])]) ).

fof(i_0_11082,plain,
    ! [X34251,X34252] :
      ( ~ class_Lattices_Odistrib__lattice(X34252)
      | class_Lattices_Odistrib__lattice(tc_fun(X34251,X34252)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Odistrib__lattice])]) ).

fof(i_0_11083,plain,
    ! [X34241,X34242] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X34242)
      | class_Complete__Lattice_Ocomplete__lattice(tc_fun(X34241,X34242)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Complete__Lattice_Ocomplete__lattice])]) ).

fof(i_0_11084,plain,
    ! [X34249,X34250] :
      ( ~ class_Lattices_Olattice(X34250)
      | class_Lattices_Osemilattice__inf(tc_fun(X34249,X34250)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__inf])]) ).

fof(i_0_11085,plain,
    ! [X34271,X34272] :
      ( ~ class_Groups_Ominus(X34272)
      | class_Groups_Ominus(tc_fun(X34271,X34272)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ominus])]) ).

fof(i_0_11086,plain,
    ! [X34245,X34246] :
      ( ~ class_Lattices_Obounded__lattice(X34246)
      | class_Lattices_Obounded__lattice__bot(tc_fun(X34245,X34246)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__bot])]) ).

fof(i_0_11087,plain,
    ! [X34259,X34260] :
      ( ~ class_Lattices_Olattice(X34260)
      | class_Lattices_Olattice(tc_fun(X34259,X34260)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Olattice])]) ).

fof(i_0_11088,plain,
    ! [X34247,X34248] :
      ( ~ class_Lattices_Olattice(X34248)
      | class_Lattices_Osemilattice__sup(tc_fun(X34247,X34248)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__sup])]) ).

fof(i_0_11089,plain,
    ! [X34265,X34266] :
      ( ~ class_Orderings_Oord(X34266)
      | class_Orderings_Oord(tc_fun(X34265,X34266)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).

fof(i_0_11090,plain,
    ! [X34261,X34262] :
      ( ~ class_Orderings_Oorder(X34262)
      | class_Orderings_Oorder(tc_fun(X34261,X34262)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).

fof(i_0_11091,plain,
    ! [X34267,X34268] :
      ( ~ class_Orderings_Obot(X34268)
      | class_Orderings_Obot(tc_fun(X34267,X34268)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Obot])]) ).

fof(i_0_11092,plain,
    ! [X34255,X34256] :
      ( ~ class_Orderings_Opreorder(X34256)
      | class_Orderings_Opreorder(tc_fun(X34255,X34256)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).

fof(i_0_11093,plain,
    ! [X28208,X28209] :
      ( ~ c_Wellfounded_Owf(X28209,X28208)
      | c_Wellfounded_Oacyclic(X28209,X28208) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__acyclic])]) ).

fof(i_0_11094,plain,
    ! [X25539] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25539)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J]) ).

fof(i_0_11095,plain,
    ! [X31284] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X31284)) = X31284,
    inference(variable_rename,[status(thm)],[fact_nat__of__of__nat]) ).

fof(i_0_11096,plain,
    ! [X31283] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X31283)) = X31283,
    inference(variable_rename,[status(thm)],[fact_of__nat__nat__of]) ).

fof(i_0_11097,plain,
    ! [X31282] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X31282)) = X31282,
    inference(variable_rename,[status(thm)],[fact_nat__of__inverse]) ).

fof(i_0_11098,plain,
    ! [X25615] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X25615)) = X25615,
    inference(variable_rename,[status(thm)],[fact_Rep__Integ__inverse]) ).

fof(i_0_11099,plain,
    ! [X24787,X24788] :
      ( ( ~ c_Int_Oiszero(X24788,X24787)
        | X24787 = c_Groups_Ozero__class_Ozero(X24788)
        | ~ class_Rings_Osemiring__1(X24788) )
      & ( X24787 != c_Groups_Ozero__class_Ozero(X24788)
        | c_Int_Oiszero(X24788,X24787)
        | ~ class_Rings_Osemiring__1(X24788) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__def])])]) ).

fof(i_0_11100,plain,
    ! [X25115] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25115) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X25115 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X25115 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25115) = 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_11101,plain,
    ! [X25168] :
      ( ~ class_Rings_Osemiring__1(X25168)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25168),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X25168) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0])]) ).

fof(i_0_11102,plain,
    ! [X25196] :
      ( ~ class_Rings_Osemiring__1(X25196)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25196),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X25196) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__1])]) ).

fof(i_0_11103,plain,
    ! [X25009] :
      ( ~ class_Rings_Oring__1(X25009)
      | hAPP(c_Int_Oring__1__class_Oof__int(X25009),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(X25009) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0])]) ).

fof(i_0_11104,plain,
    ! [X25029] :
      ( ~ class_Rings_Oring__1(X25029)
      | hAPP(c_Int_Oring__1__class_Oof__int(X25029),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X25029) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__1])]) ).

fof(i_0_11105,plain,
    ! [X24991] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24991) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X24991),
    inference(variable_rename,[status(thm)],[fact_int__number__of__def]) ).

fof(i_0_11106,plain,
    ! [X32520,X32521] :
      ( ( c_List_Oremdups(X32521,X32520) != c_List_Olist_ONil(X32521)
        | X32520 = c_List_Olist_ONil(X32521) )
      & ( X32520 != c_List_Olist_ONil(X32521)
        | c_List_Oremdups(X32521,X32520) = c_List_Olist_ONil(X32521) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remdups__eq__nil__iff])]) ).

fof(i_0_11107,plain,
    ! [X32518,X32519] :
      ( ( c_List_Olist_ONil(X32519) != c_List_Oremdups(X32519,X32518)
        | X32518 = c_List_Olist_ONil(X32519) )
      & ( X32518 != c_List_Olist_ONil(X32519)
        | c_List_Olist_ONil(X32519) = c_List_Oremdups(X32519,X32518) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remdups__eq__nil__right__iff])]) ).

fof(i_0_11108,plain,
    ! [X34341] :
      ( hBOOL(X34341)
      | hBOOL(hAPP(c_fNot,X34341)) ),
    inference(variable_rename,[status(thm)],[i_0_6099]) ).

fof(i_0_11109,plain,
    ! [X26974] :
      ( ~ class_Groups_Osgn__if(X26974)
      | c_Groups_Osgn__class_Osgn(X26974,c_Groups_Ozero__class_Ozero(X26974)) = c_Groups_Ozero__class_Ozero(X26974) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn0])]) ).

fof(i_0_11110,plain,
    ! [X25872] :
      ( ~ class_Orderings_Oord(X25872)
      | c_Orderings_Oord__class_Omax(X25872) = c_Orderings_Oord_Omax(X25872,c_Orderings_Oord__class_Oless__eq(X25872)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ord__max])]) ).

fof(i_0_11111,plain,
    ! [X25530] :
      ( ~ class_Orderings_Oord(X25530)
      | c_Orderings_Oord__class_Omin(X25530) = c_Orderings_Oord_Omin(X25530,c_Orderings_Oord__class_Oless__eq(X25530)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ord__min])]) ).

fof(i_0_11112,plain,
    ! [X32887] : hAPP(c_List_Orev(X32887),c_List_Olist_ONil(X32887)) = c_List_Olist_ONil(X32887),
    inference(variable_rename,[status(thm)],[fact_rev_Osimps_I1_J]) ).

fof(i_0_11113,plain,
    ! [X31937] : hAPP(c_List_Otl(X31937),c_List_Olist_ONil(X31937)) = c_List_Olist_ONil(X31937),
    inference(variable_rename,[status(thm)],[fact_tl_Osimps_I1_J]) ).

fof(i_0_11114,plain,
    ! [X34294,X34295] : class_Nat_Osize(tc_Nitpick_Opair__box(X34295,X34294)),
    inference(variable_rename,[status(thm)],[arity_Nitpick__Opair____box__Nat_Osize]) ).

fof(i_0_11115,plain,
    ! [X34286,X34287] : class_Nat_Osize(tc_sum(X34287,X34286)),
    inference(variable_rename,[status(thm)],[arity_sum__Nat_Osize]) ).

fof(i_0_11116,plain,
    ! [X34306,X34307] : class_Nat_Osize(tc_prod(X34307,X34306)),
    inference(variable_rename,[status(thm)],[arity_prod__Nat_Osize]) ).

fof(i_0_11117,plain,
    ! [X34292,X34293] : class_HOL_Oequal(tc_Nitpick_Opair__box(X34293,X34292)),
    inference(variable_rename,[status(thm)],[arity_Nitpick__Opair____box__HOL_Oequal]) ).

fof(i_0_11118,plain,
    ! [X34282,X34283] : class_HOL_Oequal(tc_sum(X34283,X34282)),
    inference(variable_rename,[status(thm)],[arity_sum__HOL_Oequal]) ).

fof(i_0_11119,plain,
    ! [X34302,X34303] : class_HOL_Oequal(tc_prod(X34303,X34302)),
    inference(variable_rename,[status(thm)],[arity_prod__HOL_Oequal]) ).

fof(i_0_11120,plain,
    ! [X24621] :
      ( ~ class_Int_Onumber__ring(X24621)
      | hAPP(c_Int_Onumber__class_Onumber__of(X24621),c_Int_OPls) = c_Groups_Ozero__class_Ozero(X24621) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Pls])]) ).

fof(i_0_11121,plain,
    ! [X24620] :
      ( ~ class_Int_Onumber__ring(X24620)
      | c_Groups_Ozero__class_Ozero(X24620) = hAPP(c_Int_Onumber__class_Onumber__of(X24620),c_Int_OPls) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J])]) ).

fof(i_0_11122,plain,
    ! [X32776] :
      ( ~ class_Orderings_Olinorder(X32776)
      | c_List_Olinorder__class_Osorted(X32776,c_List_Olist_ONil(X32776)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted_Oequations_I1_J])]) ).

fof(i_0_11123,plain,
    ! [X32721] :
      ( ~ class_Orderings_Olinorder(X32721)
      | c_List_Olinorder__class_Osorted(X32721,c_List_Olist_ONil(X32721)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted_ONil])]) ).

fof(i_0_11124,plain,
    ! [X24789] :
      ( ~ class_Rings_Osemiring__1(X24789)
      | c_Int_Oiszero(X24789,c_Groups_Ozero__class_Ozero(X24789)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__0])]) ).

fof(i_0_11125,plain,
    ! [X33724,X33725] : hAPP(c_New__DSequence_Opos__empty(X33725),X33724) = c_Lazy__Sequence_Oempty(X33725),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__empty__def]) ).

fof(i_0_11126,plain,
    ! [X32517] : c_List_Oremdups(X32517,c_List_Olist_ONil(X32517)) = c_List_Olist_ONil(X32517),
    inference(variable_rename,[status(thm)],[fact_remdups_Osimps_I1_J]) ).

fof(i_0_11127,plain,
    ! [X32189] : c_List_Obutlast(X32189,c_List_Olist_ONil(X32189)) = c_List_Olist_ONil(X32189),
    inference(variable_rename,[status(thm)],[fact_butlast_Osimps_I1_J]) ).

fof(i_0_11128,plain,
    ! [X22069] : hAPP(c_Nat_OSuc,X22069) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).

fof(i_0_11129,plain,
    ! [X22067] : hAPP(c_Nat_OSuc,X22067) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).

fof(i_0_11130,plain,
    ! [X22066] : hAPP(c_Nat_OSuc,X22066) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).

fof(i_0_11131,plain,
    ! [X22068] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X22068),
    inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).

fof(i_0_11132,plain,
    ! [X22065] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X22065),
    inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).

fof(i_0_11133,plain,
    ! [X22064] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X22064),
    inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).

fof(i_0_11134,plain,
    ! [X25716] :
      ( ~ class_Lattices_Osemilattice__sup(X25716)
      | ~ class_Orderings_Olinorder(X25716)
      | c_Lattices_Osemilattice__sup__class_Osup(X25716) = c_Orderings_Oord__class_Omax(X25716) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__max])]) ).

fof(i_0_11135,plain,
    ! [X25321] :
      ( ~ class_Lattices_Osemilattice__inf(X25321)
      | ~ class_Orderings_Olinorder(X25321)
      | c_Lattices_Osemilattice__inf__class_Oinf(X25321) = c_Orderings_Oord__class_Omin(X25321) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__min])]) ).

fof(i_0_11136,plain,
    ! [X21432] : hAPP(c_Nat_OSuc,X21432) != X21432,
    inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).

fof(i_0_11137,plain,
    ! [X21431] : X21431 != hAPP(c_Nat_OSuc,X21431),
    inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).

fof(i_0_11138,plain,
    ! [X27910,X27911] : hAPP(c_Fun_Oid(X27911),X27910) = X27910,
    inference(variable_rename,[status(thm)],[fact_id__apply]) ).

fof(i_0_11139,plain,
    ! [X27908,X27909] : hAPP(c_Fun_Oid(X27909),X27908) = X27908,
    inference(variable_rename,[status(thm)],[fact_id__def]) ).

fof(i_0_11140,plain,
    ! [X34312,X34313] : hAPP(c_COMBI(X34313),X34312) = X34312,
    inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).

fof(i_0_11141,plain,
    ! [X17185,X17186] : hAPP(c_Set_OCollect(X17186),X17185) = X17185,
    inference(variable_rename,[status(thm)],[fact_Collect__def]) ).

fof(i_0_11142,plain,
    ! [X22054] :
      ( ~ class_Rings_Ozero__neq__one(X22054)
      | c_Groups_Ozero__class_Ozero(X22054) != c_Groups_Oone__class_Oone(X22054) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).

fof(i_0_11143,plain,
    ! [X22053] :
      ( ~ class_Rings_Ozero__neq__one(X22053)
      | c_Groups_Oone__class_Oone(X22053) != c_Groups_Ozero__class_Ozero(X22053) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).

fof(i_0_11144,plain,
    ! [X27444] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X27444)),
    inference(variable_rename,[status(thm)],[fact_wf__int__ge__less__than]) ).

fof(i_0_11145,plain,
    ! [X27445] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X27445)),
    inference(variable_rename,[status(thm)],[fact_wf__int__ge__less__than2]) ).

fof(i_0_11146,plain,
    ! [X24005] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24005) = X24005,
    inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).

fof(i_0_11147,plain,
    ! [X22853] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X22853) = X22853,
    inference(variable_rename,[status(thm)],[fact_nat__size]) ).

fof(i_0_11148,plain,
    ! [X34277] :
      ( ~ class_Lazy__Sequence_Osmall__lazy(X34277)
      | class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X34277)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_List__Olist__Lazy__Sequence_Osmall__lazy])]) ).

fof(i_0_11149,plain,
    ! [X34288] :
      ( ~ class_Finite__Set_Ofinite(X34288)
      | class_Finite__Set_Ofinite(tc_Option_Ooption(X34288)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Finite__Set_Ofinite])]) ).

fof(i_0_11150,plain,
    ! [X34290] :
      ( ~ class_Enum_Oenum(X34290)
      | class_Enum_Oenum(tc_Option_Ooption(X34290)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Enum_Oenum])]) ).

fof(i_0_11151,plain,
    ! [X20231] : c_Equiv__Relations_Oequivp(X20231,c_fequal),
    inference(variable_rename,[status(thm)],[fact_identity__equivp]) ).

fof(i_0_11152,plain,
    ! [X33685] :
      ( ~ class_HOL_Oequal(X33685)
      | c_HOL_Oequal__class_Oequal(X33685) = c_fequal ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal])]) ).

fof(i_0_11153,plain,
    ! [X33679] :
      ( ~ class_HOL_Oequal(X33679)
      | c_fequal = c_HOL_Oequal__class_Oequal(X33679) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equal])]) ).

fof(i_0_11154,plain,
    ! [X34311] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X34311)),
    inference(variable_rename,[status(thm)],[arity_Lazy____Sequence__Olazy____sequence__Nat_Osize]) ).

fof(i_0_11155,plain,
    ! [X34279] : class_Nat_Osize(tc_List_Olist(X34279)),
    inference(variable_rename,[status(thm)],[arity_List__Olist__Nat_Osize]) ).

fof(i_0_11156,plain,
    ! [X34291] : class_Nat_Osize(tc_Option_Ooption(X34291)),
    inference(variable_rename,[status(thm)],[arity_Option__Ooption__Nat_Osize]) ).

fof(i_0_11157,plain,
    ! [X34309] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X34309)),
    inference(variable_rename,[status(thm)],[arity_Hoare____Mirabelle__Otriple__Nat_Osize]) ).

fof(i_0_11158,plain,
    ! [X34310] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(X34310)),
    inference(variable_rename,[status(thm)],[arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal]) ).

fof(i_0_11159,plain,
    ! [X34278] : class_HOL_Oequal(tc_List_Olist(X34278)),
    inference(variable_rename,[status(thm)],[arity_List__Olist__HOL_Oequal]) ).

fof(i_0_11160,plain,
    ! [X34289] : class_HOL_Oequal(tc_Option_Ooption(X34289)),
    inference(variable_rename,[status(thm)],[arity_Option__Ooption__HOL_Oequal]) ).

fof(i_0_11161,plain,
    ! [X34308] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(X34308)),
    inference(variable_rename,[status(thm)],[arity_Hoare____Mirabelle__Otriple__HOL_Oequal]) ).

fof(i_0_11162,plain,
    ~ hBOOL(c_fFalse),
    inference(fof_simplification,[status(thm)],[help_c__fFalse__1]) ).

cnf(i_0_11163,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,esk54_11(X3,X4,X5,X2,X1,X6,X7,X8,X9,X10,X11)),esk55_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_6100]),
    [final] ).

cnf(i_0_11164,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk55_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_6100]),
    [final] ).

cnf(i_0_11165,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk54_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_6100]),
    [final] ).

cnf(i_0_11166,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_6101,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11167,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_6105]),
    [final] ).

cnf(i_0_11168,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_6106]),
    [final] ).

cnf(i_0_11169,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_6107]),
    [final] ).

cnf(i_0_11170,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_6108]),
    [final] ).

cnf(i_0_11171,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_6109]),
    [final] ).

cnf(i_0_11172,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_6110]),
    [final] ).

cnf(i_0_11173,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_6111]),
    [final] ).

cnf(i_0_11174,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk279_8(X3,X4,X5,X2,X1,X6,X7,X8)),esk280_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_6112]),
    [final] ).

cnf(i_0_11175,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_6113,c_0_6114]),
    [final] ).

cnf(i_0_11176,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_6115,c_0_6114]),
    [final] ).

cnf(i_0_11177,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,esk366_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_6116]),
    [final] ).

cnf(i_0_11178,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_6117]),
    [final] ).

cnf(i_0_11179,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_6118]),
    [final] ).

cnf(i_0_11180,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_6119]),
    [final] ).

cnf(i_0_11181,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,esk478_8(X4,X5,X6,X3,X2,X1,X7,X8))),X6) != hAPP(c_Fun_Ocomp(X2,X1,X2,X6),hAPP(X5,esk478_8(X4,X5,X6,X3,X2,X1,X7,X8))) ),
    inference(split_conjunct,[status(thm)],[i_0_6120]),
    [final] ).

cnf(i_0_11182,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_6121,c_0_6122]),c_0_6122]),c_0_6122]),c_0_6122]),c_0_6123]),c_0_6123]),
    [final] ).

cnf(i_0_11183,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_6124]),
    [final] ).

cnf(i_0_11184,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_6125]),
    [final] ).

cnf(i_0_11185,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_6126]),
    [final] ).

cnf(i_0_11186,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_6127,c_0_6128]),
    [final] ).

cnf(i_0_11187,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X3)),X2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X3)))),hAPP(X3,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X3)),X2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X3))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(X3,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X3)),X2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X3))))))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6129]),
    [final] ).

cnf(i_0_11188,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_6117]),
    [final] ).

cnf(i_0_11189,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_6118]),
    [final] ).

cnf(i_0_11190,plain,
    ( X3 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk64_7(X2,X3,X4,X5,X6,X7,X1)),esk65_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_6130]),
    [final] ).

cnf(i_0_11191,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(X4,esk279_8(X5,X6,X4,X7,X8,X1,X3,X2))),hAPP(X6,esk280_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_6112]),
    [final] ).

cnf(i_0_11192,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_6124]),
    [final] ).

cnf(i_0_11193,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_6125]),
    [final] ).

cnf(i_0_11194,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_6126]),
    [final] ).

cnf(i_0_11195,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_6131,c_0_6128]),
    [final] ).

cnf(i_0_11196,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_6132,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11197,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_6133]),
    [final] ).

cnf(i_0_11198,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,esk324_8(X2,X1,X3,X4,X5,X6,X7,X8)) != hAPP(X2,hAPP(X5,esk324_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_6134]),
    [final] ).

cnf(i_0_11199,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_6135,c_0_6136]),c_0_6136]),
    [final] ).

cnf(i_0_11200,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_6137,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11201,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_6138]),
    [final] ).

cnf(i_0_11202,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk478_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_6120]),
    [final] ).

cnf(i_0_11203,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk366_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_6116]),
    [final] ).

cnf(i_0_11204,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk324_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_6134]),
    [final] ).

cnf(i_0_11205,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk186_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_6139]),
    [final] ).

cnf(i_0_11206,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk325_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_6140]),
    [final] ).

cnf(i_0_11207,plain,
    hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),X3) = hAPP(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_6141]),
    [final] ).

cnf(i_0_11208,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_6142]),
    [final] ).

cnf(i_0_11209,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_6143]),
    [final] ).

cnf(i_0_11210,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X2)))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X2)),X4))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X2)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6144]),
    [final] ).

cnf(i_0_11211,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),X1))
    | X1 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X2,tc_HOL_Obool),X3)
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X5),hAPP(X3,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X2,tc_HOL_Obool),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)),tc_fun(X2,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X2,tc_HOL_Obool),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)),tc_fun(X2,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X3)),X5))),X1))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6145]),
    [final] ).

cnf(i_0_11212,plain,
    c_Map_Omap__add(X1,X2,X3,hAPP(c_Map_Omap__of(X1,X2),X4)) = hAPP(c_List_Ofoldl(tc_fun(X1,tc_Option_Ooption(X2)),tc_prod(X1,X2),hAPP(c_COMBC(tc_prod(X1,X2),tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))))),X1),c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))),X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),X1),c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),X1,tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)))))),c_Option_Ooption_OSome(X2)))),X3),hAPP(c_List_Orev(tc_prod(X1,X2)),X4)),
    inference(rw,[status(thm)],[i_0_6146,c_0_6147]),
    [final] ).

cnf(i_0_11213,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_6148]),
    [final] ).

cnf(i_0_11214,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_6149]),
    [final] ).

cnf(i_0_11215,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,esk186_8(X2,X1,X3,X4,X5,X6,X7,X8)) != hAPP(hAPP(c_Fun_Ocomp(X6,X8,X7,X2),X5),esk186_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_6139]),
    [final] ).

cnf(i_0_11216,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,esk325_8(X2,X1,X3,X4,X5,X6,X7,X8)) != hAPP(X2,esk325_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_6140]),
    [final] ).

cnf(i_0_11217,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_6150]),
    [final] ).

cnf(i_0_11218,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_6151]),
    [final] ).

cnf(i_0_11219,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_6138]),
    [final] ).

cnf(i_0_11220,plain,
    c_Map_Omap__upds(X1,X2,X3,X4,X5) = hAPP(c_List_Ofoldl(tc_fun(X1,tc_Option_Ooption(X2)),tc_prod(X1,X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_prod(X1,X2),tc_fun(X1,tc_Option_Ooption(X2))),tc_fun(X1,tc_Option_Ooption(X2))),c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X1,tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X1,tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),tc_fun(X1,tc_Option_Ooption(X2))),c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(X1,tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),tc_fun(X1,tc_Option_Ooption(X2))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2)))),X1),c_COMBB(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)),X2))),c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2))))),c_Option_Ooption_OSome(X2))),X3),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5)),
    inference(split_conjunct,[status(thm)],[i_0_6152]),
    [final] ).

cnf(i_0_11221,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,esk56_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_6153]),
    [final] ).

cnf(i_0_11222,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,esk530_7(X2,X3,X4,X5,X1,X6,X7)),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6154]),
    [final] ).

cnf(i_0_11223,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,esk359_7(X2,X3,X1,X4,X5,X6,X7)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6155]),
    [final] ).

cnf(i_0_11224,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_6156]),
    [final] ).

cnf(i_0_11225,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_6157]),
    [final] ).

cnf(i_0_11226,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_6158]),
    [final] ).

cnf(i_0_11227,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_6159]),
    [final] ).

cnf(i_0_11228,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_6160]),
    [final] ).

cnf(i_0_11229,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_6161]),
    [final] ).

cnf(i_0_11230,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X2,X3,X4),X1),X5) = hAPP(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_6162]),
    [final] ).

cnf(i_0_11231,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)),esk401_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_6163]),
    [final] ).

cnf(i_0_11232,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_6164]),
    [final] ).

cnf(i_0_11233,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_6165]),
    [final] ).

cnf(i_0_11234,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_6166]),
    [final] ).

cnf(i_0_11235,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk325_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_6140]),
    [final] ).

cnf(i_0_11236,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_6150]),
    [final] ).

cnf(i_0_11237,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),esk29_7(X6,X7,X5,X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),esk30_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_6167]),
    [final] ).

cnf(i_0_11238,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),esk29_7(X6,X7,X5,X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),esk30_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_6167]),
    [final] ).

cnf(i_0_11239,plain,
    ( hBOOL(hAPP(hAPP(hAPP(X1,esk529_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_6168]),
    [final] ).

cnf(i_0_11240,plain,
    ( hBOOL(hAPP(hAPP(hAPP(X1,esk69_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_6169]),
    [final] ).

cnf(i_0_11241,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_6170]),
    [final] ).

cnf(i_0_11242,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_6171]),
    [final] ).

cnf(i_0_11243,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_6172,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11244,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_6173,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11245,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_6174,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11246,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_6163]),
    [final] ).

cnf(i_0_11247,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_6164]),
    [final] ).

cnf(i_0_11248,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_6165]),
    [final] ).

cnf(i_0_11249,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_6166]),
    [final] ).

cnf(i_0_11250,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_6175]),
    [final] ).

cnf(i_0_11251,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_6176,c_0_6177]),c_0_6177]),
    [final] ).

cnf(i_0_11252,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_6178,c_0_6177]),c_0_6177]),
    [final] ).

cnf(i_0_11253,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),esk243_6(X5,X4,X6,X3,X2,X1))))) != hAPP(X5,esk243_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_6179]),
    [final] ).

cnf(i_0_11254,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_6180]),
    [final] ).

cnf(i_0_11255,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_6181]),
    [final] ).

cnf(i_0_11256,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_6182,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11257,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),esk238_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_6183]),
    [final] ).

cnf(i_0_11258,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_6184]),
    [final] ).

cnf(i_0_11259,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,esk327_5(X3,X4,X5,X2,X1)))),hAPP(X2,esk327_5(X3,X4,X5,X2,X1)))),c_Transitive__Closure_Ortrancl(X1,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6185]),
    [final] ).

cnf(i_0_11260,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk141_6(X3,X4,X5,X6,X2,X1)),esk142_6(X3,X4,X5,X6,X2,X1))),hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X4)),hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3))))))
    | hBOOL(hAPP(hAPP(X3,X6),X5))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X4)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6186]),
    [final] ).

cnf(i_0_11261,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk391_6(X3,X4,X1,X5,X2,X6)),esk392_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_6187]),
    [final] ).

cnf(i_0_11262,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk390_6(X3,X4,X2,X5,X6,X1)),esk391_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_6187]),
    [final] ).

cnf(i_0_11263,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_6188]),
    [final] ).

cnf(i_0_11264,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_6189]),
    [final] ).

cnf(i_0_11265,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,esk272_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_6190]),
    [final] ).

cnf(i_0_11266,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_6191,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11267,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_6192]),
    [final] ).

cnf(i_0_11268,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_6193]),
    [final] ).

cnf(i_0_11269,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_6194,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11270,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk99_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_6195]),
    [final] ).

cnf(i_0_11271,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk29_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_6167]),
    [final] ).

cnf(i_0_11272,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk29_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_6167]),
    [final] ).

cnf(i_0_11273,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_6196]),
    [final] ).

cnf(i_0_11274,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk529_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_6168]),
    [final] ).

cnf(i_0_11275,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk69_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_6169]),
    [final] ).

cnf(i_0_11276,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk530_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_6154]),
    [final] ).

cnf(i_0_11277,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk359_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_6155]),
    [final] ).

cnf(i_0_11278,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk56_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_6153]),
    [final] ).

cnf(i_0_11279,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk65_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_6130]),
    [final] ).

cnf(i_0_11280,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk64_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_6130]),
    [final] ).

cnf(i_0_11281,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk490_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_6197]),
    [final] ).

cnf(i_0_11282,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk487_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_6198]),
    [final] ).

cnf(i_0_11283,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk351_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),esk350_4(X1,X2,X3,X4)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk350_4(X1,X2,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6199]),
    [final] ).

cnf(i_0_11284,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk351_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),esk350_4(X2,X3,X4,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X3,esk350_4(X2,X3,X4,X1))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6199]),
    [final] ).

cnf(i_0_11285,plain,
    ( hAPP(X1,esk351_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),esk350_4(X2,X1,X3,X4)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,esk350_4(X2,X1,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6199]),
    [final] ).

cnf(i_0_11286,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk272_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_6190]),
    [final] ).

cnf(i_0_11287,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,esk312_6(X3,X2,X1,X4,X5,X6))),hAPP(X3,esk312_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_6200]),
    [final] ).

cnf(i_0_11288,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,esk304_6(X3,X2,X1,X4,X5,X6)),esk305_6(X3,X2,X1,X4,X5,X6)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6201]),
    [final] ).

cnf(i_0_11289,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_6202,c_0_6102]),c_0_6102]),c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11290,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_6203,c_0_6102]),c_0_6102]),c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11291,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_6204]),
    [final] ).

cnf(i_0_11292,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_6205]),
    [final] ).

cnf(i_0_11293,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk243_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_6179]),
    [final] ).

cnf(i_0_11294,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk238_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_6183]),
    [final] ).

cnf(i_0_11295,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_6206,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11296,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_6207,c_0_6147]),c_0_6147]),
    [final] ).

cnf(i_0_11297,plain,
    ( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,esk29_7(X3,X2,X4,X5,X1,X6,X7)),esk30_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_6167]),
    [final] ).

cnf(i_0_11298,plain,
    ( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,esk29_7(X3,X2,X4,X5,X1,X6,X7)),esk30_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_6167]),
    [final] ).

cnf(i_0_11299,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_6208,c_0_6209]),c_0_6209]),
    [final] ).

cnf(i_0_11300,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_6210]),
    [final] ).

cnf(i_0_11301,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_6211]),
    [final] ).

cnf(i_0_11302,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),esk293_3(X2,X3,X1)),esk293_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))),esk292_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6212]),
    [final] ).

cnf(i_0_11303,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_6213]),
    [final] ).

cnf(i_0_11304,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk293_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))),esk292_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6212]),
    [final] ).

cnf(i_0_11305,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_6214,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11306,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_6215,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11307,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_6216,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11308,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_6217]),
    [final] ).

cnf(i_0_11309,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_6218]),
    [final] ).

cnf(i_0_11310,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_6219]),
    [final] ).

cnf(i_0_11311,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_6220]),
    [final] ).

cnf(i_0_11312,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_6221]),
    [final] ).

cnf(i_0_11313,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_6222]),
    [final] ).

cnf(i_0_11314,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_6223]),
    [final] ).

cnf(i_0_11315,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,esk306_6(X4,X3,X5,X6,X2,X1)),esk307_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_6224]),
    [final] ).

cnf(i_0_11316,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_6225]),
    [final] ).

cnf(i_0_11317,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))))),esk352_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_6226]),
    [final] ).

cnf(i_0_11318,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),esk376_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_6227]),
    [final] ).

cnf(i_0_11319,plain,
    hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Omap(tc_prod(X1,X3),tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X3,tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X3,X2),tc_fun(X3,tc_prod(X1,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(tc_fun(X3,X2),tc_fun(X3,tc_prod(X1,X2))),X1),c_COMBB(X2,tc_prod(X1,X2),X3)),c_Product__Type_OPair(X1,X2))),X4))),X5)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(X3),tc_Option_Ooption(X2),X1,hAPP(c_Option_Omap(X3,X2),X4)),hAPP(c_Map_Omap__of(X1,X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_6228]),
    [final] ).

cnf(i_0_11320,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_6229]),
    [final] ).

cnf(i_0_11321,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_6230,c_0_6102]),c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11322,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_6231,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11323,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_6232,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11324,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_6233,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11325,plain,
    ( hAPP(X1,esk64_7(X2,X3,X1,X4,X5,X6,X7)) = hAPP(X1,esk65_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_6130]),
    [final] ).

cnf(i_0_11326,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,esk291_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_6234]),
    [final] ).

cnf(i_0_11327,plain,
    ( hBOOL(hAPP(X1,esk490_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_6197]),
    [final] ).

cnf(i_0_11328,plain,
    ( hBOOL(hAPP(X1,esk487_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_6198]),
    [final] ).

cnf(i_0_11329,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,esk262_4(X3,X2,X1,X4)))),hAPP(X1,esk262_4(X3,X2,X1,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6235]),
    [final] ).

cnf(i_0_11330,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_6236]),
    [final] ).

cnf(i_0_11331,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_6237]),
    [final] ).

cnf(i_0_11332,plain,
    ( hBOOL(hAPP(hAPP(X1,X4),X3))
    | ~ hBOOL(hAPP(hAPP(X1,esk141_6(X1,X2,X3,X4,X5,X6)),esk142_6(X1,X2,X3,X4,X5,X6)))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(X6,X5),tc_HOL_Obool),tc_fun(tc_prod(X6,X5),tc_HOL_Obool),X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X5)),hAPP(hAPP(c_Product__Type_OPair(X6,X5),X4),X3)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(X6,X5),tc_HOL_Obool),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6186]),
    [final] ).

cnf(i_0_11333,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)))),esk451_3(X3,X2,X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6238,c_0_6177]),c_0_6177]),
    [final] ).

cnf(i_0_11334,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)))),esk450_3(X2,X3,X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6239,c_0_6177]),c_0_6177]),
    [final] ).

cnf(i_0_11335,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_6240]),
    [final] ).

cnf(i_0_11336,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_6212]),
    [final] ).

cnf(i_0_11337,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_6241,c_0_6242]),
    [final] ).

cnf(i_0_11338,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_6243,c_0_6102]),c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11339,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_6244]),
    [final] ).

cnf(i_0_11340,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_6245,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11341,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,esk99_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_6195]),
    [final] ).

cnf(i_0_11342,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_6246,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11343,plain,
    ( hBOOL(hAPP(X1,esk262_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_6235]),
    [final] ).

cnf(i_0_11344,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_6247]),
    [final] ).

cnf(i_0_11345,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_6248,c_0_6242]),
    [final] ).

cnf(i_0_11346,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_6249,c_0_6242]),
    [final] ).

cnf(i_0_11347,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_6218]),
    [final] ).

cnf(i_0_11348,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_6250]),
    [final] ).

cnf(i_0_11349,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_6251]),
    [final] ).

cnf(i_0_11350,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_6252]),
    [final] ).

cnf(i_0_11351,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_6219]),
    [final] ).

cnf(i_0_11352,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_6253,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11353,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_6254,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11354,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_6255]),
    [final] ).

cnf(i_0_11355,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_6256]),
    [final] ).

cnf(i_0_11356,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_6221]),
    [final] ).

cnf(i_0_11357,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_6222]),
    [final] ).

cnf(i_0_11358,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)),esk296_4(X3,X4,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6257]),
    [final] ).

cnf(i_0_11359,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_6258]),
    [final] ).

cnf(i_0_11360,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,esk274_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_6259]),
    [final] ).

cnf(i_0_11361,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,esk273_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_6260]),
    [final] ).

cnf(i_0_11362,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_6261]),
    [final] ).

cnf(i_0_11363,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_6262]),
    [final] ).

cnf(i_0_11364,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_6262]),
    [final] ).

cnf(i_0_11365,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_6262]),
    [final] ).

cnf(i_0_11366,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_6262]),
    [final] ).

cnf(i_0_11367,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)),esk218_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),esk218_4(X2,X3,X4,X1)),X3))),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6263]),
    [final] ).

cnf(i_0_11368,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_6264,c_0_6102]),c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11369,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_6265]),
    [final] ).

cnf(i_0_11370,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_6266,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11371,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_6267,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11372,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_6268,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11373,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_6269,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11374,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_6270,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11375,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_6271]),
    [final] ).

cnf(i_0_11376,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_6272,c_0_6136]),c_0_6136]),
    [final] ).

cnf(i_0_11377,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_6273]),
    [final] ).

cnf(i_0_11378,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_6274]),
    [final] ).

cnf(i_0_11379,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,esk245_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_6275]),
    [final] ).

cnf(i_0_11380,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_6276]),
    [final] ).

cnf(i_0_11381,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_6277]),
    [final] ).

cnf(i_0_11382,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_6278]),
    [final] ).

cnf(i_0_11383,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_6276]),
    [final] ).

cnf(i_0_11384,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_6277]),
    [final] ).

cnf(i_0_11385,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_6278]),
    [final] ).

cnf(i_0_11386,plain,
    ( c_Orderings_Oorder__class_Omono(X1,tc_fun(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(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))),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))),X5))
    | ~ class_Orderings_Oorder(X1)
    | ~ c_Orderings_Oorder__class_Omono(X1,tc_fun(X2,tc_HOL_Obool),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6279]),
    [final] ).

cnf(i_0_11387,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_6280]),
    [final] ).

cnf(i_0_11388,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_6281]),
    [final] ).

cnf(i_0_11389,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_6282]),
    [final] ).

cnf(i_0_11390,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_6283,c_0_6242]),
    [final] ).

cnf(i_0_11391,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_6284,c_0_6242]),
    [final] ).

cnf(i_0_11392,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_6285,c_0_6286]),c_0_6286]),c_0_6114]),c_0_6114]),
    [final] ).

cnf(i_0_11393,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_6287]),
    [final] ).

cnf(i_0_11394,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),esk86_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_6258]),
    [final] ).

cnf(i_0_11395,plain,
    ( X1 = hAPP(hAPP(X2,X3),esk376_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_6227]),
    [final] ).

cnf(i_0_11396,plain,
    ( X1 = hAPP(hAPP(X2,X3),esk352_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_6226]),
    [final] ).

cnf(i_0_11397,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk432_5(X5,X4,X3,X2,X1)),esk432_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_6288]),
    [final] ).

cnf(i_0_11398,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_6289]),
    [final] ).

cnf(i_0_11399,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk342_5(X2,X3,X4,X5,X1)),esk343_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_6290]),
    [final] ).

cnf(i_0_11400,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk341_5(X2,X3,X4,X5,X1)),esk340_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_6291]),
    [final] ).

cnf(i_0_11401,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_6292]),
    [final] ).

cnf(i_0_11402,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_6293,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11403,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_6294,c_0_6242]),
    [final] ).

cnf(i_0_11404,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_6295,c_0_6242]),
    [final] ).

cnf(i_0_11405,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk286_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),esk285_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk285_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6296]),
    [final] ).

cnf(i_0_11406,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk283_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),esk282_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk282_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6297]),
    [final] ).

cnf(i_0_11407,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk338_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk339_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_6298]),
    [final] ).

cnf(i_0_11408,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk338_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk339_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_6298]),
    [final] ).

cnf(i_0_11409,plain,
    ( hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(X2,X1)),X3),X4) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(X2),hAPP(hAPP(c_COMBC(X2,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X2),c_Smallcheck_Osmall__class_Osmall(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X2,X1)),tc_fun(X1,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X2),hAPP(c_COMBB(tc_prod(X2,X1),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),X1),X3)),c_Product__Type_OPair(X2,X1)))),X4)),X4)
    | ~ class_Smallcheck_Osmall(X1)
    | ~ class_Smallcheck_Osmall(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6299]),
    [final] ).

cnf(i_0_11410,plain,
    ( hAPP(X1,esk286_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),esk285_3(X2,X1,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,esk285_3(X2,X1,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6296]),
    [final] ).

cnf(i_0_11411,plain,
    ( hAPP(X1,esk283_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),esk282_3(X2,X1,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,esk282_3(X2,X1,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6297]),
    [final] ).

cnf(i_0_11412,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_11413,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk274_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_6259]),
    [final] ).

cnf(i_0_11414,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk273_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_6260]),
    [final] ).

cnf(i_0_11415,plain,
    ( hAPP(X1,esk397_7(X2,X3,X4,X1,X5,X6,X7)) = hAPP(c_Option_Ooption_OSome(X6),X2)
    | hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X6),X7,c_Option_Ooption_ONone(X6),X1),hAPP(X4,X3)) != hAPP(c_Option_Ooption_OSome(X6),X2) ),
    inference(rw,[status(thm)],[i_0_6300,c_0_6301]),
    [final] ).

cnf(i_0_11416,plain,
    ( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),esk397_7(X4,X2,X1,X5,X6,X7,X3))
    | hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X7),X3,c_Option_Ooption_ONone(X7),X5),hAPP(X1,X2)) != hAPP(c_Option_Ooption_OSome(X7),X4) ),
    inference(rw,[status(thm)],[i_0_6302,c_0_6301]),
    [final] ).

cnf(i_0_11417,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_6257]),
    [final] ).

cnf(i_0_11418,plain,
    ( hBOOL(hAPP(X1,esk86_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_6258]),
    [final] ).

cnf(i_0_11419,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_6303]),
    [final] ).

cnf(i_0_11420,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_6304]),
    [final] ).

cnf(i_0_11421,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_6305]),
    [final] ).

cnf(i_0_11422,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_6306,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11423,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_6307]),
    [final] ).

cnf(i_0_11424,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_6308]),
    [final] ).

cnf(i_0_11425,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_6309]),
    [final] ).

cnf(i_0_11426,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_6310,c_0_6311]),
    [final] ).

cnf(i_0_11427,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk242_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_6312]),
    [final] ).

cnf(i_0_11428,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk241_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_6312]),
    [final] ).

cnf(i_0_11429,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk312_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_6200]),
    [final] ).

cnf(i_0_11430,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_6313]),
    [final] ).

cnf(i_0_11431,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_6314,c_0_6114]),c_0_6114]),c_0_6114]),
    [final] ).

cnf(i_0_11432,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_6315,c_0_6286]),c_0_6286]),c_0_6286]),
    [final] ).

cnf(i_0_11433,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_6316]),
    [final] ).

cnf(i_0_11434,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk320_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_6317]),
    [final] ).

cnf(i_0_11435,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_6318,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11436,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_6319,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11437,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_6320]),
    [final] ).

cnf(i_0_11438,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk375_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_6321]),
    [final] ).

cnf(i_0_11439,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk245_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_6275]),
    [final] ).

cnf(i_0_11440,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_6322]),
    [final] ).

cnf(i_0_11441,plain,
    ( c_List_Olist__all2(X2,X5,X1,X3,X4)
    | ~ hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk481_5(X1,X4,X5,X3,X2))),hAPP(hAPP(c_List_Onth(X5),X4),esk481_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_6323]),
    [final] ).

cnf(i_0_11442,plain,
    ( c_List_Olist__all2(X2,X5,X1,X3,X4)
    | ~ hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk472_5(X4,X3,X1,X5,X2))),hAPP(hAPP(c_List_Onth(X5),X4),esk472_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_6324]),
    [final] ).

cnf(i_0_11443,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,esk249_5(X3,X2,X4,X5,X1))),hAPP(X3,esk249_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_6325]),
    [final] ).

cnf(i_0_11444,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_6326]),
    [final] ).

cnf(i_0_11445,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk340_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_6291]),
    [final] ).

cnf(i_0_11446,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_6327,c_0_6242]),
    [final] ).

cnf(i_0_11447,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_6328,c_0_6242]),
    [final] ).

cnf(i_0_11448,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,esk97_5(X5,X4,X3,X2,X1)),esk98_5(X5,X4,X3,X2,X1))) != hAPP(hAPP(X2,hAPP(X4,esk97_5(X5,X4,X3,X2,X1))),hAPP(X4,esk98_5(X5,X4,X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6329]),
    [final] ).

cnf(i_0_11449,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),esk452_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_6330,c_0_6209]),c_0_6209]),
    [final] ).

cnf(i_0_11450,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),esk452_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_6331,c_0_6209]),c_0_6209]),
    [final] ).

cnf(i_0_11451,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),esk452_3(X3,X1,X2))) != X3 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6332,c_0_6209]),c_0_6209]),
    [final] ).

cnf(i_0_11452,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),esk452_3(X3,X1,X2))) != X3 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6333,c_0_6209]),c_0_6209]),
    [final] ).

cnf(i_0_11453,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_6334,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11454,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk158_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),esk157_3(X1,X2,X3)),esk158_3(X1,X2,X3))))
    | hBOOL(hAPP(hAPP(X1,esk157_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)))),esk158_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_6335,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11455,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_6336]),
    [final] ).

cnf(i_0_11456,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_6337]),
    [final] ).

cnf(i_0_11457,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_6336]),
    [final] ).

cnf(i_0_11458,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_6337]),
    [final] ).

cnf(i_0_11459,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_6338]),
    [final] ).

cnf(i_0_11460,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_6339]),
    [final] ).

cnf(i_0_11461,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_6340]),
    [final] ).

cnf(i_0_11462,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),esk417_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk417_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_6341]),
    [final] ).

cnf(i_0_11463,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk149_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk148_3(X1,X2,X3)),esk149_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(X1,esk148_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)))),esk149_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_6342,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11464,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)),esk403_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_6343]),
    [final] ).

cnf(i_0_11465,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_6344,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11466,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk402_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_6343]),
    [final] ).

cnf(i_0_11467,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk346_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_6345]),
    [final] ).

cnf(i_0_11468,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk344_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_6346]),
    [final] ).

cnf(i_0_11469,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_6347,c_0_6122]),c_0_6122]),c_0_6123]),c_0_6123]),
    [final] ).

cnf(i_0_11470,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk336_5(X3,X4,X5,X2,X1))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk337_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_6348]),
    [final] ).

cnf(i_0_11471,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk336_5(X3,X4,X5,X2,X1))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk337_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_6348]),
    [final] ).

cnf(i_0_11472,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk345_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_6349]),
    [final] ).

cnf(i_0_11473,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_6350,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11474,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_6351,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11475,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk336_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_6348]),
    [final] ).

cnf(i_0_11476,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk336_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_6348]),
    [final] ).

cnf(i_0_11477,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_6352,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11478,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_6353,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11479,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_6354,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11480,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_6355,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11481,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_6356,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11482,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_6357,c_0_6242]),
    [final] ).

cnf(i_0_11483,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_6358,c_0_6242]),
    [final] ).

cnf(i_0_11484,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_6359,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11485,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_6360]),
    [final] ).

cnf(i_0_11486,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_6361,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11487,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_6362,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11488,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_6363,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11489,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_6364,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11490,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_6365,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11491,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_6366,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11492,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_6367,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11493,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_6368,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11494,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_6369,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11495,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_6370,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11496,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk70_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_6371]),
    [final] ).

cnf(i_0_11497,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk62_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_6372]),
    [final] ).

cnf(i_0_11498,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,esk241_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_6312]),
    [final] ).

cnf(i_0_11499,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,esk84_4(X4,X3,X2,X1)),esk85_4(X4,X3,X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk84_4(X4,X3,X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk85_4(X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6373]),
    [final] ).

cnf(i_0_11500,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_6374,c_0_6177]),
    [final] ).

cnf(i_0_11501,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_6375,c_0_6242]),
    [final] ).

cnf(i_0_11502,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_6376,c_0_6102]),c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11503,plain,
    ( hAPP(c_List_Oset(tc_prod(X1,X2)),X3) = 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_Option_Ooption(X2)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_Option_Ooption(X2),tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),hAPP(c_Map_Omap__of(X1,X2),X3)))),c_Option_Ooption_OSome(X2))))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6377]),
    [final] ).

cnf(i_0_11504,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_6378]),
    [final] ).

cnf(i_0_11505,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,esk320_6(X2,X3,X1,X4,X5,X6)) != hAPP(X3,esk320_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_6317]),
    [final] ).

cnf(i_0_11506,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,esk375_6(X4,X3,X2,X1,X5,X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6321]),
    [final] ).

cnf(i_0_11507,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_6379]),
    [final] ).

cnf(i_0_11508,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_6380]),
    [final] ).

cnf(i_0_11509,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk306_6(X1,X4,X3,X2,X5,X6)),esk307_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_6224]),
    [final] ).

cnf(i_0_11510,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_6381]),
    [final] ).

cnf(i_0_11511,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk390_6(X4,X5,X6,X1,X3,X2)),esk392_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_6187]),
    [final] ).

cnf(i_0_11512,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_6382,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11513,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_6383,c_0_6114]),c_0_6114]),
    [final] ).

cnf(i_0_11514,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_6384,c_0_6286]),c_0_6286]),
    [final] ).

cnf(i_0_11515,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_6385,c_0_6128]),
    [final] ).

cnf(i_0_11516,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk304_6(X4,X5,X6,X3,X2,X1)),esk305_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_6201]),
    [final] ).

cnf(i_0_11517,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_6386,c_0_6286]),c_0_6114]),
    [final] ).

cnf(i_0_11518,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_6387,c_0_6286]),c_0_6114]),
    [final] ).

cnf(i_0_11519,plain,
    hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Ofilter(X1,X4),X5)) = c_List_Omap__filter(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),X1),c_If(tc_Option_Ooption(X2))),X4)),hAPP(hAPP(c_COMBB(X2,tc_Option_Ooption(X2),X1),c_Option_Ooption_OSome(X2)),X3))),c_Option_Ooption_ONone(X2)),X5),
    inference(split_conjunct,[status(thm)],[i_0_6388]),
    [final] ).

cnf(i_0_11520,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_6389]),
    [final] ).

cnf(i_0_11521,plain,
    c_Map_Odom(X1,X2,hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),X1),c_If(tc_Option_Ooption(X2))),X3)),X4)),X5)) = 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)),c_Map_Odom(X1,X2,X4)),hAPP(c_Set_OCollect(X1),X3))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X5)),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_6390]),
    [final] ).

cnf(i_0_11522,plain,
    c_List_Omap__filter(X1,X2,X3,X4) = hAPP(hAPP(c_List_Omap(X1,X2),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2)),X3)),hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),X3)),c_Option_Ooption_ONone(X2)))),X4)),
    inference(split_conjunct,[status(thm)],[i_0_6391]),
    [final] ).

cnf(i_0_11523,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_6392]),
    [final] ).

cnf(i_0_11524,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_6308]),
    [final] ).

cnf(i_0_11525,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_6309]),
    [final] ).

cnf(i_0_11526,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Fields_Olinordered__field__inverse__zero(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_6393,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [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_6394]),
    [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_6395,c_0_6242]),
    [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_6396,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [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_6397,c_0_6242]),
    [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,esk53_5(X3,X2,X4,X5,X1))),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6398]),
    [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,esk230_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_6399]),
    [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_6400,c_0_6242]),
    [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_6401]),
    [final] ).

cnf(i_0_11535,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X1,X2),X4)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,esk22_5(X3,X2,X1,X4,X5))),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6402]),
    [final] ).

cnf(i_0_11536,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_6403]),
    [final] ).

cnf(i_0_11537,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,esk48_5(X3,X2,X4,X5,X1))),X3))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6404]),
    [final] ).

cnf(i_0_11538,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_6405,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11539,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_6406,c_0_6102]),c_0_6102]),c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11540,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_6407,c_0_6102]),c_0_6102]),c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11541,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),X2) = hAPP(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_6408]),
    [final] ).

cnf(i_0_11542,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),esk418_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk418_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_6409]),
    [final] ).

cnf(i_0_11543,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),esk418_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk418_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_6409]),
    [final] ).

cnf(i_0_11544,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_6410,c_0_6177]),
    [final] ).

cnf(i_0_11545,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_6411]),
    [final] ).

cnf(i_0_11546,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_6412]),
    [final] ).

cnf(i_0_11547,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_6413]),
    [final] ).

cnf(i_0_11548,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_6414]),
    [final] ).

cnf(i_0_11549,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_6415,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11550,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_6416]),
    [final] ).

cnf(i_0_11551,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_6417]),
    [final] ).

cnf(i_0_11552,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_6418]),
    [final] ).

cnf(i_0_11553,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_6419,c_0_6177]),
    [final] ).

cnf(i_0_11554,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_6420]),
    [final] ).

cnf(i_0_11555,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_6421,c_0_6128]),
    [final] ).

cnf(i_0_11556,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_6422]),
    [final] ).

cnf(i_0_11557,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_6423]),
    [final] ).

cnf(i_0_11558,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_6424]),
    [final] ).

cnf(i_0_11559,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk342_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_6290]),
    [final] ).

cnf(i_0_11560,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_6425]),
    [final] ).

cnf(i_0_11561,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_6426]),
    [final] ).

cnf(i_0_11562,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_6427,c_0_6242]),
    [final] ).

cnf(i_0_11563,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_6428,c_0_6242]),
    [final] ).

cnf(i_0_11564,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_6429]),
    [final] ).

cnf(i_0_11565,plain,
    ( hAPP(X1,esk241_6(X2,X3,X1,X4,X5,X6)) = hAPP(X1,esk242_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_6312]),
    [final] ).

cnf(i_0_11566,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),esk407_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_6430]),
    [final] ).

cnf(i_0_11567,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_6431,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11568,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_6432,c_0_6209]),
    [final] ).

cnf(i_0_11569,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk317_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_6433]),
    [final] ).

cnf(i_0_11570,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk406_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_6430]),
    [final] ).

cnf(i_0_11571,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_6434]),
    [final] ).

cnf(i_0_11572,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_6435]),
    [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__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_6436]),
    [final] ).

cnf(i_0_11574,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_6437]),
    [final] ).

cnf(i_0_11575,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk59_5(X3,X4,X5,X2,X1),esk60_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_6438]),
    [final] ).

cnf(i_0_11576,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk57_5(X3,X4,X5,X2,X1),esk58_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_6439]),
    [final] ).

cnf(i_0_11577,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),esk420_4(X3,X4,X2,X1))),esk419_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_6440]),
    [final] ).

cnf(i_0_11578,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_6441]),
    [final] ).

cnf(i_0_11579,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_6442]),
    [final] ).

cnf(i_0_11580,plain,
    ( hAPP(hAPP(c_Map_Omap__of(X2,X4),hAPP(hAPP(c_List_Omap(tc_prod(X1,X4),tc_prod(X2,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X4,tc_prod(X2,X4)),hAPP(hAPP(c_COMBB(X2,tc_fun(X4,tc_prod(X2,X4)),X1),c_Product__Type_OPair(X2,X4)),X3))),X5)),hAPP(X3,X6)) = hAPP(c_Option_Ooption_OSome(X4),X7)
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | hAPP(hAPP(c_Map_Omap__of(X1,X4),X5),X6) != hAPP(c_Option_Ooption_OSome(X4),X7) ),
    inference(split_conjunct,[status(thm)],[i_0_6443]),
    [final] ).

cnf(i_0_11581,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_6444,c_0_6114]),c_0_6114]),
    [final] ).

cnf(i_0_11582,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_6445,c_0_6286]),c_0_6286]),
    [final] ).

cnf(i_0_11583,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk345_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_6349]),
    [final] ).

cnf(i_0_11584,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_6446,c_0_6122]),c_0_6123]),
    [final] ).

cnf(i_0_11585,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_6447,c_0_6114]),
    [final] ).

cnf(i_0_11586,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_6448,c_0_6286]),
    [final] ).

cnf(i_0_11587,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_6449]),
    [final] ).

cnf(i_0_11588,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_6450]),
    [final] ).

cnf(i_0_11589,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_6451,c_0_6114]),
    [final] ).

cnf(i_0_11590,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_6452,c_0_6286]),
    [final] ).

cnf(i_0_11591,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),esk59_5(X2,X3,X4,X5,X1)),esk60_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_6438]),
    [final] ).

cnf(i_0_11592,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),esk57_5(X2,X3,X4,X5,X1)),esk58_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_6439]),
    [final] ).

cnf(i_0_11593,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),esk439_4(X2,X3,X4,X1)),esk438_4(X2,X3,X4,X1))),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6453]),
    [final] ).

cnf(i_0_11594,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),esk438_4(X2,X3,X4,X1)),esk439_4(X2,X3,X4,X1))),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6453]),
    [final] ).

cnf(i_0_11595,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk346_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_6345]),
    [final] ).

cnf(i_0_11596,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk344_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_6346]),
    [final] ).

cnf(i_0_11597,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_6454]),
    [final] ).

cnf(i_0_11598,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_6455]),
    [final] ).

cnf(i_0_11599,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),esk393_4(X1,X2,X3,X4)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk394_4(X1,X2,X3,X4)),esk395_4(X1,X2,X3,X4)))))
    | hBOOL(hAPP(hAPP(hAPP(X1,X4),X3),X2))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X4),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6456]),
    [final] ).

cnf(i_0_11600,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk338_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_6298]),
    [final] ).

cnf(i_0_11601,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk338_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_6298]),
    [final] ).

cnf(i_0_11602,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_6457,c_0_6242]),
    [final] ).

cnf(i_0_11603,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_6458]),
    [final] ).

cnf(i_0_11604,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_6459,c_0_6242]),
    [final] ).

cnf(i_0_11605,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_6460,c_0_6242]),
    [final] ).

cnf(i_0_11606,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_6461]),
    [final] ).

cnf(i_0_11607,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_6462]),
    [final] ).

cnf(i_0_11608,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_6463]),
    [final] ).

cnf(i_0_11609,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_6464,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11610,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X2,X1)),X3))
    | ~ c_Enum_Oex__n__lists(X1,hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_HOL_Obool,tc_List_Olist(X1)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Option_Ooption(X1)),tc_fun(X2,X1),tc_List_Olist(X1)),c_Fun_Ocomp(tc_Option_Ooption(X1),X1,X2,c_Option_Othe(X1))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X2,X1)),tc_fun(X2,tc_Option_Ooption(X1)),tc_List_Olist(X1)),c_Map_Omap__of(X2,X1)),hAPP(c_List_Ozip(X2,X1),c_Enum_Oenum__class_Oenum(X2))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_Enum_Oenum__class_Oenum(X2)))
    | ~ class_Enum_Oenum(X1)
    | ~ class_Enum_Oenum(X2)
    | ~ class_HOL_Oequal(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6465]),
    [final] ).

cnf(i_0_11611,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X2,X1)),X3))
    | ~ c_Enum_Oall__n__lists(X1,hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_HOL_Obool,tc_List_Olist(X1)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Option_Ooption(X1)),tc_fun(X2,X1),tc_List_Olist(X1)),c_Fun_Ocomp(tc_Option_Ooption(X1),X1,X2,c_Option_Othe(X1))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X2,X1)),tc_fun(X2,tc_Option_Ooption(X1)),tc_List_Olist(X1)),c_Map_Omap__of(X2,X1)),hAPP(c_List_Ozip(X2,X1),c_Enum_Oenum__class_Oenum(X2))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_Enum_Oenum__class_Oenum(X2)))
    | ~ class_Enum_Oenum(X1)
    | ~ class_Enum_Oenum(X2)
    | ~ class_HOL_Oequal(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6466]),
    [final] ).

cnf(i_0_11612,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X2,X1)),X3))
    | ~ c_Enum_Oex__n__lists(X1,hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_HOL_Obool,tc_List_Olist(X1)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Option_Ooption(X1)),tc_fun(X2,X1),tc_List_Olist(X1)),c_Fun_Ocomp(tc_Option_Ooption(X1),X1,X2,c_Option_Othe(X1))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X2,X1)),tc_fun(X2,tc_Option_Ooption(X1)),tc_List_Olist(X1)),c_Map_Omap__of(X2,X1)),hAPP(c_List_Ozip(X2,X1),c_Enum_Oenum__class_Oenum(X2))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_Enum_Oenum__class_Oenum(X2)))
    | ~ class_Enum_Oenum(X1)
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6467]),
    [final] ).

cnf(i_0_11613,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X2,X1)),X3))
    | ~ c_Enum_Oall__n__lists(X1,hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_HOL_Obool,tc_List_Olist(X1)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Option_Ooption(X1)),tc_fun(X2,X1),tc_List_Olist(X1)),c_Fun_Ocomp(tc_Option_Ooption(X1),X1,X2,c_Option_Othe(X1))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X2,X1)),tc_fun(X2,tc_Option_Ooption(X1)),tc_List_Olist(X1)),c_Map_Omap__of(X2,X1)),hAPP(c_List_Ozip(X2,X1),c_Enum_Oenum__class_Oenum(X2))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_Enum_Oenum__class_Oenum(X2)))
    | ~ class_Enum_Oenum(X1)
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6468]),
    [final] ).

cnf(i_0_11614,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)
    | esk241_6(X1,X2,X3,X4,X5,X6) != esk242_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_6312]),
    [final] ).

cnf(i_0_11615,plain,
    c_Map_Odom(X1,X2,c_Fun_Ooverride__on(X1,tc_Option_Ooption(X2),X3,X4,X5)) = 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)),c_Map_Odom(X1,X2,X3)),hAPP(c_Set_OCollect(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)),X5),c_Map_Odom(X1,X2,X4)))))),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),c_Map_Odom(X1,X2,X4))))),
    inference(split_conjunct,[status(thm)],[i_0_6469]),
    [final] ).

cnf(i_0_11616,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_6470]),
    [final] ).

cnf(i_0_11617,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_Int_Onumber__ring(X1)
    | ~ class_Fields_Olinordered__field__inverse__zero(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_6471,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11618,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_Int_Onumber__ring(X1)
    | ~ class_Fields_Olinordered__field__inverse__zero(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_6472,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11619,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_6473,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11620,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_6474,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11621,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_6475,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11622,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_6476,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11623,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_6477,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11624,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_6478,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11625,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_6479,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11626,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk356_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_6480]),
    [final] ).

cnf(i_0_11627,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk47_5(X2,X3,X4,X5,X1)),hAPP(X3,esk46_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_6481]),
    [final] ).

cnf(i_0_11628,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_6482,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11629,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_6483]),
    [final] ).

cnf(i_0_11630,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk278_5(X2,X3,X4,X1,X5)),hAPP(X2,esk277_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_6484]),
    [final] ).

cnf(i_0_11631,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_6485]),
    [final] ).

cnf(i_0_11632,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_6486]),
    [final] ).

cnf(i_0_11633,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_6394]),
    [final] ).

cnf(i_0_11634,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_6487]),
    [final] ).

cnf(i_0_11635,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_6488,c_0_6311]),c_0_6311]),
    [final] ).

cnf(i_0_11636,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_6489]),
    [final] ).

cnf(i_0_11637,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_6489]),
    [final] ).

cnf(i_0_11638,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),esk43_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_6490]),
    [final] ).

cnf(i_0_11639,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_6491]),
    [final] ).

cnf(i_0_11640,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_6492]),
    [final] ).

cnf(i_0_11641,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_6493]),
    [final] ).

cnf(i_0_11642,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_6493]),
    [final] ).

cnf(i_0_11643,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk394_4(X1,X2,X3,X4)),esk395_4(X1,X2,X3,X4)))
    | hBOOL(hAPP(hAPP(hAPP(X1,esk393_4(X1,X2,X3,X4)),esk394_4(X1,X2,X3,X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk395_4(X1,X2,X3,X4)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | hBOOL(hAPP(hAPP(hAPP(X1,X4),X3),X2))
    | hAPP(esk393_4(X1,X2,X3,X4),esk395_4(X1,X2,X3,X4)) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X4),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6456]),
    [final] ).

cnf(i_0_11644,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_6494]),
    [final] ).

cnf(i_0_11645,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_6495,c_0_6311]),
    [final] ).

cnf(i_0_11646,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_6496]),
    [final] ).

cnf(i_0_11647,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_6497]),
    [final] ).

cnf(i_0_11648,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_6498]),
    [final] ).

cnf(i_0_11649,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_6499]),
    [final] ).

cnf(i_0_11650,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_6500,c_0_6177]),
    [final] ).

cnf(i_0_11651,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_6501]),
    [final] ).

cnf(i_0_11652,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_6502]),
    [final] ).

cnf(i_0_11653,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_6503]),
    [final] ).

cnf(i_0_11654,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_6504]),
    [final] ).

cnf(i_0_11655,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)),esk227_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),esk227_4(X2,X3,X4,X1)),X3))),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6505]),
    [final] ).

cnf(i_0_11656,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),esk318_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_6433]),
    [final] ).

cnf(i_0_11657,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),esk263_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_6506]),
    [final] ).

cnf(i_0_11658,plain,
    c_Map_Oran(X1,X2,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(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),X3))),c_Option_Ooption_OSome(X2)))),
    inference(split_conjunct,[status(thm)],[i_0_6507]),
    [final] ).

cnf(i_0_11659,plain,
    ( hBOOL(hAPP(hAPP(X1,esk258_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_6508]),
    [final] ).

cnf(i_0_11660,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,esk323_3(X3,X2,X1)))),hAPP(X3,esk323_3(X3,X2,X1)))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6509]),
    [final] ).

cnf(i_0_11661,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,esk260_3(X2,X1,X3)))),hAPP(X3,esk260_3(X2,X1,X3)))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6510]),
    [final] ).

cnf(i_0_11662,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_6511]),
    [final] ).

cnf(i_0_11663,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_6512,c_0_6123]),
    [final] ).

cnf(i_0_11664,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_6513,c_0_6123]),
    [final] ).

cnf(i_0_11665,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_6514]),
    [final] ).

cnf(i_0_11666,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,esk240_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_6515]),
    [final] ).

cnf(i_0_11667,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,esk229_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_6516]),
    [final] ).

cnf(i_0_11668,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_6517]),
    [final] ).

cnf(i_0_11669,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_6518]),
    [final] ).

cnf(i_0_11670,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_6519]),
    [final] ).

cnf(i_0_11671,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_6520]),
    [final] ).

cnf(i_0_11672,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_6167]),
    [final] ).

cnf(i_0_11673,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_6503]),
    [final] ).

cnf(i_0_11674,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_6434]),
    [final] ).

cnf(i_0_11675,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_6521,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11676,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_6522]),
    [final] ).

cnf(i_0_11677,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,esk358_5(X3,X4,X5,X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6523]),
    [final] ).

cnf(i_0_11678,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,esk520_5(X3,X2,X1,X4,X5)),hAPP(X3,esk520_5(X3,X2,X1,X4,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6524]),
    [final] ).

cnf(i_0_11679,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_6525]),
    [final] ).

cnf(i_0_11680,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_6526,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11681,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),esk258_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_6508]),
    [final] ).

cnf(i_0_11682,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,esk353_5(X3,X4,X5,X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6527]),
    [final] ).

cnf(i_0_11683,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_6528]),
    [final] ).

cnf(i_0_11684,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_6503]),
    [final] ).

cnf(i_0_11685,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_6529]),
    [final] ).

cnf(i_0_11686,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,esk360_5(X2,X1,X3,X4,X5)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6530]),
    [final] ).

cnf(i_0_11687,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_6531]),
    [final] ).

cnf(i_0_11688,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_6532]),
    [final] ).

cnf(i_0_11689,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,esk357_5(X3,X4,X5,X2,X1))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6533]),
    [final] ).

cnf(i_0_11690,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,esk484_5(X3,X2,X4,X5,X1))))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6534]),
    [final] ).

cnf(i_0_11691,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,esk244_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_6535]),
    [final] ).

cnf(i_0_11692,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_6536,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11693,plain,
    ( hBOOL(hAPP(hAPP(hAPP(X1,X4),X3),X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(X1,esk393_4(X1,X2,X3,X4)),esk394_4(X1,X2,X3,X4)),esk395_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X4),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6456]),
    [final] ).

cnf(i_0_11694,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_6537]),
    [final] ).

cnf(i_0_11695,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_6538]),
    [final] ).

cnf(i_0_11696,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk488_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_6197]),
    [final] ).

cnf(i_0_11697,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk485_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_6198]),
    [final] ).

cnf(i_0_11698,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_6539,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11699,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk428_4(X2,X3,X4,X1)),esk429_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_6540]),
    [final] ).

cnf(i_0_11700,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_6541]),
    [final] ).

cnf(i_0_11701,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_6542]),
    [final] ).

cnf(i_0_11702,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_6543]),
    [final] ).

cnf(i_0_11703,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_6544]),
    [final] ).

cnf(i_0_11704,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_6503]),
    [final] ).

cnf(i_0_11705,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk317_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_6433]),
    [final] ).

cnf(i_0_11706,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_6529]),
    [final] ).

cnf(i_0_11707,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_11708,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_11709,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_6545]),
    [final] ).

cnf(i_0_11710,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_6546]),
    [final] ).

cnf(i_0_11711,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_6547]),
    [final] ).

cnf(i_0_11712,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_6548]),
    [final] ).

cnf(i_0_11713,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk106_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_6549]),
    [final] ).

cnf(i_0_11714,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_6550]),
    [final] ).

cnf(i_0_11715,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_6551]),
    [final] ).

cnf(i_0_11716,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_6552]),
    [final] ).

cnf(i_0_11717,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_6458]),
    [final] ).

cnf(i_0_11718,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_6553,c_0_6122]),c_0_6123]),
    [final] ).

cnf(i_0_11719,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_6554]),
    [final] ).

cnf(i_0_11720,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_6462]),
    [final] ).

cnf(i_0_11721,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_6555]),
    [final] ).

cnf(i_0_11722,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_6556]),
    [final] ).

cnf(i_0_11723,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_6557]),
    [final] ).

cnf(i_0_11724,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk143_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_6558]),
    [final] ).

cnf(i_0_11725,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_6559]),
    [final] ).

cnf(i_0_11726,plain,
    ( c_Enum_Oall__n__lists(X2,hAPP(hAPP(c_COMBB(tc_fun(X1,X2),tc_HOL_Obool,tc_List_Olist(X2)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,X2),tc_List_Olist(X2)),c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_fun(X1,tc_Option_Ooption(X2)),tc_List_Olist(X2)),c_Map_Omap__of(X1,X2)),hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X1,X2)),X3))
    | ~ class_Enum_Oenum(X2)
    | ~ class_Enum_Oenum(X1)
    | ~ class_HOL_Oequal(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6466]),
    [final] ).

cnf(i_0_11727,plain,
    ( c_Enum_Oex__n__lists(X2,hAPP(hAPP(c_COMBB(tc_fun(X1,X2),tc_HOL_Obool,tc_List_Olist(X2)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,X2),tc_List_Olist(X2)),c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_fun(X1,tc_Option_Ooption(X2)),tc_List_Olist(X2)),c_Map_Omap__of(X1,X2)),hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X1,X2)),X3))
    | ~ class_Enum_Oenum(X2)
    | ~ class_Enum_Oenum(X1)
    | ~ class_HOL_Oequal(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6465]),
    [final] ).

cnf(i_0_11728,plain,
    ( c_Enum_Oall__n__lists(X2,hAPP(hAPP(c_COMBB(tc_fun(X1,X2),tc_HOL_Obool,tc_List_Olist(X2)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,X2),tc_List_Olist(X2)),c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_fun(X1,tc_Option_Ooption(X2)),tc_List_Olist(X2)),c_Map_Omap__of(X1,X2)),hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X1,X2)),X3))
    | ~ class_Enum_Oenum(X2)
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6468]),
    [final] ).

cnf(i_0_11729,plain,
    ( c_Enum_Oex__n__lists(X2,hAPP(hAPP(c_COMBB(tc_fun(X1,X2),tc_HOL_Obool,tc_List_Olist(X2)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,X2),tc_List_Olist(X2)),c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_fun(X1,tc_Option_Ooption(X2)),tc_List_Olist(X2)),c_Map_Omap__of(X1,X2)),hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X1,X2)),X3))
    | ~ class_Enum_Oenum(X2)
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6467]),
    [final] ).

cnf(i_0_11730,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_6560]),
    [final] ).

cnf(i_0_11731,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_6561]),
    [final] ).

cnf(i_0_11732,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_6519]),
    [final] ).

cnf(i_0_11733,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_6520]),
    [final] ).

cnf(i_0_11734,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk25_5(X2,X3,X4,X1,X5)),X2))
    | hBOOL(hAPP(hAPP(c_member(X1),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_OCollect(X1)),X4))
    | X5 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_OCollect(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6562]),
    [final] ).

cnf(i_0_11735,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk388_4(X3,X4,X1,X2)),esk389_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_6563]),
    [final] ).

cnf(i_0_11736,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_6564]),
    [final] ).

cnf(i_0_11737,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_6565]),
    [final] ).

cnf(i_0_11738,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X5),X4))
    | ~ hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4)),esk25_5(X3,X5,X1,X2,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X5),X3))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),c_Set_OCollect(X2)),X1))
    | X4 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),c_Set_OCollect(X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_6562]),
    [final] ).

cnf(i_0_11739,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk71_5(X2,X3,X1,X4,X5)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X5),X4),c_Map_Oran(X1,X5,c_Map_Orestrict__map(X1,X5,X3,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6566]),
    [final] ).

cnf(i_0_11740,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_6567]),
    [final] ).

cnf(i_0_11741,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_6568]),
    [final] ).

cnf(i_0_11742,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_6569]),
    [final] ).

cnf(i_0_11743,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)),X5))))
    | c_Map_Omap__upds(X1,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),X6),X2),hAPP(c_Option_Ooption_OSome(X3),X7)),X5,X4) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),c_Map_Omap__upds(X1,X3,X6,X5,X4)),X2),hAPP(c_Option_Ooption_OSome(X3),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_6570]),
    [final] ).

cnf(i_0_11744,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),esk271_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_6571]),
    [final] ).

cnf(i_0_11745,plain,
    ( c_Enum_Oenum__class_Oenum(tc_fun(X1,X2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),tc_fun(X1,X2)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,X2),tc_List_Olist(X2)),c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_fun(X1,tc_Option_Ooption(X2)),tc_List_Olist(X2)),c_Map_Omap__of(X1,X2)),hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1))))),c_Enum_On__lists(X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1)),c_Enum_Oenum__class_Oenum(X2)))
    | ~ class_Enum_Oenum(X1)
    | ~ class_HOL_Oequal(X1)
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6572]),
    [final] ).

cnf(i_0_11746,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_6573]),
    [final] ).

cnf(i_0_11747,plain,
    ( c_Enum_Oenum__class_Oenum(tc_fun(X1,X2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),tc_fun(X1,X2)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,X2),tc_List_Olist(X2)),c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_fun(X1,tc_Option_Ooption(X2)),tc_List_Olist(X2)),c_Map_Omap__of(X1,X2)),hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1))))),c_Enum_On__lists(X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1)),c_Enum_Oenum__class_Oenum(X2)))
    | ~ class_Enum_Oenum(X1)
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6574]),
    [final] ).

cnf(i_0_11748,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_6575]),
    [final] ).

cnf(i_0_11749,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_6576]),
    [final] ).

cnf(i_0_11750,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_6577]),
    [final] ).

cnf(i_0_11751,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_6578]),
    [final] ).

cnf(i_0_11752,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_6579]),
    [final] ).

cnf(i_0_11753,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_6580]),
    [final] ).

cnf(i_0_11754,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_6581]),
    [final] ).

cnf(i_0_11755,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_6582]),
    [final] ).

cnf(i_0_11756,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_6583]),
    [final] ).

cnf(i_0_11757,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),esk511_2(X1,X2)),hAPP(X2,esk511_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6584]),
    [final] ).

cnf(i_0_11758,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_6569]),
    [final] ).

cnf(i_0_11759,plain,
    ( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
    | hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),esk398_6(X2,X1,X4,X5,X6,X3))
    | hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X6),X3,c_Option_Ooption_ONone(X6),X4),hAPP(X1,X2)) != c_Option_Ooption_ONone(X6) ),
    inference(rw,[status(thm)],[i_0_6585,c_0_6301]),
    [final] ).

cnf(i_0_11760,plain,
    ( hAPP(X3,X2) = c_Option_Ooption_ONone(X6)
    | hAPP(X1,esk398_6(X2,X3,X1,X4,X5,X6)) = c_Option_Ooption_ONone(X5)
    | hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X5),X6,c_Option_Ooption_ONone(X5),X1),hAPP(X3,X2)) != c_Option_Ooption_ONone(X5) ),
    inference(rw,[status(thm)],[i_0_6586,c_0_6301]),
    [final] ).

cnf(i_0_11761,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_6489]),
    [final] ).

cnf(i_0_11762,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_6587]),
    [final] ).

cnf(i_0_11763,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_6504]),
    [final] ).

cnf(i_0_11764,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk26_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_6588]),
    [final] ).

cnf(i_0_11765,plain,
    ( c_Map_Omap__upds(X1,X3,X5,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X6),c_List_Olist_ONil(X1))),X4) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),c_Map_Omap__upds(X1,X3,X5,X2,X4)),X6),hAPP(c_Option_Ooption_OSome(X3),hAPP(hAPP(c_List_Onth(X3),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))
    | ~ 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(X3)),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6589]),
    [final] ).

cnf(i_0_11766,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk17_5(X2,X3,X1,X4,X5)),X2))
    | c_Orderings_Oord__class_OLeast(X4,hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),hAPP(c_Set_Oimage(X1,X4,X3),X2))) = hAPP(X3,c_Orderings_Oord__class_OLeast(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X2))
    | ~ c_Orderings_Oorder__class_Omono(X1,X4,X3)
    | ~ class_Orderings_Oorder(X4)
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6590]),
    [final] ).

cnf(i_0_11767,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_6493]),
    [final] ).

cnf(i_0_11768,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)),esk228_3(X2,X3,X1))),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6591]),
    [final] ).

cnf(i_0_11769,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_6592]),
    [final] ).

cnf(i_0_11770,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_6593]),
    [final] ).

cnf(i_0_11771,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_6593]),
    [final] ).

cnf(i_0_11772,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_6491]),
    [final] ).

cnf(i_0_11773,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_6492]),
    [final] ).

cnf(i_0_11774,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk406_5(X3,X1,X4,X5,X2)),esk407_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_6430]),
    [final] ).

cnf(i_0_11775,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_6594]),
    [final] ).

cnf(i_0_11776,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk347_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_6595,c_0_6136]),
    [final] ).

cnf(i_0_11777,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_6322]),
    [final] ).

cnf(i_0_11778,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk348_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_6596,c_0_6136]),
    [final] ).

cnf(i_0_11779,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_6597]),
    [final] ).

cnf(i_0_11780,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_6598,c_0_6286]),
    [final] ).

cnf(i_0_11781,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_6599,c_0_6114]),
    [final] ).

cnf(i_0_11782,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_6503]),
    [final] ).

cnf(i_0_11783,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),esk473_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_6600]),
    [final] ).

cnf(i_0_11784,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),esk468_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_6601]),
    [final] ).

cnf(i_0_11785,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_6545]),
    [final] ).

cnf(i_0_11786,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_6546]),
    [final] ).

cnf(i_0_11787,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk240_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_6515]),
    [final] ).

cnf(i_0_11788,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk229_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_6516]),
    [final] ).

cnf(i_0_11789,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_6517]),
    [final] ).

cnf(i_0_11790,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_6518]),
    [final] ).

cnf(i_0_11791,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_6602]),
    [final] ).

cnf(i_0_11792,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | c_Map_Omap__upds(X1,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),X5),X2),hAPP(c_Option_Ooption_OSome(X4),X6)),X3,X7) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),c_Map_Omap__upds(X1,X4,X5,X3,X7)),X2),hAPP(c_Option_Ooption_OSome(X4),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_6603]),
    [final] ).

cnf(i_0_11793,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk230_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_6399]),
    [final] ).

cnf(i_0_11794,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk28_5(X2,X3,X4,X1,X5)),hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(c_Set_OCollect(X1),X2)))))
    | hBOOL(hAPP(X2,X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X5))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4)
    | X5 != c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6604]),
    [final] ).

cnf(i_0_11795,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk53_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_6398]),
    [final] ).

cnf(i_0_11796,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_6605]),
    [final] ).

cnf(i_0_11797,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk239_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_6606]),
    [final] ).

cnf(i_0_11798,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk231_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_6607]),
    [final] ).

cnf(i_0_11799,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk122_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_6608]),
    [final] ).

cnf(i_0_11800,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk121_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_6609]),
    [final] ).

cnf(i_0_11801,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_6610]),
    [final] ).

cnf(i_0_11802,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_6503]),
    [final] ).

cnf(i_0_11803,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk402_5(X3,X4,X5,X1,X2)),esk403_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_6343]),
    [final] ).

cnf(i_0_11804,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_6611]),
    [final] ).

cnf(i_0_11805,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_6612,c_0_6147]),
    [final] ).

cnf(i_0_11806,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_6613]),
    [final] ).

cnf(i_0_11807,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk481_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_6323]),
    [final] ).

cnf(i_0_11808,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk472_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_6324]),
    [final] ).

cnf(i_0_11809,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_6611]),
    [final] ).

cnf(i_0_11810,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk18_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_6614]),
    [final] ).

cnf(i_0_11811,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_6615,c_0_6311]),c_0_6311]),
    [final] ).

cnf(i_0_11812,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,esk50_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_6616]),
    [final] ).

cnf(i_0_11813,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_6617]),
    [final] ).

cnf(i_0_11814,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk46_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_6481]),
    [final] ).

cnf(i_0_11815,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_6618]),
    [final] ).

cnf(i_0_11816,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_6619]),
    [final] ).

cnf(i_0_11817,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk356_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_6480]),
    [final] ).

cnf(i_0_11818,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk50_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_6616]),
    [final] ).

cnf(i_0_11819,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk249_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_6325]),
    [final] ).

cnf(i_0_11820,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_6620,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11821,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk248_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_6621]),
    [final] ).

cnf(i_0_11822,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk247_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_6622]),
    [final] ).

cnf(i_0_11823,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk188_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_6623]),
    [final] ).

cnf(i_0_11824,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk187_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_6624]),
    [final] ).

cnf(i_0_11825,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)))
    | esk342_5(X1,X2,X3,X4,X5) != esk343_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_6290]),
    [final] ).

cnf(i_0_11826,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)))
    | esk341_5(X1,X2,X3,X4,X5) != esk340_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_6291]),
    [final] ).

cnf(i_0_11827,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk22_5(X2,X3,X4,X5,X1)),X5))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X3),X5)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6402]),
    [final] ).

cnf(i_0_11828,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_6625,c_0_6123]),
    [final] ).

cnf(i_0_11829,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_6626,c_0_6123]),
    [final] ).

cnf(i_0_11830,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk520_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_6524]),
    [final] ).

cnf(i_0_11831,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk44_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_6627]),
    [final] ).

cnf(i_0_11832,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk43_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_6490]),
    [final] ).

cnf(i_0_11833,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_6628]),
    [final] ).

cnf(i_0_11834,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk45_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_6481]),
    [final] ).

cnf(i_0_11835,plain,
    ( hBOOL(hAPP(hAPP(X1,esk44_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_6627]),
    [final] ).

cnf(i_0_11836,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk277_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_6484]),
    [final] ).

cnf(i_0_11837,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk358_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_6523]),
    [final] ).

cnf(i_0_11838,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_6629]),
    [final] ).

cnf(i_0_11839,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_6630]),
    [final] ).

cnf(i_0_11840,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_6631]),
    [final] ).

cnf(i_0_11841,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_6632]),
    [final] ).

cnf(i_0_11842,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk70_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_6371]),
    [final] ).

cnf(i_0_11843,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk62_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_6372]),
    [final] ).

cnf(i_0_11844,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_6633]),
    [final] ).

cnf(i_0_11845,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_6634]),
    [final] ).

cnf(i_0_11846,plain,
    ( c_Orderings_Oord__class_OLeast(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),hAPP(c_Set_Oimage(X1,X5,X4),X3))) = hAPP(X4,c_Orderings_Oord__class_OLeast(X1,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(X1),X2),esk17_5(X3,X4,X1,X5,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ c_Orderings_Oorder__class_Omono(X1,X5,X4)
    | ~ class_Orderings_Oorder(X5)
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6590]),
    [final] ).

cnf(i_0_11847,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk48_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_6404]),
    [final] ).

cnf(i_0_11848,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk353_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_6527]),
    [final] ).

cnf(i_0_11849,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(X3,esk49_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_6635]),
    [final] ).

cnf(i_0_11850,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,esk26_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_6588]),
    [final] ).

cnf(i_0_11851,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_6529]),
    [final] ).

cnf(i_0_11852,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_6529]),
    [final] ).

cnf(i_0_11853,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk360_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_6530]),
    [final] ).

cnf(i_0_11854,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk49_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_6635]),
    [final] ).

cnf(i_0_11855,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_6636]),
    [final] ).

cnf(i_0_11856,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_6637,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11857,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_6638,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11858,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_6639,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11859,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),esk93_4(X1,X3,X4,X2)),esk94_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_6640]),
    [final] ).

cnf(i_0_11860,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,esk443_4(X2,X1,X3,X4))),hAPP(X2,esk443_4(X2,X1,X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6641]),
    [final] ).

cnf(i_0_11861,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_6642]),
    [final] ).

cnf(i_0_11862,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_6643,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11863,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_6644,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11864,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_6645,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11865,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk453_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_6646]),
    [final] ).

cnf(i_0_11866,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_6647,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11867,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_6648,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11868,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk256_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_6649]),
    [final] ).

cnf(i_0_11869,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_6650]),
    [final] ).

cnf(i_0_11870,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_6651]),
    [final] ).

cnf(i_0_11871,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_6652]),
    [final] ).

cnf(i_0_11872,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk357_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_6533]),
    [final] ).

cnf(i_0_11873,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),c_Map_Orestrict__map(X1,X4,X5,X3)),X2),X6) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),c_Map_Orestrict__map(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)))))),X2),X6)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6653]),
    [final] ).

cnf(i_0_11874,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk244_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_6535]),
    [final] ).

cnf(i_0_11875,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_6654,c_0_6311]),
    [final] ).

cnf(i_0_11876,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk484_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_6534]),
    [final] ).

cnf(i_0_11877,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_6655]),
    [final] ).

cnf(i_0_11878,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_6656]),
    [final] ).

cnf(i_0_11879,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_6657]),
    [final] ).

cnf(i_0_11880,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_6550]),
    [final] ).

cnf(i_0_11881,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_6551]),
    [final] ).

cnf(i_0_11882,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_6658]),
    [final] ).

cnf(i_0_11883,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X1)),X2),X4))
    | ~ class_Orderings_Oord(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,esk3_4(X3,X4,X2,X1))),hAPP(X4,esk3_4(X3,X4,X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6659]),
    [final] ).

cnf(i_0_11884,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,esk2_4(X3,X2,X4,X1))),hAPP(X3,esk2_4(X3,X2,X4,X1))))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6660]),
    [final] ).

cnf(i_0_11885,plain,
    hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,X4)),X5),X6) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(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)))))),X5),X6),
    inference(split_conjunct,[status(thm)],[i_0_6661]),
    [final] ).

cnf(i_0_11886,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_6662]),
    [final] ).

cnf(i_0_11887,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk399_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_6663]),
    [final] ).

cnf(i_0_11888,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_6508]),
    [final] ).

cnf(i_0_11889,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_6664]),
    [final] ).

cnf(i_0_11890,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_6665]),
    [final] ).

cnf(i_0_11891,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk488_5(X1,X3,X4,X5,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X5),esk489_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_6197]),
    [final] ).

cnf(i_0_11892,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk485_5(X3,X4,X1,X5,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),esk486_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_6198]),
    [final] ).

cnf(i_0_11893,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_6666]),
    [final] ).

cnf(i_0_11894,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk427_5(X3,X4,X1,X5,X2)),X3)
    | hAPP(hAPP(c_List_Oappend(X2),esk426_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_6667]),
    [final] ).

cnf(i_0_11895,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_6668]),
    [final] ).

cnf(i_0_11896,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk101_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_6669]),
    [final] ).

cnf(i_0_11897,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_6670]),
    [final] ).

cnf(i_0_11898,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_6671]),
    [final] ).

cnf(i_0_11899,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_6672]),
    [final] ).

cnf(i_0_11900,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),esk473_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_6600]),
    [final] ).

cnf(i_0_11901,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),esk468_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_6601]),
    [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_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_6673]),
    [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_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_6674]),
    [final] ).

cnf(i_0_11904,plain,
    ( hBOOL(hAPP(hAPP(X3,hAPP(X4,X5)),hAPP(X4,X6)))
    | ~ c_Predicate_Oinv__imagep(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6675]),
    [final] ).

cnf(i_0_11905,plain,
    ( hBOOL(hAPP(hAPP(X3,hAPP(X4,X5)),hAPP(X4,X6)))
    | ~ c_Predicate_Oinv__imagep(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6676]),
    [final] ).

cnf(i_0_11906,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_6677]),
    [final] ).

cnf(i_0_11907,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_11908,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_11909,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_6678]),
    [final] ).

cnf(i_0_11910,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_6679]),
    [final] ).

cnf(i_0_11911,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_6655]),
    [final] ).

cnf(i_0_11912,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_6656]),
    [final] ).

cnf(i_0_11913,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_6680]),
    [final] ).

cnf(i_0_11914,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,esk246_3(X2,X3,X1))),hAPP(X3,esk246_3(X2,X3,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6681]),
    [final] ).

cnf(i_0_11915,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk37_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_6682]),
    [final] ).

cnf(i_0_11916,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk267_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_6683]),
    [final] ).

cnf(i_0_11917,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk265_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_6684]),
    [final] ).

cnf(i_0_11918,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_6685]),
    [final] ).

cnf(i_0_11919,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_6686]),
    [final] ).

cnf(i_0_11920,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_6687]),
    [final] ).

cnf(i_0_11921,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_6688]),
    [final] ).

cnf(i_0_11922,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_6689]),
    [final] ).

cnf(i_0_11923,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_6690]),
    [final] ).

cnf(i_0_11924,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_6691]),
    [final] ).

cnf(i_0_11925,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_6692]),
    [final] ).

cnf(i_0_11926,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_6693]),
    [final] ).

cnf(i_0_11927,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_6694]),
    [final] ).

cnf(i_0_11928,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_6695]),
    [final] ).

cnf(i_0_11929,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_6696]),
    [final] ).

cnf(i_0_11930,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_6697]),
    [final] ).

cnf(i_0_11931,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_6698]),
    [final] ).

cnf(i_0_11932,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_6699]),
    [final] ).

cnf(i_0_11933,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_6700]),
    [final] ).

cnf(i_0_11934,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_6701]),
    [final] ).

cnf(i_0_11935,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_6702]),
    [final] ).

cnf(i_0_11936,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_6703]),
    [final] ).

cnf(i_0_11937,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_6704]),
    [final] ).

cnf(i_0_11938,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_6705]),
    [final] ).

cnf(i_0_11939,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_6706]),
    [final] ).

cnf(i_0_11940,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_6707]),
    [final] ).

cnf(i_0_11941,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_6708]),
    [final] ).

cnf(i_0_11942,plain,
    ( hBOOL(hAPP(X1,X6))
    | ~ hBOOL(hAPP(X1,esk47_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_6481]),
    [final] ).

cnf(i_0_11943,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_6409]),
    [final] ).

cnf(i_0_11944,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_6709,c_0_6136]),c_0_6136]),c_0_6136]),
    [final] ).

cnf(i_0_11945,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_6710]),
    [final] ).

cnf(i_0_11946,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_6711]),
    [final] ).

cnf(i_0_11947,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_6712]),
    [final] ).

cnf(i_0_11948,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_6713]),
    [final] ).

cnf(i_0_11949,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_6714]),
    [final] ).

cnf(i_0_11950,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_6715,c_0_6136]),c_0_6136]),
    [final] ).

cnf(i_0_11951,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_6716,c_0_6136]),c_0_6136]),
    [final] ).

cnf(i_0_11952,plain,
    ( c_Map_Orestrict__map(X1,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),X5),X2),X6),X3) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),c_Map_Orestrict__map(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)))))),X2),X6)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6717]),
    [final] ).

cnf(i_0_11953,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_6718]),
    [final] ).

cnf(i_0_11954,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_6719]),
    [final] ).

cnf(i_0_11955,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_6438]),
    [final] ).

cnf(i_0_11956,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_6686]),
    [final] ).

cnf(i_0_11957,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_6687]),
    [final] ).

cnf(i_0_11958,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_6688]),
    [final] ).

cnf(i_0_11959,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),esk284_3(X2,X3,X1)),esk284_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_6720]),
    [final] ).

cnf(i_0_11960,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),esk281_3(X2,X3,X1)),esk281_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_6721]),
    [final] ).

cnf(i_0_11961,plain,
    ( hAPP(c_Map_Omap__of(X1,X3),hAPP(hAPP(c_List_Omap(X1,tc_prod(X1,X3)),hAPP(hAPP(c_COMBS(X1,X3,tc_prod(X1,X3)),c_Product__Type_OPair(X1,X3)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X3),X3,X1),c_Option_Othe(X3)),X4))),X2)) = X4
    | hAPP(c_List_Oset(X1),X2) != c_Map_Odom(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6722]),
    [final] ).

cnf(i_0_11962,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_6723]),
    [final] ).

cnf(i_0_11963,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_6724]),
    [final] ).

cnf(i_0_11964,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk348_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_6725,c_0_6136]),
    [final] ).

cnf(i_0_11965,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_6706]),
    [final] ).

cnf(i_0_11966,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_6707]),
    [final] ).

cnf(i_0_11967,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_6726]),
    [final] ).

cnf(i_0_11968,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk277_5(X4,X5,X1,X3,X2)),esk278_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_6484]),
    [final] ).

cnf(i_0_11969,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk347_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_6727,c_0_6136]),
    [final] ).

cnf(i_0_11970,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_6728]),
    [final] ).

cnf(i_0_11971,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_6729,c_0_6311]),c_0_6311]),
    [final] ).

cnf(i_0_11972,plain,
    ( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(hAPP(c_Set_Oinsert(X1),esk59_5(X4,X3,X2,X5,X1)),esk60_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_6438]),
    [final] ).

cnf(i_0_11973,plain,
    ( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(hAPP(c_Set_Oinsert(X1),esk57_5(X4,X3,X2,X5,X1)),esk58_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_6439]),
    [final] ).

cnf(i_0_11974,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,esk106_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_6549]),
    [final] ).

cnf(i_0_11975,plain,
    c_Map_Odom(X1,X2,X3) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),X3)),c_Option_Ooption_ONone(X2)))),
    inference(split_conjunct,[status(thm)],[i_0_6730]),
    [final] ).

cnf(i_0_11976,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_6701]),
    [final] ).

cnf(i_0_11977,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_6731,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11978,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_6732,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_11979,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_6699]),
    [final] ).

cnf(i_0_11980,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,esk453_5(X2,X1,X3,X4,X5)))
    | ~ class_Groups_Omonoid__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6646]),
    [final] ).

cnf(i_0_11981,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_6733]),
    [final] ).

cnf(i_0_11982,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_6734]),
    [final] ).

cnf(i_0_11983,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_6735]),
    [final] ).

cnf(i_0_11984,plain,
    ( hBOOL(hAPP(X1,X7))
    | ~ hBOOL(hAPP(X1,esk45_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_6481]),
    [final] ).

cnf(i_0_11985,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,esk28_5(X1,X2,X3,X4,X5)))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X2),X5))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X3)
    | X5 != c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X4,tc_HOL_Obool),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6604]),
    [final] ).

cnf(i_0_11986,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_6736]),
    [final] ).

cnf(i_0_11987,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_6737]),
    [final] ).

cnf(i_0_11988,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_6738]),
    [final] ).

cnf(i_0_11989,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_6739]),
    [final] ).

cnf(i_0_11990,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_6740]),
    [final] ).

cnf(i_0_11991,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_6739]),
    [final] ).

cnf(i_0_11992,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_6740]),
    [final] ).

cnf(i_0_11993,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,esk254_5(X2,X1,X3,X4,X5)) != hAPP(X2,esk254_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_6741]),
    [final] ).

cnf(i_0_11994,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,esk251_5(X2,X1,X3,X4,X5)) != hAPP(X2,esk251_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_6742]),
    [final] ).

cnf(i_0_11995,plain,
    ( hAPP(hAPP(c_List_Omap(X5,X4),X1),X3) = hAPP(hAPP(c_List_Omap(X5,X4),X2),X3)
    | hAPP(X1,esk399_5(X2,X3,X1,X4,X5)) != hAPP(X2,esk399_5(X2,X3,X1,X4,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6663]),
    [final] ).

cnf(i_0_11996,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_6743]),
    [final] ).

cnf(i_0_11997,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_6744]),
    [final] ).

cnf(i_0_11998,plain,
    ( hBOOL(hAPP(X1,esk26_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_6588]),
    [final] ).

cnf(i_0_11999,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_6745,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12000,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_6746,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12001,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_6747,c_0_6748]),c_0_6748]),c_0_6748]),
    [final] ).

cnf(i_0_12002,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_6749]),
    [final] ).

cnf(i_0_12003,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_6750]),
    [final] ).

cnf(i_0_12004,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_6751]),
    [final] ).

cnf(i_0_12005,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_6752]),
    [final] ).

cnf(i_0_12006,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_6753]),
    [final] ).

cnf(i_0_12007,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_6754]),
    [final] ).

cnf(i_0_12008,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_6755]),
    [final] ).

cnf(i_0_12009,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_6756]),
    [final] ).

cnf(i_0_12010,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_6757]),
    [final] ).

cnf(i_0_12011,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_6758]),
    [final] ).

cnf(i_0_12012,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_6759]),
    [final] ).

cnf(i_0_12013,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_6760]),
    [final] ).

cnf(i_0_12014,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_6699]),
    [final] ).

cnf(i_0_12015,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_6700]),
    [final] ).

cnf(i_0_12016,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_6701]),
    [final] ).

cnf(i_0_12017,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_6761]),
    [final] ).

cnf(i_0_12018,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),X2),esk427_5(X3,X4,X5,X2,X1)) = X4
    | hAPP(hAPP(c_List_Oappend(X1),esk426_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_6667]),
    [final] ).

cnf(i_0_12019,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk427_5(X3,X4,X1,X5,X2)),X3)
    | X5 = hAPP(hAPP(c_List_Oappend(X2),X4),esk426_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_6667]),
    [final] ).

cnf(i_0_12020,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_6762]),
    [final] ).

cnf(i_0_12021,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_6763]),
    [final] ).

cnf(i_0_12022,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_6764]),
    [final] ).

cnf(i_0_12023,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_6765]),
    [final] ).

cnf(i_0_12024,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_6766]),
    [final] ).

cnf(i_0_12025,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_6767,c_0_6768]),c_0_6768]),
    [final] ).

cnf(i_0_12026,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_6769]),
    [final] ).

cnf(i_0_12027,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X6),hAPP(c_List_Oset(X3),X4)))
    | hAPP(c_Map_Omap__of(X3,X1),hAPP(hAPP(c_List_Ozip(X3,X1),X4),X2)) = hAPP(c_Map_Omap__of(X3,X1),hAPP(hAPP(c_List_Ozip(X3,X1),X4),X5))
    | 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)),X4)
    | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X1)),hAPP(c_Map_Omap__of(X3,X1),hAPP(hAPP(c_List_Ozip(X3,X1),X4),X2))),X6),hAPP(c_Option_Ooption_OSome(X1),X7)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X1)),hAPP(c_Map_Omap__of(X3,X1),hAPP(hAPP(c_List_Ozip(X3,X1),X4),X5))),X6),hAPP(c_Option_Ooption_OSome(X1),X8)) ),
    inference(split_conjunct,[status(thm)],[i_0_6770]),
    [final] ).

cnf(i_0_12028,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_6771,c_0_6136]),c_0_6136]),
    [final] ).

cnf(i_0_12029,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_6772,c_0_6136]),c_0_6136]),
    [final] ).

cnf(i_0_12030,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_6611]),
    [final] ).

cnf(i_0_12031,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),c_Map_Omap__add(X2,X1,X3,hAPP(c_Map_Omap__of(X2,X1),X4))),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6773]),
    [final] ).

cnf(i_0_12032,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_6628]),
    [final] ).

cnf(i_0_12033,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_6774]),
    [final] ).

cnf(i_0_12034,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_6775]),
    [final] ).

cnf(i_0_12035,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_6776]),
    [final] ).

cnf(i_0_12036,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_6777,c_0_6136]),c_0_6136]),
    [final] ).

cnf(i_0_12037,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_6778,c_0_6136]),c_0_6136]),
    [final] ).

cnf(i_0_12038,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_6779]),
    [final] ).

cnf(i_0_12039,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_6780]),
    [final] ).

cnf(i_0_12040,plain,
    hAPP(c_Fun_Ocomp(tc_Option_Ooption(X1),tc_Option_Ooption(X2),tc_sum(X3,X4),hAPP(c_Option_Omap(X1,X2),X5)),c_Sum__Type_Osum_Osum__case(X3,tc_Option_Ooption(X1),X4,X6,X7)) = c_Sum__Type_Osum_Osum__case(X3,tc_Option_Ooption(X2),X4,hAPP(c_Fun_Ocomp(tc_Option_Ooption(X1),tc_Option_Ooption(X2),X3,hAPP(c_Option_Omap(X1,X2),X5)),X6),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X1),tc_Option_Ooption(X2),X4,hAPP(c_Option_Omap(X1,X2),X5)),X7)),
    inference(split_conjunct,[status(thm)],[i_0_6781]),
    [final] ).

cnf(i_0_12041,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_6782]),
    [final] ).

cnf(i_0_12042,plain,
    hAPP(c_Fun_Ocomp(tc_Option_Ooption(X1),tc_Option_Ooption(X2),X3,hAPP(c_Option_Omap(X1,X2),X4)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X1)),X5),X6),hAPP(c_Option_Ooption_OSome(X1),X7))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X2)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X1),tc_Option_Ooption(X2),X3,hAPP(c_Option_Omap(X1,X2),X4)),X5)),X6),hAPP(c_Option_Ooption_OSome(X2),hAPP(X4,X7))),
    inference(split_conjunct,[status(thm)],[i_0_6783]),
    [final] ).

cnf(i_0_12043,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_6780]),
    [final] ).

cnf(i_0_12044,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_6784]),
    [final] ).

cnf(i_0_12045,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_6785]),
    [final] ).

cnf(i_0_12046,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_6786]),
    [final] ).

cnf(i_0_12047,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_6787]),
    [final] ).

cnf(i_0_12048,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_6788]),
    [final] ).

cnf(i_0_12049,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,esk386_2(X2,X1)))
    | ~ hBOOL(hAPP(X2,esk386_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6789]),
    [final] ).

cnf(i_0_12050,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_6790,c_0_6147]),c_0_6147]),
    [final] ).

cnf(i_0_12051,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_6791]),
    [final] ).

cnf(i_0_12052,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_6792]),
    [final] ).

cnf(i_0_12053,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_6633]),
    [final] ).

cnf(i_0_12054,plain,
    ( hBOOL(hAPP(X1,esk386_2(X2,X1)))
    | hBOOL(hAPP(X2,esk386_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_6789]),
    [final] ).

cnf(i_0_12055,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk386_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_6789]),
    [final] ).

cnf(i_0_12056,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_6793]),
    [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)),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_6794]),
    [final] ).

cnf(i_0_12058,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_6794]),
    [final] ).

cnf(i_0_12059,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_6699]),
    [final] ).

cnf(i_0_12060,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_6700]),
    [final] ).

cnf(i_0_12061,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_6701]),
    [final] ).

cnf(i_0_12062,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_6795]),
    [final] ).

cnf(i_0_12063,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_6796]),
    [final] ).

cnf(i_0_12064,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk430_4(X3,X1,X4,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),esk429_4(X3,X1,X4,X2)),esk431_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_6540]),
    [final] ).

cnf(i_0_12065,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk430_4(X3,X4,X1,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),esk428_4(X3,X4,X1,X2)),esk431_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_6540]),
    [final] ).

cnf(i_0_12066,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_6797,c_0_6136]),
    [final] ).

cnf(i_0_12067,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_6798]),
    [final] ).

cnf(i_0_12068,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X2,tc_Option_Ooption(X1)),X3),X4),hAPP(c_Option_Ooption_OSome(X1),X5))),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6799]),
    [final] ).

cnf(i_0_12069,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_6701]),
    [final] ).

cnf(i_0_12070,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_6800]),
    [final] ).

cnf(i_0_12071,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_6801]),
    [final] ).

cnf(i_0_12072,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)),esk92_3(X1,X3,X2)),hAPP(hAPP(c_Set_Oinsert(X2),esk91_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_6802]),
    [final] ).

cnf(i_0_12073,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_6699]),
    [final] ).

cnf(i_0_12074,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_6341]),
    [final] ).

cnf(i_0_12075,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_6803]),
    [final] ).

cnf(i_0_12076,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk292_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),esk293_3(X2,X3,X1)),esk293_3(X2,X3,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6212]),
    [final] ).

cnf(i_0_12077,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_6804,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12078,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_6805]),
    [final] ).

cnf(i_0_12079,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_6806]),
    [final] ).

cnf(i_0_12080,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_6807]),
    [final] ).

cnf(i_0_12081,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_6440]),
    [final] ).

cnf(i_0_12082,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_6808]),
    [final] ).

cnf(i_0_12083,plain,
    ( c_Predicate_Oinv__imagep(X5,X6,X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X2,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6675]),
    [final] ).

cnf(i_0_12084,plain,
    ( c_Predicate_Oinv__imagep(X5,X6,X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X2,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6676]),
    [final] ).

cnf(i_0_12085,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_6809,c_0_6147]),c_0_6147]),c_0_6147]),
    [final] ).

cnf(i_0_12086,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_6810]),
    [final] ).

cnf(i_0_12087,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_6811]),
    [final] ).

cnf(i_0_12088,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_6812]),
    [final] ).

cnf(i_0_12089,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_6813]),
    [final] ).

cnf(i_0_12090,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_6814]),
    [final] ).

cnf(i_0_12091,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_6815]),
    [final] ).

cnf(i_0_12092,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_6816]),
    [final] ).

cnf(i_0_12093,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk437_3(X2,X3,X1)),esk437_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_6817]),
    [final] ).

cnf(i_0_12094,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_6818]),
    [final] ).

cnf(i_0_12095,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_6167]),
    [final] ).

cnf(i_0_12096,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_6819,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6242]),c_0_6242]),
    [final] ).

cnf(i_0_12097,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_6820]),
    [final] ).

cnf(i_0_12098,plain,
    ( hAPP(X1,esk143_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_6558]),
    [final] ).

cnf(i_0_12099,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_6821]),
    [final] ).

cnf(i_0_12100,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk418_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_6409]),
    [final] ).

cnf(i_0_12101,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_6822]),
    [final] ).

cnf(i_0_12102,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_6823]),
    [final] ).

cnf(i_0_12103,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk528_4(X2,X3,X1,X4)),esk527_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)),esk525_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_6824]),
    [final] ).

cnf(i_0_12104,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk528_4(X2,X3,X1,X4)),esk526_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)),esk525_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_6824]),
    [final] ).

cnf(i_0_12105,plain,
    ( hAPP(X1,esk71_5(X2,X1,X3,X4,X5)) = hAPP(c_Option_Ooption_OSome(X5),X4)
    | ~ hBOOL(hAPP(hAPP(c_member(X5),X4),c_Map_Oran(X3,X5,c_Map_Orestrict__map(X3,X5,X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6566]),
    [final] ).

cnf(i_0_12106,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_6825]),
    [final] ).

cnf(i_0_12107,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_6826]),
    [final] ).

cnf(i_0_12108,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_6827]),
    [final] ).

cnf(i_0_12109,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_6828]),
    [final] ).

cnf(i_0_12110,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_6829,c_0_6286]),
    [final] ).

cnf(i_0_12111,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_6830]),
    [final] ).

cnf(i_0_12112,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_6831,c_0_6114]),
    [final] ).

cnf(i_0_12113,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_6832]),
    [final] ).

cnf(i_0_12114,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_6833,c_0_6114]),
    [final] ).

cnf(i_0_12115,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_6834]),
    [final] ).

cnf(i_0_12116,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_6816]),
    [final] ).

cnf(i_0_12117,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_6835]),
    [final] ).

cnf(i_0_12118,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_6836]),
    [final] ).

cnf(i_0_12119,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_6837]),
    [final] ).

cnf(i_0_12120,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_6838]),
    [final] ).

cnf(i_0_12121,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_6839]),
    [final] ).

cnf(i_0_12122,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_6816]),
    [final] ).

cnf(i_0_12123,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_6840]),
    [final] ).

cnf(i_0_12124,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_6841]),
    [final] ).

cnf(i_0_12125,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_6842]),
    [final] ).

cnf(i_0_12126,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_6701]),
    [final] ).

cnf(i_0_12127,plain,
    ( c_Map_Orestrict__map(X1,X3,c_Map_Omap__upds(X1,X3,X6,X2,X4),X5) = c_Map_Omap__upds(X1,X3,c_Map_Orestrict__map(X1,X3,X6,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(c_List_Oset(X1),X2))),X2,X4)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6843]),
    [final] ).

cnf(i_0_12128,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),esk377_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_6844]),
    [final] ).

cnf(i_0_12129,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),esk381_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_6845]),
    [final] ).

cnf(i_0_12130,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk479_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X4),X1),c_Product__Type_Ofst(X1,X4)),X3))))
    | hAPP(c_Map_Omap__of(X1,X4),X3) = hAPP(c_Map_Omap__of(X1,X4),X2)
    | hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X4),X1),c_Product__Type_Ofst(X1,X4)),X3)) != hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X4),X1),c_Product__Type_Ofst(X1,X4)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6846]),
    [final] ).

cnf(i_0_12131,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk418_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_6409]),
    [final] ).

cnf(i_0_12132,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_6847,c_0_6128]),c_0_6136]),
    [final] ).

cnf(i_0_12133,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_6848]),
    [final] ).

cnf(i_0_12134,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_6699]),
    [final] ).

cnf(i_0_12135,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_6849]),
    [final] ).

cnf(i_0_12136,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_6700]),
    [final] ).

cnf(i_0_12137,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_6850,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12138,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_6851,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12139,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_6776]),
    [final] ).

cnf(i_0_12140,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_6852]),
    [final] ).

cnf(i_0_12141,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_6853]),
    [final] ).

cnf(i_0_12142,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_6854]),
    [final] ).

cnf(i_0_12143,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),esk329_3(X2,X3,X1)),esk328_3(X2,X3,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6855]),
    [final] ).

cnf(i_0_12144,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),esk328_3(X2,X3,X1)),esk329_3(X2,X3,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6855]),
    [final] ).

cnf(i_0_12145,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_6856]),
    [final] ).

cnf(i_0_12146,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | c_Smallcheck_Osmall_H(X3,X1,X2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X3,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X3,X2))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X3),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6857]),
    [final] ).

cnf(i_0_12147,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_6858]),
    [final] ).

cnf(i_0_12148,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_6859]),
    [final] ).

cnf(i_0_12149,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_6860]),
    [final] ).

cnf(i_0_12150,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_6861]),
    [final] ).

cnf(i_0_12151,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_6862]),
    [final] ).

cnf(i_0_12152,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_6863]),
    [final] ).

cnf(i_0_12153,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_6816]),
    [final] ).

cnf(i_0_12154,plain,
    c_Map_Odom(X1,X2,hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X3),tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBB(tc_fun(X3,X2),tc_fun(tc_Option_Ooption(X3),tc_Option_Ooption(X2)),X1),c_Option_Omap(X3,X2)),X4)),X5)) = c_Map_Odom(X1,X3,X5),
    inference(split_conjunct,[status(thm)],[i_0_6864]),
    [final] ).

cnf(i_0_12155,plain,
    ( hBOOL(hAPP(X2,X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk93_4(X2,X3,X4,X1)),esk94_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_6640]),
    [final] ).

cnf(i_0_12156,plain,
    ( c_List_OtakeWhile(X1,X3,X2) = hAPP(c_List_Ofilter(X1,X3),X2)
    | hBOOL(hAPP(hAPP(c_member(X1),esk464_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_6865,c_0_6311]),
    [final] ).

cnf(i_0_12157,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk318_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_6433]),
    [final] ).

cnf(i_0_12158,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk263_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_6506]),
    [final] ).

cnf(i_0_12159,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_6866,c_0_6136]),
    [final] ).

cnf(i_0_12160,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_6867,c_0_6136]),
    [final] ).

cnf(i_0_12161,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_6868]),
    [final] ).

cnf(i_0_12162,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_6848]),
    [final] ).

cnf(i_0_12163,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_6869]),
    [final] ).

cnf(i_0_12164,plain,
    ( c_Map_Omap__upds(X1,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),X6),X2),hAPP(c_Option_Ooption_OSome(X3),X7)),X5,X4) = c_Map_Omap__upds(X1,X3,X6,X5,X4)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)),X5)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6570]),
    [final] ).

cnf(i_0_12165,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),esk256_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_6649]),
    [final] ).

cnf(i_0_12166,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_6870,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12167,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_6871,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12168,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_6872,c_0_6136]),
    [final] ).

cnf(i_0_12169,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk528_4(X2,X3,X1,X4)),esk527_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),esk525_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_6824]),
    [final] ).

cnf(i_0_12170,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk528_4(X2,X3,X1,X4)),esk526_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),esk525_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_6824]),
    [final] ).

cnf(i_0_12171,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_6873]),
    [final] ).

cnf(i_0_12172,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_6874]),
    [final] ).

cnf(i_0_12173,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk269_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_6875]),
    [final] ).

cnf(i_0_12174,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk268_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_6876]),
    [final] ).

cnf(i_0_12175,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_6877]),
    [final] ).

cnf(i_0_12176,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_6878]),
    [final] ).

cnf(i_0_12177,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_6879]),
    [final] ).

cnf(i_0_12178,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_6880,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12179,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_6881]),
    [final] ).

cnf(i_0_12180,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_6882]),
    [final] ).

cnf(i_0_12181,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_6883]),
    [final] ).

cnf(i_0_12182,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk27_4(X2,X3,X4,X1)),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),X3)),hAPP(c_Set_OCollect(X1),X2)))))
    | hBOOL(hAPP(X2,X4))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6884]),
    [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)
    | 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_6885]),
    [final] ).

cnf(i_0_12184,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk14_4(X2,X3,X4,X1)),X3))
    | hBOOL(hAPP(hAPP(c_member(X1),esk13_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_6886]),
    [final] ).

cnf(i_0_12185,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_6887,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12186,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk12_4(X2,X3,X4,X1)),X3))
    | hBOOL(hAPP(hAPP(c_member(X1),esk11_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_6888]),
    [final] ).

cnf(i_0_12187,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_6889,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12188,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_6890,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12189,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_6891,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12190,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk527_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)),esk525_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_6824]),
    [final] ).

cnf(i_0_12191,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk526_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)),esk525_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_6824]),
    [final] ).

cnf(i_0_12192,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk339_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_6298]),
    [final] ).

cnf(i_0_12193,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk337_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_6348]),
    [final] ).

cnf(i_0_12194,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk339_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_6298]),
    [final] ).

cnf(i_0_12195,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk337_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_6348]),
    [final] ).

cnf(i_0_12196,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_6155]),
    [final] ).

cnf(i_0_12197,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_6892]),
    [final] ).

cnf(i_0_12198,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_6893]),
    [final] ).

cnf(i_0_12199,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_6894,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12200,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_6895,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12201,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_6433]),
    [final] ).

cnf(i_0_12202,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_6896,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12203,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_6897,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12204,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_6433]),
    [final] ).

cnf(i_0_12205,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_6433]),
    [final] ).

cnf(i_0_12206,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_6898,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12207,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_6899,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12208,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_6823]),
    [final] ).

cnf(i_0_12209,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_6900]),
    [final] ).

cnf(i_0_12210,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_6901,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12211,plain,
    ( hAPP(hAPP(c_List_Otake(X1),esk418_4(X2,X3,X4,X1)),X4) = hAPP(hAPP(c_List_Otake(X1),esk418_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_6409]),
    [final] ).

cnf(i_0_12212,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_6739]),
    [final] ).

cnf(i_0_12213,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_6740]),
    [final] ).

cnf(i_0_12214,plain,
    hAPP(c_Fun_Ocomp(X1,X2,X3,X4),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X1),X5),X6),X7)) = hAPP(hAPP(hAPP(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_6902]),
    [final] ).

cnf(i_0_12215,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_6874]),
    [final] ).

cnf(i_0_12216,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_6903,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12217,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_6904]),
    [final] ).

cnf(i_0_12218,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_6905]),
    [final] ).

cnf(i_0_12219,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk254_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_6741]),
    [final] ).

cnf(i_0_12220,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk251_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_6742]),
    [final] ).

cnf(i_0_12221,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_6906]),
    [final] ).

cnf(i_0_12222,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_6906]),
    [final] ).

cnf(i_0_12223,plain,
    c_List_Omap__filter(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(X2),X2,c_List_Omap__filter(X1,X2,X3,X5),hAPP(hAPP(c_COMBC(X2,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olist_OCons(X2)),c_List_Omap__filter(X1,X2,X3,X5))),hAPP(X3,X4)),
    inference(split_conjunct,[status(thm)],[i_0_6907]),
    [final] ).

cnf(i_0_12224,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),X2),esk427_5(X3,X4,X5,X2,X1)) = X4
    | X2 = hAPP(hAPP(c_List_Oappend(X1),X4),esk426_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_6667]),
    [final] ).

cnf(i_0_12225,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk424_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_6908]),
    [final] ).

cnf(i_0_12226,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),esk425_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_6909]),
    [final] ).

cnf(i_0_12227,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk401_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_6163]),
    [final] ).

cnf(i_0_12228,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_6910]),
    [final] ).

cnf(i_0_12229,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),esk171_2(X2,X1)),esk172_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk171_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk172_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6911]),
    [final] ).

cnf(i_0_12230,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),esk169_2(X2,X1)),esk170_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk169_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk170_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6912]),
    [final] ).

cnf(i_0_12231,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,esk275_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6913]),
    [final] ).

cnf(i_0_12232,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_6914]),
    [final] ).

cnf(i_0_12233,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_6915]),
    [final] ).

cnf(i_0_12234,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_6916]),
    [final] ).

cnf(i_0_12235,plain,
    hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Omap(X1,tc_prod(X1,X2)),hAPP(hAPP(c_COMBS(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2)),X3)),X4)) = c_Map_Orestrict__map(X1,X2,hAPP(c_Fun_Ocomp(X2,tc_Option_Ooption(X2),X1,c_Option_Ooption_OSome(X2)),X3),hAPP(c_List_Oset(X1),X4)),
    inference(split_conjunct,[status(thm)],[i_0_6917]),
    [final] ).

cnf(i_0_12236,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),esk425_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_6909]),
    [final] ).

cnf(i_0_12237,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk424_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_6908]),
    [final] ).

cnf(i_0_12238,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),esk102_2(X2,X1)),esk103_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk102_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk103_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6918]),
    [final] ).

cnf(i_0_12239,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_6919,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12240,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_6920]),
    [final] ).

cnf(i_0_12241,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_6769]),
    [final] ).

cnf(i_0_12242,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_6921]),
    [final] ).

cnf(i_0_12243,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_6922]),
    [final] ).

cnf(i_0_12244,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,esk239_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_6606]),
    [final] ).

cnf(i_0_12245,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,esk231_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_6607]),
    [final] ).

cnf(i_0_12246,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,esk122_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_6608]),
    [final] ).

cnf(i_0_12247,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,esk121_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_6609]),
    [final] ).

cnf(i_0_12248,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_6923]),
    [final] ).

cnf(i_0_12249,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_6924]),
    [final] ).

cnf(i_0_12250,plain,
    ( hAPP(hAPP(c_List_Otake(X1),esk418_4(X2,X3,X4,X1)),X4) = hAPP(hAPP(c_List_Otake(X1),esk418_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_6409]),
    [final] ).

cnf(i_0_12251,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_6925]),
    [final] ).

cnf(i_0_12252,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_6926]),
    [final] ).

cnf(i_0_12253,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_6927]),
    [final] ).

cnf(i_0_12254,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_6928]),
    [final] ).

cnf(i_0_12255,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_6929]),
    [final] ).

cnf(i_0_12256,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk420_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_6440]),
    [final] ).

cnf(i_0_12257,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk351_4(X1,X2,X3,X4)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk350_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_6199]),
    [final] ).

cnf(i_0_12258,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_6930]),
    [final] ).

cnf(i_0_12259,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_6931,c_0_6136]),c_0_6136]),
    [final] ).

cnf(i_0_12260,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_6932]),
    [final] ).

cnf(i_0_12261,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),esk11_4(X1,X2,X3,X4)),X3))
    | hBOOL(hAPP(X1,X5))
    | ~ hBOOL(hAPP(X1,esk12_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_6888]),
    [final] ).

cnf(i_0_12262,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk12_4(X2,X3,X4,X1)),X3))
    | hBOOL(hAPP(X2,X5))
    | ~ hBOOL(hAPP(X2,esk11_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_6888]),
    [final] ).

cnf(i_0_12263,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_6933]),
    [final] ).

cnf(i_0_12264,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_6934]),
    [final] ).

cnf(i_0_12265,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_6935]),
    [final] ).

cnf(i_0_12266,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_6936]),
    [final] ).

cnf(i_0_12267,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_6937]),
    [final] ).

cnf(i_0_12268,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_6937]),
    [final] ).

cnf(i_0_12269,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),esk164_2(X2,X1)),esk165_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk164_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk165_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6938]),
    [final] ).

cnf(i_0_12270,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),esk173_2(X2,X1)),esk174_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk173_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk174_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6939]),
    [final] ).

cnf(i_0_12271,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_6940]),
    [final] ).

cnf(i_0_12272,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),esk80_2(X2,X1)),esk81_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk80_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk81_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6941]),
    [final] ).

cnf(i_0_12273,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_6942]),
    [final] ).

cnf(i_0_12274,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_6943]),
    [final] ).

cnf(i_0_12275,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk381_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_6845]),
    [final] ).

cnf(i_0_12276,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk377_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_6844]),
    [final] ).

cnf(i_0_12277,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_6944]),
    [final] ).

cnf(i_0_12278,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_6945]),
    [final] ).

cnf(i_0_12279,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_6946]),
    [final] ).

cnf(i_0_12280,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk527_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),esk525_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_6824]),
    [final] ).

cnf(i_0_12281,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk526_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),esk525_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_6824]),
    [final] ).

cnf(i_0_12282,plain,
    ( hAPP(hAPP(c_Map_Omap__of(X1,X2),X5),X3) = hAPP(c_Option_Ooption_OSome(X2),esk442_5(X5,X4,X3,X2,X1))
    | ~ 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)),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6947]),
    [final] ).

cnf(i_0_12283,plain,
    ( c_Smallcheck_Osmall_H(X3,X1,X2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X3),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6857]),
    [final] ).

cnf(i_0_12284,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_6948,c_0_6136]),
    [final] ).

cnf(i_0_12285,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_6949]),
    [final] ).

cnf(i_0_12286,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_6950]),
    [final] ).

cnf(i_0_12287,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_6951]),
    [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)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6952]),
    [final] ).

cnf(i_0_12289,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,esk248_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_6621]),
    [final] ).

cnf(i_0_12290,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,esk247_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_6622]),
    [final] ).

cnf(i_0_12291,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,esk188_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_6623]),
    [final] ).

cnf(i_0_12292,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,esk187_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_6624]),
    [final] ).

cnf(i_0_12293,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_6953,c_0_6136]),
    [final] ).

cnf(i_0_12294,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_6954,c_0_6136]),
    [final] ).

cnf(i_0_12295,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_6955]),
    [final] ).

cnf(i_0_12296,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_6956]),
    [final] ).

cnf(i_0_12297,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_6601]),
    [final] ).

cnf(i_0_12298,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_6957]),
    [final] ).

cnf(i_0_12299,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_6957]),
    [final] ).

cnf(i_0_12300,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_6958]),
    [final] ).

cnf(i_0_12301,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_6959]),
    [final] ).

cnf(i_0_12302,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk451_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_6960,c_0_6177]),c_0_6177]),
    [final] ).

cnf(i_0_12303,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk450_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_6961,c_0_6177]),c_0_6177]),
    [final] ).

cnf(i_0_12304,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),esk466_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_6962]),
    [final] ).

cnf(i_0_12305,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(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_6963,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12306,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_6964,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12307,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_6965,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12308,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_6966,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12309,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_6967,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12310,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_6803]),
    [final] ).

cnf(i_0_12311,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_6968]),
    [final] ).

cnf(i_0_12312,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_6969]),
    [final] ).

cnf(i_0_12313,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_6970]),
    [final] ).

cnf(i_0_12314,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_6971]),
    [final] ).

cnf(i_0_12315,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_6972,c_0_6748]),
    [final] ).

cnf(i_0_12316,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_6973]),
    [final] ).

cnf(i_0_12317,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_6974]),
    [final] ).

cnf(i_0_12318,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_6975]),
    [final] ).

cnf(i_0_12319,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_6976]),
    [final] ).

cnf(i_0_12320,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_6977]),
    [final] ).

cnf(i_0_12321,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,esk301_3(X3,X2,X1)))),c_Predicate_ORangeP(X1,X1,hAPP(X2,esk302_3(X3,X2,X1)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ c_Wellfounded_OwfP(X1,hAPP(X2,esk300_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6978]),
    [final] ).

cnf(i_0_12322,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_6979]),
    [final] ).

cnf(i_0_12323,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_6980,c_0_6748]),c_0_6748]),
    [final] ).

cnf(i_0_12324,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_6381]),
    [final] ).

cnf(i_0_12325,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,esk453_5(X1,X2,X3,X4,X5)) != c_Groups_Ozero__class_Ozero(X5)
    | ~ class_Groups_Omonoid__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6646]),
    [final] ).

cnf(i_0_12326,plain,
    ( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk422_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk423_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk422_3(X1,X2,X3)),esk423_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_6981]),
    [final] ).

cnf(i_0_12327,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_6982]),
    [final] ).

cnf(i_0_12328,plain,
    c_Map_Omap__add(X1,X2,X3,c_Map_Omap__upds(X1,X2,X4,X5,X6)) = c_Map_Omap__upds(X1,X2,c_Map_Omap__add(X1,X2,X3,X4),X5,X6),
    inference(split_conjunct,[status(thm)],[i_0_6983]),
    [final] ).

cnf(i_0_12329,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_6984,c_0_6136]),
    [final] ).

cnf(i_0_12330,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_6985]),
    [final] ).

cnf(i_0_12331,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_6986]),
    [final] ).

cnf(i_0_12332,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_6976]),
    [final] ).

cnf(i_0_12333,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_6987,c_0_6311]),c_0_6311]),
    [final] ).

cnf(i_0_12334,plain,
    ( hBOOL(hAPP(X1,X5))
    | ~ hBOOL(hAPP(X1,esk12_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(X1,esk11_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_6888]),
    [final] ).

cnf(i_0_12335,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_6988]),
    [final] ).

cnf(i_0_12336,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),esk480_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),X4))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6989,c_0_6311]),c_0_6311]),
    [final] ).

cnf(i_0_12337,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_6827]),
    [final] ).

cnf(i_0_12338,plain,
    ( X1 = hAPP(hAPP(c_List_Olist__update(X2,X3),esk420_4(X4,X1,X3,X2)),esk419_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_6440]),
    [final] ).

cnf(i_0_12339,plain,
    ( hBOOL(hAPP(X1,esk14_4(X1,X2,X3,X4)))
    | hBOOL(hAPP(hAPP(c_member(X4),esk13_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_6886]),
    [final] ).

cnf(i_0_12340,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk14_4(X2,X3,X4,X1)),X3))
    | hBOOL(hAPP(X2,esk13_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_6886]),
    [final] ).

cnf(i_0_12341,plain,
    c_Map_Odom(X1,X2,c_Map_Omap__upds(X1,X2,X3,X4,X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)),X4))),c_Map_Odom(X1,X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_6990]),
    [final] ).

cnf(i_0_12342,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_6991,c_0_6748]),c_0_6748]),
    [final] ).

cnf(i_0_12343,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_6992]),
    [final] ).

cnf(i_0_12344,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_6993,c_0_6147]),
    [final] ).

cnf(i_0_12345,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk335_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_6994,c_0_6136]),
    [final] ).

cnf(i_0_12346,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)))
    | esk438_4(X1,X2,X3,X4) != esk439_4(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6453]),
    [final] ).

cnf(i_0_12347,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_6816]),
    [final] ).

cnf(i_0_12348,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_6995]),
    [final] ).

cnf(i_0_12349,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_6996]),
    [final] ).

cnf(i_0_12350,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_6997,c_0_6177]),c_0_6177]),c_0_6177]),
    [final] ).

cnf(i_0_12351,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,esk298_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6998]),
    [final] ).

cnf(i_0_12352,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,esk75_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6999]),
    [final] ).

cnf(i_0_12353,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_7000]),
    [final] ).

cnf(i_0_12354,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),hAPP(X5,X2)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X4,tc_HOL_Obool),X6)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X5),X3)),hAPP(X6,hAPP(c_Set_Oimage(X1,X4,X5),X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7001]),
    [final] ).

cnf(i_0_12355,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_6982]),
    [final] ).

cnf(i_0_12356,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_7002]),
    [final] ).

cnf(i_0_12357,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_7003]),
    [final] ).

cnf(i_0_12358,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_6848]),
    [final] ).

cnf(i_0_12359,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_7004]),
    [final] ).

cnf(i_0_12360,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_7005]),
    [final] ).

cnf(i_0_12361,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_6928]),
    [final] ).

cnf(i_0_12362,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_7006]),
    [final] ).

cnf(i_0_12363,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_7007]),
    [final] ).

cnf(i_0_12364,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_7008]),
    [final] ).

cnf(i_0_12365,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_7009]),
    [final] ).

cnf(i_0_12366,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk417_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_6341]),
    [final] ).

cnf(i_0_12367,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_7010]),
    [final] ).

cnf(i_0_12368,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_7011]),
    [final] ).

cnf(i_0_12369,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_7012]),
    [final] ).

cnf(i_0_12370,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_7013]),
    [final] ).

cnf(i_0_12371,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_7014]),
    [final] ).

cnf(i_0_12372,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,esk501_4(X2,X3,X4,X1))))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7015]),
    [final] ).

cnf(i_0_12373,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,esk510_4(X2,X3,X4,X1))))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7016]),
    [final] ).

cnf(i_0_12374,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk275_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_6913]),
    [final] ).

cnf(i_0_12375,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_7017]),
    [final] ).

cnf(i_0_12376,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_7018,c_0_6136]),
    [final] ).

cnf(i_0_12377,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_7019,c_0_6136]),
    [final] ).

cnf(i_0_12378,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_7020]),
    [final] ).

cnf(i_0_12379,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_7004]),
    [final] ).

cnf(i_0_12380,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_7021]),
    [final] ).

cnf(i_0_12381,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk351_4(X2,X3,X4,X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk350_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_6199]),
    [final] ).

cnf(i_0_12382,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk351_4(X1,X2,X3,X4)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk350_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_6199]),
    [final] ).

cnf(i_0_12383,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,esk276_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7022]),
    [final] ).

cnf(i_0_12384,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_7023]),
    [final] ).

cnf(i_0_12385,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_7024]),
    [final] ).

cnf(i_0_12386,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk192_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_7025]),
    [final] ).

cnf(i_0_12387,plain,
    ( hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),X4) = hAPP(c_Option_Ooption_OSome(X2),X5)
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7026]),
    [final] ).

cnf(i_0_12388,plain,
    ( hAPP(hAPP(c_Map_Omap__of(X1,X2),X5),X3) = hAPP(c_Option_Ooption_OSome(X2),X4)
    | ~ 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)),X5)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_7027]),
    [final] ).

cnf(i_0_12389,plain,
    ( hAPP(c_Option_Ooption_OSome(X2),X4) = hAPP(hAPP(c_Map_Omap__of(X1,X2),X5),X3)
    | ~ 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)),X5)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_7028]),
    [final] ).

cnf(i_0_12390,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),esk465_4(X1,X3,X2,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7029]),
    [final] ).

cnf(i_0_12391,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X2)))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X2))))) ),
    inference(split_conjunct,[status(thm)],[i_0_7030]),
    [final] ).

cnf(i_0_12392,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,esk257_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_6649]),
    [final] ).

cnf(i_0_12393,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_7031]),
    [final] ).

cnf(i_0_12394,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_7032]),
    [final] ).

cnf(i_0_12395,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),esk465_4(X4,X3,X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7029]),
    [final] ).

cnf(i_0_12396,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_7033,c_0_6136]),
    [final] ).

cnf(i_0_12397,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_6928]),
    [final] ).

cnf(i_0_12398,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)),esk525_4(X1,X2,X3,X4)),X2))
    | hAPP(X1,esk528_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_6824]),
    [final] ).

cnf(i_0_12399,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk474_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_7034]),
    [final] ).

cnf(i_0_12400,plain,
    ( X1 = X2
    | c_Sum__Type_Osum_Osum__case(X3,X4,X5,X1,X6) != c_Sum__Type_Osum_Osum__case(X3,X4,X5,X2,X7) ),
    inference(split_conjunct,[status(thm)],[i_0_7035]),
    [final] ).

cnf(i_0_12401,plain,
    ( X1 = X2
    | c_Sum__Type_Osum_Osum__case(X3,X4,X5,X6,X1) != c_Sum__Type_Osum_Osum__case(X3,X4,X5,X7,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7035]),
    [final] ).

cnf(i_0_12402,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk380_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_7036]),
    [final] ).

cnf(i_0_12403,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk378_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_7037]),
    [final] ).

cnf(i_0_12404,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_6874]),
    [final] ).

cnf(i_0_12405,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)),esk525_4(X1,X2,X3,X4)),X2))
    | esk526_4(X1,X2,X3,X4) != esk527_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_6824]),
    [final] ).

cnf(i_0_12406,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_7038]),
    [final] ).

cnf(i_0_12407,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_7039]),
    [final] ).

cnf(i_0_12408,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_7039]),
    [final] ).

cnf(i_0_12409,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_7040]),
    [final] ).

cnf(i_0_12410,plain,
    ( X1 = hAPP(c_Set_Oimage(X2,X3,X4),esk18_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_6614]),
    [final] ).

cnf(i_0_12411,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,esk480_4(X2,X1,X3,X4))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7041,c_0_6311]),c_0_6311]),
    [final] ).

cnf(i_0_12412,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(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(X3,X4)),hAPP(X3,X5))))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7042]),
    [final] ).

cnf(i_0_12413,plain,
    ( X1 = hAPP(X2,esk41_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_7043]),
    [final] ).

cnf(i_0_12414,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_7044]),
    [final] ).

cnf(i_0_12415,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_7045]),
    [final] ).

cnf(i_0_12416,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_7046,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12417,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_7047,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12418,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_7048]),
    [final] ).

cnf(i_0_12419,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_7049]),
    [final] ).

cnf(i_0_12420,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_7050]),
    [final] ).

cnf(i_0_12421,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk332_3(X3,X2,X1)),esk334_3(X3,X2,X1))),X3))
    | c_Relation_Osingle__valued(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7051]),
    [final] ).

cnf(i_0_12422,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk332_3(X3,X2,X1)),esk333_3(X3,X2,X1))),X3))
    | c_Relation_Osingle__valued(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7051]),
    [final] ).

cnf(i_0_12423,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(esk261_2(X2,X1),hAPP(c_Nat_OSuc,X3))),hAPP(esk261_2(X2,X1),X3))),X2))
    | c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6510]),
    [final] ).

cnf(i_0_12424,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_7052]),
    [final] ).

cnf(i_0_12425,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_7053]),
    [final] ).

cnf(i_0_12426,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_7054]),
    [final] ).

cnf(i_0_12427,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_7055]),
    [final] ).

cnf(i_0_12428,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk190_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_7056]),
    [final] ).

cnf(i_0_12429,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_7057]),
    [final] ).

cnf(i_0_12430,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_7058]),
    [final] ).

cnf(i_0_12431,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_7059]),
    [final] ).

cnf(i_0_12432,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),esk250_3(X2,X3,X1)),X3)),X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7060]),
    [final] ).

cnf(i_0_12433,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_7061]),
    [final] ).

cnf(i_0_12434,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_7062]),
    [final] ).

cnf(i_0_12435,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_7063]),
    [final] ).

cnf(i_0_12436,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk193_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_7025]),
    [final] ).

cnf(i_0_12437,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_7064]),
    [final] ).

cnf(i_0_12438,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_7065]),
    [final] ).

cnf(i_0_12439,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_6169]),
    [final] ).

cnf(i_0_12440,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_7066]),
    [final] ).

cnf(i_0_12441,plain,
    ( hAPP(c_Map_Omap__of(X1,X2),X3) = hAPP(c_Map_Omap__of(X1,X2),X4)
    | hAPP(c_List_Oset(tc_prod(X1,X2)),X3) != hAPP(c_List_Oset(tc_prod(X1,X2)),X4)
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X4)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7067]),
    [final] ).

cnf(i_0_12442,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_7068]),
    [final] ).

cnf(i_0_12443,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_7049]),
    [final] ).

cnf(i_0_12444,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_7050]),
    [final] ).

cnf(i_0_12445,plain,
    ( hAPP(c_Map_Omap__of(X1,X2),X3) = hAPP(c_Map_Omap__of(X1,X2),X4)
    | hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),esk479_4(X4,X3,X2,X1)) != hAPP(hAPP(c_Map_Omap__of(X1,X2),X4),esk479_4(X4,X3,X2,X1))
    | hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)) != hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6846]),
    [final] ).

cnf(i_0_12446,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_7069]),
    [final] ).

cnf(i_0_12447,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_6885]),
    [final] ).

cnf(i_0_12448,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_6885]),
    [final] ).

cnf(i_0_12449,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_7070]),
    [final] ).

cnf(i_0_12450,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_7071]),
    [final] ).

cnf(i_0_12451,plain,
    ( X1 = X2
    | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),X5),X1),X6)),X2),X7) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),X5),X2),X7)),X1),X6) ),
    inference(split_conjunct,[status(thm)],[i_0_7072]),
    [final] ).

cnf(i_0_12452,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_7073]),
    [final] ).

cnf(i_0_12453,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_7074]),
    [final] ).

cnf(i_0_12454,plain,
    ( hAPP(c_List_Oset(tc_prod(X1,X2)),X3) = hAPP(c_List_Oset(tc_prod(X1,X2)),X4)
    | hAPP(c_Map_Omap__of(X1,X2),X3) != hAPP(c_Map_Omap__of(X1,X2),X4)
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X4)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7067]),
    [final] ).

cnf(i_0_12455,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_7075]),
    [final] ).

cnf(i_0_12456,plain,
    ( hAPP(c_Set_Oimage(X2,X1,esk36_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_6682]),
    [final] ).

cnf(i_0_12457,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_7076]),
    [final] ).

cnf(i_0_12458,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_7077]),
    [final] ).

cnf(i_0_12459,plain,
    ( c_Map_Omap__upds(X1,X4,X6,X2,hAPP(hAPP(c_List_Olist__update(X4,X5),X3),X7)) = c_Map_Omap__upds(X1,X4,X6,X2,X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_7078]),
    [final] ).

cnf(i_0_12460,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_7079]),
    [final] ).

cnf(i_0_12461,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_6924]),
    [final] ).

cnf(i_0_12462,plain,
    ( X3 = X4
    | ~ class_Enum_Oenum(X1)
    | ~ class_Enum_Oenum(X2)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1))
    | hAPP(c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2)),hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1)),X3))) != hAPP(c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2)),hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1)),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7080]),
    [final] ).

cnf(i_0_12463,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk475_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),esk476_2(X2,X1))),hAPP(c_List_Oset(X1),esk477_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_7081,c_0_6177]),
    [final] ).

cnf(i_0_12464,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_6873]),
    [final] ).

cnf(i_0_12465,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_7082]),
    [final] ).

cnf(i_0_12466,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_7083]),
    [final] ).

cnf(i_0_12467,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_7084]),
    [final] ).

cnf(i_0_12468,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_7085]),
    [final] ).

cnf(i_0_12469,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_7086]),
    [final] ).

cnf(i_0_12470,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_7084]),
    [final] ).

cnf(i_0_12471,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),esk378_4(X3,X2,X4,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7037]),
    [final] ).

cnf(i_0_12472,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),esk380_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_7036]),
    [final] ).

cnf(i_0_12473,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_7087,c_0_6768]),
    [final] ).

cnf(i_0_12474,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk191_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_7056]),
    [final] ).

cnf(i_0_12475,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_7088,c_0_6136]),
    [final] ).

cnf(i_0_12476,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_7089]),
    [final] ).

cnf(i_0_12477,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_7090]),
    [final] ).

cnf(i_0_12478,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_7090]),
    [final] ).

cnf(i_0_12479,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_7091]),
    [final] ).

cnf(i_0_12480,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_7092]),
    [final] ).

cnf(i_0_12481,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_7093]),
    [final] ).

cnf(i_0_12482,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(X3,X4)),hAPP(X3,X5))),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5))))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7094]),
    [final] ).

cnf(i_0_12483,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_7052]),
    [final] ).

cnf(i_0_12484,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_7053]),
    [final] ).

cnf(i_0_12485,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_7095]),
    [final] ).

cnf(i_0_12486,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_7096,c_0_6748]),c_0_6748]),
    [final] ).

cnf(i_0_12487,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_7097]),
    [final] ).

cnf(i_0_12488,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))
    | c_Map_Omap__add(X1,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),X5),X2),hAPP(c_Option_Ooption_OSome(X3),X6)),X4) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),c_Map_Omap__add(X1,X3,X5,X4)),X2),hAPP(c_Option_Ooption_OSome(X3),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_7098]),
    [final] ).

cnf(i_0_12489,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_7099]),
    [final] ).

cnf(i_0_12490,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_7100]),
    [final] ).

cnf(i_0_12491,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_7101]),
    [final] ).

cnf(i_0_12492,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_7102]),
    [final] ).

cnf(i_0_12493,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_7103,c_0_6136]),c_0_6136]),
    [final] ).

cnf(i_0_12494,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_7104]),
    [final] ).

cnf(i_0_12495,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_7051]),
    [final] ).

cnf(i_0_12496,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_7105]),
    [final] ).

cnf(i_0_12497,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_7106]),
    [final] ).

cnf(i_0_12498,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk382_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_7107]),
    [final] ).

cnf(i_0_12499,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_7108,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12500,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_7109,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12501,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_7110,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12502,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_7111,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12503,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),c_Map_Orestrict__map(X1,X4,X5,X3)),X2),c_Option_Ooption_ONone(X4)) = c_Map_Orestrict__map(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_7112]),
    [final] ).

cnf(i_0_12504,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk284_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_6720]),
    [final] ).

cnf(i_0_12505,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk281_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_6721]),
    [final] ).

cnf(i_0_12506,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_7086]),
    [final] ).

cnf(i_0_12507,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_7113,c_0_7114]),
    [final] ).

cnf(i_0_12508,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_7115,c_0_6147]),c_0_6147]),
    [final] ).

cnf(i_0_12509,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_6398]),
    [final] ).

cnf(i_0_12510,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_7116]),
    [final] ).

cnf(i_0_12511,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_7117]),
    [final] ).

cnf(i_0_12512,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_12513,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_7118]),
    [final] ).

cnf(i_0_12514,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_7119]),
    [final] ).

cnf(i_0_12515,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_7120]),
    [final] ).

cnf(i_0_12516,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_7121]),
    [final] ).

cnf(i_0_12517,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_7122]),
    [final] ).

cnf(i_0_12518,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_7123]),
    [final] ).

cnf(i_0_12519,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_7124]),
    [final] ).

cnf(i_0_12520,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_7125]),
    [final] ).

cnf(i_0_12521,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_7126]),
    [final] ).

cnf(i_0_12522,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_7127,c_0_6136]),
    [final] ).

cnf(i_0_12523,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_7128]),
    [final] ).

cnf(i_0_12524,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_7129,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6242]),c_0_6242]),
    [final] ).

cnf(i_0_12525,plain,
    ( hAPP(hAPP(c_Map_Omap__of(X1,X4),hAPP(hAPP(c_List_Ozip(X1,X4),X3),X5)),X2) = hAPP(c_Option_Ooption_OSome(X4),esk405_5(X2,X5,X4,X3,X1))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7130]),
    [final] ).

cnf(i_0_12526,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_7131]),
    [final] ).

cnf(i_0_12527,plain,
    ( hAPP(X1,esk351_4(X2,X1,X3,X4)) = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk350_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_6199]),
    [final] ).

cnf(i_0_12528,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_7132]),
    [final] ).

cnf(i_0_12529,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(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_7133,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12530,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_7123]),
    [final] ).

cnf(i_0_12531,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_7089]),
    [final] ).

cnf(i_0_12532,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2)),X3))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ c_Orderings_Oorder__class_Omono(X1,X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2)),X3))),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7134]),
    [final] ).

cnf(i_0_12533,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_7135]),
    [final] ).

cnf(i_0_12534,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_6934]),
    [final] ).

cnf(i_0_12535,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),esk476_2(X2,X1))),hAPP(c_List_Oset(X1),esk477_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),esk475_2(X2,X1))) ),
    inference(rw,[status(thm)],[i_0_7136,c_0_6177]),
    [final] ).

cnf(i_0_12536,plain,
    ( hBOOL(hAPP(hAPP(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk136_3(X1,X2,X3))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk137_3(X1,X2,X3))))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk137_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_7137]),
    [final] ).

cnf(i_0_12537,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk206_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_7138]),
    [final] ).

cnf(i_0_12538,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_7139]),
    [final] ).

cnf(i_0_12539,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_7140]),
    [final] ).

cnf(i_0_12540,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_7140]),
    [final] ).

cnf(i_0_12541,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)))))
    | esk41_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_7043]),
    [final] ).

cnf(i_0_12542,plain,
    c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5),hAPP(hAPP(c_List_Olist_OCons(X2),X6),X7)) = c_Map_Omap__upds(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X6)),X5,X7),
    inference(split_conjunct,[status(thm)],[i_0_7141]),
    [final] ).

cnf(i_0_12543,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_7135]),
    [final] ).

cnf(i_0_12544,plain,
    ( X2 = hAPP(hAPP(c_List_Olist_OCons(X1),esk434_3(X3,X2,X1)),esk435_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_7142]),
    [final] ).

cnf(i_0_12545,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_7143]),
    [final] ).

cnf(i_0_12546,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_7144]),
    [final] ).

cnf(i_0_12547,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_7145]),
    [final] ).

cnf(i_0_12548,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_7146]),
    [final] ).

cnf(i_0_12549,plain,
    ( hBOOL(hAPP(X1,esk14_4(X1,X2,X3,X4)))
    | hBOOL(hAPP(X1,esk13_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_6886]),
    [final] ).

cnf(i_0_12550,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,esk528_4(X1,X2,X3,X4)) != c_Groups_Ozero__class_Ozero(X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),esk525_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_6824]),
    [final] ).

cnf(i_0_12551,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_7147]),
    [final] ).

cnf(i_0_12552,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk475_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk477_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_7148,c_0_6177]),
    [final] ).

cnf(i_0_12553,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk475_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk476_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_7149,c_0_6177]),
    [final] ).

cnf(i_0_12554,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_7150]),
    [final] ).

cnf(i_0_12555,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)))
    | hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),X4) != hAPP(c_Option_Ooption_OSome(X2),X5)
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7027]),
    [final] ).

cnf(i_0_12556,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),X5),X2)),hAPP(c_List_Oset(tc_prod(X3,X1)),X4)))
    | hAPP(c_Option_Ooption_OSome(X1),X2) != hAPP(hAPP(c_Map_Omap__of(X3,X1),X4),X5)
    | ~ hBOOL(hAPP(c_List_Odistinct(X3),hAPP(hAPP(c_List_Omap(tc_prod(X3,X1),X3),c_Product__Type_Ofst(X3,X1)),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7028]),
    [final] ).

cnf(i_0_12557,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)
    | esk526_4(X1,X2,X3,X4) != esk527_4(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),esk525_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_6824]),
    [final] ).

cnf(i_0_12558,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk515_3(X1,X2,X3)),esk516_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(X1,esk515_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk516_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_7151]),
    [final] ).

cnf(i_0_12559,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_7152]),
    [final] ).

cnf(i_0_12560,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_7153]),
    [final] ).

cnf(i_0_12561,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_7154,c_0_6136]),
    [final] ).

cnf(i_0_12562,plain,
    ( X1 = hAPP(c_Relation_OImage(X2,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),esk42_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_7155]),
    [final] ).

cnf(i_0_12563,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_7156,c_0_7157]),c_0_7157]),
    [final] ).

cnf(i_0_12564,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_7158,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12565,plain,
    c_Map_Omap__add(X1,X2,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X4),X5),hAPP(c_Option_Ooption_OSome(X2),X6))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Omap__add(X1,X2,X3,X4)),X5),hAPP(c_Option_Ooption_OSome(X2),X6)),
    inference(split_conjunct,[status(thm)],[i_0_7159]),
    [final] ).

cnf(i_0_12566,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_7160]),
    [final] ).

cnf(i_0_12567,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_7125]),
    [final] ).

cnf(i_0_12568,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_7126]),
    [final] ).

cnf(i_0_12569,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk466_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_6962]),
    [final] ).

cnf(i_0_12570,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk225_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_7161]),
    [final] ).

cnf(i_0_12571,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk216_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_7162]),
    [final] ).

cnf(i_0_12572,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk193_4(X2,X3,X4,X1)),esk192_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_7025]),
    [final] ).

cnf(i_0_12573,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_7163]),
    [final] ).

cnf(i_0_12574,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_7164]),
    [final] ).

cnf(i_0_12575,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_7165]),
    [final] ).

cnf(i_0_12576,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_7166]),
    [final] ).

cnf(i_0_12577,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(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_7167,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12578,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_7168,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12579,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_7169,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12580,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_7170,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12581,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_7171,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12582,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_7172,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12583,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_7173]),
    [final] ).

cnf(i_0_12584,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_7132]),
    [final] ).

cnf(i_0_12585,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_7174]),
    [final] ).

cnf(i_0_12586,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk208_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_7175]),
    [final] ).

cnf(i_0_12587,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_7176]),
    [final] ).

cnf(i_0_12588,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_7059]),
    [final] ).

cnf(i_0_12589,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_7177]),
    [final] ).

cnf(i_0_12590,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_7178]),
    [final] ).

cnf(i_0_12591,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk385_3(X2,X1,X3)),X3)),X2))
    | c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),esk383_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7107]),
    [final] ).

cnf(i_0_12592,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_6937]),
    [final] ).

cnf(i_0_12593,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),esk167_1(X1)),esk168_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_7179]),
    [final] ).

cnf(i_0_12594,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk21_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_7180]),
    [final] ).

cnf(i_0_12595,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk16_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_7181]),
    [final] ).

cnf(i_0_12596,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk207_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_7138]),
    [final] ).

cnf(i_0_12597,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_7182]),
    [final] ).

cnf(i_0_12598,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_7183]),
    [final] ).

cnf(i_0_12599,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_7184]),
    [final] ).

cnf(i_0_12600,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_7185,c_0_6177]),
    [final] ).

cnf(i_0_12601,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_7186]),
    [final] ).

cnf(i_0_12602,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(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_7187,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12603,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_7188,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12604,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_7189,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12605,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_7190]),
    [final] ).

cnf(i_0_12606,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_7191]),
    [final] ).

cnf(i_0_12607,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk291_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_6234]),
    [final] ).

cnf(i_0_12608,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),esk175_3(X3,X2,X1)),esk176_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk175_3(X3,X2,X1))),hAPP(X2,esk176_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7192]),
    [final] ).

cnf(i_0_12609,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),esk177_3(X3,X2,X1)),esk178_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk177_3(X3,X2,X1))),hAPP(X2,esk178_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7193]),
    [final] ).

cnf(i_0_12610,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_6986]),
    [final] ).

cnf(i_0_12611,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_7194]),
    [final] ).

cnf(i_0_12612,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_7195]),
    [final] ).

cnf(i_0_12613,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_6324]),
    [final] ).

cnf(i_0_12614,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_7196]),
    [final] ).

cnf(i_0_12615,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(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_HOL_Oequal__class_Oequal(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_7197,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12616,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_7198,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12617,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_7199,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12618,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_7200,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12619,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_7201,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12620,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_7202]),
    [final] ).

cnf(i_0_12621,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_7203]),
    [final] ).

cnf(i_0_12622,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_7182]),
    [final] ).

cnf(i_0_12623,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_7204]),
    [final] ).

cnf(i_0_12624,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_7205]),
    [final] ).

cnf(i_0_12625,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk298_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_6998]),
    [final] ).

cnf(i_0_12626,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk75_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_6999]),
    [final] ).

cnf(i_0_12627,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_7206]),
    [final] ).

cnf(i_0_12628,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_7207]),
    [final] ).

cnf(i_0_12629,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_7208]),
    [final] ).

cnf(i_0_12630,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_7207]),
    [final] ).

cnf(i_0_12631,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_7209]),
    [final] ).

cnf(i_0_12632,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_7210]),
    [final] ).

cnf(i_0_12633,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_7211]),
    [final] ).

cnf(i_0_12634,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),esk104_3(X3,X2,X1)),esk105_3(X3,X2,X1))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X2,esk104_3(X3,X2,X1))),hAPP(X2,esk105_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7212]),
    [final] ).

cnf(i_0_12635,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_7213]),
    [final] ).

cnf(i_0_12636,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_7214]),
    [final] ).

cnf(i_0_12637,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk314_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_7215]),
    [final] ).

cnf(i_0_12638,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk313_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_7216]),
    [final] ).

cnf(i_0_12639,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk255_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_7217]),
    [final] ).

cnf(i_0_12640,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_7218]),
    [final] ).

cnf(i_0_12641,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk477_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),esk475_2(X2,X1))) ),
    inference(rw,[status(thm)],[i_0_7219,c_0_6177]),
    [final] ).

cnf(i_0_12642,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk476_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),esk475_2(X2,X1))) ),
    inference(rw,[status(thm)],[i_0_7220,c_0_6177]),
    [final] ).

cnf(i_0_12643,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_7221]),
    [final] ).

cnf(i_0_12644,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk443_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_6641]),
    [final] ).

cnf(i_0_12645,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_7222]),
    [final] ).

cnf(i_0_12646,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk223_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_7223]),
    [final] ).

cnf(i_0_12647,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk214_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_7224]),
    [final] ).

cnf(i_0_12648,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk191_4(X2,X3,X4,X1)),esk190_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_7056]),
    [final] ).

cnf(i_0_12649,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_7225]),
    [final] ).

cnf(i_0_12650,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk15_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_6886]),
    [final] ).

cnf(i_0_12651,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk15_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_6886]),
    [final] ).

cnf(i_0_12652,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk444_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_7226]),
    [final] ).

cnf(i_0_12653,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_7227]),
    [final] ).

cnf(i_0_12654,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_12655,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_12656,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_7228]),
    [final] ).

cnf(i_0_12657,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_7229]),
    [final] ).

cnf(i_0_12658,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk42_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_7155]),
    [final] ).

cnf(i_0_12659,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_7230]),
    [final] ).

cnf(i_0_12660,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk351_4(X2,X3,X4,X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk350_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_6199]),
    [final] ).

cnf(i_0_12661,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_7231]),
    [final] ).

cnf(i_0_12662,plain,
    ( hBOOL(hAPP(X4,X2))
    | hBOOL(hAPP(hAPP(c_member(X1),esk10_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_6888]),
    [final] ).

cnf(i_0_12663,plain,
    ( hBOOL(hAPP(X4,X2))
    | hBOOL(hAPP(hAPP(c_member(X1),esk10_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_6888]),
    [final] ).

cnf(i_0_12664,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_7232]),
    [final] ).

cnf(i_0_12665,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_7233]),
    [final] ).

cnf(i_0_12666,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_7234]),
    [final] ).

cnf(i_0_12667,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_7235]),
    [final] ).

cnf(i_0_12668,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk93_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_6640]),
    [final] ).

cnf(i_0_12669,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk226_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_7161]),
    [final] ).

cnf(i_0_12670,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk217_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_7162]),
    [final] ).

cnf(i_0_12671,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_7236]),
    [final] ).

cnf(i_0_12672,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_7236]),
    [final] ).

cnf(i_0_12673,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_7049]),
    [final] ).

cnf(i_0_12674,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_7050]),
    [final] ).

cnf(i_0_12675,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_7237]),
    [final] ).

cnf(i_0_12676,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_7205]),
    [final] ).

cnf(i_0_12677,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),X1))
    | X1 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X2,tc_HOL_Obool),X3)
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X5),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X5),X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7238]),
    [final] ).

cnf(i_0_12678,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_7239]),
    [final] ).

cnf(i_0_12679,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_6669]),
    [final] ).

cnf(i_0_12680,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_7240,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12681,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk209_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_7175]),
    [final] ).

cnf(i_0_12682,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_7241]),
    [final] ).

cnf(i_0_12683,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_7242]),
    [final] ).

cnf(i_0_12684,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),esk181_3(X3,X2,X1)),esk182_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk181_3(X3,X2,X1))),hAPP(X2,esk182_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7243]),
    [final] ).

cnf(i_0_12685,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),esk179_3(X3,X2,X1)),esk180_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk179_3(X3,X2,X1))),hAPP(X2,esk180_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7244]),
    [final] ).

cnf(i_0_12686,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),esk89_3(X3,X2,X1)),esk90_3(X3,X2,X1))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X2,esk89_3(X3,X2,X1))),hAPP(X2,esk90_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7245]),
    [final] ).

cnf(i_0_12687,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),esk87_3(X3,X2,X1)),esk88_3(X3,X2,X1))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X2,esk87_3(X3,X2,X1))),hAPP(X2,esk88_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7246]),
    [final] ).

cnf(i_0_12688,plain,
    ( hBOOL(hAPP(X3,esk222_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,esk219_2(X3,X2)))
    | ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk219_2(X3,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk220_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_7247]),
    [final] ).

cnf(i_0_12689,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_7248]),
    [final] ).

cnf(i_0_12690,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),esk475_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)))
    | esk477_2(X1,X2) != esk476_2(X1,X2)
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1)) ),
    inference(rw,[status(thm)],[i_0_7249,c_0_6177]),
    [final] ).

cnf(i_0_12691,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_7250]),
    [final] ).

cnf(i_0_12692,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_7052]),
    [final] ).

cnf(i_0_12693,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_7053]),
    [final] ).

cnf(i_0_12694,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk330_2(X2,X1)),esk330_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_7251,c_0_6136]),
    [final] ).

cnf(i_0_12695,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk326_2(X2,X1)),esk326_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_7252,c_0_6136]),
    [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)),c_List_Olist_ONil(X1)),X2)),c_List_Olistrel1(X1,X3))),
    inference(split_conjunct,[status(thm)],[i_0_7253]),
    [final] ).

cnf(i_0_12697,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_7254]),
    [final] ).

cnf(i_0_12698,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_7153]),
    [final] ).

cnf(i_0_12699,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_7255]),
    [final] ).

cnf(i_0_12700,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_7256]),
    [final] ).

cnf(i_0_12701,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_7257]),
    [final] ).

cnf(i_0_12702,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_7258]),
    [final] ).

cnf(i_0_12703,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_7259]),
    [final] ).

cnf(i_0_12704,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_7260]),
    [final] ).

cnf(i_0_12705,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__flat(X3,c_Lazy__Sequence_Ohb__map(X2,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X3)),hAPP(hAPP(c_COMBC(X2,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X3))),X5),X1),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))))) ),
    inference(rw,[status(thm)],[i_0_7261,c_0_7262]),
    [final] ).

cnf(i_0_12706,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_7263]),
    [final] ).

cnf(i_0_12707,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_7264]),
    [final] ).

cnf(i_0_12708,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_7125]),
    [final] ).

cnf(i_0_12709,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_7125]),
    [final] ).

cnf(i_0_12710,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_7126]),
    [final] ).

cnf(i_0_12711,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_7126]),
    [final] ).

cnf(i_0_12712,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_7265]),
    [final] ).

cnf(i_0_12713,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_7266]),
    [final] ).

cnf(i_0_12714,plain,
    ( hAPP(c_Set_Oimage(X1,X4,hAPP(hAPP(hAPP(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_7267]),
    [final] ).

cnf(i_0_12715,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_7268]),
    [final] ).

cnf(i_0_12716,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_7269]),
    [final] ).

cnf(i_0_12717,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_7270]),
    [final] ).

cnf(i_0_12718,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_7271]),
    [final] ).

cnf(i_0_12719,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk315_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_7272]),
    [final] ).

cnf(i_0_12720,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk491_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_7273]),
    [final] ).

cnf(i_0_12721,plain,
    hAPP(c_Sum__Type_Osum_Osum__case(X1,X2,X3,hAPP(c_COMBK(X2,X1),X4),hAPP(c_COMBK(X2,X3),X4)),X5) = X4,
    inference(split_conjunct,[status(thm)],[i_0_7274]),
    [final] ).

cnf(i_0_12722,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_7275]),
    [final] ).

cnf(i_0_12723,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_7276]),
    [final] ).

cnf(i_0_12724,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_7277]),
    [final] ).

cnf(i_0_12725,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_7278]),
    [final] ).

cnf(i_0_12726,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_7279]),
    [final] ).

cnf(i_0_12727,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_7280]),
    [final] ).

cnf(i_0_12728,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_7281]),
    [final] ).

cnf(i_0_12729,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk237_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_7282]),
    [final] ).

cnf(i_0_12730,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_7283]),
    [final] ).

cnf(i_0_12731,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X3))),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X3)))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X3)))))
    | ~ c_Orderings_Oorder__class_Omono(X1,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7284]),
    [final] ).

cnf(i_0_12732,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_6341]),
    [final] ).

cnf(i_0_12733,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_6163]),
    [final] ).

cnf(i_0_12734,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_7285]),
    [final] ).

cnf(i_0_12735,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_7286]),
    [final] ).

cnf(i_0_12736,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_6976]),
    [final] ).

cnf(i_0_12737,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_7287,c_0_6147]),
    [final] ).

cnf(i_0_12738,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_6409]),
    [final] ).

cnf(i_0_12739,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_7288,c_0_6128]),
    [final] ).

cnf(i_0_12740,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_7049]),
    [final] ).

cnf(i_0_12741,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_7050]),
    [final] ).

cnf(i_0_12742,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),esk512_3(X1,X3,X2)),esk513_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_7289]),
    [final] ).

cnf(i_0_12743,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_7290]),
    [final] ).

cnf(i_0_12744,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_7202]),
    [final] ).

cnf(i_0_12745,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_7203]),
    [final] ).

cnf(i_0_12746,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_7291]),
    [final] ).

cnf(i_0_12747,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk212_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_7292]),
    [final] ).

cnf(i_0_12748,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk210_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_7293]),
    [final] ).

cnf(i_0_12749,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk424_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_6908]),
    [final] ).

cnf(i_0_12750,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk425_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_6909]),
    [final] ).

cnf(i_0_12751,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_7294]),
    [final] ).

cnf(i_0_12752,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk139_3(X3,X2,X1)),esk140_3(X3,X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7295]),
    [final] ).

cnf(i_0_12753,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk224_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_7223]),
    [final] ).

cnf(i_0_12754,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk215_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_7224]),
    [final] ).

cnf(i_0_12755,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk276_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_7022]),
    [final] ).

cnf(i_0_12756,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_7296]),
    [final] ).

cnf(i_0_12757,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk373_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_7297]),
    [final] ).

cnf(i_0_12758,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_7079]),
    [final] ).

cnf(i_0_12759,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_7298,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12760,plain,
    ( hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(c_List_Ofilter(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X6)),X3)),X4) = hAPP(c_Option_Ooption_OSome(X2),X5)
    | hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),X4) != hAPP(c_Option_Ooption_OSome(X2),X5)
    | ~ hBOOL(hAPP(hAPP(X6,X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7299]),
    [final] ).

cnf(i_0_12761,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk221_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,esk219_2(X1,X2)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk219_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk220_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_7247]),
    [final] ).

cnf(i_0_12762,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk517_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_7300]),
    [final] ).

cnf(i_0_12763,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_7301,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12764,plain,
    ( c_Nitpick_Orefl_H(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk63_2(X2,X1)),esk63_2(X2,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7302]),
    [final] ).

cnf(i_0_12765,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),esk185_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_7303]),
    [final] ).

cnf(i_0_12766,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),esk183_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_7304]),
    [final] ).

cnf(i_0_12767,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk424_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_6908]),
    [final] ).

cnf(i_0_12768,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk425_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_6909]),
    [final] ).

cnf(i_0_12769,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_6928]),
    [final] ).

cnf(i_0_12770,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_7305]),
    [final] ).

cnf(i_0_12771,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_7306,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12772,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_7307]),
    [final] ).

cnf(i_0_12773,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_7308]),
    [final] ).

cnf(i_0_12774,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk518_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_7309]),
    [final] ).

cnf(i_0_12775,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | hAPP(c_Map_Omap__upds(X1,X4,X5,X3,X6),X2) = hAPP(X5,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7310]),
    [final] ).

cnf(i_0_12776,plain,
    ( hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),X4) != c_Option_Ooption_ONone(X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7311]),
    [final] ).

cnf(i_0_12777,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_7312]),
    [final] ).

cnf(i_0_12778,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_7313]),
    [final] ).

cnf(i_0_12779,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_7314,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12780,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_7315,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12781,plain,
    ( c_Map_Omap__upds(X1,X3,X5,hAPP(hAPP(c_List_Oappend(X1),X2),X6),X4) = c_Map_Omap__upds(X1,X3,X5,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_7316]),
    [final] ).

cnf(i_0_12782,plain,
    ( c_Map_Omap__upds(X1,X3,X5,X2,hAPP(hAPP(c_List_Oappend(X3),X4),X6)) = c_Map_Omap__upds(X1,X3,X5,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_7317]),
    [final] ).

cnf(i_0_12783,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_7318,c_0_6748]),
    [final] ).

cnf(i_0_12784,plain,
    ( X1 = hAPP(c_Option_Ooption_OSome(X2),esk396_5(X3,X1,X4,X5,X2))
    | hAPP(hAPP(c_Option_Omap(X2,X5),X4),X1) != hAPP(c_Option_Ooption_OSome(X5),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7319]),
    [final] ).

cnf(i_0_12785,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_7320]),
    [final] ).

cnf(i_0_12786,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_7321]),
    [final] ).

cnf(i_0_12787,plain,
    ( hAPP(X1,esk396_5(X2,X3,X1,X4,X5)) = X2
    | hAPP(hAPP(c_Option_Omap(X5,X4),X1),X3) != hAPP(c_Option_Ooption_OSome(X4),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7319]),
    [final] ).

cnf(i_0_12788,plain,
    c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X4),X5)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,X5)),X4),hAPP(X3,X4)),
    inference(split_conjunct,[status(thm)],[i_0_7322]),
    [final] ).

cnf(i_0_12789,plain,
    ( X1 = hAPP(c_List_Ofilter(X2,X3),esk489_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_6197]),
    [final] ).

cnf(i_0_12790,plain,
    ( X1 = hAPP(c_List_Ofilter(X2,X3),esk486_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_6198]),
    [final] ).

cnf(i_0_12791,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_7323,c_0_7157]),
    [final] ).

cnf(i_0_12792,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_7324]),
    [final] ).

cnf(i_0_12793,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk510_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_7016]),
    [final] ).

cnf(i_0_12794,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk501_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_7015]),
    [final] ).

cnf(i_0_12795,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),c_Map_Orestrict__map(X1,X4,X5,X3)),X2),c_Option_Ooption_ONone(X4)) = c_Map_Orestrict__map(X1,X4,X5,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7112]),
    [final] ).

cnf(i_0_12796,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_7325]),
    [final] ).

cnf(i_0_12797,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),esk515_3(X1,X2,X3)),esk516_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_7151]),
    [final] ).

cnf(i_0_12798,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),esk422_3(X1,X2,X3)),esk423_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_6981]),
    [final] ).

cnf(i_0_12799,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),esk157_3(X1,X2,X3)),esk158_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_5336]),
    [final] ).

cnf(i_0_12800,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),esk148_3(X1,X2,X3)),esk149_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_5339]),
    [final] ).

cnf(i_0_12801,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),esk136_3(X1,X2,X3)),esk137_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_7137]),
    [final] ).

cnf(i_0_12802,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),esk252_3(X1,X2,X3)),esk253_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_7326]),
    [final] ).

cnf(i_0_12803,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_7327]),
    [final] ).

cnf(i_0_12804,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_7328]),
    [final] ).

cnf(i_0_12805,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_7329]),
    [final] ).

cnf(i_0_12806,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_7330]),
    [final] ).

cnf(i_0_12807,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_7331,c_0_6147]),
    [final] ).

cnf(i_0_12808,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk335_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_7332,c_0_6136]),
    [final] ).

cnf(i_0_12809,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)))
    | esk477_2(X1,X2) != esk476_2(X1,X2)
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1))
    | ~ hBOOL(hAPP(c_List_Odistinct(X2),esk475_2(X1,X2))) ),
    inference(rw,[status(thm)],[i_0_7333,c_0_6177]),
    [final] ).

cnf(i_0_12810,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),esk39_3(X1,X3,X2))) != esk39_3(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7334]),
    [final] ).

cnf(i_0_12811,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,esk237_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7282]),
    [final] ).

cnf(i_0_12812,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_7283]),
    [final] ).

cnf(i_0_12813,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk522_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_7335]),
    [final] ).

cnf(i_0_12814,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk509_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_7336]),
    [final] ).

cnf(i_0_12815,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_7337]),
    [final] ).

cnf(i_0_12816,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_7338]),
    [final] ).

cnf(i_0_12817,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_7321]),
    [final] ).

cnf(i_0_12818,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_7125]),
    [final] ).

cnf(i_0_12819,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_7126]),
    [final] ).

cnf(i_0_12820,plain,
    c_Map_Omap__upds(X1,X2,X3,X4,X5) = c_Map_Omap__add(X1,X2,X3,hAPP(c_Map_Omap__of(X1,X2),hAPP(c_List_Orev(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5)))),
    inference(split_conjunct,[status(thm)],[i_0_7339]),
    [final] ).

cnf(i_0_12821,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_7340]),
    [final] ).

cnf(i_0_12822,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_7341]),
    [final] ).

cnf(i_0_12823,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk296_4(X2,X3,X4,X1)),X3))
    | c_Equiv__Relations_Ocongruent(X1,X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6257]),
    [final] ).

cnf(i_0_12824,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),esk465_4(X1,X3,X2,X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7029]),
    [final] ).

cnf(i_0_12825,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_7123]),
    [final] ).

cnf(i_0_12826,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_7342]),
    [final] ).

cnf(i_0_12827,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_7343,c_0_6311]),
    [final] ).

cnf(i_0_12828,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_7344,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12829,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_7345]),
    [final] ).

cnf(i_0_12830,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_7346]),
    [final] ).

cnf(i_0_12831,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),esk465_4(X4,X3,X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7029]),
    [final] ).

cnf(i_0_12832,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_7347]),
    [final] ).

cnf(i_0_12833,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk474_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_7034]),
    [final] ).

cnf(i_0_12834,plain,
    ( hAPP(hAPP(c_List_Otake(X1),X4),X2) = hAPP(hAPP(c_List_Otake(X1),X4),X3)
    | hAPP(hAPP(c_List_Onth(X1),X2),esk444_4(X3,X2,X1,X4)) != hAPP(hAPP(c_List_Onth(X1),X3),esk444_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_7226]),
    [final] ).

cnf(i_0_12835,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk514_4(X2,X3,X1,X4)),hAPP(c_List_Oset(X1),c_Enum_Oenum__class_Oenum(X1))))
    | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X1,X4)),X3),X2))
    | ~ class_HOL_Oequal(X4)
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7348]),
    [final] ).

cnf(i_0_12836,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_6855]),
    [final] ).

cnf(i_0_12837,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_7349]),
    [final] ).

cnf(i_0_12838,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_7350]),
    [final] ).

cnf(i_0_12839,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk331_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_7351]),
    [final] ).

cnf(i_0_12840,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_7352]),
    [final] ).

cnf(i_0_12841,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_7281]),
    [final] ).

cnf(i_0_12842,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_7353]),
    [final] ).

cnf(i_0_12843,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk257_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_6649]),
    [final] ).

cnf(i_0_12844,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_7354]),
    [final] ).

cnf(i_0_12845,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_7355]),
    [final] ).

cnf(i_0_12846,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_7123]),
    [final] ).

cnf(i_0_12847,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk483_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_7356]),
    [final] ).

cnf(i_0_12848,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_7357]),
    [final] ).

cnf(i_0_12849,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk234_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_7358]),
    [final] ).

cnf(i_0_12850,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_7359]),
    [final] ).

cnf(i_0_12851,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk213_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_7292]),
    [final] ).

cnf(i_0_12852,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk211_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_7293]),
    [final] ).

cnf(i_0_12853,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_7360]),
    [final] ).

cnf(i_0_12854,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_7123]),
    [final] ).

cnf(i_0_12855,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_7052]),
    [final] ).

cnf(i_0_12856,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_7053]),
    [final] ).

cnf(i_0_12857,plain,
    ( esk253_3(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(X1,esk253_3(X1,X2,X3)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,esk252_3(X1,X2,X3),esk253_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_7326]),
    [final] ).

cnf(i_0_12858,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_7361]),
    [final] ).

cnf(i_0_12859,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_7362]),
    [final] ).

cnf(i_0_12860,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk207_4(X2,X3,X4,X1)),esk206_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_7138]),
    [final] ).

cnf(i_0_12861,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_7074]),
    [final] ).

cnf(i_0_12862,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk236_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_7363]),
    [final] ).

cnf(i_0_12863,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X2)))))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7364]),
    [final] ).

cnf(i_0_12864,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_7365]),
    [final] ).

cnf(i_0_12865,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_7241]),
    [final] ).

cnf(i_0_12866,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_7366]),
    [final] ).

cnf(i_0_12867,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_7229]),
    [final] ).

cnf(i_0_12868,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),esk465_4(X1,X3,X2,X4)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7029]),
    [final] ).

cnf(i_0_12869,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_7123]),
    [final] ).

cnf(i_0_12870,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_7367]),
    [final] ).

cnf(i_0_12871,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_7368,c_0_7369]),
    [final] ).

cnf(i_0_12872,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),esk465_4(X4,X3,X2,X1)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7029]),
    [final] ).

cnf(i_0_12873,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_7370]),
    [final] ).

cnf(i_0_12874,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_7049]),
    [final] ).

cnf(i_0_12875,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_7050]),
    [final] ).

cnf(i_0_12876,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_6372]),
    [final] ).

cnf(i_0_12877,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_7371]),
    [final] ).

cnf(i_0_12878,plain,
    hAPP(hAPP(c_Option_Omap(X1,X2),X3),hAPP(hAPP(c_Option_Omap(X4,X1),X5),X6)) = hAPP(hAPP(c_Option_Omap(X4,X2),hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X6),
    inference(split_conjunct,[status(thm)],[i_0_7372]),
    [final] ).

cnf(i_0_12879,plain,
    hAPP(hAPP(c_Option_Omap(X1,X2),X3),hAPP(hAPP(c_Option_Omap(X4,X1),X5),X6)) = hAPP(hAPP(c_Option_Omap(X4,X2),hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X6),
    inference(split_conjunct,[status(thm)],[i_0_7373]),
    [final] ).

cnf(i_0_12880,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_7374]),
    [final] ).

cnf(i_0_12881,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_7375]),
    [final] ).

cnf(i_0_12882,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_7376]),
    [final] ).

cnf(i_0_12883,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_7377]),
    [final] ).

cnf(i_0_12884,plain,
    hAPP(c_New__DSequence_Oneg__bind(X1,X2,X3,X4),X5) = c_Lazy__Sequence_Ohb__flat(X2,c_Lazy__Sequence_Ohb__map(X1,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2))),X4),X5),hAPP(X3,X5))),
    inference(rw,[status(thm)],[i_0_7378,c_0_7262]),
    [final] ).

cnf(i_0_12885,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_7379]),
    [final] ).

cnf(i_0_12886,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_7353]),
    [final] ).

cnf(i_0_12887,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_7380]),
    [final] ).

cnf(i_0_12888,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_7381]),
    [final] ).

cnf(i_0_12889,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_7382]),
    [final] ).

cnf(i_0_12890,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_7383]),
    [final] ).

cnf(i_0_12891,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_7384]),
    [final] ).

cnf(i_0_12892,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_7385]),
    [final] ).

cnf(i_0_12893,plain,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X1,X2,X3,X4,X5) = hAPP(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_7386]),
    [final] ).

cnf(i_0_12894,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_7387,c_0_6177]),c_0_6177]),
    [final] ).

cnf(i_0_12895,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_7388]),
    [final] ).

cnf(i_0_12896,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_7389]),
    [final] ).

cnf(i_0_12897,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_7390]),
    [final] ).

cnf(i_0_12898,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_7089]),
    [final] ).

cnf(i_0_12899,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_7391]),
    [final] ).

cnf(i_0_12900,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_7392]),
    [final] ).

cnf(i_0_12901,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_7393,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12902,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_7394,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12903,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_7395]),
    [final] ).

cnf(i_0_12904,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_7396]),
    [final] ).

cnf(i_0_12905,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_7397]),
    [final] ).

cnf(i_0_12906,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_7398]),
    [final] ).

cnf(i_0_12907,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk33_4(X2,X3,X4,X1)),X2))
    | c_Fun_Oinj__on(X1,X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7399]),
    [final] ).

cnf(i_0_12908,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk32_4(X2,X3,X4,X1)),X2))
    | c_Fun_Oinj__on(X1,X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7399]),
    [final] ).

cnf(i_0_12909,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_7400]),
    [final] ).

cnf(i_0_12910,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_7401]),
    [final] ).

cnf(i_0_12911,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_7163]),
    [final] ).

cnf(i_0_12912,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_7381]),
    [final] ).

cnf(i_0_12913,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_7382]),
    [final] ).

cnf(i_0_12914,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_7402]),
    [final] ).

cnf(i_0_12915,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk118_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_7403]),
    [final] ).

cnf(i_0_12916,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk389_4(X4,X1,X3,X2)),esk388_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_6563]),
    [final] ).

cnf(i_0_12917,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_7404]),
    [final] ).

cnf(i_0_12918,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_7405]),
    [final] ).

cnf(i_0_12919,plain,
    ( hBOOL(hAPP(X1,esk221_2(X1,X2)))
    | ~ hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk219_2(X1,X2)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk219_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk220_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_7247]),
    [final] ).

cnf(i_0_12920,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_7406,c_0_6128]),
    [final] ).

cnf(i_0_12921,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk226_4(X2,X3,X4,X1)),esk225_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_7161]),
    [final] ).

cnf(i_0_12922,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk217_4(X2,X3,X4,X1)),esk216_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_7162]),
    [final] ).

cnf(i_0_12923,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_7084]),
    [final] ).

cnf(i_0_12924,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk355_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_7407]),
    [final] ).

cnf(i_0_12925,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk51_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_7408]),
    [final] ).

cnf(i_0_12926,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk354_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_7409]),
    [final] ).

cnf(i_0_12927,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk52_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_7410]),
    [final] ).

cnf(i_0_12928,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X1,esk308_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_7411]),
    [final] ).

cnf(i_0_12929,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_7412]),
    [final] ).

cnf(i_0_12930,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_7413]),
    [final] ).

cnf(i_0_12931,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_7414]),
    [final] ).

cnf(i_0_12932,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_7415]),
    [final] ).

cnf(i_0_12933,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk471_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_7416]),
    [final] ).

cnf(i_0_12934,plain,
    ( hAPP(X1,esk351_4(X2,X1,X3,X4)) = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk350_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_6199]),
    [final] ).

cnf(i_0_12935,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_7417]),
    [final] ).

cnf(i_0_12936,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_7418]),
    [final] ).

cnf(i_0_12937,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_7419,c_0_6748]),c_0_6748]),
    [final] ).

cnf(i_0_12938,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_7420]),
    [final] ).

cnf(i_0_12939,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_7421]),
    [final] ).

cnf(i_0_12940,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk209_4(X2,X3,X4,X1)),esk208_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_7175]),
    [final] ).

cnf(i_0_12941,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_7422,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12942,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_7423]),
    [final] ).

cnf(i_0_12943,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)),esk367_3(X2,X3,X1)),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk368_3(X2,X3,X1)),esk369_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_7424]),
    [final] ).

cnf(i_0_12944,plain,
    ( X1 = X2
    | hAPP(hAPP(c_Map_Omap__of(X3,X4),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X3,X4)),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X1),X5)),X6)),X2) = hAPP(hAPP(c_Map_Omap__of(X3,X4),X6),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7425]),
    [final] ).

cnf(i_0_12945,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_7097]),
    [final] ).

cnf(i_0_12946,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_7426]),
    [final] ).

cnf(i_0_12947,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_7427]),
    [final] ).

cnf(i_0_12948,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_7428]),
    [final] ).

cnf(i_0_12949,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_7429,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12950,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_7430]),
    [final] ).

cnf(i_0_12951,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_7431]),
    [final] ).

cnf(i_0_12952,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_7432]),
    [final] ).

cnf(i_0_12953,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_7433]),
    [final] ).

cnf(i_0_12954,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk308_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_7411]),
    [final] ).

cnf(i_0_12955,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_7434]),
    [final] ).

cnf(i_0_12956,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_7435,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12957,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_7436]),
    [final] ).

cnf(i_0_12958,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_7202]),
    [final] ).

cnf(i_0_12959,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_7203]),
    [final] ).

cnf(i_0_12960,plain,
    ( X1 = hAPP(X2,esk40_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_7043]),
    [final] ).

cnf(i_0_12961,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_7437,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_12962,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_7438]),
    [final] ).

cnf(i_0_12963,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_7439]),
    [final] ).

cnf(i_0_12964,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_7440,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12965,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_7441,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12966,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_7442,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12967,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_7443,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12968,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_7444,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12969,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_7445,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12970,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_7446,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12971,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_7447,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_12972,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_7448]),
    [final] ).

cnf(i_0_12973,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_7449]),
    [final] ).

cnf(i_0_12974,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk369_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)),esk367_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_7424]),
    [final] ).

cnf(i_0_12975,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk368_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)),esk367_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_7424]),
    [final] ).

cnf(i_0_12976,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_7450]),
    [final] ).

cnf(i_0_12977,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_7451]),
    [final] ).

cnf(i_0_12978,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_7452]),
    [final] ).

cnf(i_0_12979,plain,
    ( hAPP(hAPP(c_Map_Omap__of(X3,X4),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X3,X4)),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X1),X5)),X6)),X2) = hAPP(c_Option_Ooption_OSome(X4),X5)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_7425]),
    [final] ).

cnf(i_0_12980,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_7453]),
    [final] ).

cnf(i_0_12981,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_7454]),
    [final] ).

cnf(i_0_12982,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_7455]),
    [final] ).

cnf(i_0_12983,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_7456]),
    [final] ).

cnf(i_0_12984,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_7457]),
    [final] ).

cnf(i_0_12985,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk27_4(X1,X2,X3,X4)))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X3),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X4,tc_HOL_Obool),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6884]),
    [final] ).

cnf(i_0_12986,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_7458]),
    [final] ).

cnf(i_0_12987,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_7459,c_0_6311]),c_0_6311]),
    [final] ).

cnf(i_0_12988,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X2),X4)))
    | ~ hBOOL(hAPP(X1,esk491_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_7273]),
    [final] ).

cnf(i_0_12989,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_7184]),
    [final] ).

cnf(i_0_12990,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_7460]),
    [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))
    | 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_7461]),
    [final] ).

cnf(i_0_12992,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_7462]),
    [final] ).

cnf(i_0_12993,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_7463]),
    [final] ).

cnf(i_0_12994,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_7101]),
    [final] ).

cnf(i_0_12995,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_7102]),
    [final] ).

cnf(i_0_12996,plain,
    ( c_Wellfounded_Owf(tc_prod(X3,X1),c_Recdef_Osame__fst(X3,X1,X4,X2))
    | ~ c_Wellfounded_Owf(X1,hAPP(X2,esk264_4(X3,X2,X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7464]),
    [final] ).

cnf(i_0_12997,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_7465]),
    [final] ).

cnf(i_0_12998,plain,
    c_Map_Orestrict__map(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = c_Map_Orestrict__map(X1,X2,X3,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[i_0_7466]),
    [final] ).

cnf(i_0_12999,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_7467,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13000,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_7468]),
    [final] ).

cnf(i_0_13001,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_7469,c_0_6136]),
    [final] ).

cnf(i_0_13002,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_7470]),
    [final] ).

cnf(i_0_13003,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_7471]),
    [final] ).

cnf(i_0_13004,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_7190]),
    [final] ).

cnf(i_0_13005,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_7191]),
    [final] ).

cnf(i_0_13006,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(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_7472,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13007,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_7473]),
    [final] ).

cnf(i_0_13008,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk224_4(X2,X3,X4,X1)),esk223_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_7223]),
    [final] ).

cnf(i_0_13009,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk215_4(X2,X3,X4,X1)),esk214_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_7224]),
    [final] ).

cnf(i_0_13010,plain,
    ( c_Map_Oran(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X3)) = hAPP(c_Set_Oimage(tc_prod(X1,X2),X2,c_Product__Type_Osnd(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7474]),
    [final] ).

cnf(i_0_13011,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_7475,c_0_6177]),c_0_6177]),
    [final] ).

cnf(i_0_13012,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_6523]),
    [final] ).

cnf(i_0_13013,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_7476]),
    [final] ).

cnf(i_0_13014,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_7477]),
    [final] ).

cnf(i_0_13015,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_7478]),
    [final] ).

cnf(i_0_13016,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_7479]),
    [final] ).

cnf(i_0_13017,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_7480]),
    [final] ).

cnf(i_0_13018,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_7481]),
    [final] ).

cnf(i_0_13019,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_7482]),
    [final] ).

cnf(i_0_13020,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_7483]),
    [final] ).

cnf(i_0_13021,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_7484]),
    [final] ).

cnf(i_0_13022,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_7485]),
    [final] ).

cnf(i_0_13023,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_7486]),
    [final] ).

cnf(i_0_13024,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_7487]),
    [final] ).

cnf(i_0_13025,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_7488]),
    [final] ).

cnf(i_0_13026,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_7489]),
    [final] ).

cnf(i_0_13027,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_7202]),
    [final] ).

cnf(i_0_13028,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_7125]),
    [final] ).

cnf(i_0_13029,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_7203]),
    [final] ).

cnf(i_0_13030,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_7126]),
    [final] ).

cnf(i_0_13031,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,esk319_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_7490]),
    [final] ).

cnf(i_0_13032,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_7491]),
    [final] ).

cnf(i_0_13033,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_7492]),
    [final] ).

cnf(i_0_13034,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_7493]),
    [final] ).

cnf(i_0_13035,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_7494]),
    [final] ).

cnf(i_0_13036,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_7495]),
    [final] ).

cnf(i_0_13037,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_7496,c_0_6177]),c_0_6177]),
    [final] ).

cnf(i_0_13038,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_7497]),
    [final] ).

cnf(i_0_13039,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_7498]),
    [final] ).

cnf(i_0_13040,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_7499]),
    [final] ).

cnf(i_0_13041,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_7500]),
    [final] ).

cnf(i_0_13042,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_7501]),
    [final] ).

cnf(i_0_13043,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_7502]),
    [final] ).

cnf(i_0_13044,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_7503]),
    [final] ).

cnf(i_0_13045,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_7504]),
    [final] ).

cnf(i_0_13046,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_7505]),
    [final] ).

cnf(i_0_13047,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_7506]),
    [final] ).

cnf(i_0_13048,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_7507,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13049,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_7508,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13050,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_7052]),
    [final] ).

cnf(i_0_13051,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_7053]),
    [final] ).

cnf(i_0_13052,plain,
    ( hBOOL(hAPP(X3,esk222_2(X3,X2)))
    | hBOOL(hAPP(X3,esk219_2(X3,X2)))
    | hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk219_2(X3,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk220_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_7247]),
    [final] ).

cnf(i_0_13053,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_7509]),
    [final] ).

cnf(i_0_13054,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_7510]),
    [final] ).

cnf(i_0_13055,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_7511]),
    [final] ).

cnf(i_0_13056,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_7512]),
    [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_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_7513,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13058,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_7514,c_0_6136]),
    [final] ).

cnf(i_0_13059,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_7163]),
    [final] ).

cnf(i_0_13060,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_7351]),
    [final] ).

cnf(i_0_13061,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_7515]),
    [final] ).

cnf(i_0_13062,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_7516]),
    [final] ).

cnf(i_0_13063,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_7217]),
    [final] ).

cnf(i_0_13064,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_7517]),
    [final] ).

cnf(i_0_13065,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_7125]),
    [final] ).

cnf(i_0_13066,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_7126]),
    [final] ).

cnf(i_0_13067,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_7518]),
    [final] ).

cnf(i_0_13068,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_7519]),
    [final] ).

cnf(i_0_13069,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_7520]),
    [final] ).

cnf(i_0_13070,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_7521]),
    [final] ).

cnf(i_0_13071,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_7522]),
    [final] ).

cnf(i_0_13072,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_7523]),
    [final] ).

cnf(i_0_13073,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_7418]),
    [final] ).

cnf(i_0_13074,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_7524]),
    [final] ).

cnf(i_0_13075,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_7525]),
    [final] ).

cnf(i_0_13076,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_7526]),
    [final] ).

cnf(i_0_13077,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_7527]),
    [final] ).

cnf(i_0_13078,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_7528]),
    [final] ).

cnf(i_0_13079,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_7255]),
    [final] ).

cnf(i_0_13080,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_7256]),
    [final] ).

cnf(i_0_13081,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(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_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OMin)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7529,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13082,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_7530,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13083,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_7531,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13084,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_7532,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13085,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_7533,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13086,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_7534,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13087,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_7535,c_0_6768]),
    [final] ).

cnf(i_0_13088,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_7536]),
    [final] ).

cnf(i_0_13089,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_7537]),
    [final] ).

cnf(i_0_13090,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_7538]),
    [final] ).

cnf(i_0_13091,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_7049]),
    [final] ).

cnf(i_0_13092,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_7050]),
    [final] ).

cnf(i_0_13093,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_7539]),
    [final] ).

cnf(i_0_13094,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_7540]),
    [final] ).

cnf(i_0_13095,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_7541]),
    [final] ).

cnf(i_0_13096,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_7542]),
    [final] ).

cnf(i_0_13097,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_7524]),
    [final] ).

cnf(i_0_13098,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_7525]),
    [final] ).

cnf(i_0_13099,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_7543]),
    [final] ).

cnf(i_0_13100,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_7052]),
    [final] ).

cnf(i_0_13101,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_7053]),
    [final] ).

cnf(i_0_13102,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_7544]),
    [final] ).

cnf(i_0_13103,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_7545]),
    [final] ).

cnf(i_0_13104,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_7546,c_0_6128]),
    [final] ).

cnf(i_0_13105,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_7547]),
    [final] ).

cnf(i_0_13106,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_7548]),
    [final] ).

cnf(i_0_13107,plain,
    ( X3 = esk40_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_7043]),
    [final] ).

cnf(i_0_13108,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_7438]),
    [final] ).

cnf(i_0_13109,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_7549]),
    [final] ).

cnf(i_0_13110,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_7550,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_13111,plain,
    ( X3 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))),X4),hAPP(c_Option_Ooption_OSome(X2),esk61_4(X4,X3,X2,X1)))
    | c_Map_Odom(X1,X2,X3) != hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7551]),
    [final] ).

cnf(i_0_13112,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_7345]),
    [final] ).

cnf(i_0_13113,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_7552]),
    [final] ).

cnf(i_0_13114,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_7553]),
    [final] ).

cnf(i_0_13115,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_7554]),
    [final] ).

cnf(i_0_13116,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_7555]),
    [final] ).

cnf(i_0_13117,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_7556]),
    [final] ).

cnf(i_0_13118,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_7557]),
    [final] ).

cnf(i_0_13119,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_7558]),
    [final] ).

cnf(i_0_13120,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_7559]),
    [final] ).

cnf(i_0_13121,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_7560]),
    [final] ).

cnf(i_0_13122,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_7561]),
    [final] ).

cnf(i_0_13123,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_7562]),
    [final] ).

cnf(i_0_13124,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_7563,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13125,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk515_3(X1,X2,X3)),esk516_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_7151]),
    [final] ).

cnf(i_0_13126,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk422_3(X1,X2,X3)),esk423_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_6981]),
    [final] ).

cnf(i_0_13127,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk252_3(X1,X2,X3)),esk253_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_7326]),
    [final] ).

cnf(i_0_13128,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk157_3(X1,X2,X3)),esk158_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_5336]),
    [final] ).

cnf(i_0_13129,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk148_3(X1,X2,X3)),esk149_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_5339]),
    [final] ).

cnf(i_0_13130,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk136_3(X1,X2,X3)),esk137_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_7137]),
    [final] ).

cnf(i_0_13131,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_6324]),
    [final] ).

cnf(i_0_13132,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_6601]),
    [final] ).

cnf(i_0_13133,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_7564]),
    [final] ).

cnf(i_0_13134,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_7565]),
    [final] ).

cnf(i_0_13135,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_7566]),
    [final] ).

cnf(i_0_13136,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,esk129_3(X2,X1,X3)),esk130_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_7567]),
    [final] ).

cnf(i_0_13137,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_7568]),
    [final] ).

cnf(i_0_13138,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X2)),X1))
    | ~ hBOOL(hAPP(X1,c_Option_Ooption_ONone(X2)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X2),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_HOL_Obool,X2),X1),c_Option_Ooption_OSome(X2))))
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7569]),
    [final] ).

cnf(i_0_13139,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_7570]),
    [final] ).

cnf(i_0_13140,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_7571]),
    [final] ).

cnf(i_0_13141,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_7572]),
    [final] ).

cnf(i_0_13142,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_7573]),
    [final] ).

cnf(i_0_13143,plain,
    hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5)),X4),X6) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X6),
    inference(split_conjunct,[status(thm)],[i_0_7574]),
    [final] ).

cnf(i_0_13144,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_7575]),
    [final] ).

cnf(i_0_13145,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_7567]),
    [final] ).

cnf(i_0_13146,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,esk127_3(X2,X1,X3)),esk128_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_7576]),
    [final] ).

cnf(i_0_13147,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_7577]),
    [final] ).

cnf(i_0_13148,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_7578]),
    [final] ).

cnf(i_0_13149,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_7579]),
    [final] ).

cnf(i_0_13150,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_7580]),
    [final] ).

cnf(i_0_13151,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_7581]),
    [final] ).

cnf(i_0_13152,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_7582]),
    [final] ).

cnf(i_0_13153,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_7583]),
    [final] ).

cnf(i_0_13154,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_7584]),
    [final] ).

cnf(i_0_13155,plain,
    ( hAPP(X4,hAPP(X3,X6)) = X6
    | ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7585]),
    [final] ).

cnf(i_0_13156,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_7576]),
    [final] ).

cnf(i_0_13157,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_7586,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13158,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_7587]),
    [final] ).

cnf(i_0_13159,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_7588]),
    [final] ).

cnf(i_0_13160,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_7589,c_0_6136]),
    [final] ).

cnf(i_0_13161,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X3,X4)),X1),X2))
    | hAPP(X1,esk514_4(X2,X1,X3,X4)) != hAPP(X2,esk514_4(X2,X1,X3,X4))
    | ~ class_HOL_Oequal(X4)
    | ~ class_Enum_Oenum(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7348]),
    [final] ).

cnf(i_0_13162,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk213_4(X2,X3,X4,X1)),esk212_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_7292]),
    [final] ).

cnf(i_0_13163,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk211_4(X2,X3,X4,X1)),esk210_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_7293]),
    [final] ).

cnf(i_0_13164,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_7125]),
    [final] ).

cnf(i_0_13165,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_7126]),
    [final] ).

cnf(i_0_13166,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,esk483_4(X2,X1,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7356]),
    [final] ).

cnf(i_0_13167,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_7590]),
    [final] ).

cnf(i_0_13168,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk221_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))
    | hBOOL(hAPP(X1,esk219_2(X1,X2)))
    | hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk219_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk220_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_7247]),
    [final] ).

cnf(i_0_13169,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_7591]),
    [final] ).

cnf(i_0_13170,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_7592]),
    [final] ).

cnf(i_0_13171,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_6876]),
    [final] ).

cnf(i_0_13172,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_7593]),
    [final] ).

cnf(i_0_13173,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_6684]),
    [final] ).

cnf(i_0_13174,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_7594]),
    [final] ).

cnf(i_0_13175,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_7595]),
    [final] ).

cnf(i_0_13176,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_7596]),
    [final] ).

cnf(i_0_13177,plain,
    ( X2 = X3
    | ~ c_List_Olist__all2(X1,X1,c_fequal,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7597]),
    [final] ).

cnf(i_0_13178,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_7125]),
    [final] ).

cnf(i_0_13179,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_7202]),
    [final] ).

cnf(i_0_13180,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_7126]),
    [final] ).

cnf(i_0_13181,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_7203]),
    [final] ).

cnf(i_0_13182,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_7448]),
    [final] ).

cnf(i_0_13183,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_7449]),
    [final] ).

cnf(i_0_13184,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_7598]),
    [final] ).

cnf(i_0_13185,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_7599]),
    [final] ).

cnf(i_0_13186,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X1)),X2))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X1),tc_HOL_Obool,X1),X2),c_Option_Ooption_OSome(X1))))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7600]),
    [final] ).

cnf(i_0_13187,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_7601,c_0_6177]),c_0_6177]),
    [final] ).

cnf(i_0_13188,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_7602]),
    [final] ).

cnf(i_0_13189,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_7603]),
    [final] ).

cnf(i_0_13190,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_7604]),
    [final] ).

cnf(i_0_13191,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_7605]),
    [final] ).

cnf(i_0_13192,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_7606,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13193,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_7142]),
    [final] ).

cnf(i_0_13194,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_7607]),
    [final] ).

cnf(i_0_13195,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk404_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_7325]),
    [final] ).

cnf(i_0_13196,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_7608]),
    [final] ).

cnf(i_0_13197,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_7609]),
    [final] ).

cnf(i_0_13198,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_7610]),
    [final] ).

cnf(i_0_13199,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_7611]),
    [final] ).

cnf(i_0_13200,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_7612]),
    [final] ).

cnf(i_0_13201,plain,
    ( c_List_Olinorder__class_Osorted(X1,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk471_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_7416]),
    [final] ).

cnf(i_0_13202,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_7613]),
    [final] ).

cnf(i_0_13203,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_7202]),
    [final] ).

cnf(i_0_13204,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_7202]),
    [final] ).

cnf(i_0_13205,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_7203]),
    [final] ).

cnf(i_0_13206,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_7203]),
    [final] ).

cnf(i_0_13207,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_7465]),
    [final] ).

cnf(i_0_13208,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | X2 != c_Inductive_Ocomplete__lattice__class_Olfp(X1,X3)
    | ~ c_Orderings_Oorder__class_Omono(X1,X1,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7614]),
    [final] ).

cnf(i_0_13209,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_7615]),
    [final] ).

cnf(i_0_13210,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_6721]),
    [final] ).

cnf(i_0_13211,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_7616]),
    [final] ).

cnf(i_0_13212,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_7617]),
    [final] ).

cnf(i_0_13213,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_7618]),
    [final] ).

cnf(i_0_13214,plain,
    hAPP(c_Fun_Ocomp(tc_Option_Ooption(X1),tc_Option_Ooption(X2),tc_Option_Ooption(X3),hAPP(c_Option_Omap(X1,X2),X4)),hAPP(c_Option_Omap(X3,X1),X5)) = hAPP(c_Option_Omap(X3,X2),hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7619]),
    [final] ).

cnf(i_0_13215,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_7353]),
    [final] ).

cnf(i_0_13216,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_7353]),
    [final] ).

cnf(i_0_13217,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_7620]),
    [final] ).

cnf(i_0_13218,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_7621]),
    [final] ).

cnf(i_0_13219,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_7622,c_0_6209]),c_0_6209]),
    [final] ).

cnf(i_0_13220,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_7623]),
    [final] ).

cnf(i_0_13221,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_7624]),
    [final] ).

cnf(i_0_13222,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_7625]),
    [final] ).

cnf(i_0_13223,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_7626]),
    [final] ).

cnf(i_0_13224,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_7626]),
    [final] ).

cnf(i_0_13225,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_7627]),
    [final] ).

cnf(i_0_13226,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_7628]),
    [final] ).

cnf(i_0_13227,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_5345]),
    [final] ).

cnf(i_0_13228,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_7381]),
    [final] ).

cnf(i_0_13229,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_7629]),
    [final] ).

cnf(i_0_13230,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk372_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_7630]),
    [final] ).

cnf(i_0_13231,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk371_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_7630]),
    [final] ).

cnf(i_0_13232,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_7631]),
    [final] ).

cnf(i_0_13233,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_7632]),
    [final] ).

cnf(i_0_13234,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_7633,c_0_6128]),c_0_6136]),
    [final] ).

cnf(i_0_13235,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_7634]),
    [final] ).

cnf(i_0_13236,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_7635]),
    [final] ).

cnf(i_0_13237,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_7636]),
    [final] ).

cnf(i_0_13238,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_7493]),
    [final] ).

cnf(i_0_13239,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_7494]),
    [final] ).

cnf(i_0_13240,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_7637]),
    [final] ).

cnf(i_0_13241,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_7637]),
    [final] ).

cnf(i_0_13242,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_7638]),
    [final] ).

cnf(i_0_13243,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_7638]),
    [final] ).

cnf(i_0_13244,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_7639]),
    [final] ).

cnf(i_0_13245,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_7640]),
    [final] ).

cnf(i_0_13246,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_7641]),
    [final] ).

cnf(i_0_13247,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_7640]),
    [final] ).

cnf(i_0_13248,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_7641]),
    [final] ).

cnf(i_0_13249,plain,
    ( hBOOL(hAPP(X4,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(X4,esk10_4(X4,X3,X5,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6888]),
    [final] ).

cnf(i_0_13250,plain,
    ( hBOOL(hAPP(X4,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(X4,esk10_4(X4,X5,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6888]),
    [final] ).

cnf(i_0_13251,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_7642]),
    [final] ).

cnf(i_0_13252,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk94_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_6640]),
    [final] ).

cnf(i_0_13253,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_7643]),
    [final] ).

cnf(i_0_13254,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_7644]),
    [final] ).

cnf(i_0_13255,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_7645]),
    [final] ).

cnf(i_0_13256,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_7646]),
    [final] ).

cnf(i_0_13257,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_7647]),
    [final] ).

cnf(i_0_13258,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_7648]),
    [final] ).

cnf(i_0_13259,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_7649]),
    [final] ).

cnf(i_0_13260,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_7049]),
    [final] ).

cnf(i_0_13261,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_7050]),
    [final] ).

cnf(i_0_13262,plain,
    ( hBOOL(hAPP(X1,esk94_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_6640]),
    [final] ).

cnf(i_0_13263,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_7650,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13264,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)),esk374_3(X2,X3,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_13265,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_7652]),
    [final] ).

cnf(i_0_13266,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_7653]),
    [final] ).

cnf(i_0_13267,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_7049]),
    [final] ).

cnf(i_0_13268,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_7050]),
    [final] ).

cnf(i_0_13269,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_7052]),
    [final] ).

cnf(i_0_13270,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_7053]),
    [final] ).

cnf(i_0_13271,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_7654]),
    [final] ).

cnf(i_0_13272,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_7655]),
    [final] ).

cnf(i_0_13273,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_7656,c_0_7369]),
    [final] ).

cnf(i_0_13274,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,esk301_3(X2,X1,X3)) != hAPP(X1,esk302_3(X2,X1,X3))
    | ~ c_Wellfounded_OwfP(X3,hAPP(X1,esk300_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6978]),
    [final] ).

cnf(i_0_13275,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_7657]),
    [final] ).

cnf(i_0_13276,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_7658]),
    [final] ).

cnf(i_0_13277,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_7659]),
    [final] ).

cnf(i_0_13278,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_7660]),
    [final] ).

cnf(i_0_13279,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_7661]),
    [final] ).

cnf(i_0_13280,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)),esk368_3(X2,X3,X1)),esk369_3(X2,X3,X1)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(X1),esk367_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_7424]),
    [final] ).

cnf(i_0_13281,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_7662,c_0_6768]),c_0_6768]),c_0_6768]),
    [final] ).

cnf(i_0_13282,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_7610]),
    [final] ).

cnf(i_0_13283,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_7663]),
    [final] ).

cnf(i_0_13284,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_7610]),
    [final] ).

cnf(i_0_13285,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_7663]),
    [final] ).

cnf(i_0_13286,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_7664]),
    [final] ).

cnf(i_0_13287,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_7665]),
    [final] ).

cnf(i_0_13288,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_7666]),
    [final] ).

cnf(i_0_13289,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_7667]),
    [final] ).

cnf(i_0_13290,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_7668]),
    [final] ).

cnf(i_0_13291,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_7669]),
    [final] ).

cnf(i_0_13292,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_7670]),
    [final] ).

cnf(i_0_13293,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_7671]),
    [final] ).

cnf(i_0_13294,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_7672]),
    [final] ).

cnf(i_0_13295,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_7673,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13296,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_7674,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13297,plain,
    ( X2 = hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk349_2(X2,X1)),esk349_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_7675,c_0_6128]),
    [final] ).

cnf(i_0_13298,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_7676,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_13299,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_7677]),
    [final] ).

cnf(i_0_13300,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_7625]),
    [final] ).

cnf(i_0_13301,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_7678,c_0_6128]),
    [final] ).

cnf(i_0_13302,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_7679,c_0_6128]),
    [final] ).

cnf(i_0_13303,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_7680]),
    [final] ).

cnf(i_0_13304,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_7681]),
    [final] ).

cnf(i_0_13305,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_7682]),
    [final] ).

cnf(i_0_13306,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_7683]),
    [final] ).

cnf(i_0_13307,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_7684]),
    [final] ).

cnf(i_0_13308,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk204_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_7685]),
    [final] ).

cnf(i_0_13309,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk194_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_7686]),
    [final] ).

cnf(i_0_13310,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_7687]),
    [final] ).

cnf(i_0_13311,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk114_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_7688]),
    [final] ).

cnf(i_0_13312,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_7689,c_0_6177]),
    [final] ).

cnf(i_0_13313,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_7568]),
    [final] ).

cnf(i_0_13314,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_7690,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_13315,plain,
    ( c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),X4,c_Map_Odom(X1,X2,X4))
    | ~ c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),c_Map_Omap__add(X1,X2,X3,X4),c_Map_Odom(X1,X2,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7691]),
    [final] ).

cnf(i_0_13316,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_7692]),
    [final] ).

cnf(i_0_13317,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X3,X4)),hAPP(X3,X5))),hAPP(X3,hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),X4),X5))))
    | ~ class_Lattices_Osemilattice__sup(X1)
    | ~ class_Orderings_Olinorder(X2)
    | ~ c_Orderings_Oorder__class_Omono(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7693]),
    [final] ).

cnf(i_0_13318,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X3,X4)),hAPP(X3,X5))),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X4),X5))))
    | ~ class_Lattices_Osemilattice__sup(X1)
    | ~ class_Lattices_Osemilattice__sup(X2)
    | ~ c_Orderings_Oorder__class_Omono(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7694]),
    [final] ).

cnf(i_0_13319,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_6404]),
    [final] ).

cnf(i_0_13320,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_7695]),
    [final] ).

cnf(i_0_13321,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_7696]),
    [final] ).

cnf(i_0_13322,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_7697]),
    [final] ).

cnf(i_0_13323,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_7698]),
    [final] ).

cnf(i_0_13324,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk369_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),esk367_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_7424]),
    [final] ).

cnf(i_0_13325,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk368_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),esk367_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_7424]),
    [final] ).

cnf(i_0_13326,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_7699]),
    [final] ).

cnf(i_0_13327,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_7052]),
    [final] ).

cnf(i_0_13328,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_7053]),
    [final] ).

cnf(i_0_13329,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_7700]),
    [final] ).

cnf(i_0_13330,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk66_2(X2,X1)),esk66_2(X2,X1))),X2))
    | c_Relation_Oirrefl(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7701]),
    [final] ).

cnf(i_0_13331,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_7702]),
    [final] ).

cnf(i_0_13332,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk126_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_7703]),
    [final] ).

cnf(i_0_13333,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_7704]),
    [final] ).

cnf(i_0_13334,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_7705]),
    [final] ).

cnf(i_0_13335,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_7706]),
    [final] ).

cnf(i_0_13336,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_7707]),
    [final] ).

cnf(i_0_13337,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_7524]),
    [final] ).

cnf(i_0_13338,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_7525]),
    [final] ).

cnf(i_0_13339,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_7708]),
    [final] ).

cnf(i_0_13340,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_7709]),
    [final] ).

cnf(i_0_13341,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_7101]),
    [final] ).

cnf(i_0_13342,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_7102]),
    [final] ).

cnf(i_0_13343,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Oimage(tc_prod(X1,X3),X1,c_Product__Type_Ofst(X1,X3)),hAPP(c_List_Oset(tc_prod(X1,X3)),X4))))
    | hAPP(hAPP(c_Map_Omap__of(X1,X3),X4),X2) = c_Option_Ooption_ONone(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7311]),
    [final] ).

cnf(i_0_13344,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_7710]),
    [final] ).

cnf(i_0_13345,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_7711]),
    [final] ).

cnf(i_0_13346,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_7163]),
    [final] ).

cnf(i_0_13347,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)),esk367_3(X1,X2,X3)),X2))
    | esk368_3(X1,X2,X3) != esk369_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_7424]),
    [final] ).

cnf(i_0_13348,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_7712]),
    [final] ).

cnf(i_0_13349,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_7713]),
    [final] ).

cnf(i_0_13350,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_7714]),
    [final] ).

cnf(i_0_13351,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_7715]),
    [final] ).

cnf(i_0_13352,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_7701]),
    [final] ).

cnf(i_0_13353,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_7716]),
    [final] ).

cnf(i_0_13354,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_7717]),
    [final] ).

cnf(i_0_13355,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_7524]),
    [final] ).

cnf(i_0_13356,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_7524]),
    [final] ).

cnf(i_0_13357,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_7525]),
    [final] ).

cnf(i_0_13358,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_7525]),
    [final] ).

cnf(i_0_13359,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_7718,c_0_6128]),
    [final] ).

cnf(i_0_13360,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_7719]),
    [final] ).

cnf(i_0_13361,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_7720]),
    [final] ).

cnf(i_0_13362,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_7721]),
    [final] ).

cnf(i_0_13363,plain,
    c_Lazy__Sequence_Ohb__flat(X1,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1))),X2,X3)) = c_Lazy__Sequence_Oappend(tc_Option_Ooption(X1),hAPP(c_Option_Ooption_Ooption__case(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1)),tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1)),c_Lazy__Sequence_Ohit__bound(X1),c_COMBI(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1)))),X2),c_Lazy__Sequence_Ohb__flat(X1,X3)),
    inference(split_conjunct,[status(thm)],[i_0_7722]),
    [final] ).

cnf(i_0_13364,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_7476]),
    [final] ).

cnf(i_0_13365,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_7477]),
    [final] ).

cnf(i_0_13366,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_7478]),
    [final] ).

cnf(i_0_13367,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X3,hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),X4),X5))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X3,X4)),hAPP(X3,X5))))
    | ~ class_Lattices_Osemilattice__inf(X1)
    | ~ class_Orderings_Olinorder(X2)
    | ~ c_Orderings_Oorder__class_Omono(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7723]),
    [final] ).

cnf(i_0_13368,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X4),X5))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X3,X4)),hAPP(X3,X5))))
    | ~ class_Lattices_Osemilattice__inf(X1)
    | ~ class_Lattices_Osemilattice__inf(X2)
    | ~ c_Orderings_Oorder__class_Omono(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7724]),
    [final] ).

cnf(i_0_13369,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk126_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_7703]),
    [final] ).

cnf(i_0_13370,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),esk460_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk461_2(X2,X1))))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7725]),
    [final] ).

cnf(i_0_13371,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),esk459_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk458_2(X2,X1))))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7726]),
    [final] ).

cnf(i_0_13372,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_6527]),
    [final] ).

cnf(i_0_13373,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_7727]),
    [final] ).

cnf(i_0_13374,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_7728]),
    [final] ).

cnf(i_0_13375,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_7729]),
    [final] ).

cnf(i_0_13376,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_7730]),
    [final] ).

cnf(i_0_13377,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_7731]),
    [final] ).

cnf(i_0_13378,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3))),esk536_3(X1,X2,X3))
    | X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3))),esk534_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_7732]),
    [final] ).

cnf(i_0_13379,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_7733]),
    [final] ).

cnf(i_0_13380,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X1))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(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_7734,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13381,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_7735,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13382,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_7736,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13383,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_7737,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13384,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_7738,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13385,plain,
    ( hBOOL(hAPP(X1,X2))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(X1,esk518_4(X1,X2,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7309]),
    [final] ).

cnf(i_0_13386,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_7739]),
    [final] ).

cnf(i_0_13387,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_7740]),
    [final] ).

cnf(i_0_13388,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_7741]),
    [final] ).

cnf(i_0_13389,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_7742]),
    [final] ).

cnf(i_0_13390,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk539_3(X1,X2,X3))),esk540_3(X1,X2,X3))
    | X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk537_3(X1,X2,X3))),esk538_3(X1,X2,X3))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_13391,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_7744]),
    [final] ).

cnf(i_0_13392,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_7745]),
    [final] ).

cnf(i_0_13393,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk286_3(X1,X2,X3)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk285_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_6296]),
    [final] ).

cnf(i_0_13394,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk283_3(X1,X2,X3)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk282_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_6297]),
    [final] ).

cnf(i_0_13395,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_7746]),
    [final] ).

cnf(i_0_13396,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_7747]),
    [final] ).

cnf(i_0_13397,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_7748,c_0_6103]),
    [final] ).

cnf(i_0_13398,plain,
    hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(X1),tc_Option_Ooption(X2),X3,hAPP(c_Option_Omap(X1,X2),X4)),hAPP(c_COMBK(tc_Option_Ooption(X1),X3),c_Option_Ooption_ONone(X1))),X5) = c_Option_Ooption_ONone(X2),
    inference(split_conjunct,[status(thm)],[i_0_7749]),
    [final] ).

cnf(i_0_13399,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_7750]),
    [final] ).

cnf(i_0_13400,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Set_Oimage(X1,X2,X3),X4)))
    | c_Fun_Oinj__on(X1,X2,hAPP(hAPP(hAPP(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_7751]),
    [final] ).

cnf(i_0_13401,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_7752]),
    [final] ).

cnf(i_0_13402,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_7753]),
    [final] ).

cnf(i_0_13403,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_7754]),
    [final] ).

cnf(i_0_13404,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_7755]),
    [final] ).

cnf(i_0_13405,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_7756]),
    [final] ).

cnf(i_0_13406,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_7610]),
    [final] ).

cnf(i_0_13407,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_7610]),
    [final] ).

cnf(i_0_13408,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_7757]),
    [final] ).

cnf(i_0_13409,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_7758]),
    [final] ).

cnf(i_0_13410,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_7759,c_0_6311]),
    [final] ).

cnf(i_0_13411,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_7760]),
    [final] ).

cnf(i_0_13412,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_7202]),
    [final] ).

cnf(i_0_13413,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_7203]),
    [final] ).

cnf(i_0_13414,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_7761,c_0_6147]),
    [final] ).

cnf(i_0_13415,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_7497]),
    [final] ).

cnf(i_0_13416,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_7762]),
    [final] ).

cnf(i_0_13417,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_7763,c_0_6209]),
    [final] ).

cnf(i_0_13418,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,esk126_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_7703]),
    [final] ).

cnf(i_0_13419,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_7764]),
    [final] ).

cnf(i_0_13420,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_7765]),
    [final] ).

cnf(i_0_13421,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk539_3(X1,X2,X3))),esk540_3(X1,X2,X3))
    | X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk537_3(X1,X2,X3))),esk538_3(X1,X2,X3))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_13422,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3))),esk536_3(X1,X2,X3))
    | X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3))),esk534_3(X1,X2,X3))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_13423,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_7766,c_0_6768]),c_0_6768]),c_0_6768]),
    [final] ).

cnf(i_0_13424,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk129_3(X1,X3,X2))),esk130_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_7567]),
    [final] ).

cnf(i_0_13425,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_7610]),
    [final] ).

cnf(i_0_13426,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_7354]),
    [final] ).

cnf(i_0_13427,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_7354]),
    [final] ).

cnf(i_0_13428,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_7767,c_0_6147]),
    [final] ).

cnf(i_0_13429,plain,
    ( hBOOL(hAPP(X1,esk221_2(X1,X2)))
    | hBOOL(hAPP(X1,esk219_2(X1,X2)))
    | hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk219_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk220_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_7247]),
    [final] ).

cnf(i_0_13430,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_7768]),
    [final] ).

cnf(i_0_13431,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_7769]),
    [final] ).

cnf(i_0_13432,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk127_3(X1,X3,X2))),esk128_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_7576]),
    [final] ).

cnf(i_0_13433,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_7770]),
    [final] ).

cnf(i_0_13434,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_7771]),
    [final] ).

cnf(i_0_13435,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk31_3(X3,X2,X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7772]),
    [final] ).

cnf(i_0_13436,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_7773]),
    [final] ).

cnf(i_0_13437,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_7774]),
    [final] ).

cnf(i_0_13438,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_7775]),
    [final] ).

cnf(i_0_13439,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_7776]),
    [final] ).

cnf(i_0_13440,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,esk373_4(X3,X2,X1,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7297]),
    [final] ).

cnf(i_0_13441,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_7777]),
    [final] ).

cnf(i_0_13442,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_7777]),
    [final] ).

cnf(i_0_13443,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,esk126_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_7703]),
    [final] ).

cnf(i_0_13444,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_7778]),
    [final] ).

cnf(i_0_13445,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_7779]),
    [final] ).

cnf(i_0_13446,plain,
    ( hBOOL(hAPP(X1,esk264_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_7464]),
    [final] ).

cnf(i_0_13447,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_7703]),
    [final] ).

cnf(i_0_13448,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_7780]),
    [final] ).

cnf(i_0_13449,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_7334]),
    [final] ).

cnf(i_0_13450,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(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_7781,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13451,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_6999]),
    [final] ).

cnf(i_0_13452,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_7782]),
    [final] ).

cnf(i_0_13453,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_7783]),
    [final] ).

cnf(i_0_13454,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_7784]),
    [final] ).

cnf(i_0_13455,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_7785]),
    [final] ).

cnf(i_0_13456,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_7786]),
    [final] ).

cnf(i_0_13457,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_7787]),
    [final] ).

cnf(i_0_13458,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_7788,c_0_6768]),c_0_6768]),
    [final] ).

cnf(i_0_13459,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_7553]),
    [final] ).

cnf(i_0_13460,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_7789]),
    [final] ).

cnf(i_0_13461,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_7790]),
    [final] ).

cnf(i_0_13462,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_7791]),
    [final] ).

cnf(i_0_13463,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_7792]),
    [final] ).

cnf(i_0_13464,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_7793]),
    [final] ).

cnf(i_0_13465,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_7489]),
    [final] ).

cnf(i_0_13466,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_7125]),
    [final] ).

cnf(i_0_13467,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_7126]),
    [final] ).

cnf(i_0_13468,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_7794]),
    [final] ).

cnf(i_0_13469,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_7794]),
    [final] ).

cnf(i_0_13470,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_7795]),
    [final] ).

cnf(i_0_13471,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_7795]),
    [final] ).

cnf(i_0_13472,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_7796,c_0_6128]),
    [final] ).

cnf(i_0_13473,plain,
    ( hAPP(hAPP(c_Map_Omap__of(X1,X4),hAPP(hAPP(c_List_Ozip(X1,X4),X3),hAPP(hAPP(c_List_Omap(X1,X4),X5),X3))),X2) = hAPP(c_Option_Ooption_OSome(X4),hAPP(X5,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7797]),
    [final] ).

cnf(i_0_13474,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_7798]),
    [final] ).

cnf(i_0_13475,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_6816]),
    [final] ).

cnf(i_0_13476,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_7799]),
    [final] ).

cnf(i_0_13477,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_7800]),
    [final] ).

cnf(i_0_13478,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_7801]),
    [final] ).

cnf(i_0_13479,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_7802]),
    [final] ).

cnf(i_0_13480,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_7803,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13481,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_7804]),
    [final] ).

cnf(i_0_13482,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)))
    | hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),X4) != hAPP(c_Option_Ooption_OSome(X2),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7805]),
    [final] ).

cnf(i_0_13483,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)))
    | hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),X4) != hAPP(c_Option_Ooption_OSome(X2),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7806]),
    [final] ).

cnf(i_0_13484,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(c_Set_Oimage(X1,tc_Option_Ooption(X4),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),X5),X2),hAPP(c_Option_Ooption_OSome(X4),X6))),X3) = hAPP(c_Set_Oimage(X1,tc_Option_Ooption(X4),X5),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7807]),
    [final] ).

cnf(i_0_13485,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_7808,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13486,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_7809,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13487,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_7810,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13488,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_7811,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13489,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_7812]),
    [final] ).

cnf(i_0_13490,plain,
    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) = 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),
    inference(rw,[status(thm)],[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_7813,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6242]),c_0_6242]),c_0_6242]),
    [final] ).

cnf(i_0_13491,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_7814]),
    [final] ).

cnf(i_0_13492,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_7815]),
    [final] ).

cnf(i_0_13493,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_7816,c_0_6136]),
    [final] ).

cnf(i_0_13494,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk205_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_7685]),
    [final] ).

cnf(i_0_13495,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk195_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_7686]),
    [final] ).

cnf(i_0_13496,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_7760]),
    [final] ).

cnf(i_0_13497,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_7817]),
    [final] ).

cnf(i_0_13498,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_7818]),
    [final] ).

cnf(i_0_13499,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_7819]),
    [final] ).

cnf(i_0_13500,plain,
    ( hBOOL(hAPP(X2,X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk512_3(X2,X3,X1)),esk513_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_7289]),
    [final] ).

cnf(i_0_13501,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_7820]),
    [final] ).

cnf(i_0_13502,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_7821,c_0_6128]),
    [final] ).

cnf(i_0_13503,plain,
    c_Map_Omap__add(X1,X2,X3,c_Map_Omap__add(X1,X2,X4,X5)) = c_Map_Omap__add(X1,X2,c_Map_Omap__add(X1,X2,X3,X4),X5),
    inference(split_conjunct,[status(thm)],[i_0_7822]),
    [final] ).

cnf(i_0_13504,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_7823]),
    [final] ).

cnf(i_0_13505,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_7824]),
    [final] ).

cnf(i_0_13506,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_7825]),
    [final] ).

cnf(i_0_13507,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_7826]),
    [final] ).

cnf(i_0_13508,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_7827]),
    [final] ).

cnf(i_0_13509,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_7828]),
    [final] ).

cnf(i_0_13510,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_7829]),
    [final] ).

cnf(i_0_13511,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_7830]),
    [final] ).

cnf(i_0_13512,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_7831]),
    [final] ).

cnf(i_0_13513,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_7832]),
    [final] ).

cnf(i_0_13514,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_7833,c_0_6311]),
    [final] ).

cnf(i_0_13515,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_7834]),
    [final] ).

cnf(i_0_13516,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_7835]),
    [final] ).

cnf(i_0_13517,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_7836]),
    [final] ).

cnf(i_0_13518,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_7837]),
    [final] ).

cnf(i_0_13519,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ c_Orderings_Oorder__class_Omono(X1,X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2))))) ),
    inference(split_conjunct,[status(thm)],[i_0_7838]),
    [final] ).

cnf(i_0_13520,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_7839,c_0_6177]),
    [final] ).

cnf(i_0_13521,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,esk315_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_7272]),
    [final] ).

cnf(i_0_13522,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_7819]),
    [final] ).

cnf(i_0_13523,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_7840]),
    [final] ).

cnf(i_0_13524,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_7841]),
    [final] ).

cnf(i_0_13525,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_7842]),
    [final] ).

cnf(i_0_13526,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_7843]),
    [final] ).

cnf(i_0_13527,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_7844]),
    [final] ).

cnf(i_0_13528,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_7845]),
    [final] ).

cnf(i_0_13529,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_7846]),
    [final] ).

cnf(i_0_13530,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_7847]),
    [final] ).

cnf(i_0_13531,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_7848]),
    [final] ).

cnf(i_0_13532,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_7849]),
    [final] ).

cnf(i_0_13533,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_7850]),
    [final] ).

cnf(i_0_13534,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_7851]),
    [final] ).

cnf(i_0_13535,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_7852,c_0_6177]),
    [final] ).

cnf(i_0_13536,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_7853]),
    [final] ).

cnf(i_0_13537,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_7819]),
    [final] ).

cnf(i_0_13538,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk162_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_7854]),
    [final] ).

cnf(i_0_13539,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk162_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_7854]),
    [final] ).

cnf(i_0_13540,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk160_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_7855]),
    [final] ).

cnf(i_0_13541,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk160_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_7855]),
    [final] ).

cnf(i_0_13542,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_6530]),
    [final] ).

cnf(i_0_13543,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_7856]),
    [final] ).

cnf(i_0_13544,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_7857]),
    [final] ).

cnf(i_0_13545,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_7858]),
    [final] ).

cnf(i_0_13546,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_7859]),
    [final] ).

cnf(i_0_13547,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_7860]),
    [final] ).

cnf(i_0_13548,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_7861]),
    [final] ).

cnf(i_0_13549,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_7862]),
    [final] ).

cnf(i_0_13550,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_7863]),
    [final] ).

cnf(i_0_13551,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_7637]),
    [final] ).

cnf(i_0_13552,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_7638]),
    [final] ).

cnf(i_0_13553,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_7864]),
    [final] ).

cnf(i_0_13554,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_7434]),
    [final] ).

cnf(i_0_13555,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_7865]),
    [final] ).

cnf(i_0_13556,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,esk287_3(X1,X2,X3))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7866]),
    [final] ).

cnf(i_0_13557,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,esk120_3(X1,X2,X3))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7867]),
    [final] ).

cnf(i_0_13558,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_7868]),
    [final] ).

cnf(i_0_13559,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_7869]),
    [final] ).

cnf(i_0_13560,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_7870]),
    [final] ).

cnf(i_0_13561,plain,
    hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))),X3),c_Option_Ooption_ONone(X2)),X4) = c_Option_Ooption_ONone(X2),
    inference(split_conjunct,[status(thm)],[i_0_7871]),
    [final] ).

cnf(i_0_13562,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_7872]),
    [final] ).

cnf(i_0_13563,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_7873]),
    [final] ).

cnf(i_0_13564,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_7874]),
    [final] ).

cnf(i_0_13565,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_7123]),
    [final] ).

cnf(i_0_13566,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_5346]),
    [final] ).

cnf(i_0_13567,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_7875]),
    [final] ).

cnf(i_0_13568,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_7876]),
    [final] ).

cnf(i_0_13569,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_7877]),
    [final] ).

cnf(i_0_13570,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_7878]),
    [final] ).

cnf(i_0_13571,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_7879]),
    [final] ).

cnf(i_0_13572,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_7880]),
    [final] ).

cnf(i_0_13573,plain,
    ( X1 = hAPP(X2,esk21_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_7180]),
    [final] ).

cnf(i_0_13574,plain,
    ( X1 = hAPP(X2,esk16_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_7181]),
    [final] ).

cnf(i_0_13575,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),hAPP(c_Map_Omap__of(X2,X1),X3)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))),
    inference(split_conjunct,[status(thm)],[i_0_7881]),
    [final] ).

cnf(i_0_13576,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_7882]),
    [final] ).

cnf(i_0_13577,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_7580]),
    [final] ).

cnf(i_0_13578,plain,
    ( c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),c_Map_Omap__add(X1,X2,X4,X3),c_Map_Odom(X1,X2,X3))
    | ~ c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),X3,c_Map_Odom(X1,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7691]),
    [final] ).

cnf(i_0_13579,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_6614]),
    [final] ).

cnf(i_0_13580,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_7883]),
    [final] ).

cnf(i_0_13581,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_7884]),
    [final] ).

cnf(i_0_13582,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_7885,c_0_6147]),
    [final] ).

cnf(i_0_13583,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_7886]),
    [final] ).

cnf(i_0_13584,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_7887]),
    [final] ).

cnf(i_0_13585,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_7888]),
    [final] ).

cnf(i_0_13586,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_7888]),
    [final] ).

cnf(i_0_13587,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_7889]),
    [final] ).

cnf(i_0_13588,plain,
    ( hBOOL(hAPP(X1,esk522_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_7335]),
    [final] ).

cnf(i_0_13589,plain,
    ( hBOOL(hAPP(X1,esk509_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_7336]),
    [final] ).

cnf(i_0_13590,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_7890,c_0_6128]),
    [final] ).

cnf(i_0_13591,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_7891,c_0_6128]),
    [final] ).

cnf(i_0_13592,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_7049]),
    [final] ).

cnf(i_0_13593,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_7050]),
    [final] ).

cnf(i_0_13594,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk536_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3))),esk534_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_7732]),
    [final] ).

cnf(i_0_13595,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_7892,c_0_6311]),
    [final] ).

cnf(i_0_13596,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_7893]),
    [final] ).

cnf(i_0_13597,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3))),esk536_3(X1,X2,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X1,X2,X3)),X2))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_13598,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_7163]),
    [final] ).

cnf(i_0_13599,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk540_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk537_3(X1,X2,X3))),esk538_3(X1,X2,X3))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_13600,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_7894]),
    [final] ).

cnf(i_0_13601,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_7895]),
    [final] ).

cnf(i_0_13602,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_7896]),
    [final] ).

cnf(i_0_13603,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_7897]),
    [final] ).

cnf(i_0_13604,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_7898]),
    [final] ).

cnf(i_0_13605,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_7899,c_0_6128]),
    [final] ).

cnf(i_0_13606,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_7900]),
    [final] ).

cnf(i_0_13607,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_7901]),
    [final] ).

cnf(i_0_13608,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_7902]),
    [final] ).

cnf(i_0_13609,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_7903]),
    [final] ).

cnf(i_0_13610,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_7904]),
    [final] ).

cnf(i_0_13611,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk539_3(X1,X2,X3))),esk540_3(X1,X2,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk538_3(X1,X2,X3)),X2))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_13612,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_7905]),
    [final] ).

cnf(i_0_13613,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_7906]),
    [final] ).

cnf(i_0_13614,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_7907]),
    [final] ).

cnf(i_0_13615,plain,
    ( c_Fun_Oinj__on(X1,X2,esk101_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_6669]),
    [final] ).

cnf(i_0_13616,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_7908]),
    [final] ).

cnf(i_0_13617,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_7909]),
    [final] ).

cnf(i_0_13618,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_7910,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13619,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_7911]),
    [final] ).

cnf(i_0_13620,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_7912]),
    [final] ).

cnf(i_0_13621,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_7913]),
    [final] ).

cnf(i_0_13622,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_7901]),
    [final] ).

cnf(i_0_13623,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_7900]),
    [final] ).

cnf(i_0_13624,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_7914]),
    [final] ).

cnf(i_0_13625,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_7915]),
    [final] ).

cnf(i_0_13626,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_7916]),
    [final] ).

cnf(i_0_13627,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_7917]),
    [final] ).

cnf(i_0_13628,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_7918]),
    [final] ).

cnf(i_0_13629,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_7919]),
    [final] ).

cnf(i_0_13630,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | hAPP(hAPP(c_Map_Omap__of(X1,X4),hAPP(hAPP(c_List_Ozip(X1,X4),X3),hAPP(hAPP(c_List_Omap(X1,X4),X5),X3))),X2) = c_Option_Ooption_ONone(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7797]),
    [final] ).

cnf(i_0_13631,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk374_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_7651]),
    [final] ).

cnf(i_0_13632,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_7920,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13633,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_7900]),
    [final] ).

cnf(i_0_13634,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_7901]),
    [final] ).

cnf(i_0_13635,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_7921]),
    [final] ).

cnf(i_0_13636,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_7922]),
    [final] ).

cnf(i_0_13637,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_7760]),
    [final] ).

cnf(i_0_13638,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_7923]),
    [final] ).

cnf(i_0_13639,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_7924]),
    [final] ).

cnf(i_0_13640,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk412_3(X1,X3,X2))))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7925]),
    [final] ).

cnf(i_0_13641,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_7926]),
    [final] ).

cnf(i_0_13642,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_7549]),
    [final] ).

cnf(i_0_13643,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_7927,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13644,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_7928,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13645,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_7901]),
    [final] ).

cnf(i_0_13646,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_7900]),
    [final] ).

cnf(i_0_13647,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_7640]),
    [final] ).

cnf(i_0_13648,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_7641]),
    [final] ).

cnf(i_0_13649,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_7929,c_0_6136]),
    [final] ).

cnf(i_0_13650,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_7930]),
    [final] ).

cnf(i_0_13651,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk540_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk537_3(X1,X2,X3))),esk538_3(X1,X2,X3))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_13652,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk536_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3))),esk534_3(X1,X2,X3))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_13653,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_6480]),
    [final] ).

cnf(i_0_13654,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),esk455_3(X2,X3,X1)),esk456_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_7931]),
    [final] ).

cnf(i_0_13655,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_7932]),
    [final] ).

cnf(i_0_13656,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk539_3(X1,X2,X3))),esk540_3(X1,X2,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk538_3(X1,X2,X3)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_13657,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3))),esk536_3(X1,X2,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X1,X2,X3)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_13658,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_7202]),
    [final] ).

cnf(i_0_13659,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_7203]),
    [final] ).

cnf(i_0_13660,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_7933]),
    [final] ).

cnf(i_0_13661,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_7934]),
    [final] ).

cnf(i_0_13662,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk130_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_7567]),
    [final] ).

cnf(i_0_13663,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_7935]),
    [final] ).

cnf(i_0_13664,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_7524]),
    [final] ).

cnf(i_0_13665,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_7525]),
    [final] ).

cnf(i_0_13666,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_7936]),
    [final] ).

cnf(i_0_13667,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_7937]),
    [final] ).

cnf(i_0_13668,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk128_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_7576]),
    [final] ).

cnf(i_0_13669,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk205_3(X2,X1,X3)),esk204_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_7685]),
    [final] ).

cnf(i_0_13670,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk195_3(X2,X1,X3)),esk194_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_7686]),
    [final] ).

cnf(i_0_13671,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_7938]),
    [final] ).

cnf(i_0_13672,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_7939]),
    [final] ).

cnf(i_0_13673,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_7940]),
    [final] ).

cnf(i_0_13674,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_7637]),
    [final] ).

cnf(i_0_13675,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_7524]),
    [final] ).

cnf(i_0_13676,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_7941]),
    [final] ).

cnf(i_0_13677,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_7942]),
    [final] ).

cnf(i_0_13678,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_7943]),
    [final] ).

cnf(i_0_13679,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_7638]),
    [final] ).

cnf(i_0_13680,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_7525]),
    [final] ).

cnf(i_0_13681,plain,
    ( X2 = hAPP(c_Set_Oimage(tc_Nat_Onat,X1,esk96_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)),esk95_2(X2,X1))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7645]),
    [final] ).

cnf(i_0_13682,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | c_Smallcheck_Osmall_H(X3,X1,X2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X3,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7944]),
    [final] ).

cnf(i_0_13683,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_7886]),
    [final] ).

cnf(i_0_13684,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_7945]),
    [final] ).

cnf(i_0_13685,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_7565]),
    [final] ).

cnf(i_0_13686,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_7566]),
    [final] ).

cnf(i_0_13687,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk293_3(X2,X3,X1)),X3))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk292_3(X2,X3,X1)),X2))
    | c_Relation_Orefl__on(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6212]),
    [final] ).

cnf(i_0_13688,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_7946]),
    [final] ).

cnf(i_0_13689,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_7947]),
    [final] ).

cnf(i_0_13690,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_7711]),
    [final] ).

cnf(i_0_13691,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_7948,c_0_6768]),
    [final] ).

cnf(i_0_13692,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_7949,c_0_6177]),
    [final] ).

cnf(i_0_13693,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_7950,c_0_6177]),
    [final] ).

cnf(i_0_13694,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_7951]),
    [final] ).

cnf(i_0_13695,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_7952]),
    [final] ).

cnf(i_0_13696,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_7953]),
    [final] ).

cnf(i_0_13697,plain,
    ( c_Map_Odom(X2,X3,X1) = hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))
    | X1 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X2,tc_Option_Ooption(X3)),hAPP(c_COMBK(tc_Option_Ooption(X3),X2),c_Option_Ooption_ONone(X3))),X4),hAPP(c_Option_Ooption_OSome(X3),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7551]),
    [final] ).

cnf(i_0_13698,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_7954]),
    [final] ).

cnf(i_0_13699,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_7955]),
    [final] ).

cnf(i_0_13700,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_7956]),
    [final] ).

cnf(i_0_13701,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_7902]),
    [final] ).

cnf(i_0_13702,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_7957]),
    [final] ).

cnf(i_0_13703,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_7958]),
    [final] ).

cnf(i_0_13704,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_7959]),
    [final] ).

cnf(i_0_13705,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_7960]),
    [final] ).

cnf(i_0_13706,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_7961,c_0_6209]),c_0_6209]),c_0_6209]),
    [final] ).

cnf(i_0_13707,plain,
    ( hBOOL(hAPP(X2,X4))
    | ~ c_Enum_Oall__n__lists(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X3,c_Enum_Oenum__class_Oenum(X1)))))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7962]),
    [final] ).

cnf(i_0_13708,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_7963]),
    [final] ).

cnf(i_0_13709,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_5347]),
    [final] ).

cnf(i_0_13710,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_7568]),
    [final] ).

cnf(i_0_13711,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_7964]),
    [final] ).

cnf(i_0_13712,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_7965]),
    [final] ).

cnf(i_0_13713,plain,
    ( hBOOL(hAPP(X2,c_Option_Ooption_ONone(X1)))
    | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X1),tc_HOL_Obool,X1),X2),c_Option_Ooption_OSome(X1))))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X1)),X2))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7600]),
    [final] ).

cnf(i_0_13714,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)),esk371_3(X2,X3,X1)),esk372_3(X2,X3,X1)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7630]),
    [final] ).

cnf(i_0_13715,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_7966]),
    [final] ).

cnf(i_0_13716,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_7967]),
    [final] ).

cnf(i_0_13717,plain,
    ( c_Enum_Oex__n__lists(X1,X4,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,c_Enum_Oenum__class_Oenum(X1)))))
    | ~ hBOOL(hAPP(X4,X2))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7968]),
    [final] ).

cnf(i_0_13718,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_7969]),
    [final] ).

cnf(i_0_13719,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_6212]),
    [final] ).

cnf(i_0_13720,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_6721]),
    [final] ).

cnf(i_0_13721,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_7970]),
    [final] ).

cnf(i_0_13722,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_7971]),
    [final] ).

cnf(i_0_13723,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_7972]),
    [final] ).

cnf(i_0_13724,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_7973]),
    [final] ).

cnf(i_0_13725,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_7974]),
    [final] ).

cnf(i_0_13726,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_6816]),
    [final] ).

cnf(i_0_13727,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_7716]),
    [final] ).

cnf(i_0_13728,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_7975]),
    [final] ).

cnf(i_0_13729,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_7976]),
    [final] ).

cnf(i_0_13730,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_7977]),
    [final] ).

cnf(i_0_13731,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk408_3(X2,X3,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X2,c_Enum_Oenum__class_Oenum(X1)))))
    | ~ c_Enum_Oex__n__lists(X1,X3,X2)
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7968]),
    [final] ).

cnf(i_0_13732,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_7978,c_0_6311]),
    [final] ).

cnf(i_0_13733,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),esk519_3(X3,X2,X1))))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7979]),
    [final] ).

cnf(i_0_13734,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_7663]),
    [final] ).

cnf(i_0_13735,plain,
    c_Map_Orestrict__map(X1,X2,c_Map_Orestrict__map(X1,X2,X3,X4),X5) = c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5)),
    inference(split_conjunct,[status(thm)],[i_0_7980]),
    [final] ).

cnf(i_0_13736,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_7981]),
    [final] ).

cnf(i_0_13737,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_7982]),
    [final] ).

cnf(i_0_13738,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_7983]),
    [final] ).

cnf(i_0_13739,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_7984]),
    [final] ).

cnf(i_0_13740,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_7985]),
    [final] ).

cnf(i_0_13741,plain,
    ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,esk108_2(X2,X1))),hAPP(X2,hAPP(c_Nat_OSuc,esk108_2(X2,X1)))))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7986]),
    [final] ).

cnf(i_0_13742,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_7987]),
    [final] ).

cnf(i_0_13743,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_7988]),
    [final] ).

cnf(i_0_13744,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_7989]),
    [final] ).

cnf(i_0_13745,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_7990]),
    [final] ).

cnf(i_0_13746,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_7991]),
    [final] ).

cnf(i_0_13747,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_7992]),
    [final] ).

cnf(i_0_13748,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_7993,c_0_6311]),
    [final] ).

cnf(i_0_13749,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_7994]),
    [final] ).

cnf(i_0_13750,plain,
    ( c_Map_Omap__add(X1,X2,X3,X4) = c_Map_Omap__add(X1,X2,X4,X3)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),c_Map_Odom(X1,X2,X4)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7995]),
    [final] ).

cnf(i_0_13751,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_7996]),
    [final] ).

cnf(i_0_13752,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_7626]),
    [final] ).

cnf(i_0_13753,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_7997]),
    [final] ).

cnf(i_0_13754,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_7052]),
    [final] ).

cnf(i_0_13755,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_7053]),
    [final] ).

cnf(i_0_13756,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_7998,c_0_6748]),
    [final] ).

cnf(i_0_13757,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_7999]),
    [final] ).

cnf(i_0_13758,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_8000]),
    [final] ).

cnf(i_0_13759,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_7625]),
    [final] ).

cnf(i_0_13760,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X1),tc_HOL_Obool,X1),X2),c_Option_Ooption_OSome(X1))))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X1)),X2))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7569]),
    [final] ).

cnf(i_0_13761,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,esk288_2(X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8001]),
    [final] ).

cnf(i_0_13762,plain,
    ( hAPP(X1,esk32_4(X2,X1,X3,X4)) = hAPP(X1,esk33_4(X2,X1,X3,X4))
    | c_Fun_Oinj__on(X4,X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7399]),
    [final] ).

cnf(i_0_13763,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_7634]),
    [final] ).

cnf(i_0_13764,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_8002]),
    [final] ).

cnf(i_0_13765,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_13766,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_8003]),
    [final] ).

cnf(i_0_13767,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_8004]),
    [final] ).

cnf(i_0_13768,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_8005]),
    [final] ).

cnf(i_0_13769,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_8006]),
    [final] ).

cnf(i_0_13770,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_8007]),
    [final] ).

cnf(i_0_13771,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_8008]),
    [final] ).

cnf(i_0_13772,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_8009]),
    [final] ).

cnf(i_0_13773,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_8010]),
    [final] ).

cnf(i_0_13774,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3))),esk536_3(X1,X2,X3))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk533_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_13775,plain,
    ( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk533_3(X2,X3,X1))),esk534_3(X2,X3,X1))
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk535_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_13776,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_8011]),
    [final] ).

cnf(i_0_13777,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_8012]),
    [final] ).

cnf(i_0_13778,plain,
    c_Option_Ooption_Ooption__rec(X1,X2,X3,X4,hAPP(c_Option_Ooption_OSome(X2),X5)) = hAPP(X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_8013]),
    [final] ).

cnf(i_0_13779,plain,
    hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),X3),X4)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_Map_Omap__of(X1,X2),X4)),hAPP(c_Product__Type_Ofst(X1,X2),X3)),hAPP(c_Option_Ooption_OSome(X2),hAPP(c_Product__Type_Osnd(X1,X2),X3))),
    inference(split_conjunct,[status(thm)],[i_0_8014]),
    [final] ).

cnf(i_0_13780,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_8015]),
    [final] ).

cnf(i_0_13781,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_6616]),
    [final] ).

cnf(i_0_13782,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_8016]),
    [final] ).

cnf(i_0_13783,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_8017]),
    [final] ).

cnf(i_0_13784,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_8018]),
    [final] ).

cnf(i_0_13785,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_8019]),
    [final] ).

cnf(i_0_13786,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_8020,c_0_6311]),
    [final] ).

cnf(i_0_13787,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_8021]),
    [final] ).

cnf(i_0_13788,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk539_3(X1,X2,X3))),esk540_3(X1,X2,X3))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk538_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_13789,plain,
    ( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk537_3(X2,X3,X1))),esk538_3(X2,X3,X1))
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk540_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_13790,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk498_3(X3,X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8022]),
    [final] ).

cnf(i_0_13791,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk495_3(X3,X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8023]),
    [final] ).

cnf(i_0_13792,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk409_3(X2,X3,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X2,c_Enum_Oenum__class_Oenum(X1)))))
    | c_Enum_Oall__n__lists(X1,X3,X2)
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7962]),
    [final] ).

cnf(i_0_13793,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_8024,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_13794,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_8025]),
    [final] ).

cnf(i_0_13795,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_8026]),
    [final] ).

cnf(i_0_13796,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_8027]),
    [final] ).

cnf(i_0_13797,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_8028]),
    [final] ).

cnf(i_0_13798,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_8029]),
    [final] ).

cnf(i_0_13799,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_8030]),
    [final] ).

cnf(i_0_13800,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_8031]),
    [final] ).

cnf(i_0_13801,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_8032]),
    [final] ).

cnf(i_0_13802,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_8033]),
    [final] ).

cnf(i_0_13803,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_7726]),
    [final] ).

cnf(i_0_13804,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_13805,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_8034]),
    [final] ).

cnf(i_0_13806,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_8035]),
    [final] ).

cnf(i_0_13807,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_8036]),
    [final] ).

cnf(i_0_13808,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_8037]),
    [final] ).

cnf(i_0_13809,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_7912]),
    [final] ).

cnf(i_0_13810,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_8038,c_0_6103]),
    [final] ).

cnf(i_0_13811,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_8039,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13812,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_8040]),
    [final] ).

cnf(i_0_13813,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_6816]),
    [final] ).

cnf(i_0_13814,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_8041]),
    [final] ).

cnf(i_0_13815,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_8042]),
    [final] ).

cnf(i_0_13816,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_8043]),
    [final] ).

cnf(i_0_13817,plain,
    ( hBOOL(hAPP(X1,esk15_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X5),X2))
    | ~ hBOOL(hAPP(X1,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6886]),
    [final] ).

cnf(i_0_13818,plain,
    ( hBOOL(hAPP(X1,esk15_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X5),X3))
    | ~ hBOOL(hAPP(X1,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6886]),
    [final] ).

cnf(i_0_13819,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_8044,c_0_6748]),
    [final] ).

cnf(i_0_13820,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_8045,c_0_8046]),c_0_8047]),c_0_8047]),
    [final] ).

cnf(i_0_13821,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),esk115_3(X2,X3,X1)),esk116_3(X2,X3,X1)))
    | hAPP(c_Finite__Set_Ocard(X1),X3) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8048]),
    [final] ).

cnf(i_0_13822,plain,
    ( hAPP(X1,esk286_3(X2,X1,X3)) = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk285_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_6296]),
    [final] ).

cnf(i_0_13823,plain,
    ( hAPP(X1,esk283_3(X2,X1,X3)) = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk282_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_6297]),
    [final] ).

cnf(i_0_13824,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_8049]),
    [final] ).

cnf(i_0_13825,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_8050]),
    [final] ).

cnf(i_0_13826,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_8051]),
    [final] ).

cnf(i_0_13827,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_8052]),
    [final] ).

cnf(i_0_13828,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_8053]),
    [final] ).

cnf(i_0_13829,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_8054]),
    [final] ).

cnf(i_0_13830,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_8055]),
    [final] ).

cnf(i_0_13831,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),esk463_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2))) ),
    inference(rw,[status(thm)],[i_0_8056,c_0_6311]),
    [final] ).

cnf(i_0_13832,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_7591]),
    [final] ).

cnf(i_0_13833,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_7592]),
    [final] ).

cnf(i_0_13834,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_7939]),
    [final] ).

cnf(i_0_13835,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_8057]),
    [final] ).

cnf(i_0_13836,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_7524]),
    [final] ).

cnf(i_0_13837,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_7938]),
    [final] ).

cnf(i_0_13838,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_7637]),
    [final] ).

cnf(i_0_13839,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_7942]),
    [final] ).

cnf(i_0_13840,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_8058]),
    [final] ).

cnf(i_0_13841,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_7525]),
    [final] ).

cnf(i_0_13842,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_7941]),
    [final] ).

cnf(i_0_13843,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_7638]),
    [final] ).

cnf(i_0_13844,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_8059]),
    [final] ).

cnf(i_0_13845,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_8060]),
    [final] ).

cnf(i_0_13846,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_7610]),
    [final] ).

cnf(i_0_13847,plain,
    ( X3 = X2
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_fequal),esk404_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_7325]),
    [final] ).

cnf(i_0_13848,plain,
    c_Map_Omap__upds(X1,X2,X3,c_List_Olist_ONil(X1),X4) = X3,
    inference(split_conjunct,[status(thm)],[i_0_8061]),
    [final] ).

cnf(i_0_13849,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_8062]),
    [final] ).

cnf(i_0_13850,plain,
    c_Map_Omap__upds(X1,X2,X3,X4,c_List_Olist_ONil(X2)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_8063]),
    [final] ).

cnf(i_0_13851,plain,
    c_Option_Ooption_Ooption__rec(X1,X2,X3,X4,c_Option_Ooption_ONone(X2)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_8064]),
    [final] ).

cnf(i_0_13852,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_8065]),
    [final] ).

cnf(i_0_13853,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_8066]),
    [final] ).

cnf(i_0_13854,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_8067]),
    [final] ).

cnf(i_0_13855,plain,
    ( c_List_Olist__all2(X3,X3,c_fequal,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_7597]),
    [final] ).

cnf(i_0_13856,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_7902]),
    [final] ).

cnf(i_0_13857,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk539_3(X1,X2,X3))),esk540_3(X1,X2,X3))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk538_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_13858,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3))),esk536_3(X1,X2,X3))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk533_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_13859,plain,
    ( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk537_3(X2,X3,X1))),esk538_3(X2,X3,X1))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk540_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_13860,plain,
    ( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk533_3(X2,X3,X1))),esk534_3(X2,X3,X1))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk535_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_13861,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_8068,c_0_6748]),
    [final] ).

cnf(i_0_13862,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_8069]),
    [final] ).

cnf(i_0_13863,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_8070]),
    [final] ).

cnf(i_0_13864,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_8071]),
    [final] ).

cnf(i_0_13865,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_8072]),
    [final] ).

cnf(i_0_13866,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_7524]),
    [final] ).

cnf(i_0_13867,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_7525]),
    [final] ).

cnf(i_0_13868,plain,
    ( hBOOL(hAPP(X1,esk185_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_7303]),
    [final] ).

cnf(i_0_13869,plain,
    ( hBOOL(hAPP(X1,esk183_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_7304]),
    [final] ).

cnf(i_0_13870,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_8073]),
    [final] ).

cnf(i_0_13871,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_8074]),
    [final] ).

cnf(i_0_13872,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3))),esk536_3(X1,X2,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_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_7732]),
    [final] ).

cnf(i_0_13873,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_8075,c_0_6209]),c_0_6209]),
    [final] ).

cnf(i_0_13874,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk411_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_7925]),
    [final] ).

cnf(i_0_13875,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_8076]),
    [final] ).

cnf(i_0_13876,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_8077]),
    [final] ).

cnf(i_0_13877,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_8078]),
    [final] ).

cnf(i_0_13878,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_8079,c_0_6768]),c_0_6768]),
    [final] ).

cnf(i_0_13879,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_8080,c_0_6136]),c_0_6136]),
    [final] ).

cnf(i_0_13880,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk539_3(X1,X2,X3))),esk540_3(X1,X2,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk538_3(X1,X2,X3)))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_13881,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,esk234_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_7358]),
    [final] ).

cnf(i_0_13882,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_8081]),
    [final] ).

cnf(i_0_13883,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_8082]),
    [final] ).

cnf(i_0_13884,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_8083]),
    [final] ).

cnf(i_0_13885,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_7049]),
    [final] ).

cnf(i_0_13886,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_7050]),
    [final] ).

cnf(i_0_13887,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk536_3(X2,X1,X3)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk533_3(X2,X1,X3))),esk534_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_7732]),
    [final] ).

cnf(i_0_13888,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_8084]),
    [final] ).

cnf(i_0_13889,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_8085]),
    [final] ).

cnf(i_0_13890,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_8086]),
    [final] ).

cnf(i_0_13891,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_8087]),
    [final] ).

cnf(i_0_13892,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_7992]),
    [final] ).

cnf(i_0_13893,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_7992]),
    [final] ).

cnf(i_0_13894,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_8088]),
    [final] ).

cnf(i_0_13895,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_6848]),
    [final] ).

cnf(i_0_13896,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_8089]),
    [final] ).

cnf(i_0_13897,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk540_3(X2,X1,X3)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk537_3(X2,X1,X3))),esk538_3(X2,X1,X3))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_13898,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_8090]),
    [final] ).

cnf(i_0_13899,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_8091]),
    [final] ).

cnf(i_0_13900,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_8092]),
    [final] ).

cnf(i_0_13901,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_8093]),
    [final] ).

cnf(i_0_13902,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_8091]),
    [final] ).

cnf(i_0_13903,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_8093]),
    [final] ).

cnf(i_0_13904,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_8041]),
    [final] ).

cnf(i_0_13905,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_8094]),
    [final] ).

cnf(i_0_13906,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_8042]),
    [final] ).

cnf(i_0_13907,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_8095]),
    [final] ).

cnf(i_0_13908,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_7912]),
    [final] ).

cnf(i_0_13909,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_8096]),
    [final] ).

cnf(i_0_13910,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_8097]),
    [final] ).

cnf(i_0_13911,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_6690]),
    [final] ).

cnf(i_0_13912,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_6816]),
    [final] ).

cnf(i_0_13913,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_8098]),
    [final] ).

cnf(i_0_13914,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk536_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X1,X2,X3)),X2))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_13915,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_8099]),
    [final] ).

cnf(i_0_13916,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_8100,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13917,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_7225]),
    [final] ).

cnf(i_0_13918,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_8101]),
    [final] ).

cnf(i_0_13919,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_8102]),
    [final] ).

cnf(i_0_13920,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_7052]),
    [final] ).

cnf(i_0_13921,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_7053]),
    [final] ).

cnf(i_0_13922,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_8103]),
    [final] ).

cnf(i_0_13923,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_8104]),
    [final] ).

cnf(i_0_13924,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk540_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk538_3(X1,X2,X3)),X2))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_13925,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,esk236_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_7363]),
    [final] ).

cnf(i_0_13926,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_8105]),
    [final] ).

cnf(i_0_13927,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_8106,c_0_6147]),
    [final] ).

cnf(i_0_13928,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_8107]),
    [final] ).

cnf(i_0_13929,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_8108]),
    [final] ).

cnf(i_0_13930,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_8109,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13931,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | hAPP(hAPP(c_List_Omap(X1,X4),hAPP(hAPP(hAPP(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_8110]),
    [final] ).

cnf(i_0_13932,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_8111]),
    [final] ).

cnf(i_0_13933,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_8112]),
    [final] ).

cnf(i_0_13934,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_8113]),
    [final] ).

cnf(i_0_13935,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_7202]),
    [final] ).

cnf(i_0_13936,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_7203]),
    [final] ).

cnf(i_0_13937,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))
    | esk368_3(X1,X2,X3) != esk369_3(X1,X2,X3)
    | hAPP(c_Finite__Set_Ocard(X3),esk367_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_7424]),
    [final] ).

cnf(i_0_13938,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_8114]),
    [final] ).

cnf(i_0_13939,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_8115]),
    [final] ).

cnf(i_0_13940,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_8116]),
    [final] ).

cnf(i_0_13941,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_8117]),
    [final] ).

cnf(i_0_13942,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_8118]),
    [final] ).

cnf(i_0_13943,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_8119]),
    [final] ).

cnf(i_0_13944,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_8120]),
    [final] ).

cnf(i_0_13945,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_8121]),
    [final] ).

cnf(i_0_13946,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_8122]),
    [final] ).

cnf(i_0_13947,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk539_3(X1,X2,X3))),esk540_3(X1,X2,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk538_3(X1,X2,X3)))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_13948,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3))),esk536_3(X1,X2,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X1,X2,X3)))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_13949,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_8123]),
    [final] ).

cnf(i_0_13950,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_8124]),
    [final] ).

cnf(i_0_13951,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_8125,c_0_6209]),
    [final] ).

cnf(i_0_13952,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_8126]),
    [final] ).

cnf(i_0_13953,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_5346]),
    [final] ).

cnf(i_0_13954,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk130_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_7567]),
    [final] ).

cnf(i_0_13955,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_8127]),
    [final] ).

cnf(i_0_13956,plain,
    ( hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1)),X3)),X4) = hAPP(c_Option_Ooption_OSome(X2),esk436_4(X4,X3,X2,X1))
    | ~ class_Enum_Oenum(X1)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8128]),
    [final] ).

cnf(i_0_13957,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_8129,c_0_6103]),
    [final] ).

cnf(i_0_13958,plain,
    ( hBOOL(hAPP(X1,esk523_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_8130]),
    [final] ).

cnf(i_0_13959,plain,
    c_Fun_Oinj__on(X1,tc_prod(X2,X1),esk271_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_6571]),
    [final] ).

cnf(i_0_13960,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_8131]),
    [final] ).

cnf(i_0_13961,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_8132]),
    [final] ).

cnf(i_0_13962,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_8133]),
    [final] ).

cnf(i_0_13963,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk38_3(X2,X3,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8134]),
    [final] ).

cnf(i_0_13964,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk540_3(X2,X1,X3)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk537_3(X2,X1,X3))),esk538_3(X2,X1,X3))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_13965,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk536_3(X2,X1,X3)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk533_3(X2,X1,X3))),esk534_3(X2,X1,X3))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_13966,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(c_Set_Oimage(X1,X4,hAPP(hAPP(hAPP(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_7267]),
    [final] ).

cnf(i_0_13967,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_7637]),
    [final] ).

cnf(i_0_13968,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_7637]),
    [final] ).

cnf(i_0_13969,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_7638]),
    [final] ).

cnf(i_0_13970,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_7638]),
    [final] ).

cnf(i_0_13971,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_7637]),
    [final] ).

cnf(i_0_13972,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_7638]),
    [final] ).

cnf(i_0_13973,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_8135]),
    [final] ).

cnf(i_0_13974,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_8136]),
    [final] ).

cnf(i_0_13975,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_8137]),
    [final] ).

cnf(i_0_13976,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_8138]),
    [final] ).

cnf(i_0_13977,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(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_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X1)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8139,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13978,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_8140,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13979,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_8141,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13980,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_8142,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13981,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_8143,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_13982,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_7654]),
    [final] ).

cnf(i_0_13983,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_8144]),
    [final] ).

cnf(i_0_13984,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_8145]),
    [final] ).

cnf(i_0_13985,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_6816]),
    [final] ).

cnf(i_0_13986,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_8146]),
    [final] ).

cnf(i_0_13987,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_8147]),
    [final] ).

cnf(i_0_13988,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_8148]),
    [final] ).

cnf(i_0_13989,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk128_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_7576]),
    [final] ).

cnf(i_0_13990,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | X2 != c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X3)
    | ~ c_Orderings_Oorder__class_Omono(X1,X1,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8149]),
    [final] ).

cnf(i_0_13991,plain,
    hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X2),X2,hAPP(X3,X5),c_Option_Ooption_OSome(X2)),hAPP(X4,X5)),
    inference(split_conjunct,[status(thm)],[i_0_8150]),
    [final] ).

cnf(i_0_13992,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_8151]),
    [final] ).

cnf(i_0_13993,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_8152]),
    [final] ).

cnf(i_0_13994,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_8153]),
    [final] ).

cnf(i_0_13995,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_8154]),
    [final] ).

cnf(i_0_13996,plain,
    ( c_Map_Odom(X3,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X2)),X4),X5),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),c_Map_Odom(X3,X2,X4)),hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
    | X1 != c_Option_Ooption_ONone(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8155]),
    [final] ).

cnf(i_0_13997,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_8156]),
    [final] ).

cnf(i_0_13998,plain,
    ( hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)),X5) != c_Option_Ooption_ONone(X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(c_List_Oset(X1),X3)))
    | 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_8157]),
    [final] ).

cnf(i_0_13999,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_8088]),
    [final] ).

cnf(i_0_14000,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk387_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_8158]),
    [final] ).

cnf(i_0_14001,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_8159]),
    [final] ).

cnf(i_0_14002,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk74_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_8160]),
    [final] ).

cnf(i_0_14003,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_8161]),
    [final] ).

cnf(i_0_14004,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_8162]),
    [final] ).

cnf(i_0_14005,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk540_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk538_3(X1,X2,X3)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14006,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk536_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X1,X2,X3)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14007,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_8163]),
    [final] ).

cnf(i_0_14008,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_8164]),
    [final] ).

cnf(i_0_14009,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_8165]),
    [final] ).

cnf(i_0_14010,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_8166]),
    [final] ).

cnf(i_0_14011,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_8167]),
    [final] ).

cnf(i_0_14012,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_8168]),
    [final] ).

cnf(i_0_14013,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_8169]),
    [final] ).

cnf(i_0_14014,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_7709]),
    [final] ).

cnf(i_0_14015,plain,
    c_Lazy__Sequence_Ohb__map(X1,X2,X3,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X1),X4,X5)) = c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X2),hAPP(hAPP(c_Option_Omap(X1,X2),X3),X4),c_Lazy__Sequence_Ohb__map(X1,X2,X3,X5)),
    inference(split_conjunct,[status(thm)],[i_0_8170]),
    [final] ).

cnf(i_0_14016,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_8171]),
    [final] ).

cnf(i_0_14017,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_7900]),
    [final] ).

cnf(i_0_14018,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_8172]),
    [final] ).

cnf(i_0_14019,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_7901]),
    [final] ).

cnf(i_0_14020,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_8173]),
    [final] ).

cnf(i_0_14021,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_8174]),
    [final] ).

cnf(i_0_14022,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_7848]),
    [final] ).

cnf(i_0_14023,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_8175]),
    [final] ).

cnf(i_0_14024,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_8176]),
    [final] ).

cnf(i_0_14025,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_8177]),
    [final] ).

cnf(i_0_14026,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_8178]),
    [final] ).

cnf(i_0_14027,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_8179]),
    [final] ).

cnf(i_0_14028,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_7851]),
    [final] ).

cnf(i_0_14029,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_8180]),
    [final] ).

cnf(i_0_14030,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_8181]),
    [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),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_8182]),
    [final] ).

cnf(i_0_14032,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_8183]),
    [final] ).

cnf(i_0_14033,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_8184]),
    [final] ).

cnf(i_0_14034,plain,
    ( c_Big__Operators_Olinorder__class_OMax(X1,X3) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk322_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_8185]),
    [final] ).

cnf(i_0_14035,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_5497]),
    [final] ).

cnf(i_0_14036,plain,
    ( c_List_Olist__all(X2,X1,X3)
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk502_3(X3,X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8186]),
    [final] ).

cnf(i_0_14037,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_7867]),
    [final] ).

cnf(i_0_14038,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_8187]),
    [final] ).

cnf(i_0_14039,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_8188]),
    [final] ).

cnf(i_0_14040,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_8189]),
    [final] ).

cnf(i_0_14041,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_8190]),
    [final] ).

cnf(i_0_14042,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(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_8191,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_14043,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_8192,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_14044,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_8193,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_14045,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_8168]),
    [final] ).

cnf(i_0_14046,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_8167]),
    [final] ).

cnf(i_0_14047,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_8194]),
    [final] ).

cnf(i_0_14048,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_8195,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_14049,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_8196,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_14050,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_8197]),
    [final] ).

cnf(i_0_14051,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_8198]),
    [final] ).

cnf(i_0_14052,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_8199]),
    [final] ).

cnf(i_0_14053,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_8200,c_0_6748]),
    [final] ).

cnf(i_0_14054,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_7982]),
    [final] ).

cnf(i_0_14055,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_8201]),
    [final] ).

cnf(i_0_14056,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_8202]),
    [final] ).

cnf(i_0_14057,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_8203]),
    [final] ).

cnf(i_0_14058,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | c_Map_Orestrict__map(X1,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),X5),X2),X6),X3) = c_Map_Orestrict__map(X1,X4,X5,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6717]),
    [final] ).

cnf(i_0_14059,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_8204]),
    [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),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_8181]),
    [final] ).

cnf(i_0_14061,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_8181]),
    [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),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_8182]),
    [final] ).

cnf(i_0_14063,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_8182]),
    [final] ).

cnf(i_0_14064,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_8183]),
    [final] ).

cnf(i_0_14065,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_8183]),
    [final] ).

cnf(i_0_14066,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_6873]),
    [final] ).

cnf(i_0_14067,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_6873]),
    [final] ).

cnf(i_0_14068,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_7771]),
    [final] ).

cnf(i_0_14069,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_8205]),
    [final] ).

cnf(i_0_14070,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_7859]),
    [final] ).

cnf(i_0_14071,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_8206]),
    [final] ).

cnf(i_0_14072,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_7860]),
    [final] ).

cnf(i_0_14073,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_8207]),
    [final] ).

cnf(i_0_14074,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_7900]),
    [final] ).

cnf(i_0_14075,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_8208]),
    [final] ).

cnf(i_0_14076,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_7901]),
    [final] ).

cnf(i_0_14077,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_7869]),
    [final] ).

cnf(i_0_14078,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_8209]),
    [final] ).

cnf(i_0_14079,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_8210]),
    [final] ).

cnf(i_0_14080,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_8211]),
    [final] ).

cnf(i_0_14081,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_7870]),
    [final] ).

cnf(i_0_14082,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_8212]),
    [final] ).

cnf(i_0_14083,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_7163]),
    [final] ).

cnf(i_0_14084,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_7897]),
    [final] ).

cnf(i_0_14085,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_7898]),
    [final] ).

cnf(i_0_14086,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_7815]),
    [final] ).

cnf(i_0_14087,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_8213,c_0_6311]),
    [final] ).

cnf(i_0_14088,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk314_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7215]),
    [final] ).

cnf(i_0_14089,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk313_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7216]),
    [final] ).

cnf(i_0_14090,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk255_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7217]),
    [final] ).

cnf(i_0_14091,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_8214]),
    [final] ).

cnf(i_0_14092,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_8215]),
    [final] ).

cnf(i_0_14093,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_8088]),
    [final] ).

cnf(i_0_14094,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_8181]),
    [final] ).

cnf(i_0_14095,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_8182]),
    [final] ).

cnf(i_0_14096,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_8183]),
    [final] ).

cnf(i_0_14097,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_8216]),
    [final] ).

cnf(i_0_14098,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_8217,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_14099,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_6533]),
    [final] ).

cnf(i_0_14100,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_7699]),
    [final] ).

cnf(i_0_14101,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_8218]),
    [final] ).

cnf(i_0_14102,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_8219]),
    [final] ).

cnf(i_0_14103,plain,
    ( hBOOL(hAPP(X1,esk517_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_7300]),
    [final] ).

cnf(i_0_14104,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_8220]),
    [final] ).

cnf(i_0_14105,plain,
    hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_8221]),
    [final] ).

cnf(i_0_14106,plain,
    hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_8222]),
    [final] ).

cnf(i_0_14107,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X1) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X1),c_Nat_OSuc)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8223]),
    [final] ).

cnf(i_0_14108,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_7302]),
    [final] ).

cnf(i_0_14109,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_8224]),
    [final] ).

cnf(i_0_14110,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_8225]),
    [final] ).

cnf(i_0_14111,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_8226]),
    [final] ).

cnf(i_0_14112,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_8227]),
    [final] ).

cnf(i_0_14113,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_8228]),
    [final] ).

cnf(i_0_14114,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_8229]),
    [final] ).

cnf(i_0_14115,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_8230]),
    [final] ).

cnf(i_0_14116,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_8231]),
    [final] ).

cnf(i_0_14117,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_7834]),
    [final] ).

cnf(i_0_14118,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_8232]),
    [final] ).

cnf(i_0_14119,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_8233]),
    [final] ).

cnf(i_0_14120,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_8234]),
    [final] ).

cnf(i_0_14121,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_8235]),
    [final] ).

cnf(i_0_14122,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_8236]),
    [final] ).

cnf(i_0_14123,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_8237]),
    [final] ).

cnf(i_0_14124,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_8238]),
    [final] ).

cnf(i_0_14125,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_8239]),
    [final] ).

cnf(i_0_14126,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_8240]),
    [final] ).

cnf(i_0_14127,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_8241]),
    [final] ).

cnf(i_0_14128,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_6627]),
    [final] ).

cnf(i_0_14129,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_8242]),
    [final] ).

cnf(i_0_14130,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),esk361_3(X2,X3,X1)),X2))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8243]),
    [final] ).

cnf(i_0_14131,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_6848]),
    [final] ).

cnf(i_0_14132,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_8089]),
    [final] ).

cnf(i_0_14133,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_8244]),
    [final] ).

cnf(i_0_14134,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_8245]),
    [final] ).

cnf(i_0_14135,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_8246]),
    [final] ).

cnf(i_0_14136,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_8247]),
    [final] ).

cnf(i_0_14137,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_8248]),
    [final] ).

cnf(i_0_14138,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,esk355_4(X1,X2,X3,X4)) != c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7407]),
    [final] ).

cnf(i_0_14139,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,esk51_4(X1,X2,X3,X4)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7408]),
    [final] ).

cnf(i_0_14140,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,esk354_4(X1,X2,X3,X4)) != c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7409]),
    [final] ).

cnf(i_0_14141,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,esk52_4(X1,X2,X3,X4)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7410]),
    [final] ).

cnf(i_0_14142,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_8249]),
    [final] ).

cnf(i_0_14143,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_8250]),
    [final] ).

cnf(i_0_14144,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk134_3(X2,X1,X3))),esk135_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_8251]),
    [final] ).

cnf(i_0_14145,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk287_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_7866]),
    [final] ).

cnf(i_0_14146,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk120_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_7867]),
    [final] ).

cnf(i_0_14147,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk416_3(X2,X3,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8252]),
    [final] ).

cnf(i_0_14148,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_8253]),
    [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),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_7886]),
    [final] ).

cnf(i_0_14150,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_7663]),
    [final] ).

cnf(i_0_14151,plain,
    c_Map_Orestrict__map(X1,X2,X3,hAPP(c_Groups_Ouminus__class_Ouminus(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(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),c_Option_Ooption_ONone(X2)),
    inference(split_conjunct,[status(thm)],[i_0_8254]),
    [final] ).

cnf(i_0_14152,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_8255]),
    [final] ).

cnf(i_0_14153,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_7812]),
    [final] ).

cnf(i_0_14154,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_8256]),
    [final] ).

cnf(i_0_14155,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_8257]),
    [final] ).

cnf(i_0_14156,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_7300]),
    [final] ).

cnf(i_0_14157,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_7309]),
    [final] ).

cnf(i_0_14158,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_8258,c_0_6147]),
    [final] ).

cnf(i_0_14159,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_8127]),
    [final] ).

cnf(i_0_14160,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_8259]),
    [final] ).

cnf(i_0_14161,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_8260,c_0_6177]),
    [final] ).

cnf(i_0_14162,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_8261,c_0_6177]),
    [final] ).

cnf(i_0_14163,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_8262]),
    [final] ).

cnf(i_0_14164,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_8263]),
    [final] ).

cnf(i_0_14165,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_8264]),
    [final] ).

cnf(i_0_14166,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(c_List_Oset(X1),X3)))
    | hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)),X5) != hAPP(c_Option_Ooption_OSome(X2),X6)
    | 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_7130]),
    [final] ).

cnf(i_0_14167,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_8265]),
    [final] ).

cnf(i_0_14168,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk365_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_8144]),
    [final] ).

cnf(i_0_14169,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_8266]),
    [final] ).

cnf(i_0_14170,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_8267]),
    [final] ).

cnf(i_0_14171,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk124_3(X2,X1,X3))),esk125_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_8268]),
    [final] ).

cnf(i_0_14172,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_8269]),
    [final] ).

cnf(i_0_14173,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_8270]),
    [final] ).

cnf(i_0_14174,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_8271,c_0_6768]),c_0_6768]),
    [final] ).

cnf(i_0_14175,plain,
    ( c_Fun_Oinj__on(X4,X3,X2,X1)
    | esk32_4(X1,X2,X3,X4) != esk33_4(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7399]),
    [final] ).

cnf(i_0_14176,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_8272]),
    [final] ).

cnf(i_0_14177,plain,
    ( hAPP(c_Map_Omap__add(X1,X3,X5,X4),X2) = hAPP(X4,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8273]),
    [final] ).

cnf(i_0_14178,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk536_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk533_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14179,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_8138]),
    [final] ).

cnf(i_0_14180,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_8274,c_0_6209]),c_0_6209]),
    [final] ).

cnf(i_0_14181,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_8275]),
    [final] ).

cnf(i_0_14182,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X2,X3,X1)),X3))
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk535_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14183,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk540_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk538_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14184,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_8091]),
    [final] ).

cnf(i_0_14185,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_8276]),
    [final] ).

cnf(i_0_14186,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_7300]),
    [final] ).

cnf(i_0_14187,plain,
    c_Map_Odom(X1,X2,c_Map_Omap__add(X1,X2,X3,X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X4)),c_Map_Odom(X1,X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_8277]),
    [final] ).

cnf(i_0_14188,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_8278]),
    [final] ).

cnf(i_0_14189,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk538_3(X2,X3,X1)),X3))
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk540_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14190,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_8279]),
    [final] ).

cnf(i_0_14191,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_8279]),
    [final] ).

cnf(i_0_14192,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_8280]),
    [final] ).

cnf(i_0_14193,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_8281]),
    [final] ).

cnf(i_0_14194,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_8282]),
    [final] ).

cnf(i_0_14195,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_8282]),
    [final] ).

cnf(i_0_14196,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_8283]),
    [final] ).

cnf(i_0_14197,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk134_3(X2,X1,X3))),esk135_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_8251]),
    [final] ).

cnf(i_0_14198,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_8284]),
    [final] ).

cnf(i_0_14199,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_8285]),
    [final] ).

cnf(i_0_14200,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_8286]),
    [final] ).

cnf(i_0_14201,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk91_3(X2,X3,X1)),esk92_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_6802]),
    [final] ).

cnf(i_0_14202,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_5348]),
    [final] ).

cnf(i_0_14203,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_7309]),
    [final] ).

cnf(i_0_14204,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_8133]),
    [final] ).

cnf(i_0_14205,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_8287]),
    [final] ).

cnf(i_0_14206,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_8287]),
    [final] ).

cnf(i_0_14207,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_8288]),
    [final] ).

cnf(i_0_14208,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_8288]),
    [final] ).

cnf(i_0_14209,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_8289]),
    [final] ).

cnf(i_0_14210,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_8290]),
    [final] ).

cnf(i_0_14211,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,esk463_3(X2,X1,X3))) ),
    inference(rw,[status(thm)],[i_0_8291,c_0_6311]),
    [final] ).

cnf(i_0_14212,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_8292]),
    [final] ).

cnf(i_0_14213,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_8293]),
    [final] ).

cnf(i_0_14214,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk311_2(X2,X1)),hAPP(c_Relation_OImage(X1,X1,X2),esk311_2(X2,X1))))
    | c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8294]),
    [final] ).

cnf(i_0_14215,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_8295]),
    [final] ).

cnf(i_0_14216,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_8296]),
    [final] ).

cnf(i_0_14217,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_8118]),
    [final] ).

cnf(i_0_14218,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_8297]),
    [final] ).

cnf(i_0_14219,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_8298]),
    [final] ).

cnf(i_0_14220,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_8299]),
    [final] ).

cnf(i_0_14221,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_6808]),
    [final] ).

cnf(i_0_14222,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X2),esk74_3(X3,X1,X2)),esk74_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_8160]),
    [final] ).

cnf(i_0_14223,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_8300]),
    [final] ).

cnf(i_0_14224,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_8301]),
    [final] ).

cnf(i_0_14225,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_5348]),
    [final] ).

cnf(i_0_14226,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_8302,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6242]),
    [final] ).

cnf(i_0_14227,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_8303]),
    [final] ).

cnf(i_0_14228,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_8304,c_0_6136]),
    [final] ).

cnf(i_0_14229,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3))),esk536_3(X1,X2,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14230,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_8305,c_0_6209]),c_0_6209]),
    [final] ).

cnf(i_0_14231,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_8306,c_0_6209]),c_0_6209]),
    [final] ).

cnf(i_0_14232,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_7524]),
    [final] ).

cnf(i_0_14233,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_7525]),
    [final] ).

cnf(i_0_14234,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_8307]),
    [final] ).

cnf(i_0_14235,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_8308]),
    [final] ).

cnf(i_0_14236,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_8309]),
    [final] ).

cnf(i_0_14237,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk124_3(X2,X1,X3))),esk125_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_8268]),
    [final] ).

cnf(i_0_14238,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_7922]),
    [final] ).

cnf(i_0_14239,plain,
    ( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
    | X2 = X5
    | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X6,tc_Option_Ooption(X3)),X1),X5),hAPP(c_Option_Ooption_OSome(X3),X7)),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8310]),
    [final] ).

cnf(i_0_14240,plain,
    ( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
    | X5 = X4
    | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X6,tc_Option_Ooption(X3)),X1),X7),hAPP(c_Option_Ooption_OSome(X3),X5)),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8310]),
    [final] ).

cnf(i_0_14241,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_8311]),
    [final] ).

cnf(i_0_14242,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_8311]),
    [final] ).

cnf(i_0_14243,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_8312]),
    [final] ).

cnf(i_0_14244,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_8313]),
    [final] ).

cnf(i_0_14245,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),esk533_3(X2,X1,X3))),esk534_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_7732]),
    [final] ).

cnf(i_0_14246,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_8314,c_0_6768]),c_0_6768]),
    [final] ).

cnf(i_0_14247,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_8315]),
    [final] ).

cnf(i_0_14248,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_8316]),
    [final] ).

cnf(i_0_14249,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk539_3(X1,X2,X3))),esk540_3(X1,X2,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14250,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_8317,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_14251,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk540_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk538_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14252,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk536_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk533_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14253,plain,
    ( X2 = X5
    | 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)),X4)
    | ~ hBOOL(hAPP(c_List_Odistinct(X3),X4))
    | hAPP(c_Map_Omap__of(X3,X1),hAPP(hAPP(c_List_Ozip(X3,X1),X4),X2)) != hAPP(c_Map_Omap__of(X3,X1),hAPP(hAPP(c_List_Ozip(X3,X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8318]),
    [final] ).

cnf(i_0_14254,plain,
    ( X1 = hAPP(c_Int_ORep__Integ,esk290_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_8319]),
    [final] ).

cnf(i_0_14255,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk379_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_8320]),
    [final] ).

cnf(i_0_14256,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk441_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_8321]),
    [final] ).

cnf(i_0_14257,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk412_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_7925]),
    [final] ).

cnf(i_0_14258,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_8322]),
    [final] ).

cnf(i_0_14259,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),esk537_3(X2,X1,X3))),esk538_3(X2,X1,X3))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14260,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk538_3(X2,X3,X1)),X3))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk540_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14261,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X2,X3,X1)),X3))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk535_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14262,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X2),X4)))
    | ~ hBOOL(hAPP(X1,esk411_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_7925]),
    [final] ).

cnf(i_0_14263,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_8323]),
    [final] ).

cnf(i_0_14264,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_8324]),
    [final] ).

cnf(i_0_14265,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_8325]),
    [final] ).

cnf(i_0_14266,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_8326]),
    [final] ).

cnf(i_0_14267,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_8322]),
    [final] ).

cnf(i_0_14268,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk536_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)),esk534_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_7732]),
    [final] ).

cnf(i_0_14269,plain,
    ( c_Fun_Oinj__on(X1,X2,esk37_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_6682]),
    [final] ).

cnf(i_0_14270,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_8316]),
    [final] ).

cnf(i_0_14271,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,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14272,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,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14273,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_8327]),
    [final] ).

cnf(i_0_14274,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_8328]),
    [final] ).

cnf(i_0_14275,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_8329]),
    [final] ).

cnf(i_0_14276,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_8330]),
    [final] ).

cnf(i_0_14277,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),esk299_2(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8331]),
    [final] ).

cnf(i_0_14278,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_8332]),
    [final] ).

cnf(i_0_14279,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_8333]),
    [final] ).

cnf(i_0_14280,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(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(X4,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8334]),
    [final] ).

cnf(i_0_14281,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_7854]),
    [final] ).

cnf(i_0_14282,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_7855]),
    [final] ).

cnf(i_0_14283,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_8335]),
    [final] ).

cnf(i_0_14284,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_8336]),
    [final] ).

cnf(i_0_14285,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_8337]),
    [final] ).

cnf(i_0_14286,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_8338]),
    [final] ).

cnf(i_0_14287,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_8041]),
    [final] ).

cnf(i_0_14288,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_8339]),
    [final] ).

cnf(i_0_14289,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_8340]),
    [final] ).

cnf(i_0_14290,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_8167]),
    [final] ).

cnf(i_0_14291,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_8341]),
    [final] ).

cnf(i_0_14292,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_8168]),
    [final] ).

cnf(i_0_14293,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_8004]),
    [final] ).

cnf(i_0_14294,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_8342]),
    [final] ).

cnf(i_0_14295,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_8343]),
    [final] ).

cnf(i_0_14296,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_8344]),
    [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),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_8006]),
    [final] ).

cnf(i_0_14298,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk540_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)),esk538_3(X1,X2,X3)))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14299,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_8345]),
    [final] ).

cnf(i_0_14300,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_8346]),
    [final] ).

cnf(i_0_14301,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_8347]),
    [final] ).

cnf(i_0_14302,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_8348]),
    [final] ).

cnf(i_0_14303,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_8349]),
    [final] ).

cnf(i_0_14304,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_8350]),
    [final] ).

cnf(i_0_14305,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_6808]),
    [final] ).

cnf(i_0_14306,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_6808]),
    [final] ).

cnf(i_0_14307,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk161_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_8351]),
    [final] ).

cnf(i_0_14308,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk159_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_8352]),
    [final] ).

cnf(i_0_14309,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk100_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_8353]),
    [final] ).

cnf(i_0_14310,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_7123]),
    [final] ).

cnf(i_0_14311,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_8354]),
    [final] ).

cnf(i_0_14312,plain,
    ( X3 = X4
    | X1 != X2
    | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X6)),X7),X2),hAPP(c_Option_Ooption_OSome(X6),X3)),X1) != hAPP(c_Option_Ooption_OSome(X6),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8310]),
    [final] ).

cnf(i_0_14313,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)),esk448_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
    inference(rw,[status(thm)],[i_0_8355,c_0_6177]),
    [final] ).

cnf(i_0_14314,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)),esk449_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
    inference(rw,[status(thm)],[i_0_8356,c_0_6177]),
    [final] ).

cnf(i_0_14315,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_8357]),
    [final] ).

cnf(i_0_14316,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_8358]),
    [final] ).

cnf(i_0_14317,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk536_3(X2,X1,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X2,X1,X3)),X1))
    | epred1_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14318,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_8359]),
    [final] ).

cnf(i_0_14319,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_8360,c_0_8361]),
    [final] ).

cnf(i_0_14320,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,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14321,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,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14322,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_8362]),
    [final] ).

cnf(i_0_14323,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_8363]),
    [final] ).

cnf(i_0_14324,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_8364]),
    [final] ).

cnf(i_0_14325,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_8365]),
    [final] ).

cnf(i_0_14326,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_8366]),
    [final] ).

cnf(i_0_14327,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_8367]),
    [final] ).

cnf(i_0_14328,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_8368]),
    [final] ).

cnf(i_0_14329,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_8369]),
    [final] ).

cnf(i_0_14330,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk415_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_8370]),
    [final] ).

cnf(i_0_14331,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk540_3(X2,X1,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk538_3(X2,X1,X3)),X1))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14332,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_8371]),
    [final] ).

cnf(i_0_14333,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_8372]),
    [final] ).

cnf(i_0_14334,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_8373]),
    [final] ).

cnf(i_0_14335,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_8374]),
    [final] ).

cnf(i_0_14336,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_8375]),
    [final] ).

cnf(i_0_14337,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_8376]),
    [final] ).

cnf(i_0_14338,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_8083]),
    [final] ).

cnf(i_0_14339,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_8377]),
    [final] ).

cnf(i_0_14340,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_8378]),
    [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(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_8379]),
    [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(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_8380]),
    [final] ).

cnf(i_0_14343,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_8381]),
    [final] ).

cnf(i_0_14344,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_8382]),
    [final] ).

cnf(i_0_14345,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_8383,c_0_6128]),
    [final] ).

cnf(i_0_14346,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_7461]),
    [final] ).

cnf(i_0_14347,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_8384]),
    [final] ).

cnf(i_0_14348,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_8385]),
    [final] ).

cnf(i_0_14349,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_8181]),
    [final] ).

cnf(i_0_14350,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_8181]),
    [final] ).

cnf(i_0_14351,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_8386]),
    [final] ).

cnf(i_0_14352,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_8387]),
    [final] ).

cnf(i_0_14353,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_8388]),
    [final] ).

cnf(i_0_14354,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_8389]),
    [final] ).

cnf(i_0_14355,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_8390]),
    [final] ).

cnf(i_0_14356,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_8182]),
    [final] ).

cnf(i_0_14357,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_8182]),
    [final] ).

cnf(i_0_14358,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_8391]),
    [final] ).

cnf(i_0_14359,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_8392]),
    [final] ).

cnf(i_0_14360,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_8391]),
    [final] ).

cnf(i_0_14361,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_8393]),
    [final] ).

cnf(i_0_14362,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_8183]),
    [final] ).

cnf(i_0_14363,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_8183]),
    [final] ).

cnf(i_0_14364,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_8394]),
    [final] ).

cnf(i_0_14365,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_8395]),
    [final] ).

cnf(i_0_14366,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk539_3(X1,X2,X3))),esk540_3(X1,X2,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,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14367,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3))),esk536_3(X1,X2,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,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14368,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_8396]),
    [final] ).

cnf(i_0_14369,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_Int_Onumber__ring(X1)
    | ~ class_Fields_Ofield(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8397,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_14370,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_Int_Onumber__ring(X1)
    | ~ class_Fields_Ofield(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8398,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_14371,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_8399]),
    [final] ).

cnf(i_0_14372,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_8399]),
    [final] ).

cnf(i_0_14373,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_8400]),
    [final] ).

cnf(i_0_14374,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_8401]),
    [final] ).

cnf(i_0_14375,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_8400]),
    [final] ).

cnf(i_0_14376,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_8401]),
    [final] ).

cnf(i_0_14377,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_8402]),
    [final] ).

cnf(i_0_14378,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_8403]),
    [final] ).

cnf(i_0_14379,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_8402]),
    [final] ).

cnf(i_0_14380,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_8403]),
    [final] ).

cnf(i_0_14381,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_8404]),
    [final] ).

cnf(i_0_14382,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_8405]),
    [final] ).

cnf(i_0_14383,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_8406]),
    [final] ).

cnf(i_0_14384,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk299_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_8331]),
    [final] ).

cnf(i_0_14385,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_8407]),
    [final] ).

cnf(i_0_14386,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_8408]),
    [final] ).

cnf(i_0_14387,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_8406]),
    [final] ).

cnf(i_0_14388,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),esk537_3(X2,X1,X3))),esk538_3(X2,X1,X3))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14389,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),esk533_3(X2,X1,X3))),esk534_3(X2,X1,X3))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14390,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_8409]),
    [final] ).

cnf(i_0_14391,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_8410,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_14392,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_8411,c_0_8412]),c_0_8412]),
    [final] ).

cnf(i_0_14393,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_8413]),
    [final] ).

cnf(i_0_14394,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_6689]),
    [final] ).

cnf(i_0_14395,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_6691]),
    [final] ).

cnf(i_0_14396,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)),esk365_3(X2,X3,X1)),X2) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8144]),
    [final] ).

cnf(i_0_14397,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_8414]),
    [final] ).

cnf(i_0_14398,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_8415]),
    [final] ).

cnf(i_0_14399,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_8416]),
    [final] ).

cnf(i_0_14400,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_8417]),
    [final] ).

cnf(i_0_14401,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),esk161_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8351]),
    [final] ).

cnf(i_0_14402,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),esk159_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8352]),
    [final] ).

cnf(i_0_14403,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),esk100_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8353]),
    [final] ).

cnf(i_0_14404,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_8418]),
    [final] ).

cnf(i_0_14405,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_8132]),
    [final] ).

cnf(i_0_14406,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_8419,c_0_6768]),
    [final] ).

cnf(i_0_14407,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_5349]),
    [final] ).

cnf(i_0_14408,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_8420]),
    [final] ).

cnf(i_0_14409,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_8251]),
    [final] ).

cnf(i_0_14410,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_8421]),
    [final] ).

cnf(i_0_14411,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_8422]),
    [final] ).

cnf(i_0_14412,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_8423]),
    [final] ).

cnf(i_0_14413,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_8424]),
    [final] ).

cnf(i_0_14414,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_8215]),
    [final] ).

cnf(i_0_14415,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_8425]),
    [final] ).

cnf(i_0_14416,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_8426]),
    [final] ).

cnf(i_0_14417,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_8427]),
    [final] ).

cnf(i_0_14418,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_8428]),
    [final] ).

cnf(i_0_14419,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_8429]),
    [final] ).

cnf(i_0_14420,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_8430]),
    [final] ).

cnf(i_0_14421,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_8431]),
    [final] ).

cnf(i_0_14422,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_8432]),
    [final] ).

cnf(i_0_14423,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_8433]),
    [final] ).

cnf(i_0_14424,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_8434]),
    [final] ).

cnf(i_0_14425,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_8435]),
    [final] ).

cnf(i_0_14426,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_8436]),
    [final] ).

cnf(i_0_14427,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_8437]),
    [final] ).

cnf(i_0_14428,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk540_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)),esk538_3(X1,X2,X3)))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14429,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk536_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)),esk534_3(X1,X2,X3)))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14430,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_8438]),
    [final] ).

cnf(i_0_14431,plain,
    c_Map_Odom(X1,X2,c_Map_Orestrict__map(X1,X2,X3,X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),X4),
    inference(split_conjunct,[status(thm)],[i_0_8439]),
    [final] ).

cnf(i_0_14432,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_8105]),
    [final] ).

cnf(i_0_14433,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_OCollect(X2),X3)),hAPP(c_Set_OCollect(X2),X1)))
    | ~ hBOOL(hAPP(X1,esk9_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8440]),
    [final] ).

cnf(i_0_14434,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_6635]),
    [final] ).

cnf(i_0_14435,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_8441]),
    [final] ).

cnf(i_0_14436,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_8113]),
    [final] ).

cnf(i_0_14437,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_7819]),
    [final] ).

cnf(i_0_14438,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_8256]),
    [final] ).

cnf(i_0_14439,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_8442]),
    [final] ).

cnf(i_0_14440,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_8443]),
    [final] ).

cnf(i_0_14441,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_8444]),
    [final] ).

cnf(i_0_14442,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_8445]),
    [final] ).

cnf(i_0_14443,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_8446]),
    [final] ).

cnf(i_0_14444,plain,
    ( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
    | hAPP(X5,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
    | hAPP(c_Map_Omap__add(X6,X3,X1,X5),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8447]),
    [final] ).

cnf(i_0_14445,plain,
    ( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
    | hAPP(X5,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
    | hAPP(c_Map_Omap__add(X6,X3,X1,X5),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8448]),
    [final] ).

cnf(i_0_14446,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_7430]),
    [final] ).

cnf(i_0_14447,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_7431]),
    [final] ).

cnf(i_0_14448,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_8449]),
    [final] ).

cnf(i_0_14449,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_8450]),
    [final] ).

cnf(i_0_14450,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_8451]),
    [final] ).

cnf(i_0_14451,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_8452]),
    [final] ).

cnf(i_0_14452,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_8453]),
    [final] ).

cnf(i_0_14453,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_8025]),
    [final] ).

cnf(i_0_14454,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_8454]),
    [final] ).

cnf(i_0_14455,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_8027]),
    [final] ).

cnf(i_0_14456,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_8455]),
    [final] ).

cnf(i_0_14457,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_8030]),
    [final] ).

cnf(i_0_14458,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_8456]),
    [final] ).

cnf(i_0_14459,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_8032]),
    [final] ).

cnf(i_0_14460,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_8457]),
    [final] ).

cnf(i_0_14461,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_8458]),
    [final] ).

cnf(i_0_14462,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_8459]),
    [final] ).

cnf(i_0_14463,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_8265]),
    [final] ).

cnf(i_0_14464,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_8460]),
    [final] ).

cnf(i_0_14465,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_8461]),
    [final] ).

cnf(i_0_14466,plain,
    ( X5 = X7
    | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X6),X4),hAPP(c_Option_Ooption_OSome(X2),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_8462]),
    [final] ).

cnf(i_0_14467,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_8463]),
    [final] ).

cnf(i_0_14468,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_8464]),
    [final] ).

cnf(i_0_14469,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_8465]),
    [final] ).

cnf(i_0_14470,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk540_3(X2,X1,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk538_3(X2,X1,X3)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14471,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk536_3(X2,X1,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X2,X1,X3)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14472,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_8466]),
    [final] ).

cnf(i_0_14473,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_8467]),
    [final] ).

cnf(i_0_14474,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_8468]),
    [final] ).

cnf(i_0_14475,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_8298]),
    [final] ).

cnf(i_0_14476,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_8299]),
    [final] ).

cnf(i_0_14477,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_8469]),
    [final] ).

cnf(i_0_14478,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_8345]),
    [final] ).

cnf(i_0_14479,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_8470]),
    [final] ).

cnf(i_0_14480,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_8471]),
    [final] ).

cnf(i_0_14481,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_8472]),
    [final] ).

cnf(i_0_14482,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_8473]),
    [final] ).

cnf(i_0_14483,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_8474]),
    [final] ).

cnf(i_0_14484,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_8475]),
    [final] ).

cnf(i_0_14485,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_8476]),
    [final] ).

cnf(i_0_14486,plain,
    ( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
    | hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
    | hAPP(c_Map_Omap__add(X5,X3,X6,X1),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8447]),
    [final] ).

cnf(i_0_14487,plain,
    ( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
    | hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
    | hAPP(c_Map_Omap__add(X5,X3,X6,X1),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8448]),
    [final] ).

cnf(i_0_14488,plain,
    ( epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk535_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,esk533_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14489,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk364_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_8477]),
    [final] ).

cnf(i_0_14490,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk364_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_8477]),
    [final] ).

cnf(i_0_14491,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_8478]),
    [final] ).

cnf(i_0_14492,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_8479]),
    [final] ).

cnf(i_0_14493,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_8480]),
    [final] ).

cnf(i_0_14494,plain,
    hAPP(c_Option_Omap(X1,X2),X3) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(X2),X1,c_Option_Ooption_ONone(X2),hAPP(hAPP(c_COMBB(X2,tc_Option_Ooption(X2),X1),c_Option_Ooption_OSome(X2)),X3)),
    inference(split_conjunct,[status(thm)],[i_0_8481]),
    [final] ).

cnf(i_0_14495,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_8482]),
    [final] ).

cnf(i_0_14496,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_8483]),
    [final] ).

cnf(i_0_14497,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_8484]),
    [final] ).

cnf(i_0_14498,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_8485]),
    [final] ).

cnf(i_0_14499,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_7931]),
    [final] ).

cnf(i_0_14500,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_8486]),
    [final] ).

cnf(i_0_14501,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_8487]),
    [final] ).

cnf(i_0_14502,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_8268]),
    [final] ).

cnf(i_0_14503,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk497_3(X1,X3,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk498_3(X1,X3,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8022]),
    [final] ).

cnf(i_0_14504,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk495_3(X1,X3,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk496_3(X1,X3,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8023]),
    [final] ).

cnf(i_0_14505,plain,
    ( X3 = hAPP(hAPP(c_List_Oappend(X1),esk499_3(X3,X2,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk500_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8488]),
    [final] ).

cnf(i_0_14506,plain,
    ( epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk540_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,esk538_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14507,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_8489]),
    [final] ).

cnf(i_0_14508,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_8490]),
    [final] ).

cnf(i_0_14509,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_8351]),
    [final] ).

cnf(i_0_14510,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_8353]),
    [final] ).

cnf(i_0_14511,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_8352]),
    [final] ).

cnf(i_0_14512,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_8491]),
    [final] ).

cnf(i_0_14513,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_8415]),
    [final] ).

cnf(i_0_14514,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_8415]),
    [final] ).

cnf(i_0_14515,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_8492]),
    [final] ).

cnf(i_0_14516,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_7637]),
    [final] ).

cnf(i_0_14517,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_7638]),
    [final] ).

cnf(i_0_14518,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk440_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_8321]),
    [final] ).

cnf(i_0_14519,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_8493]),
    [final] ).

cnf(i_0_14520,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_8494]),
    [final] ).

cnf(i_0_14521,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_8495]),
    [final] ).

cnf(i_0_14522,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_8496]),
    [final] ).

cnf(i_0_14523,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_7482]),
    [final] ).

cnf(i_0_14524,plain,
    ( hAPP(X3,X5) = hAPP(X4,X5)
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X1,X2)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(c_List_Oset(X1),c_Enum_Oenum__class_Oenum(X1))))
    | ~ class_HOL_Oequal(X2)
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7348]),
    [final] ).

cnf(i_0_14525,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_8497]),
    [final] ).

cnf(i_0_14526,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_8498]),
    [final] ).

cnf(i_0_14527,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_8499]),
    [final] ).

cnf(i_0_14528,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_8500]),
    [final] ).

cnf(i_0_14529,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_8501]),
    [final] ).

cnf(i_0_14530,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_8502]),
    [final] ).

cnf(i_0_14531,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_5356]),
    [final] ).

cnf(i_0_14532,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_8503]),
    [final] ).

cnf(i_0_14533,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_8504]),
    [final] ).

cnf(i_0_14534,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_8505]),
    [final] ).

cnf(i_0_14535,plain,
    ( hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)) = hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X4))
    | hAPP(c_Map_Omap__of(X1,X2),X3) != hAPP(c_Map_Omap__of(X1,X2),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8506]),
    [final] ).

cnf(i_0_14536,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_8399]),
    [final] ).

cnf(i_0_14537,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_8402]),
    [final] ).

cnf(i_0_14538,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_8507]),
    [final] ).

cnf(i_0_14539,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_8508]),
    [final] ).

cnf(i_0_14540,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_8400]),
    [final] ).

cnf(i_0_14541,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_8509]),
    [final] ).

cnf(i_0_14542,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_8510]),
    [final] ).

cnf(i_0_14543,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_8511]),
    [final] ).

cnf(i_0_14544,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_8512]),
    [final] ).

cnf(i_0_14545,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_8513]),
    [final] ).

cnf(i_0_14546,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_8514]),
    [final] ).

cnf(i_0_14547,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_8515,c_0_6768]),
    [final] ).

cnf(i_0_14548,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_8516]),
    [final] ).

cnf(i_0_14549,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_8517]),
    [final] ).

cnf(i_0_14550,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_8518]),
    [final] ).

cnf(i_0_14551,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_8519]),
    [final] ).

cnf(i_0_14552,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_8520]),
    [final] ).

cnf(i_0_14553,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_8521]),
    [final] ).

cnf(i_0_14554,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_8522]),
    [final] ).

cnf(i_0_14555,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_8523]),
    [final] ).

cnf(i_0_14556,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_8524]),
    [final] ).

cnf(i_0_14557,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_8073]),
    [final] ).

cnf(i_0_14558,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_8097]),
    [final] ).

cnf(i_0_14559,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk385_3(X2,X1,X3)),esk383_2(X2,X1)))
    | c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),esk383_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7107]),
    [final] ).

cnf(i_0_14560,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_7483]),
    [final] ).

cnf(i_0_14561,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_7484]),
    [final] ).

cnf(i_0_14562,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_7485]),
    [final] ).

cnf(i_0_14563,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_7486]),
    [final] ).

cnf(i_0_14564,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_8525]),
    [final] ).

cnf(i_0_14565,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_8241]),
    [final] ).

cnf(i_0_14566,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_8526]),
    [final] ).

cnf(i_0_14567,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_8527]),
    [final] ).

cnf(i_0_14568,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_8528]),
    [final] ).

cnf(i_0_14569,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_8529]),
    [final] ).

cnf(i_0_14570,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_8530]),
    [final] ).

cnf(i_0_14571,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_8531]),
    [final] ).

cnf(i_0_14572,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),c_Map_Odom(X4,X3,X1)),hAPP(hAPP(c_Set_Oinsert(X4),X2),X5)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),c_Map_Odom(X4,X3,X1)),X5)
    | hAPP(X1,X2) != c_Option_Ooption_ONone(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8532]),
    [final] ).

cnf(i_0_14573,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_7976]),
    [final] ).

cnf(i_0_14574,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_8533]),
    [final] ).

cnf(i_0_14575,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_8534]),
    [final] ).

cnf(i_0_14576,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_7976]),
    [final] ).

cnf(i_0_14577,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_8535]),
    [final] ).

cnf(i_0_14578,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_8534]),
    [final] ).

cnf(i_0_14579,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_8536]),
    [final] ).

cnf(i_0_14580,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_8537]),
    [final] ).

cnf(i_0_14581,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_8538]),
    [final] ).

cnf(i_0_14582,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_8539]),
    [final] ).

cnf(i_0_14583,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))
    | hAPP(c_Map_Omap__add(X1,X3,X4,X5),X2) = hAPP(X5,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8540]),
    [final] ).

cnf(i_0_14584,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))
    | hAPP(c_Map_Omap__add(X1,X3,X5,X4),X2) = hAPP(X5,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8541]),
    [final] ).

cnf(i_0_14585,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_8542]),
    [final] ).

cnf(i_0_14586,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_8543]),
    [final] ).

cnf(i_0_14587,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_8544]),
    [final] ).

cnf(i_0_14588,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_8545]),
    [final] ).

cnf(i_0_14589,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_8546]),
    [final] ).

cnf(i_0_14590,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_8547]),
    [final] ).

cnf(i_0_14591,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_8548]),
    [final] ).

cnf(i_0_14592,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_8549]),
    [final] ).

cnf(i_0_14593,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_8550]),
    [final] ).

cnf(i_0_14594,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_8551]),
    [final] ).

cnf(i_0_14595,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_8552]),
    [final] ).

cnf(i_0_14596,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_7456]),
    [final] ).

cnf(i_0_14597,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_7457]),
    [final] ).

cnf(i_0_14598,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_8553]),
    [final] ).

cnf(i_0_14599,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_8554]),
    [final] ).

cnf(i_0_14600,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_8555]),
    [final] ).

cnf(i_0_14601,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_8256]),
    [final] ).

cnf(i_0_14602,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_8556]),
    [final] ).

cnf(i_0_14603,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_8557]),
    [final] ).

cnf(i_0_14604,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_8558]),
    [final] ).

cnf(i_0_14605,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_8559]),
    [final] ).

cnf(i_0_14606,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk540_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,esk538_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14607,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk535_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,esk533_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14608,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_8560]),
    [final] ).

cnf(i_0_14609,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_8561]),
    [final] ).

cnf(i_0_14610,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_8562]),
    [final] ).

cnf(i_0_14611,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_8563,c_0_6103]),
    [final] ).

cnf(i_0_14612,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_8564,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_14613,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_8247]),
    [final] ).

cnf(i_0_14614,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_8247]),
    [final] ).

cnf(i_0_14615,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk38_3(X2,X3,X1)),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_8134]),
    [final] ).

cnf(i_0_14616,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_8565]),
    [final] ).

cnf(i_0_14617,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_6462]),
    [final] ).

cnf(i_0_14618,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_8566]),
    [final] ).

cnf(i_0_14619,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_8265]),
    [final] ).

cnf(i_0_14620,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_8495]),
    [final] ).

cnf(i_0_14621,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_8567]),
    [final] ).

cnf(i_0_14622,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_8568]),
    [final] ).

cnf(i_0_14623,plain,
    ( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
    | hAPP(c_Map_Omap__add(X4,X3,X1,X5),X2) != c_Option_Ooption_ONone(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8569]),
    [final] ).

cnf(i_0_14624,plain,
    ( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
    | hAPP(c_Map_Omap__add(X4,X3,X5,X1),X2) != c_Option_Ooption_ONone(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8569]),
    [final] ).

cnf(i_0_14625,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_8570]),
    [final] ).

cnf(i_0_14626,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_8571]),
    [final] ).

cnf(i_0_14627,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_8572]),
    [final] ).

cnf(i_0_14628,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_8259]),
    [final] ).

cnf(i_0_14629,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk416_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_8252]),
    [final] ).

cnf(i_0_14630,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_8573]),
    [final] ).

cnf(i_0_14631,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_8574]),
    [final] ).

cnf(i_0_14632,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_8575]),
    [final] ).

cnf(i_0_14633,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X2,X3,X1)))
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk535_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14634,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_8576]),
    [final] ).

cnf(i_0_14635,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_8577]),
    [final] ).

cnf(i_0_14636,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_8578]),
    [final] ).

cnf(i_0_14637,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_8578]),
    [final] ).

cnf(i_0_14638,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_8578]),
    [final] ).

cnf(i_0_14639,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_8578]),
    [final] ).

cnf(i_0_14640,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_8133]),
    [final] ).

cnf(i_0_14641,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_8579]),
    [final] ).

cnf(i_0_14642,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_7163]),
    [final] ).

cnf(i_0_14643,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_8580]),
    [final] ).

cnf(i_0_14644,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_8581]),
    [final] ).

cnf(i_0_14645,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_8581]),
    [final] ).

cnf(i_0_14646,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_8582]),
    [final] ).

cnf(i_0_14647,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_8583]),
    [final] ).

cnf(i_0_14648,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk135_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_8251]),
    [final] ).

cnf(i_0_14649,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk538_3(X2,X3,X1)))
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk540_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14650,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_8584]),
    [final] ).

cnf(i_0_14651,plain,
    ( c_Map_Oran(X4,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),X1),X2),hAPP(c_Option_Ooption_OSome(X3),X5))) = hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Map_Oran(X4,X3,X1))
    | hAPP(X1,X2) != c_Option_Ooption_ONone(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8585]),
    [final] ).

cnf(i_0_14652,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_8245]),
    [final] ).

cnf(i_0_14653,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk536_3(X2,X1,X3)))
    | epred1_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,esk533_3(X2,X1,X3)))
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14654,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_8586]),
    [final] ).

cnf(i_0_14655,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_8587]),
    [final] ).

cnf(i_0_14656,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_8588]),
    [final] ).

cnf(i_0_14657,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OPls)) ),
    inference(rw,[status(thm)],[i_0_8589,c_0_6103]),
    [final] ).

cnf(i_0_14658,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_8590,c_0_6103]),
    [final] ).

cnf(i_0_14659,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_8591,c_0_6103]),
    [final] ).

cnf(i_0_14660,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_8592,c_0_6103]),
    [final] ).

cnf(i_0_14661,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_8593,c_0_6103]),
    [final] ).

cnf(i_0_14662,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_8594,c_0_6103]),
    [final] ).

cnf(i_0_14663,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_8595,c_0_6103]),
    [final] ).

cnf(i_0_14664,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_8596]),
    [final] ).

cnf(i_0_14665,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_8597]),
    [final] ).

cnf(i_0_14666,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_6827]),
    [final] ).

cnf(i_0_14667,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk363_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_8598]),
    [final] ).

cnf(i_0_14668,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_8599]),
    [final] ).

cnf(i_0_14669,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_8600,c_0_6128]),
    [final] ).

cnf(i_0_14670,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_8601]),
    [final] ).

cnf(i_0_14671,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_8602]),
    [final] ).

cnf(i_0_14672,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk540_3(X2,X1,X3)))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,esk538_3(X2,X1,X3)))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14673,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_8316]),
    [final] ).

cnf(i_0_14674,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_8603]),
    [final] ).

cnf(i_0_14675,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_8604]),
    [final] ).

cnf(i_0_14676,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_8184]),
    [final] ).

cnf(i_0_14677,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk321_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_8605]),
    [final] ).

cnf(i_0_14678,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk322_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_8185]),
    [final] ).

cnf(i_0_14679,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_8606]),
    [final] ).

cnf(i_0_14680,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk370_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_8607]),
    [final] ).

cnf(i_0_14681,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_8608]),
    [final] ).

cnf(i_0_14682,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_8609]),
    [final] ).

cnf(i_0_14683,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_8610]),
    [final] ).

cnf(i_0_14684,plain,
    hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X2),X1,c_Option_Ooption_ONone(X2),hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))),hAPP(X4,X5)) = c_Option_Ooption_ONone(X2),
    inference(rw,[status(thm)],[i_0_8611,c_0_6301]),
    [final] ).

cnf(i_0_14685,plain,
    hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X2),X1,c_Option_Ooption_ONone(X2),X4),hAPP(hAPP(c_COMBK(tc_Option_Ooption(X1),X3),c_Option_Ooption_ONone(X1)),X5)) = c_Option_Ooption_ONone(X2),
    inference(rw,[status(thm)],[i_0_8612,c_0_6301]),
    [final] ).

cnf(i_0_14686,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk125_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_8268]),
    [final] ).

cnf(i_0_14687,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_8613,c_0_6242]),
    [final] ).

cnf(i_0_14688,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_8614,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_14689,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_8615]),
    [final] ).

cnf(i_0_14690,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_8290]),
    [final] ).

cnf(i_0_14691,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_8616]),
    [final] ).

cnf(i_0_14692,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_8297]),
    [final] ).

cnf(i_0_14693,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_8617]),
    [final] ).

cnf(i_0_14694,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_8618]),
    [final] ).

cnf(i_0_14695,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_8321]),
    [final] ).

cnf(i_0_14696,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_8619]),
    [final] ).

cnf(i_0_14697,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_8620]),
    [final] ).

cnf(i_0_14698,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_8620]),
    [final] ).

cnf(i_0_14699,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_8620]),
    [final] ).

cnf(i_0_14700,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_8620]),
    [final] ).

cnf(i_0_14701,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_8621]),
    [final] ).

cnf(i_0_14702,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_8621]),
    [final] ).

cnf(i_0_14703,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_8622]),
    [final] ).

cnf(i_0_14704,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_8622]),
    [final] ).

cnf(i_0_14705,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_8621]),
    [final] ).

cnf(i_0_14706,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_8621]),
    [final] ).

cnf(i_0_14707,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_8622]),
    [final] ).

cnf(i_0_14708,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_8622]),
    [final] ).

cnf(i_0_14709,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk532_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_8623]),
    [final] ).

cnf(i_0_14710,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_7518]),
    [final] ).

cnf(i_0_14711,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_7519]),
    [final] ).

cnf(i_0_14712,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_7520]),
    [final] ).

cnf(i_0_14713,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_7521]),
    [final] ).

cnf(i_0_14714,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(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_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8624,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_14715,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_8625,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_14716,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_8626,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_14717,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_8627]),
    [final] ).

cnf(i_0_14718,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_8628]),
    [final] ).

cnf(i_0_14719,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_8194]),
    [final] ).

cnf(i_0_14720,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_8629,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_14721,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_8630,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_14722,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_8631]),
    [final] ).

cnf(i_0_14723,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_8632]),
    [final] ).

cnf(i_0_14724,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_8633]),
    [final] ).

cnf(i_0_14725,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_8197]),
    [final] ).

cnf(i_0_14726,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_8005]),
    [final] ).

cnf(i_0_14727,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_8634]),
    [final] ).

cnf(i_0_14728,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_8007]),
    [final] ).

cnf(i_0_14729,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_8635]),
    [final] ).

cnf(i_0_14730,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_8636]),
    [final] ).

cnf(i_0_14731,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_8637]),
    [final] ).

cnf(i_0_14732,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_8638]),
    [final] ).

cnf(i_0_14733,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_8639]),
    [final] ).

cnf(i_0_14734,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_8640]),
    [final] ).

cnf(i_0_14735,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_8641]),
    [final] ).

cnf(i_0_14736,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_8642]),
    [final] ).

cnf(i_0_14737,plain,
    ( c_List_Olist__ex1(X3,X2,X1)
    | esk522_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_7335]),
    [final] ).

cnf(i_0_14738,plain,
    ( c_List_Olist__ex1(X3,X2,X1)
    | esk509_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_7336]),
    [final] ).

cnf(i_0_14739,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_8643]),
    [final] ).

cnf(i_0_14740,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_8644,c_0_6104]),
    [final] ).

cnf(i_0_14741,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_8645]),
    [final] ).

cnf(i_0_14742,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_8646]),
    [final] ).

cnf(i_0_14743,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_8646]),
    [final] ).

cnf(i_0_14744,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk456_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_7931]),
    [final] ).

cnf(i_0_14745,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk455_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_7931]),
    [final] ).

cnf(i_0_14746,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk433_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_8245]),
    [final] ).

cnf(i_0_14747,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_8647]),
    [final] ).

cnf(i_0_14748,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_8648]),
    [final] ).

cnf(i_0_14749,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_7181]),
    [final] ).

cnf(i_0_14750,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_8649]),
    [final] ).

cnf(i_0_14751,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X3,X2),X4),X5)))
    | ~ hBOOL(hAPP(X1,esk138_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7295]),
    [final] ).

cnf(i_0_14752,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_6213]),
    [final] ).

cnf(i_0_14753,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_8576]),
    [final] ).

cnf(i_0_14754,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_8577]),
    [final] ).

cnf(i_0_14755,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 != esk234_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_7358]),
    [final] ).

cnf(i_0_14756,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_8650]),
    [final] ).

cnf(i_0_14757,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_8651]),
    [final] ).

cnf(i_0_14758,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_8652]),
    [final] ).

cnf(i_0_14759,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_7399]),
    [final] ).

cnf(i_0_14760,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_8653]),
    [final] ).

cnf(i_0_14761,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_8654]),
    [final] ).

cnf(i_0_14762,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_8655]),
    [final] ).

cnf(i_0_14763,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_8656]),
    [final] ).

cnf(i_0_14764,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_8657]),
    [final] ).

cnf(i_0_14765,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_8579]),
    [final] ).

cnf(i_0_14766,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_8658]),
    [final] ).

cnf(i_0_14767,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_8659]),
    [final] ).

cnf(i_0_14768,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk135_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_8251]),
    [final] ).

cnf(i_0_14769,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_8660]),
    [final] ).

cnf(i_0_14770,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_8661]),
    [final] ).

cnf(i_0_14771,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_6660]),
    [final] ).

cnf(i_0_14772,plain,
    ( hBOOL(hAPP(X1,esk9_3(X2,X3,X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_OCollect(X2),X1)),hAPP(c_Set_OCollect(X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8440]),
    [final] ).

cnf(i_0_14773,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk538_3(X2,X3,X1)))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk540_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14774,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X2,X3,X1)))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk535_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14775,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_8662]),
    [final] ).

cnf(i_0_14776,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_8663]),
    [final] ).

cnf(i_0_14777,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_8664]),
    [final] ).

cnf(i_0_14778,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_8665]),
    [final] ).

cnf(i_0_14779,plain,
    ( c_Big__Operators_Olinorder__class_OMin(X1,X3) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk321_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_8605]),
    [final] ).

cnf(i_0_14780,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk233_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_7358]),
    [final] ).

cnf(i_0_14781,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_8666]),
    [final] ).

cnf(i_0_14782,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_8484]),
    [final] ).

cnf(i_0_14783,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_8667]),
    [final] ).

cnf(i_0_14784,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_8668]),
    [final] ).

cnf(i_0_14785,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_8669]),
    [final] ).

cnf(i_0_14786,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_8670]),
    [final] ).

cnf(i_0_14787,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk492_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_8671]),
    [final] ).

cnf(i_0_14788,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk457_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_8672]),
    [final] ).

cnf(i_0_14789,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk454_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_8673]),
    [final] ).

cnf(i_0_14790,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_8674]),
    [final] ).

cnf(i_0_14791,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_7637]),
    [final] ).

cnf(i_0_14792,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_7638]),
    [final] ).

cnf(i_0_14793,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_8675]),
    [final] ).

cnf(i_0_14794,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_8620]),
    [final] ).

cnf(i_0_14795,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_8676]),
    [final] ).

cnf(i_0_14796,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_8677]),
    [final] ).

cnf(i_0_14797,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_8678]),
    [final] ).

cnf(i_0_14798,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_8679]),
    [final] ).

cnf(i_0_14799,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_8680]),
    [final] ).

cnf(i_0_14800,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_8681]),
    [final] ).

cnf(i_0_14801,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_8621]),
    [final] ).

cnf(i_0_14802,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_8682]),
    [final] ).

cnf(i_0_14803,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_8683]),
    [final] ).

cnf(i_0_14804,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_8622]),
    [final] ).

cnf(i_0_14805,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_8684]),
    [final] ).

cnf(i_0_14806,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk319_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_7490]),
    [final] ).

cnf(i_0_14807,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_8685]),
    [final] ).

cnf(i_0_14808,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_8686]),
    [final] ).

cnf(i_0_14809,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_8687]),
    [final] ).

cnf(i_0_14810,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_8688,c_0_6128]),
    [final] ).

cnf(i_0_14811,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_8689]),
    [final] ).

cnf(i_0_14812,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),esk379_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8320]),
    [final] ).

cnf(i_0_14813,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_8690,c_0_6209]),c_0_6209]),
    [final] ).

cnf(i_0_14814,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_8691,c_0_6209]),c_0_6209]),
    [final] ).

cnf(i_0_14815,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_8692]),
    [final] ).

cnf(i_0_14816,plain,
    hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),X3),X4)) = c_Map_Omap__add(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X4),hAPP(c_Map_Omap__of(X1,X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_8693]),
    [final] ).

cnf(i_0_14817,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk361_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_8243]),
    [final] ).

cnf(i_0_14818,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_8694]),
    [final] ).

cnf(i_0_14819,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_8695]),
    [final] ).

cnf(i_0_14820,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk410_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_8696]),
    [final] ).

cnf(i_0_14821,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk540_3(X2,X1,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,esk538_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14822,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk536_3(X2,X1,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,esk533_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14823,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_8697]),
    [final] ).

cnf(i_0_14824,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_8698]),
    [final] ).

cnf(i_0_14825,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_8699]),
    [final] ).

cnf(i_0_14826,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk493_3(X3,X1,X2))))
    | ~ c_List_Olist__ex(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8656]),
    [final] ).

cnf(i_0_14827,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_8700]),
    [final] ).

cnf(i_0_14828,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_8701]),
    [final] ).

cnf(i_0_14829,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_8702]),
    [final] ).

cnf(i_0_14830,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_8703]),
    [final] ).

cnf(i_0_14831,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_8704]),
    [final] ).

cnf(i_0_14832,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_8705]),
    [final] ).

cnf(i_0_14833,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_8706]),
    [final] ).

cnf(i_0_14834,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_8216]),
    [final] ).

cnf(i_0_14835,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_8707]),
    [final] ).

cnf(i_0_14836,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_8282]),
    [final] ).

cnf(i_0_14837,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk536_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)),X2))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14838,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_8708]),
    [final] ).

cnf(i_0_14839,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),esk531_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_8709]),
    [final] ).

cnf(i_0_14840,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_8710]),
    [final] ).

cnf(i_0_14841,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_8711]),
    [final] ).

cnf(i_0_14842,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_8712]),
    [final] ).

cnf(i_0_14843,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_8713]),
    [final] ).

cnf(i_0_14844,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_8714]),
    [final] ).

cnf(i_0_14845,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_8705]),
    [final] ).

cnf(i_0_14846,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_8706]),
    [final] ).

cnf(i_0_14847,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_8715]),
    [final] ).

cnf(i_0_14848,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | hAPP(hAPP(c_Map_Omap__of(X1,X4),hAPP(hAPP(c_List_Ozip(X1,X4),X3),X5)),X2) = c_Option_Ooption_ONone(X4)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_8157]),
    [final] ).

cnf(i_0_14849,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_8716]),
    [final] ).

cnf(i_0_14850,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_8717]),
    [final] ).

cnf(i_0_14851,plain,
    ( hAPP(X1,esk118_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_7403]),
    [final] ).

cnf(i_0_14852,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_8718]),
    [final] ).

cnf(i_0_14853,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_8719]),
    [final] ).

cnf(i_0_14854,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_8720]),
    [final] ).

cnf(i_0_14855,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_8007]),
    [final] ).

cnf(i_0_14856,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_8005]),
    [final] ).

cnf(i_0_14857,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk536_3(X2,X1,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_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_7732]),
    [final] ).

cnf(i_0_14858,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 != esk236_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_7363]),
    [final] ).

cnf(i_0_14859,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk197_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_8721]),
    [final] ).

cnf(i_0_14860,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk235_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_7363]),
    [final] ).

cnf(i_0_14861,plain,
    hAPP(c_Map_Orestrict__map(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)),X3),X4) = c_Option_Ooption_ONone(X2),
    inference(split_conjunct,[status(thm)],[i_0_8722]),
    [final] ).

cnf(i_0_14862,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_8723]),
    [final] ).

cnf(i_0_14863,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk294_2(X1,X2)),c_Int_OInteg))
    | hBOOL(hAPP(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8724]),
    [final] ).

cnf(i_0_14864,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_8126]),
    [final] ).

cnf(i_0_14865,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_8725,c_0_6103]),
    [final] ).

cnf(i_0_14866,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk540_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)),X2))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14867,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_8726]),
    [final] ).

cnf(i_0_14868,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_8727]),
    [final] ).

cnf(i_0_14869,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_8728]),
    [final] ).

cnf(i_0_14870,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_8686]),
    [final] ).

cnf(i_0_14871,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_8729]),
    [final] ).

cnf(i_0_14872,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk125_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_8268]),
    [final] ).

cnf(i_0_14873,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_8730]),
    [final] ).

cnf(i_0_14874,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_8731]),
    [final] ).

cnf(i_0_14875,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_8732]),
    [final] ).

cnf(i_0_14876,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),esk534_3(X2,X1,X3)),X1))
    | epred1_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14877,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_8733]),
    [final] ).

cnf(i_0_14878,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk493_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_8656]),
    [final] ).

cnf(i_0_14879,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_8734]),
    [final] ).

cnf(i_0_14880,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_8735]),
    [final] ).

cnf(i_0_14881,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk540_3(X2,X1,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk538_3(X2,X1,X3)))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14882,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_8736]),
    [final] ).

cnf(i_0_14883,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_8737]),
    [final] ).

cnf(i_0_14884,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_8738]),
    [final] ).

cnf(i_0_14885,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_8739]),
    [final] ).

cnf(i_0_14886,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_8740]),
    [final] ).

cnf(i_0_14887,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_8741]),
    [final] ).

cnf(i_0_14888,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_8742]),
    [final] ).

cnf(i_0_14889,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_8743]),
    [final] ).

cnf(i_0_14890,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_8744]),
    [final] ).

cnf(i_0_14891,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_8745]),
    [final] ).

cnf(i_0_14892,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_8746]),
    [final] ).

cnf(i_0_14893,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_8747]),
    [final] ).

cnf(i_0_14894,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_8123]),
    [final] ).

cnf(i_0_14895,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_8124]),
    [final] ).

cnf(i_0_14896,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_8748]),
    [final] ).

cnf(i_0_14897,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_8749]),
    [final] ).

cnf(i_0_14898,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_8655]),
    [final] ).

cnf(i_0_14899,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_8750]),
    [final] ).

cnf(i_0_14900,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),esk538_3(X2,X1,X3)),X1))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14901,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_8751]),
    [final] ).

cnf(i_0_14902,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_8752]),
    [final] ).

cnf(i_0_14903,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_8753]),
    [final] ).

cnf(i_0_14904,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_8754]),
    [final] ).

cnf(i_0_14905,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_8755]),
    [final] ).

cnf(i_0_14906,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk382_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_7107]),
    [final] ).

cnf(i_0_14907,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_8756]),
    [final] ).

cnf(i_0_14908,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_8757]),
    [final] ).

cnf(i_0_14909,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk198_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_8758]),
    [final] ).

cnf(i_0_14910,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_8328]),
    [final] ).

cnf(i_0_14911,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_8329]),
    [final] ).

cnf(i_0_14912,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_8759]),
    [final] ).

cnf(i_0_14913,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_8330]),
    [final] ).

cnf(i_0_14914,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_8760]),
    [final] ).

cnf(i_0_14915,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_8761]),
    [final] ).

cnf(i_0_14916,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_8252]),
    [final] ).

cnf(i_0_14917,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_8762]),
    [final] ).

cnf(i_0_14918,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_8763]),
    [final] ).

cnf(i_0_14919,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_8620]),
    [final] ).

cnf(i_0_14920,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_8764]),
    [final] ).

cnf(i_0_14921,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_8765]),
    [final] ).

cnf(i_0_14922,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_8621]),
    [final] ).

cnf(i_0_14923,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_8622]),
    [final] ).

cnf(i_0_14924,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_8684]),
    [final] ).

cnf(i_0_14925,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_8766]),
    [final] ).

cnf(i_0_14926,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_8601]),
    [final] ).

cnf(i_0_14927,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_8602]),
    [final] ).

cnf(i_0_14928,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_8767]),
    [final] ).

cnf(i_0_14929,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_8768]),
    [final] ).

cnf(i_0_14930,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_8769]),
    [final] ).

cnf(i_0_14931,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),esk387_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_8158]),
    [final] ).

cnf(i_0_14932,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_8770]),
    [final] ).

cnf(i_0_14933,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_8655]),
    [final] ).

cnf(i_0_14934,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_8771]),
    [final] ).

cnf(i_0_14935,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_6394]),
    [final] ).

cnf(i_0_14936,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_8772]),
    [final] ).

cnf(i_0_14937,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_8773]),
    [final] ).

cnf(i_0_14938,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_8774,c_0_6242]),
    [final] ).

cnf(i_0_14939,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_8775]),
    [final] ).

cnf(i_0_14940,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_8776]),
    [final] ).

cnf(i_0_14941,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),
    inference(rw,[status(thm)],[i_0_8777,c_0_6103]),
    [final] ).

cnf(i_0_14942,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_8778]),
    [final] ).

cnf(i_0_14943,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_8779]),
    [final] ).

cnf(i_0_14944,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_8780]),
    [final] ).

cnf(i_0_14945,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_8781]),
    [final] ).

cnf(i_0_14946,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_8782]),
    [final] ).

cnf(i_0_14947,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_8783,c_0_6102]),c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_14948,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_8784]),
    [final] ).

cnf(i_0_14949,plain,
    ( X1 = c_Option_Ooption_ONone(X2)
    | c_Map_Odom(X3,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X2)),X4),X5),X1)) = hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Map_Odom(X3,X2,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8155]),
    [final] ).

cnf(i_0_14950,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk440_3(X3,X1,X2)),esk441_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_8321]),
    [final] ).

cnf(i_0_14951,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_8785]),
    [final] ).

cnf(i_0_14952,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk24_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_8786]),
    [final] ).

cnf(i_0_14953,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk23_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_8786]),
    [final] ).

cnf(i_0_14954,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))
    | esk371_3(X1,X2,X3) != esk372_3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7630]),
    [final] ).

cnf(i_0_14955,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_8787]),
    [final] ).

cnf(i_0_14956,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_8788]),
    [final] ).

cnf(i_0_14957,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_8357]),
    [final] ).

cnf(i_0_14958,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_8358]),
    [final] ).

cnf(i_0_14959,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_8789]),
    [final] ).

cnf(i_0_14960,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_8790]),
    [final] ).

cnf(i_0_14961,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_8791]),
    [final] ).

cnf(i_0_14962,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_8792]),
    [final] ).

cnf(i_0_14963,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk502_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_8186]),
    [final] ).

cnf(i_0_14964,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_8793]),
    [final] ).

cnf(i_0_14965,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_8794]),
    [final] ).

cnf(i_0_14966,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk362_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_8795]),
    [final] ).

cnf(i_0_14967,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_8796]),
    [final] ).

cnf(i_0_14968,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_8797]),
    [final] ).

cnf(i_0_14969,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_7801]),
    [final] ).

cnf(i_0_14970,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk470_2(X3,X1)),X2))
    | X3 = c_List_Olist_ONil(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk469_2(X3,X1))))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7416]),
    [final] ).

cnf(i_0_14971,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk521_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | ~ c_List_Olist__ex1(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7335]),
    [final] ).

cnf(i_0_14972,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk508_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | ~ c_List_Olist__ex1(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7336]),
    [final] ).

cnf(i_0_14973,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk494_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | ~ c_List_Olist__ex(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8798]),
    [final] ).

cnf(i_0_14974,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_8799]),
    [final] ).

cnf(i_0_14975,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_8800]),
    [final] ).

cnf(i_0_14976,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_8378]),
    [final] ).

cnf(i_0_14977,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_8381]),
    [final] ).

cnf(i_0_14978,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_8382]),
    [final] ).

cnf(i_0_14979,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_8379]),
    [final] ).

cnf(i_0_14980,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_8380]),
    [final] ).

cnf(i_0_14981,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk540_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)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_14982,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk536_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)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_14983,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk467_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_8801]),
    [final] ).

cnf(i_0_14984,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_5357]),
    [final] ).

cnf(i_0_14985,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_8802]),
    [final] ).

cnf(i_0_14986,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_8803]),
    [final] ).

cnf(i_0_14987,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_8804]),
    [final] ).

cnf(i_0_14988,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_8805]),
    [final] ).

cnf(i_0_14989,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_8806]),
    [final] ).

cnf(i_0_14990,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_8807]),
    [final] ).

cnf(i_0_14991,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_8808,c_0_6177]),
    [final] ).

cnf(i_0_14992,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_8266]),
    [final] ).

cnf(i_0_14993,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_8809]),
    [final] ).

cnf(i_0_14994,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_8266]),
    [final] ).

cnf(i_0_14995,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_8810]),
    [final] ).

cnf(i_0_14996,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_8811]),
    [final] ).

cnf(i_0_14997,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_8812]),
    [final] ).

cnf(i_0_14998,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_8813]),
    [final] ).

cnf(i_0_14999,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_8267]),
    [final] ).

cnf(i_0_15000,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_8814]),
    [final] ).

cnf(i_0_15001,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_8267]),
    [final] ).

cnf(i_0_15002,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_8815]),
    [final] ).

cnf(i_0_15003,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_8816]),
    [final] ).

cnf(i_0_15004,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_8817]),
    [final] ).

cnf(i_0_15005,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk232_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_8818]),
    [final] ).

cnf(i_0_15006,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk119_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_8819]),
    [final] ).

cnf(i_0_15007,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_8782]),
    [final] ).

cnf(i_0_15008,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_8782]),
    [final] ).

cnf(i_0_15009,plain,
    ( hAPP(c_Map_Orestrict__map(X1,X4,X5,X3),X2) = hAPP(X5,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8820]),
    [final] ).

cnf(i_0_15010,plain,
    ( hAPP(c_Map_Orestrict__map(X1,X4,X5,X3),X2) = hAPP(X5,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8821]),
    [final] ).

cnf(i_0_15011,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,esk113_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8822]),
    [final] ).

cnf(i_0_15012,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,esk112_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8823]),
    [final] ).

cnf(i_0_15013,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_8824]),
    [final] ).

cnf(i_0_15014,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_8825]),
    [final] ).

cnf(i_0_15015,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk540_3(X2,X1,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk538_3(X2,X1,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_15016,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk536_3(X2,X1,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X2,X1,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_15017,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_8826]),
    [final] ).

cnf(i_0_15018,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_8218]),
    [final] ).

cnf(i_0_15019,plain,
    ( hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X6),X3,c_Option_Ooption_ONone(X6),X5),hAPP(X1,X2)) = hAPP(c_Option_Ooption_OSome(X6),X7)
    | hAPP(X5,X4) != hAPP(c_Option_Ooption_OSome(X6),X7)
    | hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
    inference(rw,[status(thm)],[i_0_8827,c_0_6301]),
    [final] ).

cnf(i_0_15020,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_8828]),
    [final] ).

cnf(i_0_15021,plain,
    ( c_Map_Odom(X1,X3,hAPP(c_Map_Omap__of(X1,X3),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4))) = hAPP(c_List_Oset(X1),X2)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8829]),
    [final] ).

cnf(i_0_15022,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_8830,c_0_8412]),c_0_8412]),
    [final] ).

cnf(i_0_15023,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_8831]),
    [final] ).

cnf(i_0_15024,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),esk538_3(X2,X1,X3)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_15025,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),esk534_3(X2,X1,X3)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_15026,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_8832]),
    [final] ).

cnf(i_0_15027,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_8833]),
    [final] ).

cnf(i_0_15028,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_8834]),
    [final] ).

cnf(i_0_15029,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_8834]),
    [final] ).

cnf(i_0_15030,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_8835]),
    [final] ).

cnf(i_0_15031,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_8406]),
    [final] ).

cnf(i_0_15032,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_8836]),
    [final] ).

cnf(i_0_15033,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_8837]),
    [final] ).

cnf(i_0_15034,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_8838]),
    [final] ).

cnf(i_0_15035,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_8839]),
    [final] ).

cnf(i_0_15036,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_8840]),
    [final] ).

cnf(i_0_15037,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_8841]),
    [final] ).

cnf(i_0_15038,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_8842]),
    [final] ).

cnf(i_0_15039,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_8843]),
    [final] ).

cnf(i_0_15040,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_8844]),
    [final] ).

cnf(i_0_15041,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_8845]),
    [final] ).

cnf(i_0_15042,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_8846]),
    [final] ).

cnf(i_0_15043,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_8847]),
    [final] ).

cnf(i_0_15044,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_8848]),
    [final] ).

cnf(i_0_15045,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_5354]),
    [final] ).

cnf(i_0_15046,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_8849,c_0_6209]),c_0_6209]),
    [final] ).

cnf(i_0_15047,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_8850]),
    [final] ).

cnf(i_0_15048,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
    | hAPP(X3,esk303_3(X3,X2,X1)) = c_Option_Ooption_ONone(X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Map_Odom(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8851]),
    [final] ).

cnf(i_0_15049,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_8537]),
    [final] ).

cnf(i_0_15050,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_8852]),
    [final] ).

cnf(i_0_15051,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_8852]),
    [final] ).

cnf(i_0_15052,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_8853]),
    [final] ).

cnf(i_0_15053,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_8539]),
    [final] ).

cnf(i_0_15054,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_8854]),
    [final] ).

cnf(i_0_15055,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_8854]),
    [final] ).

cnf(i_0_15056,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_8303]),
    [final] ).

cnf(i_0_15057,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_8855]),
    [final] ).

cnf(i_0_15058,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_8856]),
    [final] ).

cnf(i_0_15059,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_8553]),
    [final] ).

cnf(i_0_15060,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_8857,c_0_6768]),
    [final] ).

cnf(i_0_15061,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_8858]),
    [final] ).

cnf(i_0_15062,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_8859]),
    [final] ).

cnf(i_0_15063,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_8782]),
    [final] ).

cnf(i_0_15064,plain,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)))
    | ~ hBOOL(hAPP(X1,esk135_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8251]),
    [final] ).

cnf(i_0_15065,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_8860]),
    [final] ).

cnf(i_0_15066,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),esk362_3(X3,X2,X1)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8795]),
    [final] ).

cnf(i_0_15067,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_8861]),
    [final] ).

cnf(i_0_15068,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_8862]),
    [final] ).

cnf(i_0_15069,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_8186]),
    [final] ).

cnf(i_0_15070,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk310_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_8863]),
    [final] ).

cnf(i_0_15071,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk462_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | c_List_OtakeWhile(X1,X3,X2) = X2 ),
    inference(split_conjunct,[status(thm)],[i_0_8864]),
    [final] ).

cnf(i_0_15072,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_8865]),
    [final] ).

cnf(i_0_15073,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_8866]),
    [final] ).

cnf(i_0_15074,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk504_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))
    | c_List_Olist__all(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8867]),
    [final] ).

cnf(i_0_15075,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk505_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | c_List_Olist__all(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8868]),
    [final] ).

cnf(i_0_15076,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk503_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | c_List_Olist__all(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8869]),
    [final] ).

cnf(i_0_15077,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_8870]),
    [final] ).

cnf(i_0_15078,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_8871]),
    [final] ).

cnf(i_0_15079,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_8872,c_0_6311]),
    [final] ).

cnf(i_0_15080,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_8873]),
    [final] ).

cnf(i_0_15081,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_8874]),
    [final] ).

cnf(i_0_15082,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_8875]),
    [final] ).

cnf(i_0_15083,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_8876]),
    [final] ).

cnf(i_0_15084,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_8877]),
    [final] ).

cnf(i_0_15085,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_8878]),
    [final] ).

cnf(i_0_15086,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_8879]),
    [final] ).

cnf(i_0_15087,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_8880]),
    [final] ).

cnf(i_0_15088,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_8881]),
    [final] ).

cnf(i_0_15089,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_8882]),
    [final] ).

cnf(i_0_15090,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk250_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_7060]),
    [final] ).

cnf(i_0_15091,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_8883]),
    [final] ).

cnf(i_0_15092,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_8604]),
    [final] ).

cnf(i_0_15093,plain,
    c_Map_Odom(X1,X2,hAPP(hAPP(c_COMBB(X2,tc_Option_Ooption(X2),X1),c_Option_Ooption_OSome(X2)),X3)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_8884]),
    [final] ).

cnf(i_0_15094,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_8885]),
    [final] ).

cnf(i_0_15095,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_8886]),
    [final] ).

cnf(i_0_15096,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk203_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_8887]),
    [final] ).

cnf(i_0_15097,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_8888]),
    [final] ).

cnf(i_0_15098,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_7123]),
    [final] ).

cnf(i_0_15099,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_8889]),
    [final] ).

cnf(i_0_15100,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_8890,c_0_6209]),c_0_6209]),
    [final] ).

cnf(i_0_15101,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_8891]),
    [final] ).

cnf(i_0_15102,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_8891]),
    [final] ).

cnf(i_0_15103,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_8892]),
    [final] ).

cnf(i_0_15104,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk446_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_8893]),
    [final] ).

cnf(i_0_15105,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_8717]),
    [final] ).

cnf(i_0_15106,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_8894]),
    [final] ).

cnf(i_0_15107,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_8895]),
    [final] ).

cnf(i_0_15108,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_8896]),
    [final] ).

cnf(i_0_15109,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_8897]),
    [final] ).

cnf(i_0_15110,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_8898]),
    [final] ).

cnf(i_0_15111,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_8899]),
    [final] ).

cnf(i_0_15112,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_8900]),
    [final] ).

cnf(i_0_15113,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk198_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_8758]),
    [final] ).

cnf(i_0_15114,plain,
    ( X1 = X2
    | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X6,tc_Option_Ooption(X4)),X3),X2),hAPP(c_Option_Ooption_OSome(X4),X7)),X1) = hAPP(c_Option_Ooption_OSome(X4),X5)
    | hAPP(X3,X1) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_8310]),
    [final] ).

cnf(i_0_15115,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_8901]),
    [final] ).

cnf(i_0_15116,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_8902]),
    [final] ).

cnf(i_0_15117,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(X1,esk124_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_8268]),
    [final] ).

cnf(i_0_15118,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(X1,esk113_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_8822]),
    [final] ).

cnf(i_0_15119,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(X1,esk112_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_8823]),
    [final] ).

cnf(i_0_15120,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk447_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_8903]),
    [final] ).

cnf(i_0_15121,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),esk492_3(X2,X3,X1)))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8671]),
    [final] ).

cnf(i_0_15122,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),esk457_3(X3,X2,X1)))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8672]),
    [final] ).

cnf(i_0_15123,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),esk454_3(X3,X2,X1)))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8673]),
    [final] ).

cnf(i_0_15124,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_8904]),
    [final] ).

cnf(i_0_15125,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_8905]),
    [final] ).

cnf(i_0_15126,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_8906,c_0_6768]),
    [final] ).

cnf(i_0_15127,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_8907]),
    [final] ).

cnf(i_0_15128,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_8908]),
    [final] ).

cnf(i_0_15129,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_8909]),
    [final] ).

cnf(i_0_15130,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_8910]),
    [final] ).

cnf(i_0_15131,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_8909]),
    [final] ).

cnf(i_0_15132,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_8911]),
    [final] ).

cnf(i_0_15133,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_8912]),
    [final] ).

cnf(i_0_15134,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_8913]),
    [final] ).

cnf(i_0_15135,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_8914]),
    [final] ).

cnf(i_0_15136,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_8289]),
    [final] ).

cnf(i_0_15137,plain,
    ( hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X6),X3,c_Option_Ooption_ONone(X6),X5),hAPP(X1,X2)) = c_Option_Ooption_ONone(X6)
    | hAPP(X5,X4) != c_Option_Ooption_ONone(X6)
    | hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
    inference(rw,[status(thm)],[i_0_8915,c_0_6301]),
    [final] ).

cnf(i_0_15138,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_7819]),
    [final] ).

cnf(i_0_15139,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_8916]),
    [final] ).

cnf(i_0_15140,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_8917]),
    [final] ).

cnf(i_0_15141,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_8918]),
    [final] ).

cnf(i_0_15142,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_8919]),
    [final] ).

cnf(i_0_15143,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_8920]),
    [final] ).

cnf(i_0_15144,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_8921]),
    [final] ).

cnf(i_0_15145,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk200_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_8922]),
    [final] ).

cnf(i_0_15146,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_8923]),
    [final] ).

cnf(i_0_15147,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_8924]),
    [final] ).

cnf(i_0_15148,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_8473]),
    [final] ).

cnf(i_0_15149,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_8474]),
    [final] ).

cnf(i_0_15150,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_8925]),
    [final] ).

cnf(i_0_15151,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_8476]),
    [final] ).

cnf(i_0_15152,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_8926,c_0_6136]),
    [final] ).

cnf(i_0_15153,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_8927,c_0_6136]),
    [final] ).

cnf(i_0_15154,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_8928]),
    [final] ).

cnf(i_0_15155,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_8929]),
    [final] ).

cnf(i_0_15156,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_8930]),
    [final] ).

cnf(i_0_15157,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_8931]),
    [final] ).

cnf(i_0_15158,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_8932]),
    [final] ).

cnf(i_0_15159,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_8933]),
    [final] ).

cnf(i_0_15160,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_8934]),
    [final] ).

cnf(i_0_15161,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_8935,c_0_6103]),c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_15162,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_8936,c_0_6103]),c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_15163,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_8937]),
    [final] ).

cnf(i_0_15164,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_8938]),
    [final] ).

cnf(i_0_15165,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_8939]),
    [final] ).

cnf(i_0_15166,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_8940]),
    [final] ).

cnf(i_0_15167,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_8941]),
    [final] ).

cnf(i_0_15168,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_8942]),
    [final] ).

cnf(i_0_15169,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_8943]),
    [final] ).

cnf(i_0_15170,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_8944]),
    [final] ).

cnf(i_0_15171,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_8945]),
    [final] ).

cnf(i_0_15172,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_8837]),
    [final] ).

cnf(i_0_15173,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk297_1(X1)),c_Int_OInteg)),
    inference(split_conjunct,[status(thm)],[i_0_8946]),
    [final] ).

cnf(i_0_15174,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_8947,c_0_6209]),c_0_6209]),
    [final] ).

cnf(i_0_15175,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_8948,c_0_6209]),c_0_6209]),
    [final] ).

cnf(i_0_15176,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_8949]),
    [final] ).

cnf(i_0_15177,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_8950]),
    [final] ).

cnf(i_0_15178,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_8527]),
    [final] ).

cnf(i_0_15179,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_8951]),
    [final] ).

cnf(i_0_15180,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_8952]),
    [final] ).

cnf(i_0_15181,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_8953]),
    [final] ).

cnf(i_0_15182,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_8954]),
    [final] ).

cnf(i_0_15183,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_8955]),
    [final] ).

cnf(i_0_15184,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_8956]),
    [final] ).

cnf(i_0_15185,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_8957]),
    [final] ).

cnf(i_0_15186,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_8958]),
    [final] ).

cnf(i_0_15187,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_8959]),
    [final] ).

cnf(i_0_15188,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_8959]),
    [final] ).

cnf(i_0_15189,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,esk135_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8251]),
    [final] ).

cnf(i_0_15190,plain,
    ( hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X5),X3,c_Option_Ooption_ONone(X5),X7),hAPP(X1,X2)) = hAPP(X7,X4)
    | hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
    inference(rw,[status(thm)],[i_0_8960,c_0_6301]),
    [final] ).

cnf(i_0_15191,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_8918]),
    [final] ).

cnf(i_0_15192,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_8961]),
    [final] ).

cnf(i_0_15193,plain,
    ( hBOOL(hAPP(X1,esk197_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_8721]),
    [final] ).

cnf(i_0_15194,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_8962]),
    [final] ).

cnf(i_0_15195,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_8963]),
    [final] ).

cnf(i_0_15196,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_8964]),
    [final] ).

cnf(i_0_15197,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_8965]),
    [final] ).

cnf(i_0_15198,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_8966]),
    [final] ).

cnf(i_0_15199,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_8967]),
    [final] ).

cnf(i_0_15200,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_8968]),
    [final] ).

cnf(i_0_15201,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_8969]),
    [final] ).

cnf(i_0_15202,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_8970]),
    [final] ).

cnf(i_0_15203,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_8971]),
    [final] ).

cnf(i_0_15204,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_8972]),
    [final] ).

cnf(i_0_15205,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_8973]),
    [final] ).

cnf(i_0_15206,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_8974]),
    [final] ).

cnf(i_0_15207,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_8975]),
    [final] ).

cnf(i_0_15208,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_8976]),
    [final] ).

cnf(i_0_15209,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_8977]),
    [final] ).

cnf(i_0_15210,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_8978]),
    [final] ).

cnf(i_0_15211,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_8979]),
    [final] ).

cnf(i_0_15212,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_8980]),
    [final] ).

cnf(i_0_15213,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_8750]),
    [final] ).

cnf(i_0_15214,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_8981]),
    [final] ).

cnf(i_0_15215,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_8982]),
    [final] ).

cnf(i_0_15216,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_8983]),
    [final] ).

cnf(i_0_15217,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_8984]),
    [final] ).

cnf(i_0_15218,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_8985]),
    [final] ).

cnf(i_0_15219,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_8986]),
    [final] ).

cnf(i_0_15220,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_8987]),
    [final] ).

cnf(i_0_15221,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_8988]),
    [final] ).

cnf(i_0_15222,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_8989]),
    [final] ).

cnf(i_0_15223,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_8990]),
    [final] ).

cnf(i_0_15224,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_8991]),
    [final] ).

cnf(i_0_15225,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,X3)),hAPP(X2,X4)))
    | ~ c_Orderings_Oorder__class_Ostrict__mono(X5,X1,X2)
    | ~ class_Orderings_Oorder(X1)
    | ~ class_Orderings_Olinorder(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_8992]),
    [final] ).

cnf(i_0_15226,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(X2,X4)))
    | ~ c_Orderings_Oorder__class_Ostrict__mono(X5,X1,X2)
    | ~ class_Orderings_Oorder(X1)
    | ~ class_Orderings_Olinorder(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_8993]),
    [final] ).

cnf(i_0_15227,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_8994]),
    [final] ).

cnf(i_0_15228,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_8995]),
    [final] ).

cnf(i_0_15229,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_8996,c_0_6103]),
    [final] ).

cnf(i_0_15230,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_8837]),
    [final] ).

cnf(i_0_15231,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_8997]),
    [final] ).

cnf(i_0_15232,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(c_Map_Orestrict__map(X1,X4,X5,X3),X2) = c_Option_Ooption_ONone(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8820]),
    [final] ).

cnf(i_0_15233,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(c_Map_Orestrict__map(X1,X4,X5,X3),X2) = c_Option_Ooption_ONone(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8998]),
    [final] ).

cnf(i_0_15234,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_8322]),
    [final] ).

cnf(i_0_15235,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_8999]),
    [final] ).

cnf(i_0_15236,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk295_3(X2,X3,X1)),X2))
    | hBOOL(hAPP(c_Predicate_OPowp(X1,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9000]),
    [final] ).

cnf(i_0_15237,plain,
    hAPP(c_Map_Orestrict__map(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X4) = c_Option_Ooption_ONone(X2),
    inference(split_conjunct,[status(thm)],[i_0_9001]),
    [final] ).

cnf(i_0_15238,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk196_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_8721]),
    [final] ).

cnf(i_0_15239,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_9002]),
    [final] ).

cnf(i_0_15240,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_9003]),
    [final] ).

cnf(i_0_15241,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_9004]),
    [final] ).

cnf(i_0_15242,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_9005,c_0_6103]),
    [final] ).

cnf(i_0_15243,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_8243]),
    [final] ).

cnf(i_0_15244,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_8370]),
    [final] ).

cnf(i_0_15245,plain,
    ( hBOOL(hAPP(X1,esk126_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_7703]),
    [final] ).

cnf(i_0_15246,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_9006]),
    [final] ).

cnf(i_0_15247,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_9007]),
    [final] ).

cnf(i_0_15248,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_8023]),
    [final] ).

cnf(i_0_15249,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_8022]),
    [final] ).

cnf(i_0_15250,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_9008,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_15251,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_8505]),
    [final] ).

cnf(i_0_15252,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_8505]),
    [final] ).

cnf(i_0_15253,plain,
    ( hAPP(c_Map_Omap__add(X6,X3,X4,X1),X2) = hAPP(c_Option_Ooption_OSome(X3),X5)
    | hAPP(X1,X2) != c_Option_Ooption_ONone(X3)
    | hAPP(X4,X2) != hAPP(c_Option_Ooption_OSome(X3),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_8447]),
    [final] ).

cnf(i_0_15254,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_8572]),
    [final] ).

cnf(i_0_15255,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_7688]),
    [final] ).

cnf(i_0_15256,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_7801]),
    [final] ).

cnf(i_0_15257,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_9009]),
    [final] ).

cnf(i_0_15258,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_8786]),
    [final] ).

cnf(i_0_15259,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_7819]),
    [final] ).

cnf(i_0_15260,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_6663]),
    [final] ).

cnf(i_0_15261,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X6)),X7),X2),hAPP(c_Option_Ooption_OSome(X6),X3)),X1) = hAPP(c_Option_Ooption_OSome(X6),X4)
    | X1 != X2
    | X3 != X4 ),
    inference(split_conjunct,[status(thm)],[i_0_8310]),
    [final] ).

cnf(i_0_15262,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_9010,c_0_6209]),
    [final] ).

cnf(i_0_15263,plain,
    ( X2 = X3
    | hAPP(hAPP(c_List_Onth(X1),X2),esk410_3(X1,X3,X2)) != hAPP(hAPP(c_List_Onth(X1),X3),esk410_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_8696]),
    [final] ).

cnf(i_0_15264,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_8779]),
    [final] ).

cnf(i_0_15265,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_8771]),
    [final] ).

cnf(i_0_15266,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_8995]),
    [final] ).

cnf(i_0_15267,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_9011]),
    [final] ).

cnf(i_0_15268,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_7123]),
    [final] ).

cnf(i_0_15269,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_8894]),
    [final] ).

cnf(i_0_15270,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_8894]),
    [final] ).

cnf(i_0_15271,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_8898]),
    [final] ).

cnf(i_0_15272,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_9012]),
    [final] ).

cnf(i_0_15273,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_8898]),
    [final] ).

cnf(i_0_15274,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_9012]),
    [final] ).

cnf(i_0_15275,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_8895]),
    [final] ).

cnf(i_0_15276,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_9013]),
    [final] ).

cnf(i_0_15277,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_8895]),
    [final] ).

cnf(i_0_15278,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_9013]),
    [final] ).

cnf(i_0_15279,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk535_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_15280,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_9014]),
    [final] ).

cnf(i_0_15281,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_9015]),
    [final] ).

cnf(i_0_15282,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_9016]),
    [final] ).

cnf(i_0_15283,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_9017]),
    [final] ).

cnf(i_0_15284,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_9018]),
    [final] ).

cnf(i_0_15285,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_9019]),
    [final] ).

cnf(i_0_15286,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_9020]),
    [final] ).

cnf(i_0_15287,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_9021]),
    [final] ).

cnf(i_0_15288,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_8824]),
    [final] ).

cnf(i_0_15289,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_9022]),
    [final] ).

cnf(i_0_15290,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_8521]),
    [final] ).

cnf(i_0_15291,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_9023]),
    [final] ).

cnf(i_0_15292,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_8420]),
    [final] ).

cnf(i_0_15293,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_9024]),
    [final] ).

cnf(i_0_15294,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_9025]),
    [final] ).

cnf(i_0_15295,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_9026]),
    [final] ).

cnf(i_0_15296,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_9027]),
    [final] ).

cnf(i_0_15297,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,esk124_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8268]),
    [final] ).

cnf(i_0_15298,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk199_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_8758]),
    [final] ).

cnf(i_0_15299,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | epred1_3(X2,X1,X3)
    | ~ hBOOL(hAPP(X2,esk533_3(X3,X1,X2)))
    | ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_15300,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(rw,[status(thm)],[i_0_9028,c_0_6103]),
    [final] ).

cnf(i_0_15301,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_9029,c_0_6103]),
    [final] ).

cnf(i_0_15302,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_9030,c_0_6103]),
    [final] ).

cnf(i_0_15303,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_9031,c_0_6103]),
    [final] ).

cnf(i_0_15304,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_9032,c_0_6103]),
    [final] ).

cnf(i_0_15305,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_9033,c_0_6103]),
    [final] ).

cnf(i_0_15306,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_9034]),
    [final] ).

cnf(i_0_15307,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_9035,c_0_9036]),c_0_9036]),
    [final] ).

cnf(i_0_15308,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_9037,c_0_6136]),
    [final] ).

cnf(i_0_15309,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_8461]),
    [final] ).

cnf(i_0_15310,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk540_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_15311,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_9038]),
    [final] ).

cnf(i_0_15312,plain,
    ( hBOOL(hAPP(hAPP(X1,esk132_3(X2,X1,X3)),X2))
    | hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9039]),
    [final] ).

cnf(i_0_15313,plain,
    ( hBOOL(hAPP(hAPP(X1,esk131_3(X2,X1,X3)),X2))
    | hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9040]),
    [final] ).

cnf(i_0_15314,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_9041,c_0_6128]),
    [final] ).

cnf(i_0_15315,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_8623]),
    [final] ).

cnf(i_0_15316,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_9042]),
    [final] ).

cnf(i_0_15317,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_9043,c_0_6242]),
    [final] ).

cnf(i_0_15318,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_9044]),
    [final] ).

cnf(i_0_15319,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_9045]),
    [final] ).

cnf(i_0_15320,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_9046]),
    [final] ).

cnf(i_0_15321,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_9047]),
    [final] ).

cnf(i_0_15322,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_9048]),
    [final] ).

cnf(i_0_15323,plain,
    ( hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X4),X3,c_Option_Ooption_ONone(X4),X6),hAPP(X1,X2)) = c_Option_Ooption_ONone(X4)
    | hAPP(X1,X2) != c_Option_Ooption_ONone(X3) ),
    inference(rw,[status(thm)],[i_0_9049,c_0_6301]),
    [final] ).

cnf(i_0_15324,plain,
    ( hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X4),X3,c_Option_Ooption_ONone(X4),X6),hAPP(X1,X2)) = c_Option_Ooption_ONone(X4)
    | hAPP(X1,X2) != c_Option_Ooption_ONone(X3) ),
    inference(rw,[status(thm)],[i_0_9050,c_0_6301]),
    [final] ).

cnf(i_0_15325,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_9051]),
    [final] ).

cnf(i_0_15326,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_9052]),
    [final] ).

cnf(i_0_15327,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk329_3(X2,X3,X1)),X3))
    | c_Relation_Ototal__on(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6855]),
    [final] ).

cnf(i_0_15328,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk328_3(X2,X3,X1)),X3))
    | c_Relation_Ototal__on(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6855]),
    [final] ).

cnf(i_0_15329,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)
    | esk448_2(X1,X2) != c_List_Olist_ONil(X2) ),
    inference(rw,[status(thm)],[i_0_9053,c_0_6177]),
    [final] ).

cnf(i_0_15330,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)
    | esk449_2(X1,X2) != c_List_Olist_ONil(X2) ),
    inference(rw,[status(thm)],[i_0_9054,c_0_6177]),
    [final] ).

cnf(i_0_15331,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_9055]),
    [final] ).

cnf(i_0_15332,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_9056]),
    [final] ).

cnf(i_0_15333,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | epred2_3(X2,X1,X3)
    | ~ hBOOL(hAPP(X2,esk538_3(X3,X1,X2)))
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_15334,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_9057]),
    [final] ).

cnf(i_0_15335,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_9058]),
    [final] ).

cnf(i_0_15336,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_9059]),
    [final] ).

cnf(i_0_15337,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_9060]),
    [final] ).

cnf(i_0_15338,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_9061]),
    [final] ).

cnf(i_0_15339,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_8672]),
    [final] ).

cnf(i_0_15340,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_8673]),
    [final] ).

cnf(i_0_15341,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_9062]),
    [final] ).

cnf(i_0_15342,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_15343,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_9063,c_0_6136]),
    [final] ).

cnf(i_0_15344,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_9064]),
    [final] ).

cnf(i_0_15345,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_9065]),
    [final] ).

cnf(i_0_15346,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_9066,c_0_6136]),
    [final] ).

cnf(i_0_15347,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),esk363_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_8598]),
    [final] ).

cnf(i_0_15348,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_9067]),
    [final] ).

cnf(i_0_15349,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_9068]),
    [final] ).

cnf(i_0_15350,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_9069]),
    [final] ).

cnf(i_0_15351,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_9069]),
    [final] ).

cnf(i_0_15352,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_8303]),
    [final] ).

cnf(i_0_15353,plain,
    ( hAPP(c_Map_Omap__add(X5,X3,X6,X1),X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
    | hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8447]),
    [final] ).

cnf(i_0_15354,plain,
    ( hAPP(c_Map_Omap__add(X5,X3,X6,X1),X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
    | hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9070]),
    [final] ).

cnf(i_0_15355,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_9071]),
    [final] ).

cnf(i_0_15356,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_9072]),
    [final] ).

cnf(i_0_15357,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_9073]),
    [final] ).

cnf(i_0_15358,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_9074]),
    [final] ).

cnf(i_0_15359,plain,
    ( hBOOL(hAPP(X1,esk126_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_7703]),
    [final] ).

cnf(i_0_15360,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_9075,c_0_6177]),
    [final] ).

cnf(i_0_15361,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_9076]),
    [final] ).

cnf(i_0_15362,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_9077]),
    [final] ).

cnf(i_0_15363,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_9078]),
    [final] ).

cnf(i_0_15364,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_9079]),
    [final] ).

cnf(i_0_15365,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_9080]),
    [final] ).

cnf(i_0_15366,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_9081]),
    [final] ).

cnf(i_0_15367,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_8825]),
    [final] ).

cnf(i_0_15368,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_9082]),
    [final] ).

cnf(i_0_15369,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_9083]),
    [final] ).

cnf(i_0_15370,plain,
    ( c_Orderings_Oord__class_OLeast(X1,X3) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk8_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X3,X2))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9084]),
    [final] ).

cnf(i_0_15371,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_9085]),
    [final] ).

cnf(i_0_15372,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_8529]),
    [final] ).

cnf(i_0_15373,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_9086]),
    [final] ).

cnf(i_0_15374,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_9087]),
    [final] ).

cnf(i_0_15375,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_9088]),
    [final] ).

cnf(i_0_15376,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_9089]),
    [final] ).

cnf(i_0_15377,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_9090]),
    [final] ).

cnf(i_0_15378,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk200_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_8922]),
    [final] ).

cnf(i_0_15379,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_9091]),
    [final] ).

cnf(i_0_15380,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_9092]),
    [final] ).

cnf(i_0_15381,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_9093]),
    [final] ).

cnf(i_0_15382,plain,
    ( hBOOL(hAPP(hAPP(X3,esk266_2(X4,X3)),X4))
    | ~ hBOOL(hAPP(c_Predicate_ORangeP(X1,X2,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9094]),
    [final] ).

cnf(i_0_15383,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_9095]),
    [final] ).

cnf(i_0_15384,plain,
    ( hAPP(c_Map_Omap__add(X5,X3,X4,X1),X2) = c_Option_Ooption_ONone(X3)
    | hAPP(X1,X2) != c_Option_Ooption_ONone(X3)
    | hAPP(X4,X2) != c_Option_Ooption_ONone(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8569]),
    [final] ).

cnf(i_0_15385,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_9096]),
    [final] ).

cnf(i_0_15386,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Map_Odom(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X3)))),
    inference(split_conjunct,[status(thm)],[i_0_9097]),
    [final] ).

cnf(i_0_15387,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_9098]),
    [final] ).

cnf(i_0_15388,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_9099]),
    [final] ).

cnf(i_0_15389,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_9100]),
    [final] ).

cnf(i_0_15390,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_9101,c_0_6209]),
    [final] ).

cnf(i_0_15391,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_9102]),
    [final] ).

cnf(i_0_15392,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_9103]),
    [final] ).

cnf(i_0_15393,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_7717]),
    [final] ).

cnf(i_0_15394,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_9104]),
    [final] ).

cnf(i_0_15395,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_9105]),
    [final] ).

cnf(i_0_15396,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk513_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_7289]),
    [final] ).

cnf(i_0_15397,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_9106]),
    [final] ).

cnf(i_0_15398,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2))),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ c_Orderings_Oorder__class_Omono(X1,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9107]),
    [final] ).

cnf(i_0_15399,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2))),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ c_Orderings_Oorder__class_Omono(X1,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9108]),
    [final] ).

cnf(i_0_15400,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk202_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_8887]),
    [final] ).

cnf(i_0_15401,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_9109]),
    [final] ).

cnf(i_0_15402,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_9110]),
    [final] ).

cnf(i_0_15403,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_8477]),
    [final] ).

cnf(i_0_15404,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_9111]),
    [final] ).

cnf(i_0_15405,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_9112]),
    [final] ).

cnf(i_0_15406,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_9113]),
    [final] ).

cnf(i_0_15407,plain,
    hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
    inference(split_conjunct,[status(thm)],[i_0_9114]),
    [final] ).

cnf(i_0_15408,plain,
    hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_9115]),
    [final] ).

cnf(i_0_15409,plain,
    hAPP(c_Option_Ooption_Ooption__case(X1,X2,X3,X4),hAPP(c_Option_Ooption_OSome(X2),X5)) = hAPP(X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_9116]),
    [final] ).

cnf(i_0_15410,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_9117]),
    [final] ).

cnf(i_0_15411,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_8980]),
    [final] ).

cnf(i_0_15412,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_8980]),
    [final] ).

cnf(i_0_15413,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_9118]),
    [final] ).

cnf(i_0_15414,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_9119]),
    [final] ).

cnf(i_0_15415,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_7479]),
    [final] ).

cnf(i_0_15416,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_7480]),
    [final] ).

cnf(i_0_15417,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_7481]),
    [final] ).

cnf(i_0_15418,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_9120]),
    [final] ).

cnf(i_0_15419,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_9121]),
    [final] ).

cnf(i_0_15420,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_9122]),
    [final] ).

cnf(i_0_15421,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_9123]),
    [final] ).

cnf(i_0_15422,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_7379]),
    [final] ).

cnf(i_0_15423,plain,
    ( hBOOL(hAPP(X1,esk513_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_7289]),
    [final] ).

cnf(i_0_15424,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_9124]),
    [final] ).

cnf(i_0_15425,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_9125]),
    [final] ).

cnf(i_0_15426,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_9126]),
    [final] ).

cnf(i_0_15427,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_9127]),
    [final] ).

cnf(i_0_15428,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_9128]),
    [final] ).

cnf(i_0_15429,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_9129]),
    [final] ).

cnf(i_0_15430,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_9130]),
    [final] ).

cnf(i_0_15431,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_9131]),
    [final] ).

cnf(i_0_15432,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_9132]),
    [final] ).

cnf(i_0_15433,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_9133]),
    [final] ).

cnf(i_0_15434,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk540_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_15435,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk535_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_15436,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_8496]),
    [final] ).

cnf(i_0_15437,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_9134]),
    [final] ).

cnf(i_0_15438,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_8865]),
    [final] ).

cnf(i_0_15439,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_9135]),
    [final] ).

cnf(i_0_15440,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_8866]),
    [final] ).

cnf(i_0_15441,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_9136]),
    [final] ).

cnf(i_0_15442,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2)),X3))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9137]),
    [final] ).

cnf(i_0_15443,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_9138]),
    [final] ).

cnf(i_0_15444,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_8957]),
    [final] ).

cnf(i_0_15445,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_8958]),
    [final] ).

cnf(i_0_15446,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_9139]),
    [final] ).

cnf(i_0_15447,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_8959]),
    [final] ).

cnf(i_0_15448,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_8959]),
    [final] ).

cnf(i_0_15449,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_9140]),
    [final] ).

cnf(i_0_15450,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_9141]),
    [final] ).

cnf(i_0_15451,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk132_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9039]),
    [final] ).

cnf(i_0_15452,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk131_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9040]),
    [final] ).

cnf(i_0_15453,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_8496]),
    [final] ).

cnf(i_0_15454,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_9142,c_0_6128]),c_0_6128]),
    [final] ).

cnf(i_0_15455,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_9143]),
    [final] ).

cnf(i_0_15456,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_9144]),
    [final] ).

cnf(i_0_15457,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),esk370_2(X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8607]),
    [final] ).

cnf(i_0_15458,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_9145]),
    [final] ).

cnf(i_0_15459,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_9146]),
    [final] ).

cnf(i_0_15460,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk201_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_8922]),
    [final] ).

cnf(i_0_15461,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(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_9147]),
    [final] ).

cnf(i_0_15462,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_9148]),
    [final] ).

cnf(i_0_15463,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_8825]),
    [final] ).

cnf(i_0_15464,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_9149]),
    [final] ).

cnf(i_0_15465,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_9150]),
    [final] ).

cnf(i_0_15466,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_9151]),
    [final] ).

cnf(i_0_15467,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_9152]),
    [final] ).

cnf(i_0_15468,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_9153]),
    [final] ).

cnf(i_0_15469,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_9154]),
    [final] ).

cnf(i_0_15470,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_9155]),
    [final] ).

cnf(i_0_15471,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_9156]),
    [final] ).

cnf(i_0_15472,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_9157]),
    [final] ).

cnf(i_0_15473,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_9158]),
    [final] ).

cnf(i_0_15474,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_9159]),
    [final] ).

cnf(i_0_15475,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_9160]),
    [final] ).

cnf(i_0_15476,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_8599]),
    [final] ).

cnf(i_0_15477,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_9161]),
    [final] ).

cnf(i_0_15478,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_9162]),
    [final] ).

cnf(i_0_15479,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_9163]),
    [final] ).

cnf(i_0_15480,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_9164]),
    [final] ).

cnf(i_0_15481,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,X1,X3)
    | ~ hBOOL(hAPP(X2,esk538_3(X3,X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_15482,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,X1,X3)
    | ~ hBOOL(hAPP(X2,esk533_3(X3,X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_15483,plain,
    ( hBOOL(hAPP(X1,esk203_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_8887]),
    [final] ).

cnf(i_0_15484,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_9165]),
    [final] ).

cnf(i_0_15485,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_9166,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_15486,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_9167]),
    [final] ).

cnf(i_0_15487,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_9168]),
    [final] ).

cnf(i_0_15488,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_9169]),
    [final] ).

cnf(i_0_15489,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_9170]),
    [final] ).

cnf(i_0_15490,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_9171]),
    [final] ).

cnf(i_0_15491,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_8551]),
    [final] ).

cnf(i_0_15492,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)
    | esk433_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_8245]),
    [final] ).

cnf(i_0_15493,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_9172]),
    [final] ).

cnf(i_0_15494,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_9173]),
    [final] ).

cnf(i_0_15495,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_9173]),
    [final] ).

cnf(i_0_15496,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_9174]),
    [final] ).

cnf(i_0_15497,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_7407]),
    [final] ).

cnf(i_0_15498,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_7408]),
    [final] ).

cnf(i_0_15499,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_7409]),
    [final] ).

cnf(i_0_15500,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_7410]),
    [final] ).

cnf(i_0_15501,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_9175]),
    [final] ).

cnf(i_0_15502,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_7965]),
    [final] ).

cnf(i_0_15503,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_7123]),
    [final] ).

cnf(i_0_15504,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_9095]),
    [final] ).

cnf(i_0_15505,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_9176]),
    [final] ).

cnf(i_0_15506,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_9177]),
    [final] ).

cnf(i_0_15507,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_9178]),
    [final] ).

cnf(i_0_15508,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_9179]),
    [final] ).

cnf(i_0_15509,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_8746]),
    [final] ).

cnf(i_0_15510,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_8747]),
    [final] ).

cnf(i_0_15511,plain,
    hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5)) != hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)),
    inference(split_conjunct,[status(thm)],[i_0_9180]),
    [final] ).

cnf(i_0_15512,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_9181]),
    [final] ).

cnf(i_0_15513,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_9182]),
    [final] ).

cnf(i_0_15514,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_9183]),
    [final] ).

cnf(i_0_15515,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_9184]),
    [final] ).

cnf(i_0_15516,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_9185]),
    [final] ).

cnf(i_0_15517,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_9186]),
    [final] ).

cnf(i_0_15518,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_9187]),
    [final] ).

cnf(i_0_15519,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_9188]),
    [final] ).

cnf(i_0_15520,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_9189]),
    [final] ).

cnf(i_0_15521,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_9190]),
    [final] ).

cnf(i_0_15522,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)),esk534_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_7732]),
    [final] ).

cnf(i_0_15523,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_9145]),
    [final] ).

cnf(i_0_15524,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_9145]),
    [final] ).

cnf(i_0_15525,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_9191]),
    [final] ).

cnf(i_0_15526,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_9192]),
    [final] ).

cnf(i_0_15527,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_9193]),
    [final] ).

cnf(i_0_15528,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_9194]),
    [final] ).

cnf(i_0_15529,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))
    | hAPP(X4,X2) != c_Option_Ooption_ONone(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9195]),
    [final] ).

cnf(i_0_15530,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_8987]),
    [final] ).

cnf(i_0_15531,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_9196]),
    [final] ).

cnf(i_0_15532,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_9197]),
    [final] ).

cnf(i_0_15533,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_9198]),
    [final] ).

cnf(i_0_15534,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_9199]),
    [final] ).

cnf(i_0_15535,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_9200]),
    [final] ).

cnf(i_0_15536,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_9201]),
    [final] ).

cnf(i_0_15537,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_8795]),
    [final] ).

cnf(i_0_15538,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X3,X4)),hAPP(X3,X5)))
    | ~ class_Orderings_Oorder(X1)
    | ~ class_Orderings_Oorder(X2)
    | ~ c_Orderings_Oorder__class_Ostrict__mono(X2,X1,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_9202]),
    [final] ).

cnf(i_0_15539,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(X5,X2)),hAPP(X5,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ c_Orderings_Oorder__class_Ostrict__mono(X1,X4,X5)
    | ~ class_Orderings_Oorder(X4)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8992]),
    [final] ).

cnf(i_0_15540,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X3,X4)),hAPP(X3,X5)))
    | ~ class_Orderings_Oorder(X1)
    | ~ class_Orderings_Oorder(X2)
    | ~ c_Orderings_Oorder__class_Omono(X2,X1,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_9203]),
    [final] ).

cnf(i_0_15541,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(X5,X2)),hAPP(X5,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ c_Orderings_Oorder__class_Ostrict__mono(X1,X4,X5)
    | ~ class_Orderings_Oorder(X4)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8993]),
    [final] ).

cnf(i_0_15542,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_9204]),
    [final] ).

cnf(i_0_15543,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_9205]),
    [final] ).

cnf(i_0_15544,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_9206]),
    [final] ).

cnf(i_0_15545,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_9207]),
    [final] ).

cnf(i_0_15546,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_9208]),
    [final] ).

cnf(i_0_15547,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk536_3(X2,X1,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | epred1_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_15548,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_9209]),
    [final] ).

cnf(i_0_15549,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_9210]),
    [final] ).

cnf(i_0_15550,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_9211]),
    [final] ).

cnf(i_0_15551,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_9212]),
    [final] ).

cnf(i_0_15552,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_9213]),
    [final] ).

cnf(i_0_15553,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_9213]),
    [final] ).

cnf(i_0_15554,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_9214]),
    [final] ).

cnf(i_0_15555,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_9215]),
    [final] ).

cnf(i_0_15556,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)),esk538_3(X2,X1,X3)))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_15557,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_8578]),
    [final] ).

cnf(i_0_15558,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_9216]),
    [final] ).

cnf(i_0_15559,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_9217]),
    [final] ).

cnf(i_0_15560,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_9218]),
    [final] ).

cnf(i_0_15561,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_9219]),
    [final] ).

cnf(i_0_15562,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_9220]),
    [final] ).

cnf(i_0_15563,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_9221]),
    [final] ).

cnf(i_0_15564,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_9222]),
    [final] ).

cnf(i_0_15565,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_9223]),
    [final] ).

cnf(i_0_15566,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_8573]),
    [final] ).

cnf(i_0_15567,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_9159]),
    [final] ).

cnf(i_0_15568,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_9224]),
    [final] ).

cnf(i_0_15569,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_9225]),
    [final] ).

cnf(i_0_15570,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_9226]),
    [final] ).

cnf(i_0_15571,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_8537]),
    [final] ).

cnf(i_0_15572,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_8539]),
    [final] ).

cnf(i_0_15573,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_9227]),
    [final] ).

cnf(i_0_15574,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_9228]),
    [final] ).

cnf(i_0_15575,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_9229]),
    [final] ).

cnf(i_0_15576,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_9230]),
    [final] ).

cnf(i_0_15577,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_9231]),
    [final] ).

cnf(i_0_15578,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_9232]),
    [final] ).

cnf(i_0_15579,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_9233]),
    [final] ).

cnf(i_0_15580,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_9234]),
    [final] ).

cnf(i_0_15581,plain,
    c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(X1)),c_Option_Ooption_ONone(X1)),hAPP(c_Set_Oimage(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_9235]),
    [final] ).

cnf(i_0_15582,plain,
    hAPP(c_Fun_Ocomp(X1,X1,X2,c_Fun_Oid(X1)),X3) = X3,
    inference(split_conjunct,[status(thm)],[i_0_9236]),
    [final] ).

cnf(i_0_15583,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_9237]),
    [final] ).

cnf(i_0_15584,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_9238,c_0_8412]),
    [final] ).

cnf(i_0_15585,plain,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ c_Partial__Function_Omk__less(X4,X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9239]),
    [final] ).

cnf(i_0_15586,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_9240]),
    [final] ).

cnf(i_0_15587,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_9241]),
    [final] ).

cnf(i_0_15588,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_9242]),
    [final] ).

cnf(i_0_15589,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk540_3(X2,X1,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_15590,plain,
    ( hBOOL(hAPP(hAPP(X3,X4),esk270_2(X4,X3)))
    | ~ hBOOL(hAPP(c_Predicate_ODomainP(X1,X2,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9243]),
    [final] ).

cnf(i_0_15591,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_9244]),
    [final] ).

cnf(i_0_15592,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_9245]),
    [final] ).

cnf(i_0_15593,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_9019]),
    [final] ).

cnf(i_0_15594,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_9246]),
    [final] ).

cnf(i_0_15595,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_5577]),
    [final] ).

cnf(i_0_15596,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_7756]),
    [final] ).

cnf(i_0_15597,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_8822]),
    [final] ).

cnf(i_0_15598,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_8823]),
    [final] ).

cnf(i_0_15599,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_9247]),
    [final] ).

cnf(i_0_15600,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_9248]),
    [final] ).

cnf(i_0_15601,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_9249,c_0_6242]),
    [final] ).

cnf(i_0_15602,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk117_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_9250]),
    [final] ).

cnf(i_0_15603,plain,
    hAPP(c_List_Ofoldl(X1,X2,X3,X4),c_List_Olist_ONil(X2)) = X4,
    inference(split_conjunct,[status(thm)],[i_0_9251]),
    [final] ).

cnf(i_0_15604,plain,
    hAPP(c_List_Olist_Olist__case(X1,X2,X3,X4),c_List_Olist_ONil(X2)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_9252]),
    [final] ).

cnf(i_0_15605,plain,
    hAPP(c_Option_Ooption_Ooption__case(X1,X2,X3,X4),c_Option_Ooption_ONone(X2)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_9253]),
    [final] ).

cnf(i_0_15606,plain,
    hAPP(c_Fun_Ocomp(X1,X2,X1,X3),c_Fun_Oid(X1)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_9254]),
    [final] ).

cnf(i_0_15607,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_9255]),
    [final] ).

cnf(i_0_15608,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_9255]),
    [final] ).

cnf(i_0_15609,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_9256,c_0_6209]),
    [final] ).

cnf(i_0_15610,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_9257]),
    [final] ).

cnf(i_0_15611,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_9258]),
    [final] ).

cnf(i_0_15612,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_9259]),
    [final] ).

cnf(i_0_15613,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_8919]),
    [final] ).

cnf(i_0_15614,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_8920]),
    [final] ).

cnf(i_0_15615,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_9260]),
    [final] ).

cnf(i_0_15616,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_8921]),
    [final] ).

cnf(i_0_15617,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_9261]),
    [final] ).

cnf(i_0_15618,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X1))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))) ),
    inference(rw,[status(thm)],[i_0_9262,c_0_6103]),
    [final] ).

cnf(i_0_15619,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_9263,c_0_6103]),
    [final] ).

cnf(i_0_15620,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_9264,c_0_6103]),
    [final] ).

cnf(i_0_15621,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_9265,c_0_6103]),
    [final] ).

cnf(i_0_15622,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_9266,c_0_6103]),
    [final] ).

cnf(i_0_15623,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_9267]),
    [final] ).

cnf(i_0_15624,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_9268]),
    [final] ).

cnf(i_0_15625,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_9269]),
    [final] ).

cnf(i_0_15626,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_8598]),
    [final] ).

cnf(i_0_15627,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_9270]),
    [final] ).

cnf(i_0_15628,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_9271]),
    [final] ).

cnf(i_0_15629,plain,
    ( c_FunDef_OTHE__default(X2,X1,X3) = c_HOL_OThe(X2,X3)
    | esk523_4(X1,X2,X3,X4) != X4
    | ~ hBOOL(hAPP(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8130]),
    [final] ).

cnf(i_0_15630,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_9272]),
    [final] ).

cnf(i_0_15631,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk92_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_6802]),
    [final] ).

cnf(i_0_15632,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_9273]),
    [final] ).

cnf(i_0_15633,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_15634,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_9274]),
    [final] ).

cnf(i_0_15635,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_9275]),
    [final] ).

cnf(i_0_15636,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_9276]),
    [final] ).

cnf(i_0_15637,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_9277]),
    [final] ).

cnf(i_0_15638,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_9278]),
    [final] ).

cnf(i_0_15639,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_8773]),
    [final] ).

cnf(i_0_15640,plain,
    c_Map_Odom(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X3)) = hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9279]),
    [final] ).

cnf(i_0_15641,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_8929]),
    [final] ).

cnf(i_0_15642,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_8930]),
    [final] ).

cnf(i_0_15643,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_9280]),
    [final] ).

cnf(i_0_15644,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_9281]),
    [final] ).

cnf(i_0_15645,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_9282]),
    [final] ).

cnf(i_0_15646,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_9283]),
    [final] ).

cnf(i_0_15647,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_9284]),
    [final] ).

cnf(i_0_15648,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_8847]),
    [final] ).

cnf(i_0_15649,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_9285]),
    [final] ).

cnf(i_0_15650,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_8309]),
    [final] ).

cnf(i_0_15651,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_8309]),
    [final] ).

cnf(i_0_15652,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_9286]),
    [final] ).

cnf(i_0_15653,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_9287]),
    [final] ).

cnf(i_0_15654,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_8695]),
    [final] ).

cnf(i_0_15655,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_15656,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_9288]),
    [final] ).

cnf(i_0_15657,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_9289]),
    [final] ).

cnf(i_0_15658,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_9290]),
    [final] ).

cnf(i_0_15659,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_9291]),
    [final] ).

cnf(i_0_15660,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_9292]),
    [final] ).

cnf(i_0_15661,plain,
    ( hBOOL(hAPP(X1,esk92_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_6802]),
    [final] ).

cnf(i_0_15662,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_9293]),
    [final] ).

cnf(i_0_15663,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_9255]),
    [final] ).

cnf(i_0_15664,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_9294,c_0_6768]),
    [final] ).

cnf(i_0_15665,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_9295]),
    [final] ).

cnf(i_0_15666,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_9296,c_0_6768]),
    [final] ).

cnf(i_0_15667,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_9297]),
    [final] ).

cnf(i_0_15668,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_9298]),
    [final] ).

cnf(i_0_15669,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_8942]),
    [final] ).

cnf(i_0_15670,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_8941]),
    [final] ).

cnf(i_0_15671,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_8945]),
    [final] ).

cnf(i_0_15672,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_8944]),
    [final] ).

cnf(i_0_15673,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_9299]),
    [final] ).

cnf(i_0_15674,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_9300]),
    [final] ).

cnf(i_0_15675,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_9301]),
    [final] ).

cnf(i_0_15676,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_9302]),
    [final] ).

cnf(i_0_15677,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_9303]),
    [final] ).

cnf(i_0_15678,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_9304]),
    [final] ).

cnf(i_0_15679,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_9305]),
    [final] ).

cnf(i_0_15680,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_9306]),
    [final] ).

cnf(i_0_15681,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_9307]),
    [final] ).

cnf(i_0_15682,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_8775]),
    [final] ).

cnf(i_0_15683,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_9308]),
    [final] ).

cnf(i_0_15684,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_8775]),
    [final] ).

cnf(i_0_15685,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_9309]),
    [final] ).

cnf(i_0_15686,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_9310]),
    [final] ).

cnf(i_0_15687,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_9311]),
    [final] ).

cnf(i_0_15688,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_9312]),
    [final] ).

cnf(i_0_15689,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_8776]),
    [final] ).

cnf(i_0_15690,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_9313]),
    [final] ).

cnf(i_0_15691,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_8776]),
    [final] ).

cnf(i_0_15692,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_9314]),
    [final] ).

cnf(i_0_15693,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_9315]),
    [final] ).

cnf(i_0_15694,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_9316,c_0_6103]),
    [final] ).

cnf(i_0_15695,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_9099]),
    [final] ).

cnf(i_0_15696,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_9317]),
    [final] ).

cnf(i_0_15697,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_9104]),
    [final] ).

cnf(i_0_15698,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_9105]),
    [final] ).

cnf(i_0_15699,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_9318]),
    [final] ).

cnf(i_0_15700,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_9319]),
    [final] ).

cnf(i_0_15701,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_9320]),
    [final] ).

cnf(i_0_15702,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_9321]),
    [final] ).

cnf(i_0_15703,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_9322]),
    [final] ).

cnf(i_0_15704,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_8839]),
    [final] ).

cnf(i_0_15705,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_9323]),
    [final] ).

cnf(i_0_15706,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_9191]),
    [final] ).

cnf(i_0_15707,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_9324]),
    [final] ).

cnf(i_0_15708,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)),esk538_3(X2,X1,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_15709,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)),esk534_3(X2,X1,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_15710,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_9325]),
    [final] ).

cnf(i_0_15711,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_9326]),
    [final] ).

cnf(i_0_15712,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_9327]),
    [final] ).

cnf(i_0_15713,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_9026]),
    [final] ).

cnf(i_0_15714,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_9328]),
    [final] ).

cnf(i_0_15715,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_9329]),
    [final] ).

cnf(i_0_15716,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_9330]),
    [final] ).

cnf(i_0_15717,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_9330]),
    [final] ).

cnf(i_0_15718,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_9331]),
    [final] ).

cnf(i_0_15719,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_9331]),
    [final] ).

cnf(i_0_15720,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_9332]),
    [final] ).

cnf(i_0_15721,plain,
    ( X2 = esk521_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_7335]),
    [final] ).

cnf(i_0_15722,plain,
    ( X2 = esk508_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_7336]),
    [final] ).

cnf(i_0_15723,plain,
    ( hBOOL(hAPP(X1,esk319_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_7490]),
    [final] ).

cnf(i_0_15724,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_9333]),
    [final] ).

cnf(i_0_15725,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_9334]),
    [final] ).

cnf(i_0_15726,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_9335]),
    [final] ).

cnf(i_0_15727,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_9336,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_15728,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_9337,c_0_9338]),
    [final] ).

cnf(i_0_15729,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_9339]),
    [final] ).

cnf(i_0_15730,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_9340]),
    [final] ).

cnf(i_0_15731,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_8463]),
    [final] ).

cnf(i_0_15732,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_9341,c_0_6209]),
    [final] ).

cnf(i_0_15733,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_9342]),
    [final] ).

cnf(i_0_15734,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_9343]),
    [final] ).

cnf(i_0_15735,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk540_3(X2,X1,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,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_15736,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk536_3(X2,X1,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,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_15737,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_8718]),
    [final] ).

cnf(i_0_15738,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_9344]),
    [final] ).

cnf(i_0_15739,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_9143]),
    [final] ).

cnf(i_0_15740,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_9144]),
    [final] ).

cnf(i_0_15741,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ c_Partial__Function_Omk__less(X4,X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9239]),
    [final] ).

cnf(i_0_15742,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_9345]),
    [final] ).

cnf(i_0_15743,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_9139]),
    [final] ).

cnf(i_0_15744,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_9346]),
    [final] ).

cnf(i_0_15745,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_9346]),
    [final] ).

cnf(i_0_15746,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_9347]),
    [final] ).

cnf(i_0_15747,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_9348]),
    [final] ).

cnf(i_0_15748,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_9349]),
    [final] ).

cnf(i_0_15749,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_9350,c_0_6242]),
    [final] ).

cnf(i_0_15750,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_9351]),
    [final] ).

cnf(i_0_15751,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_9352]),
    [final] ).

cnf(i_0_15752,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_9353]),
    [final] ).

cnf(i_0_15753,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_9354]),
    [final] ).

cnf(i_0_15754,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_9355]),
    [final] ).

cnf(i_0_15755,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_9356]),
    [final] ).

cnf(i_0_15756,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_9357]),
    [final] ).

cnf(i_0_15757,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_9358]),
    [final] ).

cnf(i_0_15758,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_9359]),
    [final] ).

cnf(i_0_15759,plain,
    ( esk233_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_7358]),
    [final] ).

cnf(i_0_15760,plain,
    ( hBOOL(hAPP(c_List_Olistsp(X3,X1),X2))
    | ~ hBOOL(hAPP(X1,esk467_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8801]),
    [final] ).

cnf(i_0_15761,plain,
    ( hBOOL(hAPP(c_Predicate_OPowp(X3,X1),X2))
    | ~ hBOOL(hAPP(X1,esk295_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9000]),
    [final] ).

cnf(i_0_15762,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_7123]),
    [final] ).

cnf(i_0_15763,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_9360]),
    [final] ).

cnf(i_0_15764,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_9361]),
    [final] ).

cnf(i_0_15765,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_9362,c_0_6209]),c_0_6209]),
    [final] ).

cnf(i_0_15766,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_9363]),
    [final] ).

cnf(i_0_15767,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_9364]),
    [final] ).

cnf(i_0_15768,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_9191]),
    [final] ).

cnf(i_0_15769,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_9365]),
    [final] ).

cnf(i_0_15770,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_9366]),
    [final] ).

cnf(i_0_15771,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_9367]),
    [final] ).

cnf(i_0_15772,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_9368]),
    [final] ).

cnf(i_0_15773,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_9369]),
    [final] ).

cnf(i_0_15774,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_9370]),
    [final] ).

cnf(i_0_15775,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_9371]),
    [final] ).

cnf(i_0_15776,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_9372]),
    [final] ).

cnf(i_0_15777,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_9373]),
    [final] ).

cnf(i_0_15778,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_8855]),
    [final] ).

cnf(i_0_15779,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_9374]),
    [final] ).

cnf(i_0_15780,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | c_Partial__Function_Omk__less(X4,X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9239]),
    [final] ).

cnf(i_0_15781,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_9375]),
    [final] ).

cnf(i_0_15782,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2)),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ c_Orderings_Oorder__class_Omono(X1,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9376]),
    [final] ).

cnf(i_0_15783,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2)),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ c_Orderings_Oorder__class_Omono(X1,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9377]),
    [final] ).

cnf(i_0_15784,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_9378]),
    [final] ).

cnf(i_0_15785,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk113_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_8822]),
    [final] ).

cnf(i_0_15786,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk112_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_8823]),
    [final] ).

cnf(i_0_15787,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_8706]),
    [final] ).

cnf(i_0_15788,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_9379]),
    [final] ).

cnf(i_0_15789,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_9139]),
    [final] ).

cnf(i_0_15790,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_9380]),
    [final] ).

cnf(i_0_15791,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_9381]),
    [final] ).

cnf(i_0_15792,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_9382]),
    [final] ).

cnf(i_0_15793,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_9383]),
    [final] ).

cnf(i_0_15794,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_9384]),
    [final] ).

cnf(i_0_15795,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_9385]),
    [final] ).

cnf(i_0_15796,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk519_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_7979]),
    [final] ).

cnf(i_0_15797,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk250_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_7060]),
    [final] ).

cnf(i_0_15798,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_9386]),
    [final] ).

cnf(i_0_15799,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_9387]),
    [final] ).

cnf(i_0_15800,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_9388]),
    [final] ).

cnf(i_0_15801,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_9110]),
    [final] ).

cnf(i_0_15802,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_8870]),
    [final] ).

cnf(i_0_15803,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_8870]),
    [final] ).

cnf(i_0_15804,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_9389]),
    [final] ).

cnf(i_0_15805,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_9390]),
    [final] ).

cnf(i_0_15806,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_9391]),
    [final] ).

cnf(i_0_15807,plain,
    hAPP(c_Lazy__Sequence_Oyield(X1),c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3)) = hAPP(c_Option_Ooption_OSome(tc_prod(X1,tc_Lazy__Sequence_Olazy__sequence(X1))),hAPP(hAPP(c_Product__Type_OPair(X1,tc_Lazy__Sequence_Olazy__sequence(X1)),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9392]),
    [final] ).

cnf(i_0_15808,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_9393]),
    [final] ).

cnf(i_0_15809,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_9394]),
    [final] ).

cnf(i_0_15810,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_9395]),
    [final] ).

cnf(i_0_15811,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_9396]),
    [final] ).

cnf(i_0_15812,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_9397]),
    [final] ).

cnf(i_0_15813,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_9398]),
    [final] ).

cnf(i_0_15814,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_9399]),
    [final] ).

cnf(i_0_15815,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_9400]),
    [final] ).

cnf(i_0_15816,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_9401]),
    [final] ).

cnf(i_0_15817,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_9402]),
    [final] ).

cnf(i_0_15818,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_9297]),
    [final] ).

cnf(i_0_15819,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_9057]),
    [final] ).

cnf(i_0_15820,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_9058]),
    [final] ).

cnf(i_0_15821,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_9059]),
    [final] ).

cnf(i_0_15822,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_9060]),
    [final] ).

cnf(i_0_15823,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_9403]),
    [final] ).

cnf(i_0_15824,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_9404]),
    [final] ).

cnf(i_0_15825,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_9405]),
    [final] ).

cnf(i_0_15826,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_9406]),
    [final] ).

cnf(i_0_15827,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_9407]),
    [final] ).

cnf(i_0_15828,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_9408]),
    [final] ).

cnf(i_0_15829,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_9409]),
    [final] ).

cnf(i_0_15830,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_9410]),
    [final] ).

cnf(i_0_15831,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_9411]),
    [final] ).

cnf(i_0_15832,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_9412]),
    [final] ).

cnf(i_0_15833,plain,
    ( hAPP(hAPP(c_List_Onth(X1),X2),esk415_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_8370]),
    [final] ).

cnf(i_0_15834,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_8801]),
    [final] ).

cnf(i_0_15835,plain,
    ( esk235_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_7363]),
    [final] ).

cnf(i_0_15836,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_9413]),
    [final] ).

cnf(i_0_15837,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_9414]),
    [final] ).

cnf(i_0_15838,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_9414]),
    [final] ).

cnf(i_0_15839,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_9415]),
    [final] ).

cnf(i_0_15840,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_9415]),
    [final] ).

cnf(i_0_15841,plain,
    ( c_Enum_Oall__n__lists(X3,X1,X2)
    | ~ hBOOL(hAPP(X1,esk409_3(X2,X1,X3)))
    | ~ class_Enum_Oenum(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7962]),
    [final] ).

cnf(i_0_15842,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(X2,hAPP(c_Nat_OSuc,X3))))
    | ~ c_Orderings_Oorder__class_Omono(tc_Nat_Onat,X1,X2)
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7986]),
    [final] ).

cnf(i_0_15843,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_9416]),
    [final] ).

cnf(i_0_15844,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_9417]),
    [final] ).

cnf(i_0_15845,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_9418,c_0_6128]),
    [final] ).

cnf(i_0_15846,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_9301]),
    [final] ).

cnf(i_0_15847,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_9419,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_15848,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_9420]),
    [final] ).

cnf(i_0_15849,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_9421]),
    [final] ).

cnf(i_0_15850,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_9422,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_15851,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_9423,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_15852,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_9424]),
    [final] ).

cnf(i_0_15853,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_9425]),
    [final] ).

cnf(i_0_15854,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_9426]),
    [final] ).

cnf(i_0_15855,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_9427]),
    [final] ).

cnf(i_0_15856,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_9428]),
    [final] ).

cnf(i_0_15857,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_9429]),
    [final] ).

cnf(i_0_15858,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_9430]),
    [final] ).

cnf(i_0_15859,plain,
    ( c_List_OtakeWhile(X3,X1,X2) = X2
    | ~ hBOOL(hAPP(X1,esk462_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8864]),
    [final] ).

cnf(i_0_15860,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_9431]),
    [final] ).

cnf(i_0_15861,plain,
    ( c_List_Oall__interval__int(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk532_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8623]),
    [final] ).

cnf(i_0_15862,plain,
    ( c_List_Olist__all(X3,X1,X2)
    | ~ hBOOL(hAPP(X1,esk505_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8868]),
    [final] ).

cnf(i_0_15863,plain,
    ( c_List_Olist__all(X3,X1,X2)
    | ~ hBOOL(hAPP(X1,esk504_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8867]),
    [final] ).

cnf(i_0_15864,plain,
    ( c_List_Olist__all(X3,X1,X2)
    | ~ hBOOL(hAPP(X1,esk503_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8869]),
    [final] ).

cnf(i_0_15865,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_8913]),
    [final] ).

cnf(i_0_15866,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_9182]),
    [final] ).

cnf(i_0_15867,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_9183]),
    [final] ).

cnf(i_0_15868,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_9432]),
    [final] ).

cnf(i_0_15869,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_9433]),
    [final] ).

cnf(i_0_15870,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_8822]),
    [final] ).

cnf(i_0_15871,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_8823]),
    [final] ).

cnf(i_0_15872,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(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_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9147]),
    [final] ).

cnf(i_0_15873,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_9149]),
    [final] ).

cnf(i_0_15874,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_9150]),
    [final] ).

cnf(i_0_15875,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_9148]),
    [final] ).

cnf(i_0_15876,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_9152]),
    [final] ).

cnf(i_0_15877,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_9153]),
    [final] ).

cnf(i_0_15878,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_9151]),
    [final] ).

cnf(i_0_15879,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_8928]),
    [final] ).

cnf(i_0_15880,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_9154]),
    [final] ).

cnf(i_0_15881,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_9141]),
    [final] ).

cnf(i_0_15882,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_9156]),
    [final] ).

cnf(i_0_15883,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_9155]),
    [final] ).

cnf(i_0_15884,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_9434]),
    [final] ).

cnf(i_0_15885,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_9435]),
    [final] ).

cnf(i_0_15886,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_6649]),
    [final] ).

cnf(i_0_15887,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_9024]),
    [final] ).

cnf(i_0_15888,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_9436]),
    [final] ).

cnf(i_0_15889,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_9437,c_0_6103]),
    [final] ).

cnf(i_0_15890,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_9438]),
    [final] ).

cnf(i_0_15891,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_9439]),
    [final] ).

cnf(i_0_15892,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Wellfounded_Omax__extp(X1,X3,X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6649]),
    [final] ).

cnf(i_0_15893,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Wellfounded_Omax__extp(X1,X3,X4,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6649]),
    [final] ).

cnf(i_0_15894,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_9440]),
    [final] ).

cnf(i_0_15895,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_9002]),
    [final] ).

cnf(i_0_15896,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_8553]),
    [final] ).

cnf(i_0_15897,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_8553]),
    [final] ).

cnf(i_0_15898,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_8847]),
    [final] ).

cnf(i_0_15899,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_9441]),
    [final] ).

cnf(i_0_15900,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_9442,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_15901,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_8928]),
    [final] ).

cnf(i_0_15902,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_9443]),
    [final] ).

cnf(i_0_15903,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_9444]),
    [final] ).

cnf(i_0_15904,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_9445,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_15905,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_9446,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_15906,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_9447,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_15907,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_9448,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_15908,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_9449]),
    [final] ).

cnf(i_0_15909,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_9450]),
    [final] ).

cnf(i_0_15910,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_9451]),
    [final] ).

cnf(i_0_15911,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_9193]),
    [final] ).

cnf(i_0_15912,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_9194]),
    [final] ).

cnf(i_0_15913,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_9452]),
    [final] ).

cnf(i_0_15914,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_9453]),
    [final] ).

cnf(i_0_15915,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_9454]),
    [final] ).

cnf(i_0_15916,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_9455]),
    [final] ).

cnf(i_0_15917,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_9456]),
    [final] ).

cnf(i_0_15918,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_9457]),
    [final] ).

cnf(i_0_15919,plain,
    ( epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9458]),
    [final] ).

cnf(i_0_15920,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_9459]),
    [final] ).

cnf(i_0_15921,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_9460]),
    [final] ).

cnf(i_0_15922,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_9461]),
    [final] ).

cnf(i_0_15923,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_9462]),
    [final] ).

cnf(i_0_15924,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_9463]),
    [final] ).

cnf(i_0_15925,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_9464]),
    [final] ).

cnf(i_0_15926,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_9465]),
    [final] ).

cnf(i_0_15927,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_8488]),
    [final] ).

cnf(i_0_15928,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_9466]),
    [final] ).

cnf(i_0_15929,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_8891]),
    [final] ).

cnf(i_0_15930,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_5799]),
    [final] ).

cnf(i_0_15931,plain,
    ( c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk259_2(X2,X1)),c_Wellfounded_Oacc(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9467]),
    [final] ).

cnf(i_0_15932,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_9468]),
    [final] ).

cnf(i_0_15933,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_9469]),
    [final] ).

cnf(i_0_15934,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_9470]),
    [final] ).

cnf(i_0_15935,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_9095]),
    [final] ).

cnf(i_0_15936,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_9471]),
    [final] ).

cnf(i_0_15937,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_9472]),
    [final] ).

cnf(i_0_15938,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_9473,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_15939,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_9474,c_0_6102]),c_0_6103]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_15940,plain,
    ( X1 = hAPP(hAPP(c_Set_Oinsert(X2),esk115_3(X3,X1,X2)),esk116_3(X3,X1,X2))
    | hAPP(c_Finite__Set_Ocard(X2),X1) != hAPP(c_Nat_OSuc,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8048]),
    [final] ).

cnf(i_0_15941,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_9475]),
    [final] ).

cnf(i_0_15942,plain,
    ( hAPP(c_List_Ofilter(X3,X1),X2) = X2
    | ~ hBOOL(hAPP(X1,esk447_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8903]),
    [final] ).

cnf(i_0_15943,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_9476]),
    [final] ).

cnf(i_0_15944,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_9477]),
    [final] ).

cnf(i_0_15945,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_9267]),
    [final] ).

cnf(i_0_15946,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_9478]),
    [final] ).

cnf(i_0_15947,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_9479]),
    [final] ).

cnf(i_0_15948,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_9480]),
    [final] ).

cnf(i_0_15949,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_9481]),
    [final] ).

cnf(i_0_15950,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_9482]),
    [final] ).

cnf(i_0_15951,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_9483]),
    [final] ).

cnf(i_0_15952,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_9484,c_0_7157]),
    [final] ).

cnf(i_0_15953,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_9485]),
    [final] ).

cnf(i_0_15954,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_9486]),
    [final] ).

cnf(i_0_15955,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_9487]),
    [final] ).

cnf(i_0_15956,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_9488]),
    [final] ).

cnf(i_0_15957,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_9489]),
    [final] ).

cnf(i_0_15958,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_9490]),
    [final] ).

cnf(i_0_15959,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_9491]),
    [final] ).

cnf(i_0_15960,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_9492]),
    [final] ).

cnf(i_0_15961,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_9493]),
    [final] ).

cnf(i_0_15962,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_9494]),
    [final] ).

cnf(i_0_15963,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_9495]),
    [final] ).

cnf(i_0_15964,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk110_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_9496]),
    [final] ).

cnf(i_0_15965,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk113_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_8822]),
    [final] ).

cnf(i_0_15966,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk112_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_8823]),
    [final] ).

cnf(i_0_15967,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))),
    inference(rw,[status(thm)],[i_0_9497,c_0_6103]),
    [final] ).

cnf(i_0_15968,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_9498,c_0_8361]),
    [final] ).

cnf(i_0_15969,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_9361]),
    [final] ).

cnf(i_0_15970,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_9499]),
    [final] ).

cnf(i_0_15971,plain,
    ( X1 = X2
    | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),X5),X2),X6),X1) = hAPP(X5,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9500]),
    [final] ).

cnf(i_0_15972,plain,
    ( X1 = X2
    | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),X5),X2),X6),X1) = hAPP(X5,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9501]),
    [final] ).

cnf(i_0_15973,plain,
    ( X1 = X2
    | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),X5),X2),X6),X1) = hAPP(X5,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9502]),
    [final] ).

cnf(i_0_15974,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_9503,c_0_6209]),
    [final] ).

cnf(i_0_15975,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_9504]),
    [final] ).

cnf(i_0_15976,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_9505]),
    [final] ).

cnf(i_0_15977,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_9506]),
    [final] ).

cnf(i_0_15978,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_9507]),
    [final] ).

cnf(i_0_15979,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_9508]),
    [final] ).

cnf(i_0_15980,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_9509]),
    [final] ).

cnf(i_0_15981,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_9510]),
    [final] ).

cnf(i_0_15982,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_9511]),
    [final] ).

cnf(i_0_15983,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_9512]),
    [final] ).

cnf(i_0_15984,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_9513]),
    [final] ).

cnf(i_0_15985,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_9514]),
    [final] ).

cnf(i_0_15986,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_9515]),
    [final] ).

cnf(i_0_15987,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_9516]),
    [final] ).

cnf(i_0_15988,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_9517]),
    [final] ).

cnf(i_0_15989,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_9518]),
    [final] ).

cnf(i_0_15990,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_9519]),
    [final] ).

cnf(i_0_15991,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_9520]),
    [final] ).

cnf(i_0_15992,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_9521]),
    [final] ).

cnf(i_0_15993,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_9522]),
    [final] ).

cnf(i_0_15994,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_9523]),
    [final] ).

cnf(i_0_15995,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_9524]),
    [final] ).

cnf(i_0_15996,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_9525]),
    [final] ).

cnf(i_0_15997,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_9526]),
    [final] ).

cnf(i_0_15998,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_9527]),
    [final] ).

cnf(i_0_15999,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_9528]),
    [final] ).

cnf(i_0_16000,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_9529]),
    [final] ).

cnf(i_0_16001,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_9530]),
    [final] ).

cnf(i_0_16002,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_9531]),
    [final] ).

cnf(i_0_16003,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_9333]),
    [final] ).

cnf(i_0_16004,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_5358]),
    [final] ).

cnf(i_0_16005,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_9532]),
    [final] ).

cnf(i_0_16006,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_9533]),
    [final] ).

cnf(i_0_16007,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_9534]),
    [final] ).

cnf(i_0_16008,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X3)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9535]),
    [final] ).

cnf(i_0_16009,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_9173]),
    [final] ).

cnf(i_0_16010,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_9536]),
    [final] ).

cnf(i_0_16011,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_9537]),
    [final] ).

cnf(i_0_16012,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_9538]),
    [final] ).

cnf(i_0_16013,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_9539]),
    [final] ).

cnf(i_0_16014,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_9540]),
    [final] ).

cnf(i_0_16015,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_9541]),
    [final] ).

cnf(i_0_16016,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_9542]),
    [final] ).

cnf(i_0_16017,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_9543]),
    [final] ).

cnf(i_0_16018,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_9544]),
    [final] ).

cnf(i_0_16019,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_9545]),
    [final] ).

cnf(i_0_16020,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_9546]),
    [final] ).

cnf(i_0_16021,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_9547]),
    [final] ).

cnf(i_0_16022,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_9548]),
    [final] ).

cnf(i_0_16023,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_8251]),
    [final] ).

cnf(i_0_16024,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_9549]),
    [final] ).

cnf(i_0_16025,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_9345]),
    [final] ).

cnf(i_0_16026,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_9550]),
    [final] ).

cnf(i_0_16027,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_9551]),
    [final] ).

cnf(i_0_16028,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_9552]),
    [final] ).

cnf(i_0_16029,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk445_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_9318]),
    [final] ).

cnf(i_0_16030,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),X5),X2),X6),X1) = X6
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9500]),
    [final] ).

cnf(i_0_16031,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),X5),X2),X6),X1) = X6
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9502]),
    [final] ).

cnf(i_0_16032,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X1)) ),
    inference(rw,[status(thm)],[i_0_9553,c_0_6103]),
    [final] ).

cnf(i_0_16033,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_9554,c_0_6103]),
    [final] ).

cnf(i_0_16034,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_9555,c_0_6103]),
    [final] ).

cnf(i_0_16035,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_9556,c_0_6103]),
    [final] ).

cnf(i_0_16036,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_9557,c_0_6103]),
    [final] ).

cnf(i_0_16037,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_9558]),
    [final] ).

cnf(i_0_16038,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_9559]),
    [final] ).

cnf(i_0_16039,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_9560]),
    [final] ).

cnf(i_0_16040,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_9561]),
    [final] ).

cnf(i_0_16041,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_8864]),
    [final] ).

cnf(i_0_16042,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_8893]),
    [final] ).

cnf(i_0_16043,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_9562]),
    [final] ).

cnf(i_0_16044,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_9563]),
    [final] ).

cnf(i_0_16045,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_8868]),
    [final] ).

cnf(i_0_16046,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_8867]),
    [final] ).

cnf(i_0_16047,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_8869]),
    [final] ).

cnf(i_0_16048,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_9564,c_0_6128]),
    [final] ).

cnf(i_0_16049,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_9565,c_0_6128]),
    [final] ).

cnf(i_0_16050,plain,
    hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5),X4) = X5,
    inference(split_conjunct,[status(thm)],[i_0_9566]),
    [final] ).

cnf(i_0_16051,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_9567]),
    [final] ).

cnf(i_0_16052,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_9568]),
    [final] ).

cnf(i_0_16053,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_9569]),
    [final] ).

cnf(i_0_16054,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_9570]),
    [final] ).

cnf(i_0_16055,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_9571]),
    [final] ).

cnf(i_0_16056,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_9572]),
    [final] ).

cnf(i_0_16057,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_9573]),
    [final] ).

cnf(i_0_16058,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_9574]),
    [final] ).

cnf(i_0_16059,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_9401]),
    [final] ).

cnf(i_0_16060,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_9402]),
    [final] ).

cnf(i_0_16061,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_9575]),
    [final] ).

cnf(i_0_16062,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_9576]),
    [final] ).

cnf(i_0_16063,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_9577]),
    [final] ).

cnf(i_0_16064,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_9578]),
    [final] ).

cnf(i_0_16065,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_9579]),
    [final] ).

cnf(i_0_16066,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_9580]),
    [final] ).

cnf(i_0_16067,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_9581]),
    [final] ).

cnf(i_0_16068,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_5357]),
    [final] ).

cnf(i_0_16069,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_9582]),
    [final] ).

cnf(i_0_16070,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_9583]),
    [final] ).

cnf(i_0_16071,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_9584]),
    [final] ).

cnf(i_0_16072,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_9585]),
    [final] ).

cnf(i_0_16073,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_9586,c_0_6136]),
    [final] ).

cnf(i_0_16074,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_9587]),
    [final] ).

cnf(i_0_16075,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_9472]),
    [final] ).

cnf(i_0_16076,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_9588]),
    [final] ).

cnf(i_0_16077,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_9589]),
    [final] ).

cnf(i_0_16078,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_9590]),
    [final] ).

cnf(i_0_16079,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_9438]),
    [final] ).

cnf(i_0_16080,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_9591,c_0_8412]),
    [final] ).

cnf(i_0_16081,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_9592,c_0_8412]),
    [final] ).

cnf(i_0_16082,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_9378]),
    [final] ).

cnf(i_0_16083,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_9593]),
    [final] ).

cnf(i_0_16084,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_9073]),
    [final] ).

cnf(i_0_16085,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_9072]),
    [final] ).

cnf(i_0_16086,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_9594]),
    [final] ).

cnf(i_0_16087,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_16088,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_9595]),
    [final] ).

cnf(i_0_16089,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_9596,c_0_6128]),
    [final] ).

cnf(i_0_16090,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_9597]),
    [final] ).

cnf(i_0_16091,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_9598]),
    [final] ).

cnf(i_0_16092,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_8818]),
    [final] ).

cnf(i_0_16093,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_8819]),
    [final] ).

cnf(i_0_16094,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_8798]),
    [final] ).

cnf(i_0_16095,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_9332]),
    [final] ).

cnf(i_0_16096,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_9599]),
    [final] ).

cnf(i_0_16097,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_9600]),
    [final] ).

cnf(i_0_16098,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_9601]),
    [final] ).

cnf(i_0_16099,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_6162]),
    [final] ).

cnf(i_0_16100,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_9069]),
    [final] ).

cnf(i_0_16101,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_9602]),
    [final] ).

cnf(i_0_16102,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_9603]),
    [final] ).

cnf(i_0_16103,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_9604]),
    [final] ).

cnf(i_0_16104,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_9605]),
    [final] ).

cnf(i_0_16105,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_9606]),
    [final] ).

cnf(i_0_16106,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_9607]),
    [final] ).

cnf(i_0_16107,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_9608]),
    [final] ).

cnf(i_0_16108,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_9609]),
    [final] ).

cnf(i_0_16109,plain,
    ( epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9610]),
    [final] ).

cnf(i_0_16110,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_9611]),
    [final] ).

cnf(i_0_16111,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk151_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_9612]),
    [final] ).

cnf(i_0_16112,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_9613]),
    [final] ).

cnf(i_0_16113,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_9614]),
    [final] ).

cnf(i_0_16114,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_9042]),
    [final] ).

cnf(i_0_16115,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_9042]),
    [final] ).

cnf(i_0_16116,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_9378]),
    [final] ).

cnf(i_0_16117,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_9615]),
    [final] ).

cnf(i_0_16118,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_9616]),
    [final] ).

cnf(i_0_16119,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_8903]),
    [final] ).

cnf(i_0_16120,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_9617]),
    [final] ).

cnf(i_0_16121,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_9428]),
    [final] ).

cnf(i_0_16122,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_9427]),
    [final] ).

cnf(i_0_16123,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_9429]),
    [final] ).

cnf(i_0_16124,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_9618]),
    [final] ).

cnf(i_0_16125,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_9476]),
    [final] ).

cnf(i_0_16126,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_9477]),
    [final] ).

cnf(i_0_16127,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_9619]),
    [final] ).

cnf(i_0_16128,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_9380]),
    [final] ).

cnf(i_0_16129,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_9379]),
    [final] ).

cnf(i_0_16130,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_9382]),
    [final] ).

cnf(i_0_16131,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_9620]),
    [final] ).

cnf(i_0_16132,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_9384]),
    [final] ).

cnf(i_0_16133,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_9383]),
    [final] ).

cnf(i_0_16134,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_9385]),
    [final] ).

cnf(i_0_16135,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_9621]),
    [final] ).

cnf(i_0_16136,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_9622]),
    [final] ).

cnf(i_0_16137,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_9623]),
    [final] ).

cnf(i_0_16138,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_9479]),
    [final] ).

cnf(i_0_16139,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_9624]),
    [final] ).

cnf(i_0_16140,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_9625]),
    [final] ).

cnf(i_0_16141,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_9626]),
    [final] ).

cnf(i_0_16142,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_9627]),
    [final] ).

cnf(i_0_16143,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_9628]),
    [final] ).

cnf(i_0_16144,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_9629]),
    [final] ).

cnf(i_0_16145,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_9524]),
    [final] ).

cnf(i_0_16146,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_9630]),
    [final] ).

cnf(i_0_16147,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_9631]),
    [final] ).

cnf(i_0_16148,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_9632]),
    [final] ).

cnf(i_0_16149,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_9633]),
    [final] ).

cnf(i_0_16150,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_9634]),
    [final] ).

cnf(i_0_16151,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_9635]),
    [final] ).

cnf(i_0_16152,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,esk155_2(X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9636]),
    [final] ).

cnf(i_0_16153,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_9538]),
    [final] ).

cnf(i_0_16154,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_9539]),
    [final] ).

cnf(i_0_16155,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_9637,c_0_6209]),
    [final] ).

cnf(i_0_16156,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_9638]),
    [final] ).

cnf(i_0_16157,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_9639]),
    [final] ).

cnf(i_0_16158,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_9640]),
    [final] ).

cnf(i_0_16159,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_9641]),
    [final] ).

cnf(i_0_16160,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X4),c_Map_Oran(X5,X3,X1)))
    | hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9642]),
    [final] ).

cnf(i_0_16161,plain,
    ( hBOOL(hAPP(hAPP(c_member(X5),X2),c_Map_Odom(X5,X3,X1)))
    | hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9643]),
    [final] ).

cnf(i_0_16162,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_7403]),
    [final] ).

cnf(i_0_16163,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_9644]),
    [final] ).

cnf(i_0_16164,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(X4,X5,X1),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9243]),
    [final] ).

cnf(i_0_16165,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(X4,X5,X1),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9645]),
    [final] ).

cnf(i_0_16166,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(X4,X5,X1),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9094]),
    [final] ).

cnf(i_0_16167,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(X4,X5,X1),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9646]),
    [final] ).

cnf(i_0_16168,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_8268]),
    [final] ).

cnf(i_0_16169,plain,
    ( c_Enum_Oenum__class_Oenum(tc_Option_Ooption(X1)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(X1)),c_Option_Ooption_ONone(X1)),hAPP(hAPP(c_List_Omap(X1,tc_Option_Ooption(X1)),c_Option_Ooption_OSome(X1)),c_Enum_Oenum__class_Oenum(X1)))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9647]),
    [final] ).

cnf(i_0_16170,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_9648]),
    [final] ).

cnf(i_0_16171,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_9649]),
    [final] ).

cnf(i_0_16172,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_9650]),
    [final] ).

cnf(i_0_16173,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_9651]),
    [final] ).

cnf(i_0_16174,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_9652,c_0_8361]),
    [final] ).

cnf(i_0_16175,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_9653]),
    [final] ).

cnf(i_0_16176,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_9208]),
    [final] ).

cnf(i_0_16177,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_9160]),
    [final] ).

cnf(i_0_16178,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_9654]),
    [final] ).

cnf(i_0_16179,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_9655]),
    [final] ).

cnf(i_0_16180,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_9656,c_0_6209]),
    [final] ).

cnf(i_0_16181,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_9657]),
    [final] ).

cnf(i_0_16182,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_9658]),
    [final] ).

cnf(i_0_16183,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_8085]),
    [final] ).

cnf(i_0_16184,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_9659]),
    [final] ).

cnf(i_0_16185,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_9660]),
    [final] ).

cnf(i_0_16186,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk414_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_8405]),
    [final] ).

cnf(i_0_16187,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk413_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_8405]),
    [final] ).

cnf(i_0_16188,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_9661]),
    [final] ).

cnf(i_0_16189,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_9662]),
    [final] ).

cnf(i_0_16190,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_9663,c_0_6128]),
    [final] ).

cnf(i_0_16191,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_9664]),
    [final] ).

cnf(i_0_16192,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_9665]),
    [final] ).

cnf(i_0_16193,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_8653]),
    [final] ).

cnf(i_0_16194,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_9666]),
    [final] ).

cnf(i_0_16195,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_9667]),
    [final] ).

cnf(i_0_16196,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_9117]),
    [final] ).

cnf(i_0_16197,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_9668]),
    [final] ).

cnf(i_0_16198,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_9669]),
    [final] ).

cnf(i_0_16199,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_9670]),
    [final] ).

cnf(i_0_16200,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_9378]),
    [final] ).

cnf(i_0_16201,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_9671]),
    [final] ).

cnf(i_0_16202,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_9672]),
    [final] ).

cnf(i_0_16203,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_9673]),
    [final] ).

cnf(i_0_16204,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_9674]),
    [final] ).

cnf(i_0_16205,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_9675]),
    [final] ).

cnf(i_0_16206,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_9676]),
    [final] ).

cnf(i_0_16207,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_8278]),
    [final] ).

cnf(i_0_16208,plain,
    ( hAPP(X1,esk233_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_7358]),
    [final] ).

cnf(i_0_16209,plain,
    c_Map_Omap__add(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)),X3) = X3,
    inference(split_conjunct,[status(thm)],[i_0_9677]),
    [final] ).

cnf(i_0_16210,plain,
    c_Map_Omap__add(X1,X2,X3,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))) = X3,
    inference(split_conjunct,[status(thm)],[i_0_9678]),
    [final] ).

cnf(i_0_16211,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),esk117_2(X2,X3)))
    | ~ hBOOL(hAPP(X3,X1))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9250]),
    [final] ).

cnf(i_0_16212,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_9679]),
    [final] ).

cnf(i_0_16213,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_9680]),
    [final] ).

cnf(i_0_16214,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_9681]),
    [final] ).

cnf(i_0_16215,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_9682]),
    [final] ).

cnf(i_0_16216,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_9683]),
    [final] ).

cnf(i_0_16217,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_9684]),
    [final] ).

cnf(i_0_16218,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_9685]),
    [final] ).

cnf(i_0_16219,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_9686]),
    [final] ).

cnf(i_0_16220,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_9687]),
    [final] ).

cnf(i_0_16221,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_9688]),
    [final] ).

cnf(i_0_16222,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_9689]),
    [final] ).

cnf(i_0_16223,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_9690]),
    [final] ).

cnf(i_0_16224,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_9691]),
    [final] ).

cnf(i_0_16225,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_9692]),
    [final] ).

cnf(i_0_16226,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_9693]),
    [final] ).

cnf(i_0_16227,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_9694]),
    [final] ).

cnf(i_0_16228,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_9456]),
    [final] ).

cnf(i_0_16229,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_9457]),
    [final] ).

cnf(i_0_16230,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_9695]),
    [final] ).

cnf(i_0_16231,plain,
    ( hBOOL(hAPP(X1,esk506_3(X1,X2,X3)))
    | c_List_Olist__ex1(X2,X1,c_Enum_Oenum__class_Oenum(X2))
    | ~ hBOOL(hAPP(X1,X3))
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9696]),
    [final] ).

cnf(i_0_16232,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_9697]),
    [final] ).

cnf(i_0_16233,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_9698]),
    [final] ).

cnf(i_0_16234,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_9699]),
    [final] ).

cnf(i_0_16235,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_9577]),
    [final] ).

cnf(i_0_16236,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_9575]),
    [final] ).

cnf(i_0_16237,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_9578]),
    [final] ).

cnf(i_0_16238,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_9576]),
    [final] ).

cnf(i_0_16239,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_9388]),
    [final] ).

cnf(i_0_16240,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_9700]),
    [final] ).

cnf(i_0_16241,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_9701]),
    [final] ).

cnf(i_0_16242,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_9664]),
    [final] ).

cnf(i_0_16243,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_9702]),
    [final] ).

cnf(i_0_16244,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_9703,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_16245,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_9704,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_16246,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_9014]),
    [final] ).

cnf(i_0_16247,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_9705]),
    [final] ).

cnf(i_0_16248,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_9706]),
    [final] ).

cnf(i_0_16249,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_9707]),
    [final] ).

cnf(i_0_16250,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_9708,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_16251,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_9709,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_16252,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_9710]),
    [final] ).

cnf(i_0_16253,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_9711]),
    [final] ).

cnf(i_0_16254,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_9712]),
    [final] ).

cnf(i_0_16255,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_9713]),
    [final] ).

cnf(i_0_16256,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_9714,c_0_8412]),
    [final] ).

cnf(i_0_16257,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_9715,c_0_8412]),
    [final] ).

cnf(i_0_16258,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_9716]),
    [final] ).

cnf(i_0_16259,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,esk232_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_8818]),
    [final] ).

cnf(i_0_16260,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,esk119_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_8819]),
    [final] ).

cnf(i_0_16261,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_9717]),
    [final] ).

cnf(i_0_16262,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_9718]),
    [final] ).

cnf(i_0_16263,plain,
    ( c_Fun_Oinj__on(X2,X1,X3,X4)
    | ~ class_Orderings_Oorder(X1)
    | ~ class_Orderings_Olinorder(X2)
    | ~ c_Orderings_Oorder__class_Ostrict__mono(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9719]),
    [final] ).

cnf(i_0_16264,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_9720]),
    [final] ).

cnf(i_0_16265,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk79_2(X1,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9721]),
    [final] ).

cnf(i_0_16266,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk77_2(X1,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9722]),
    [final] ).

cnf(i_0_16267,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_9723]),
    [final] ).

cnf(i_0_16268,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_9724]),
    [final] ).

cnf(i_0_16269,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_9552]),
    [final] ).

cnf(i_0_16270,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_9725]),
    [final] ).

cnf(i_0_16271,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X3,X4)),hAPP(X3,X5)) = hAPP(X3,hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),X4),X5))
    | ~ class_Orderings_Olinorder(X1)
    | ~ class_Orderings_Olinorder(X2)
    | ~ c_Orderings_Oorder__class_Omono(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9726]),
    [final] ).

cnf(i_0_16272,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X3,X4)),hAPP(X3,X5)) = hAPP(X3,hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),X4),X5))
    | ~ class_Orderings_Olinorder(X1)
    | ~ class_Orderings_Olinorder(X2)
    | ~ c_Orderings_Oorder__class_Omono(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9727]),
    [final] ).

cnf(i_0_16273,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_9629]),
    [final] ).

cnf(i_0_16274,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_9728]),
    [final] ).

cnf(i_0_16275,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_9729]),
    [final] ).

cnf(i_0_16276,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_9730]),
    [final] ).

cnf(i_0_16277,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_9731]),
    [final] ).

cnf(i_0_16278,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_9732]),
    [final] ).

cnf(i_0_16279,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_9733]),
    [final] ).

cnf(i_0_16280,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_9734]),
    [final] ).

cnf(i_0_16281,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_9735]),
    [final] ).

cnf(i_0_16282,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_9736]),
    [final] ).

cnf(i_0_16283,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_9737]),
    [final] ).

cnf(i_0_16284,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_9738]),
    [final] ).

cnf(i_0_16285,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_9739]),
    [final] ).

cnf(i_0_16286,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_9740]),
    [final] ).

cnf(i_0_16287,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk461_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_7725]),
    [final] ).

cnf(i_0_16288,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk458_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_7726]),
    [final] ).

cnf(i_0_16289,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_9741]),
    [final] ).

cnf(i_0_16290,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_9742]),
    [final] ).

cnf(i_0_16291,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_9743]),
    [final] ).

cnf(i_0_16292,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_9744]),
    [final] ).

cnf(i_0_16293,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_9745]),
    [final] ).

cnf(i_0_16294,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_9746]),
    [final] ).

cnf(i_0_16295,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_9747]),
    [final] ).

cnf(i_0_16296,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_9748]),
    [final] ).

cnf(i_0_16297,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_9749]),
    [final] ).

cnf(i_0_16298,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_9750]),
    [final] ).

cnf(i_0_16299,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_9751]),
    [final] ).

cnf(i_0_16300,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_9752]),
    [final] ).

cnf(i_0_16301,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_9753]),
    [final] ).

cnf(i_0_16302,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_9600]),
    [final] ).

cnf(i_0_16303,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_9754]),
    [final] ).

cnf(i_0_16304,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_9755]),
    [final] ).

cnf(i_0_16305,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_9756]),
    [final] ).

cnf(i_0_16306,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_9757]),
    [final] ).

cnf(i_0_16307,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_9039]),
    [final] ).

cnf(i_0_16308,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_9040]),
    [final] ).

cnf(i_0_16309,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_9758]),
    [final] ).

cnf(i_0_16310,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_9759]),
    [final] ).

cnf(i_0_16311,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_9760]),
    [final] ).

cnf(i_0_16312,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_9761]),
    [final] ).

cnf(i_0_16313,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_9762]),
    [final] ).

cnf(i_0_16314,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_9763]),
    [final] ).

cnf(i_0_16315,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_9764]),
    [final] ).

cnf(i_0_16316,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_9640]),
    [final] ).

cnf(i_0_16317,plain,
    ( hBOOL(hAPP(X1,esk464_3(X2,X1,X3)))
    | c_List_OtakeWhile(X3,X1,X2) = hAPP(c_List_Ofilter(X3,X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5476]),
    [final] ).

cnf(i_0_16318,plain,
    ( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
    | hBOOL(hAPP(hAPP(c_member(X4),X2),c_Map_Odom(X4,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9195]),
    [final] ).

cnf(i_0_16319,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X3)),X1),X2),hAPP(c_Option_Ooption_OSome(X3),X4)) = X1
    | hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9765]),
    [final] ).

cnf(i_0_16320,plain,
    ( hBOOL(hAPP(X1,esk408_3(X2,X1,X3)))
    | ~ c_Enum_Oex__n__lists(X3,X1,X2)
    | ~ class_Enum_Oenum(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7968]),
    [final] ).

cnf(i_0_16321,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_9766]),
    [final] ).

cnf(i_0_16322,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_9767]),
    [final] ).

cnf(i_0_16323,plain,
    ( hBOOL(hAPP(X2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk152_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_9768]),
    [final] ).

cnf(i_0_16324,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_9603]),
    [final] ).

cnf(i_0_16325,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_9604]),
    [final] ).

cnf(i_0_16326,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_9769]),
    [final] ).

cnf(i_0_16327,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_9770]),
    [final] ).

cnf(i_0_16328,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_9771]),
    [final] ).

cnf(i_0_16329,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_9772]),
    [final] ).

cnf(i_0_16330,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_9773]),
    [final] ).

cnf(i_0_16331,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_9774]),
    [final] ).

cnf(i_0_16332,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_9775,c_0_6209]),
    [final] ).

cnf(i_0_16333,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_6611]),
    [final] ).

cnf(i_0_16334,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_9776]),
    [final] ).

cnf(i_0_16335,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_9777]),
    [final] ).

cnf(i_0_16336,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_9778]),
    [final] ).

cnf(i_0_16337,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_9779]),
    [final] ).

cnf(i_0_16338,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_9780]),
    [final] ).

cnf(i_0_16339,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_9781]),
    [final] ).

cnf(i_0_16340,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_9782]),
    [final] ).

cnf(i_0_16341,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_9783]),
    [final] ).

cnf(i_0_16342,plain,
    ( hBOOL(hAPP(X2,esk147_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_9784]),
    [final] ).

cnf(i_0_16343,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_9778]),
    [final] ).

cnf(i_0_16344,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_9785]),
    [final] ).

cnf(i_0_16345,plain,
    ( hBOOL(hAPP(X1,esk521_3(X2,X1,X3)))
    | ~ c_List_Olist__ex1(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7335]),
    [final] ).

cnf(i_0_16346,plain,
    ( hBOOL(hAPP(X1,esk508_3(X2,X1,X3)))
    | ~ c_List_Olist__ex1(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7336]),
    [final] ).

cnf(i_0_16347,plain,
    ( hBOOL(hAPP(X1,esk494_3(X2,X1,X3)))
    | ~ c_List_Olist__ex(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8798]),
    [final] ).

cnf(i_0_16348,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_9786,c_0_6103]),
    [final] ).

cnf(i_0_16349,plain,
    ( hAPP(X1,esk235_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_7363]),
    [final] ).

cnf(i_0_16350,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_9787]),
    [final] ).

cnf(i_0_16351,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_9788]),
    [final] ).

cnf(i_0_16352,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_9789]),
    [final] ).

cnf(i_0_16353,hypothesis,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga)),
    inference(split_conjunct,[status(thm)],[conj_2]),
    [final] ).

cnf(i_0_16354,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_9790]),
    [final] ).

cnf(i_0_16355,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_9791]),
    [final] ).

cnf(i_0_16356,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_9792]),
    [final] ).

cnf(i_0_16357,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_9793]),
    [final] ).

cnf(i_0_16358,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_9794]),
    [final] ).

cnf(i_0_16359,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_9795]),
    [final] ).

cnf(i_0_16360,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_9796,c_0_6209]),
    [final] ).

cnf(i_0_16361,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_9000]),
    [final] ).

cnf(i_0_16362,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_9797]),
    [final] ).

cnf(i_0_16363,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_9798]),
    [final] ).

cnf(i_0_16364,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_9799]),
    [final] ).

cnf(i_0_16365,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_9800]),
    [final] ).

cnf(i_0_16366,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_9660]),
    [final] ).

cnf(i_0_16367,plain,
    ( hAPP(X3,X4) = X5
    | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_9801]),
    [final] ).

cnf(i_0_16368,plain,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)))
    | ~ epred2_3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9458]),
    [final] ).

cnf(i_0_16369,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_9802]),
    [final] ).

cnf(i_0_16370,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_9803]),
    [final] ).

cnf(i_0_16371,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_9804]),
    [final] ).

cnf(i_0_16372,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_9805]),
    [final] ).

cnf(i_0_16373,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_9806]),
    [final] ).

cnf(i_0_16374,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_9807]),
    [final] ).

cnf(i_0_16375,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_9808]),
    [final] ).

cnf(i_0_16376,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_9809]),
    [final] ).

cnf(i_0_16377,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_9810]),
    [final] ).

cnf(i_0_16378,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_9811]),
    [final] ).

cnf(i_0_16379,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_9062]),
    [final] ).

cnf(i_0_16380,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_9729]),
    [final] ).

cnf(i_0_16381,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_9812]),
    [final] ).

cnf(i_0_16382,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,X1,X3)
    | ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_16383,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_9813]),
    [final] ).

cnf(i_0_16384,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_9814]),
    [final] ).

cnf(i_0_16385,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_9815]),
    [final] ).

cnf(i_0_16386,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_9816]),
    [final] ).

cnf(i_0_16387,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_9817]),
    [final] ).

cnf(i_0_16388,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_9818]),
    [final] ).

cnf(i_0_16389,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_9819]),
    [final] ).

cnf(i_0_16390,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_9820]),
    [final] ).

cnf(i_0_16391,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_9821]),
    [final] ).

cnf(i_0_16392,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_9822]),
    [final] ).

cnf(i_0_16393,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_9823,c_0_6768]),
    [final] ).

cnf(i_0_16394,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_9824]),
    [final] ).

cnf(i_0_16395,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_9825]),
    [final] ).

cnf(i_0_16396,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_9826]),
    [final] ).

cnf(i_0_16397,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_9827]),
    [final] ).

cnf(i_0_16398,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_9828]),
    [final] ).

cnf(i_0_16399,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_9829,c_0_7157]),
    [final] ).

cnf(i_0_16400,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_9830,c_0_8361]),
    [final] ).

cnf(i_0_16401,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_9831,c_0_6209]),
    [final] ).

cnf(i_0_16402,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_9832]),
    [final] ).

cnf(i_0_16403,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_9833]),
    [final] ).

cnf(i_0_16404,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_9834]),
    [final] ).

cnf(i_0_16405,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_9835]),
    [final] ).

cnf(i_0_16406,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_9836]),
    [final] ).

cnf(i_0_16407,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_9837]),
    [final] ).

cnf(i_0_16408,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_9838]),
    [final] ).

cnf(i_0_16409,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_9839]),
    [final] ).

cnf(i_0_16410,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_9840]),
    [final] ).

cnf(i_0_16411,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_9841]),
    [final] ).

cnf(i_0_16412,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_9842]),
    [final] ).

cnf(i_0_16413,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_9843]),
    [final] ).

cnf(i_0_16414,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_9844]),
    [final] ).

cnf(i_0_16415,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_9845]),
    [final] ).

cnf(i_0_16416,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_9846]),
    [final] ).

cnf(i_0_16417,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_9847]),
    [final] ).

cnf(i_0_16418,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_9848]),
    [final] ).

cnf(i_0_16419,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_9026]),
    [final] ).

cnf(i_0_16420,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_9329]),
    [final] ).

cnf(i_0_16421,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_9849]),
    [final] ).

cnf(i_0_16422,plain,
    ( hBOOL(hAPP(X1,esk8_3(X2,X1,X3)))
    | c_Orderings_Oord__class_OLeast(X3,X1) = X2
    | ~ hBOOL(hAPP(X1,X2))
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9084]),
    [final] ).

cnf(i_0_16423,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_9850]),
    [final] ).

cnf(i_0_16424,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_9851]),
    [final] ).

cnf(i_0_16425,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_9441]),
    [final] ).

cnf(i_0_16426,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_9852]),
    [final] ).

cnf(i_0_16427,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_9853]),
    [final] ).

cnf(i_0_16428,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_9854]),
    [final] ).

cnf(i_0_16429,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_9855]),
    [final] ).

cnf(i_0_16430,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_9856]),
    [final] ).

cnf(i_0_16431,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_9857]),
    [final] ).

cnf(i_0_16432,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,esk294_2(X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8724]),
    [final] ).

cnf(i_0_16433,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_9858]),
    [final] ).

cnf(i_0_16434,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_9859]),
    [final] ).

cnf(i_0_16435,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),esk78_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_9721]),
    [final] ).

cnf(i_0_16436,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),esk76_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_9722]),
    [final] ).

cnf(i_0_16437,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_5265]),
    [final] ).

cnf(i_0_16438,plain,
    ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(X1,esk144_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_9860]),
    [final] ).

cnf(i_0_16439,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))),
    inference(split_conjunct,[status(thm)],[i_0_9861]),
    [final] ).

cnf(i_0_16440,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_9496]),
    [final] ).

cnf(i_0_16441,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_16442,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,X1,X3)
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_16443,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_9700]),
    [final] ).

cnf(i_0_16444,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_9862]),
    [final] ).

cnf(i_0_16445,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_9863]),
    [final] ).

cnf(i_0_16446,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_9095]),
    [final] ).

cnf(i_0_16447,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_9864,c_0_6104]),
    [final] ).

cnf(i_0_16448,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_9865,c_0_6242]),
    [final] ).

cnf(i_0_16449,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_9866]),
    [final] ).

cnf(i_0_16450,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_8917]),
    [final] ).

cnf(i_0_16451,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk201_2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8922]),
    [final] ).

cnf(i_0_16452,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk199_2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8758]),
    [final] ).

cnf(i_0_16453,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_9867]),
    [final] ).

cnf(i_0_16454,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_9868]),
    [final] ).

cnf(i_0_16455,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_9869]),
    [final] ).

cnf(i_0_16456,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,esk156_2(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9849]),
    [final] ).

cnf(i_0_16457,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_9439]),
    [final] ).

cnf(i_0_16458,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_9870]),
    [final] ).

cnf(i_0_16459,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_9871]),
    [final] ).

cnf(i_0_16460,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_9872,c_0_6242]),
    [final] ).

cnf(i_0_16461,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_9873]),
    [final] ).

cnf(i_0_16462,plain,
    ( ~ class_Orderings_Owellorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Orderings_Oord__class_OLeast(X1,X3)))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9874]),
    [final] ).

cnf(i_0_16463,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_9875]),
    [final] ).

cnf(i_0_16464,plain,
    ( c_Enum_Oenum__class_Oenum(tc_prod(X1,X2)) = c_Enum_Oproduct(X1,X2,c_Enum_Oenum__class_Oenum(X1),c_Enum_Oenum__class_Oenum(X2))
    | ~ class_Enum_Oenum(X1)
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9876]),
    [final] ).

cnf(i_0_16465,plain,
    ( X2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk107_2(X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9877]),
    [final] ).

cnf(i_0_16466,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_9878]),
    [final] ).

cnf(i_0_16467,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_9879]),
    [final] ).

cnf(i_0_16468,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_9880]),
    [final] ).

cnf(i_0_16469,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_9881]),
    [final] ).

cnf(i_0_16470,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_9882]),
    [final] ).

cnf(i_0_16471,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_9883]),
    [final] ).

cnf(i_0_16472,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_9438]),
    [final] ).

cnf(i_0_16473,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_6487]),
    [final] ).

cnf(i_0_16474,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_9378]),
    [final] ).

cnf(i_0_16475,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_9884]),
    [final] ).

cnf(i_0_16476,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_8723]),
    [final] ).

cnf(i_0_16477,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_9787]),
    [final] ).

cnf(i_0_16478,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_9787]),
    [final] ).

cnf(i_0_16479,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_9885]),
    [final] ).

cnf(i_0_16480,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_9886]),
    [final] ).

cnf(i_0_16481,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_6205]),
    [final] ).

cnf(i_0_16482,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_8048]),
    [final] ).

cnf(i_0_16483,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_9095]),
    [final] ).

cnf(i_0_16484,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk316_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_9887]),
    [final] ).

cnf(i_0_16485,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[conj_3]),
    [final] ).

cnf(i_0_16486,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[conj_0]),
    [final] ).

cnf(i_0_16487,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_9888]),
    [final] ).

cnf(i_0_16488,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_9889]),
    [final] ).

cnf(i_0_16489,plain,
    ( hBOOL(hAPP(X1,esk524_3(X2,X3,X1)))
    | c_FunDef_OTHE__default(X3,X2,X1) = X2 ),
    inference(split_conjunct,[status(thm)],[i_0_8130]),
    [final] ).

cnf(i_0_16490,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_9890]),
    [final] ).

cnf(i_0_16491,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_9891]),
    [final] ).

cnf(i_0_16492,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_9892]),
    [final] ).

cnf(i_0_16493,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_9893,c_0_6209]),
    [final] ).

cnf(i_0_16494,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_9894]),
    [final] ).

cnf(i_0_16495,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_9895]),
    [final] ).

cnf(i_0_16496,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_9896]),
    [final] ).

cnf(i_0_16497,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_9897]),
    [final] ).

cnf(i_0_16498,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_9898]),
    [final] ).

cnf(i_0_16499,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X2)))
    | ~ epred1_3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9610]),
    [final] ).

cnf(i_0_16500,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_9899]),
    [final] ).

cnf(i_0_16501,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_9899]),
    [final] ).

cnf(i_0_16502,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_9900]),
    [final] ).

cnf(i_0_16503,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_9901]),
    [final] ).

cnf(i_0_16504,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_9902]),
    [final] ).

cnf(i_0_16505,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_9903]),
    [final] ).

cnf(i_0_16506,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_9904]),
    [final] ).

cnf(i_0_16507,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_9905]),
    [final] ).

cnf(i_0_16508,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_9906]),
    [final] ).

cnf(i_0_16509,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_9907]),
    [final] ).

cnf(i_0_16510,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_9908]),
    [final] ).

cnf(i_0_16511,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_9791]),
    [final] ).

cnf(i_0_16512,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_9792]),
    [final] ).

cnf(i_0_16513,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_9909,c_0_7157]),
    [final] ).

cnf(i_0_16514,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_9910,c_0_7157]),
    [final] ).

cnf(i_0_16515,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_9911]),
    [final] ).

cnf(i_0_16516,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_16517,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_8422]),
    [final] ).

cnf(i_0_16518,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_8422]),
    [final] ).

cnf(i_0_16519,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_9912]),
    [final] ).

cnf(i_0_16520,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_9912]),
    [final] ).

cnf(i_0_16521,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_8705]),
    [final] ).

cnf(i_0_16522,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_9913]),
    [final] ).

cnf(i_0_16523,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_9914]),
    [final] ).

cnf(i_0_16524,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_9110]),
    [final] ).

cnf(i_0_16525,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_9651]),
    [final] ).

cnf(i_0_16526,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_9915]),
    [final] ).

cnf(i_0_16527,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_9916]),
    [final] ).

cnf(i_0_16528,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_9917]),
    [final] ).

cnf(i_0_16529,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_8251]),
    [final] ).

cnf(i_0_16530,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_9885]),
    [final] ).

cnf(i_0_16531,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_9636]),
    [final] ).

cnf(i_0_16532,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_9918]),
    [final] ).

cnf(i_0_16533,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_9919]),
    [final] ).

cnf(i_0_16534,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_9920]),
    [final] ).

cnf(i_0_16535,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_9919]),
    [final] ).

cnf(i_0_16536,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_9920]),
    [final] ).

cnf(i_0_16537,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_9921]),
    [final] ).

cnf(i_0_16538,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_9922]),
    [final] ).

cnf(i_0_16539,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_9923]),
    [final] ).

cnf(i_0_16540,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_9141]),
    [final] ).

cnf(i_0_16541,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_9742]),
    [final] ).

cnf(i_0_16542,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_9924]),
    [final] ).

cnf(i_0_16543,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_9925]),
    [final] ).

cnf(i_0_16544,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_9926]),
    [final] ).

cnf(i_0_16545,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_9927]),
    [final] ).

cnf(i_0_16546,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_9928]),
    [final] ).

cnf(i_0_16547,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_9929]),
    [final] ).

cnf(i_0_16548,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_9828]),
    [final] ).

cnf(i_0_16549,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_9847]),
    [final] ).

cnf(i_0_16550,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_9930]),
    [final] ).

cnf(i_0_16551,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_9793]),
    [final] ).

cnf(i_0_16552,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_9931]),
    [final] ).

cnf(i_0_16553,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_9759]),
    [final] ).

cnf(i_0_16554,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_9207]),
    [final] ).

cnf(i_0_16555,plain,
    ( hBOOL(hAPP(X1,esk446_3(X2,X1,X3)))
    | hAPP(c_List_Ofilter(X3,X1),X2) = c_List_Olist_ONil(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8893]),
    [final] ).

cnf(i_0_16556,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_9932]),
    [final] ).

cnf(i_0_16557,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_9933]),
    [final] ).

cnf(i_0_16558,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_9664]),
    [final] ).

cnf(i_0_16559,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_9934]),
    [final] ).

cnf(i_0_16560,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_9935]),
    [final] ).

cnf(i_0_16561,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_9936]),
    [final] ).

cnf(i_0_16562,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_9430]),
    [final] ).

cnf(i_0_16563,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk189_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_9937]),
    [final] ).

cnf(i_0_16564,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_9938]),
    [final] ).

cnf(i_0_16565,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_9938]),
    [final] ).

cnf(i_0_16566,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_9939]),
    [final] ).

cnf(i_0_16567,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_9940]),
    [final] ).

cnf(i_0_16568,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_9941]),
    [final] ).

cnf(i_0_16569,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_9942]),
    [final] ).

cnf(i_0_16570,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_9943]),
    [final] ).

cnf(i_0_16571,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_9944]),
    [final] ).

cnf(i_0_16572,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_9945]),
    [final] ).

cnf(i_0_16573,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_9946]),
    [final] ).

cnf(i_0_16574,plain,
    c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Nat_OSuc,X4)) = hAPP(X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_9947]),
    [final] ).

cnf(i_0_16575,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_9948]),
    [final] ).

cnf(i_0_16576,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_9949]),
    [final] ).

cnf(i_0_16577,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_9950]),
    [final] ).

cnf(i_0_16578,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_9951]),
    [final] ).

cnf(i_0_16579,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_9952]),
    [final] ).

cnf(i_0_16580,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_9953]),
    [final] ).

cnf(i_0_16581,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_9954]),
    [final] ).

cnf(i_0_16582,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_9730]),
    [final] ).

cnf(i_0_16583,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_9955]),
    [final] ).

cnf(i_0_16584,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_9956]),
    [final] ).

cnf(i_0_16585,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_9957]),
    [final] ).

cnf(i_0_16586,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_9958]),
    [final] ).

cnf(i_0_16587,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_9959]),
    [final] ).

cnf(i_0_16588,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_9960]),
    [final] ).

cnf(i_0_16589,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_9961]),
    [final] ).

cnf(i_0_16590,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_9962]),
    [final] ).

cnf(i_0_16591,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_9963]),
    [final] ).

cnf(i_0_16592,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_9964]),
    [final] ).

cnf(i_0_16593,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_9965]),
    [final] ).

cnf(i_0_16594,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_9966]),
    [final] ).

cnf(i_0_16595,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_16596,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_16597,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_16598,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_16599,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_9967]),
    [final] ).

cnf(i_0_16600,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_9968]),
    [final] ).

cnf(i_0_16601,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_9969]),
    [final] ).

cnf(i_0_16602,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_9970]),
    [final] ).

cnf(i_0_16603,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk117_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_9250]),
    [final] ).

cnf(i_0_16604,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),X2))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9574]),
    [final] ).

cnf(i_0_16605,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_9971]),
    [final] ).

cnf(i_0_16606,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_9664]),
    [final] ).

cnf(i_0_16607,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_9953]),
    [final] ).

cnf(i_0_16608,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_9954]),
    [final] ).

cnf(i_0_16609,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_9972]),
    [final] ).

cnf(i_0_16610,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_9600]),
    [final] ).

cnf(i_0_16611,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_9973]),
    [final] ).

cnf(i_0_16612,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_9974]),
    [final] ).

cnf(i_0_16613,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_16614,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_9975]),
    [final] ).

cnf(i_0_16615,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_9425]),
    [final] ).

cnf(i_0_16616,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_9976]),
    [final] ).

cnf(i_0_16617,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_9977]),
    [final] ).

cnf(i_0_16618,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_9978,c_0_6104]),
    [final] ).

cnf(i_0_16619,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_9588]),
    [final] ).

cnf(i_0_16620,plain,
    ( esk23_3(X1,X2,X3) = esk24_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_8786]),
    [final] ).

cnf(i_0_16621,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_9979]),
    [final] ).

cnf(i_0_16622,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_9980]),
    [final] ).

cnf(i_0_16623,plain,
    ( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk154_2(X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9981]),
    [final] ).

cnf(i_0_16624,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_9982]),
    [final] ).

cnf(i_0_16625,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_9983]),
    [final] ).

cnf(i_0_16626,plain,
    ( hBOOL(hAPP(X1,esk202_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_8887]),
    [final] ).

cnf(i_0_16627,plain,
    ( hBOOL(hAPP(X1,esk196_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_8721]),
    [final] ).

cnf(i_0_16628,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_9984]),
    [final] ).

cnf(i_0_16629,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_9984]),
    [final] ).

cnf(i_0_16630,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,esk184_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_9985]),
    [final] ).

cnf(i_0_16631,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_9986]),
    [final] ).

cnf(i_0_16632,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_9987]),
    [final] ).

cnf(i_0_16633,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_9988]),
    [final] ).

cnf(i_0_16634,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_9989]),
    [final] ).

cnf(i_0_16635,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_9778]),
    [final] ).

cnf(i_0_16636,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_9990]),
    [final] ).

cnf(i_0_16637,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_9991]),
    [final] ).

cnf(i_0_16638,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_9644]),
    [final] ).

cnf(i_0_16639,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_9992]),
    [final] ).

cnf(i_0_16640,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_9885]),
    [final] ).

cnf(i_0_16641,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_9993]),
    [final] ).

cnf(i_0_16642,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk384_2(X2,X1)),esk383_2(X2,X1)))
    | c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7107]),
    [final] ).

cnf(i_0_16643,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_9994]),
    [final] ).

cnf(i_0_16644,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_9995]),
    [final] ).

cnf(i_0_16645,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_9006]),
    [final] ).

cnf(i_0_16646,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_9996]),
    [final] ).

cnf(i_0_16647,plain,
    c_Lazy__Sequence_Ohb__map(X1,X2,X3,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(X1))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(X2)),
    inference(split_conjunct,[status(thm)],[i_0_9997]),
    [final] ).

cnf(i_0_16648,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_9664]),
    [final] ).

cnf(i_0_16649,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_9998]),
    [final] ).

cnf(i_0_16650,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_9999]),
    [final] ).

cnf(i_0_16651,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_10000]),
    [final] ).

cnf(i_0_16652,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_10000]),
    [final] ).

cnf(i_0_16653,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_10001]),
    [final] ).

cnf(i_0_16654,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_10002]),
    [final] ).

cnf(i_0_16655,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_10003]),
    [final] ).

cnf(i_0_16656,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_10004]),
    [final] ).

cnf(i_0_16657,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_10005]),
    [final] ).

cnf(i_0_16658,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_10006]),
    [final] ).

cnf(i_0_16659,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_10007]),
    [final] ).

cnf(i_0_16660,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_10008]),
    [final] ).

cnf(i_0_16661,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_10009]),
    [final] ).

cnf(i_0_16662,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_10009]),
    [final] ).

cnf(i_0_16663,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_10008]),
    [final] ).

cnf(i_0_16664,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_7703]),
    [final] ).

cnf(i_0_16665,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_8268]),
    [final] ).

cnf(i_0_16666,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_6611]),
    [final] ).

cnf(i_0_16667,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_10010]),
    [final] ).

cnf(i_0_16668,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_10011]),
    [final] ).

cnf(i_0_16669,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_9595]),
    [final] ).

cnf(i_0_16670,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_10012]),
    [final] ).

cnf(i_0_16671,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_6667]),
    [final] ).

cnf(i_0_16672,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_10013]),
    [final] ).

cnf(i_0_16673,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_6908]),
    [final] ).

cnf(i_0_16674,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_6667]),
    [final] ).

cnf(i_0_16675,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_6909]),
    [final] ).

cnf(i_0_16676,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_10014]),
    [final] ).

cnf(i_0_16677,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_10015]),
    [final] ).

cnf(i_0_16678,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_10016]),
    [final] ).

cnf(i_0_16679,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_10017]),
    [final] ).

cnf(i_0_16680,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_9984]),
    [final] ).

cnf(i_0_16681,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk460_2(X1,X2)),esk461_2(X1,X2)))
    | c_List_Olinorder__class_Osorted(X2,X1)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7725]),
    [final] ).

cnf(i_0_16682,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk459_2(X1,X2)),esk458_2(X1,X2)))
    | c_List_Olinorder__class_Osorted(X2,X1)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7726]),
    [final] ).

cnf(i_0_16683,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_10018]),
    [final] ).

cnf(i_0_16684,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_10019]),
    [final] ).

cnf(i_0_16685,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_10020]),
    [final] ).

cnf(i_0_16686,plain,
    ( X3 = hAPP(c_Option_Ooption_OSome(X1),X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Option_Oset(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_10021]),
    [final] ).

cnf(i_0_16687,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_10022]),
    [final] ).

cnf(i_0_16688,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_10023]),
    [final] ).

cnf(i_0_16689,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_10024]),
    [final] ).

cnf(i_0_16690,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_10024]),
    [final] ).

cnf(i_0_16691,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_10025]),
    [final] ).

cnf(i_0_16692,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_9664]),
    [final] ).

cnf(i_0_16693,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_10026]),
    [final] ).

cnf(i_0_16694,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk153_1(X1)))
    | ~ hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9768]),
    [final] ).

cnf(i_0_16695,plain,
    ( hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Map_Odom(X5,X3,X1)) = c_Map_Odom(X5,X3,X1)
    | hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_10027]),
    [final] ).

cnf(i_0_16696,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_10028]),
    [final] ).

cnf(i_0_16697,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_10029]),
    [final] ).

cnf(i_0_16698,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_10030]),
    [final] ).

cnf(i_0_16699,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_10029]),
    [final] ).

cnf(i_0_16700,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,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_16701,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,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_16702,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_10031]),
    [final] ).

cnf(i_0_16703,negated_conjecture,
    ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)),
    inference(split_conjunct,[status(thm)],[i_0_10032]),
    [final] ).

cnf(i_0_16704,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Orderings_Oord__class_OLeast(X1,X2)),X3))
    | ~ class_Orderings_Owellorder(X1)
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10033]),
    [final] ).

cnf(i_0_16705,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_10034]),
    [final] ).

cnf(i_0_16706,plain,
    ( c_Equiv__Relations_Oequivp(X2,X1)
    | ~ hBOOL(hAPP(hAPP(X1,esk72_1(X1)),esk73_1(X1)))
    | hAPP(X1,esk72_1(X1)) != hAPP(X1,esk73_1(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10035]),
    [final] ).

cnf(i_0_16707,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_10036]),
    [final] ).

cnf(i_0_16708,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_10037]),
    [final] ).

cnf(i_0_16709,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_10038]),
    [final] ).

cnf(i_0_16710,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_10039]),
    [final] ).

cnf(i_0_16711,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_10040]),
    [final] ).

cnf(i_0_16712,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk110_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_9496]),
    [final] ).

cnf(i_0_16713,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_9551]),
    [final] ).

cnf(i_0_16714,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_9160]),
    [final] ).

cnf(i_0_16715,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_10041]),
    [final] ).

cnf(i_0_16716,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_10042]),
    [final] ).

cnf(i_0_16717,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_9792]),
    [final] ).

cnf(i_0_16718,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_9791]),
    [final] ).

cnf(i_0_16719,plain,
    ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,esk156_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9849]),
    [final] ).

cnf(i_0_16720,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_9862]),
    [final] ).

cnf(i_0_16721,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_10043]),
    [final] ).

cnf(i_0_16722,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_10044]),
    [final] ).

cnf(i_0_16723,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_10045]),
    [final] ).

cnf(i_0_16724,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_9003]),
    [final] ).

cnf(i_0_16725,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_9003]),
    [final] ).

cnf(i_0_16726,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_10046]),
    [final] ).

cnf(i_0_16727,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_10047]),
    [final] ).

cnf(i_0_16728,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_10048]),
    [final] ).

cnf(i_0_16729,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_10049]),
    [final] ).

cnf(i_0_16730,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_8048]),
    [final] ).

cnf(i_0_16731,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_10050]),
    [final] ).

cnf(i_0_16732,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_10051]),
    [final] ).

cnf(i_0_16733,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_10052]),
    [final] ).

cnf(i_0_16734,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_10053]),
    [final] ).

cnf(i_0_16735,plain,
    c_Fun_Oinj__on(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10054]),
    [final] ).

cnf(i_0_16736,plain,
    c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10055]),
    [final] ).

cnf(i_0_16737,plain,
    c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10056]),
    [final] ).

cnf(i_0_16738,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_5989]),
    [final] ).

cnf(i_0_16739,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_5990]),
    [final] ).

cnf(i_0_16740,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_9899]),
    [final] ).

cnf(i_0_16741,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_10057]),
    [final] ).

cnf(i_0_16742,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_9933]),
    [final] ).

cnf(i_0_16743,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_10058]),
    [final] ).

cnf(i_0_16744,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_10059]),
    [final] ).

cnf(i_0_16745,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_10059]),
    [final] ).

cnf(i_0_16746,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_10060]),
    [final] ).

cnf(i_0_16747,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_10061]),
    [final] ).

cnf(i_0_16748,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_10008]),
    [final] ).

cnf(i_0_16749,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_10009]),
    [final] ).

cnf(i_0_16750,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_5359]),
    [final] ).

cnf(i_0_16751,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_10062]),
    [final] ).

cnf(i_0_16752,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_10063]),
    [final] ).

cnf(i_0_16753,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_10064]),
    [final] ).

cnf(i_0_16754,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_10065]),
    [final] ).

cnf(i_0_16755,plain,
    c_List_Omaps(X1,X2,X3,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X2),
    inference(split_conjunct,[status(thm)],[i_0_10066]),
    [final] ).

cnf(i_0_16756,plain,
    c_List_Omap__filter(X1,X2,X3,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X2),
    inference(split_conjunct,[status(thm)],[i_0_10067]),
    [final] ).

cnf(i_0_16757,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_9877]),
    [final] ).

cnf(i_0_16758,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_10068,c_0_8361]),c_0_8361]),
    [final] ).

cnf(i_0_16759,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_10069]),
    [final] ).

cnf(i_0_16760,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_10070]),
    [final] ).

cnf(i_0_16761,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_10071]),
    [final] ).

cnf(i_0_16762,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_10072]),
    [final] ).

cnf(i_0_16763,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_10073]),
    [final] ).

cnf(i_0_16764,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_10074]),
    [final] ).

cnf(i_0_16765,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_10075]),
    [final] ).

cnf(i_0_16766,plain,
    c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10076]),
    [final] ).

cnf(i_0_16767,plain,
    c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10077]),
    [final] ).

cnf(i_0_16768,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_7972]),
    [final] ).

cnf(i_0_16769,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_10078]),
    [final] ).

cnf(i_0_16770,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_10079]),
    [final] ).

cnf(i_0_16771,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_10080]),
    [final] ).

cnf(i_0_16772,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_10081,c_0_6136]),
    [final] ).

cnf(i_0_16773,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_10082]),
    [final] ).

cnf(i_0_16774,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_10083,c_0_8361]),
    [final] ).

cnf(i_0_16775,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_10084]),
    [final] ).

cnf(i_0_16776,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_10085]),
    [final] ).

cnf(i_0_16777,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_10086]),
    [final] ).

cnf(i_0_16778,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_6862]),
    [final] ).

cnf(i_0_16779,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_10087]),
    [final] ).

cnf(i_0_16780,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_10088]),
    [final] ).

cnf(i_0_16781,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_10089]),
    [final] ).

cnf(i_0_16782,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_10090]),
    [final] ).

cnf(i_0_16783,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_10091]),
    [final] ).

cnf(i_0_16784,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_10092]),
    [final] ).

cnf(i_0_16785,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_10093]),
    [final] ).

cnf(i_0_16786,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_10094]),
    [final] ).

cnf(i_0_16787,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_10095]),
    [final] ).

cnf(i_0_16788,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_10096,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_16789,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_10097]),
    [final] ).

cnf(i_0_16790,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_10098]),
    [final] ).

cnf(i_0_16791,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_10099]),
    [final] ).

cnf(i_0_16792,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_10100]),
    [final] ).

cnf(i_0_16793,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_5359]),
    [final] ).

cnf(i_0_16794,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_10101]),
    [final] ).

cnf(i_0_16795,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_10101]),
    [final] ).

cnf(i_0_16796,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),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)],[i_0_10102,c_0_6102]),c_0_6103]),c_0_6104]),c_0_6104]),
    [final] ).

cnf(i_0_16797,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_10103]),
    [final] ).

cnf(i_0_16798,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_10104]),
    [final] ).

cnf(i_0_16799,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_10105]),
    [final] ).

cnf(i_0_16800,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_10106]),
    [final] ).

cnf(i_0_16801,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_10107]),
    [final] ).

cnf(i_0_16802,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_10108]),
    [final] ).

cnf(i_0_16803,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_10109]),
    [final] ).

cnf(i_0_16804,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_10110]),
    [final] ).

cnf(i_0_16805,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_10111]),
    [final] ).

cnf(i_0_16806,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_10112,c_0_8046]),c_0_8047]),
    [final] ).

cnf(i_0_16807,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_10113]),
    [final] ).

cnf(i_0_16808,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_10114]),
    [final] ).

cnf(i_0_16809,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_10115]),
    [final] ).

cnf(i_0_16810,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_10116]),
    [final] ).

cnf(i_0_16811,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_10117]),
    [final] ).

cnf(i_0_16812,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_10118]),
    [final] ).

cnf(i_0_16813,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_10119]),
    [final] ).

cnf(i_0_16814,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_10120]),
    [final] ).

cnf(i_0_16815,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_10121]),
    [final] ).

cnf(i_0_16816,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_10122]),
    [final] ).

cnf(i_0_16817,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_10123]),
    [final] ).

cnf(i_0_16818,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_9701]),
    [final] ).

cnf(i_0_16819,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_9701]),
    [final] ).

cnf(i_0_16820,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_9776]),
    [final] ).

cnf(i_0_16821,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_10124]),
    [final] ).

cnf(i_0_16822,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_10108]),
    [final] ).

cnf(i_0_16823,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_10125]),
    [final] ).

cnf(i_0_16824,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_10126]),
    [final] ).

cnf(i_0_16825,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_10110]),
    [final] ).

cnf(i_0_16826,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_10111]),
    [final] ).

cnf(i_0_16827,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_10127]),
    [final] ).

cnf(i_0_16828,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_10128]),
    [final] ).

cnf(i_0_16829,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_10129]),
    [final] ).

cnf(i_0_16830,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_16831,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_10130]),
    [final] ).

cnf(i_0_16832,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_10131,c_0_6104]),
    [final] ).

cnf(i_0_16833,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_9095]),
    [final] ).

cnf(i_0_16834,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_10132]),
    [final] ).

cnf(i_0_16835,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(X2),esk19_2(X1,X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10133]),
    [final] ).

cnf(i_0_16836,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk20_2(X2,X1)),X2))
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_10134]),
    [final] ).

cnf(i_0_16837,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_10135]),
    [final] ).

cnf(i_0_16838,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_10136,c_0_6209]),
    [final] ).

cnf(i_0_16839,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_9827]),
    [final] ).

cnf(i_0_16840,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9574]),
    [final] ).

cnf(i_0_16841,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_10137]),
    [final] ).

cnf(i_0_16842,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_10138]),
    [final] ).

cnf(i_0_16843,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_10139]),
    [final] ).

cnf(i_0_16844,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_10140]),
    [final] ).

cnf(i_0_16845,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_9649]),
    [final] ).

cnf(i_0_16846,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_10141]),
    [final] ).

cnf(i_0_16847,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_10142]),
    [final] ).

cnf(i_0_16848,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_10143]),
    [final] ).

cnf(i_0_16849,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_10144]),
    [final] ).

cnf(i_0_16850,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_10145]),
    [final] ).

cnf(i_0_16851,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_10146]),
    [final] ).

cnf(i_0_16852,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_10147]),
    [final] ).

cnf(i_0_16853,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_10148]),
    [final] ).

cnf(i_0_16854,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_10149]),
    [final] ).

cnf(i_0_16855,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_10150]),
    [final] ).

cnf(i_0_16856,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_10151,c_0_6209]),
    [final] ).

cnf(i_0_16857,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_10152,c_0_6209]),
    [final] ).

cnf(i_0_16858,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_10153,c_0_6209]),
    [final] ).

cnf(i_0_16859,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_10154]),
    [final] ).

cnf(i_0_16860,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_9655]),
    [final] ).

cnf(i_0_16861,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_10155]),
    [final] ).

cnf(i_0_16862,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_10156]),
    [final] ).

cnf(i_0_16863,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk79_2(X1,X2)),X1))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9721]),
    [final] ).

cnf(i_0_16864,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk77_2(X1,X2)),X1))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9722]),
    [final] ).

cnf(i_0_16865,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_9675]),
    [final] ).

cnf(i_0_16866,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_9676]),
    [final] ).

cnf(i_0_16867,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_10157]),
    [final] ).

cnf(i_0_16868,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_10158]),
    [final] ).

cnf(i_0_16869,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_10159]),
    [final] ).

cnf(i_0_16870,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_10160]),
    [final] ).

cnf(i_0_16871,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_10161]),
    [final] ).

cnf(i_0_16872,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_10162]),
    [final] ).

cnf(i_0_16873,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_10163]),
    [final] ).

cnf(i_0_16874,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_10164]),
    [final] ).

cnf(i_0_16875,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_9723]),
    [final] ).

cnf(i_0_16876,plain,
    hAPP(c_New__DSequence_Oneg__union(X1,X2,X3),X4) = c_Lazy__Sequence_Oappend(tc_Option_Ooption(X1),hAPP(X2,X4),hAPP(X3,X4)),
    inference(split_conjunct,[status(thm)],[i_0_10165]),
    [final] ).

cnf(i_0_16877,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_10166]),
    [final] ).

cnf(i_0_16878,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_10167]),
    [final] ).

cnf(i_0_16879,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_10168]),
    [final] ).

cnf(i_0_16880,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_10169]),
    [final] ).

cnf(i_0_16881,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_10170]),
    [final] ).

cnf(i_0_16882,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_10171]),
    [final] ).

cnf(i_0_16883,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_10172]),
    [final] ).

cnf(i_0_16884,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_10173]),
    [final] ).

cnf(i_0_16885,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_10174]),
    [final] ).

cnf(i_0_16886,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_10175]),
    [final] ).

cnf(i_0_16887,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_9819]),
    [final] ).

cnf(i_0_16888,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_10176]),
    [final] ).

cnf(i_0_16889,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_6007]),
    [final] ).

cnf(i_0_16890,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_10177]),
    [final] ).

cnf(i_0_16891,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_10178]),
    [final] ).

cnf(i_0_16892,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_10179]),
    [final] ).

cnf(i_0_16893,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_10180]),
    [final] ).

cnf(i_0_16894,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_10101]),
    [final] ).

cnf(i_0_16895,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_10181]),
    [final] ).

cnf(i_0_16896,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_10182]),
    [final] ).

cnf(i_0_16897,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_10183]),
    [final] ).

cnf(i_0_16898,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_10184]),
    [final] ).

cnf(i_0_16899,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_10185]),
    [final] ).

cnf(i_0_16900,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_10186]),
    [final] ).

cnf(i_0_16901,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_10187]),
    [final] ).

cnf(i_0_16902,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_10188]),
    [final] ).

cnf(i_0_16903,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_10189]),
    [final] ).

cnf(i_0_16904,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_10190]),
    [final] ).

cnf(i_0_16905,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_10191]),
    [final] ).

cnf(i_0_16906,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_10192]),
    [final] ).

cnf(i_0_16907,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_10193]),
    [final] ).

cnf(i_0_16908,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_10194]),
    [final] ).

cnf(i_0_16909,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_10195]),
    [final] ).

cnf(i_0_16910,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_10196]),
    [final] ).

cnf(i_0_16911,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_10197]),
    [final] ).

cnf(i_0_16912,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_10198]),
    [final] ).

cnf(i_0_16913,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_9916]),
    [final] ).

cnf(i_0_16914,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_10199]),
    [final] ).

cnf(i_0_16915,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_10200]),
    [final] ).

cnf(i_0_16916,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_10201,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_16917,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_10202,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_16918,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_10203,c_0_6209]),
    [final] ).

cnf(i_0_16919,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_10204]),
    [final] ).

cnf(i_0_16920,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_10205]),
    [final] ).

cnf(i_0_16921,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_10206]),
    [final] ).

cnf(i_0_16922,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_10207]),
    [final] ).

cnf(i_0_16923,plain,
    ( c_Relation_Osingle__valued(X3,X2,X1)
    | esk333_3(X1,X2,X3) != esk334_3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7051]),
    [final] ).

cnf(i_0_16924,plain,
    ( c_Relation_Ototal__on(X3,X2,X1)
    | esk328_3(X1,X2,X3) != esk329_3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6855]),
    [final] ).

cnf(i_0_16925,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_10208]),
    [final] ).

cnf(i_0_16926,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_10209]),
    [final] ).

cnf(i_0_16927,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_10210]),
    [final] ).

cnf(i_0_16928,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_10211]),
    [final] ).

cnf(i_0_16929,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_9302]),
    [final] ).

cnf(i_0_16930,plain,
    ( c_Wellfounded_OwfP(X1,X2)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk289_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_10212]),
    [final] ).

cnf(i_0_16931,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_10213]),
    [final] ).

cnf(i_0_16932,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_10214,c_0_6209]),
    [final] ).

cnf(i_0_16933,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_9641]),
    [final] ).

cnf(i_0_16934,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_10215]),
    [final] ).

cnf(i_0_16935,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_10216]),
    [final] ).

cnf(i_0_16936,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_9955]),
    [final] ).

cnf(i_0_16937,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_10217]),
    [final] ).

cnf(i_0_16938,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_10218]),
    [final] ).

cnf(i_0_16939,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_10219]),
    [final] ).

cnf(i_0_16940,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_10220]),
    [final] ).

cnf(i_0_16941,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_10221]),
    [final] ).

cnf(i_0_16942,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_10222]),
    [final] ).

cnf(i_0_16943,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_10223]),
    [final] ).

cnf(i_0_16944,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_9746]),
    [final] ).

cnf(i_0_16945,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_10224]),
    [final] ).

cnf(i_0_16946,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_10225]),
    [final] ).

cnf(i_0_16947,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_10226]),
    [final] ).

cnf(i_0_16948,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_10227]),
    [final] ).

cnf(i_0_16949,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_10228]),
    [final] ).

cnf(i_0_16950,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_10229]),
    [final] ).

cnf(i_0_16951,plain,
    hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),hAPP(X3,X4)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_10230]),
    [final] ).

cnf(i_0_16952,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_10231]),
    [final] ).

cnf(i_0_16953,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_10232]),
    [final] ).

cnf(i_0_16954,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_10233,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_16955,plain,
    ( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk109_2(X2,X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10234]),
    [final] ).

cnf(i_0_16956,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_10235]),
    [final] ).

cnf(i_0_16957,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),esk156_2(X1,X2))
    | hBOOL(hAPP(X2,hAPP(c_Int_Onat,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9849]),
    [final] ).

cnf(i_0_16958,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_10236]),
    [final] ).

cnf(i_0_16959,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_9984]),
    [final] ).

cnf(i_0_16960,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_10237]),
    [final] ).

cnf(i_0_16961,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_10238]),
    [final] ).

cnf(i_0_16962,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_9749]),
    [final] ).

cnf(i_0_16963,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_10239]),
    [final] ).

cnf(i_0_16964,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_9748]),
    [final] ).

cnf(i_0_16965,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_10240]),
    [final] ).

cnf(i_0_16966,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_10241]),
    [final] ).

cnf(i_0_16967,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X5),X1),X2),X3) = X1
    | hAPP(X1,X2) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_10242]),
    [final] ).

cnf(i_0_16968,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X5),X1),X2),X3) = X1
    | hAPP(X1,X2) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_9801]),
    [final] ).

cnf(i_0_16969,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_10243,c_0_6209]),
    [final] ).

cnf(i_0_16970,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_10244,c_0_6209]),
    [final] ).

cnf(i_0_16971,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_9757]),
    [final] ).

cnf(i_0_16972,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_10245]),
    [final] ).

cnf(i_0_16973,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_10246]),
    [final] ).

cnf(i_0_16974,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_10247]),
    [final] ).

cnf(i_0_16975,plain,
    c_Option_Ooption_Ooption__size(X1,X2,hAPP(c_Option_Ooption_OSome(X1),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X2,X3)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_10248]),
    [final] ).

cnf(i_0_16976,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_10249]),
    [final] ).

cnf(i_0_16977,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_10250,c_0_6104]),c_0_6242]),
    [final] ).

cnf(i_0_16978,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_9981]),
    [final] ).

cnf(i_0_16979,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_10041]),
    [final] ).

cnf(i_0_16980,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_10042]),
    [final] ).

cnf(i_0_16981,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_10251]),
    [final] ).

cnf(i_0_16982,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_10252]),
    [final] ).

cnf(i_0_16983,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_10253]),
    [final] ).

cnf(i_0_16984,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_10254]),
    [final] ).

cnf(i_0_16985,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_10255]),
    [final] ).

cnf(i_0_16986,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_10256]),
    [final] ).

cnf(i_0_16987,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_10257]),
    [final] ).

cnf(i_0_16988,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_10258]),
    [final] ).

cnf(i_0_16989,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_10259]),
    [final] ).

cnf(i_0_16990,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_10260]),
    [final] ).

cnf(i_0_16991,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_10261]),
    [final] ).

cnf(i_0_16992,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_10262]),
    [final] ).

cnf(i_0_16993,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_10263]),
    [final] ).

cnf(i_0_16994,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_10264]),
    [final] ).

cnf(i_0_16995,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_10265]),
    [final] ).

cnf(i_0_16996,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_10266,c_0_6104]),
    [final] ).

cnf(i_0_16997,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_8321]),
    [final] ).

cnf(i_0_16998,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_10267]),
    [final] ).

cnf(i_0_16999,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_10268]),
    [final] ).

cnf(i_0_17000,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_10269]),
    [final] ).

cnf(i_0_17001,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_10270]),
    [final] ).

cnf(i_0_17002,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_Enum_Oenum__class_Oenum(X1))))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10271]),
    [final] ).

cnf(i_0_17003,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_10272]),
    [final] ).

cnf(i_0_17004,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_10273]),
    [final] ).

cnf(i_0_17005,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_10274]),
    [final] ).

cnf(i_0_17006,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_10275]),
    [final] ).

cnf(i_0_17007,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_10276]),
    [final] ).

cnf(i_0_17008,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_10277]),
    [final] ).

cnf(i_0_17009,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_10278]),
    [final] ).

cnf(i_0_17010,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_10279]),
    [final] ).

cnf(i_0_17011,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_10280]),
    [final] ).

cnf(i_0_17012,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_10281]),
    [final] ).

cnf(i_0_17013,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_10282]),
    [final] ).

cnf(i_0_17014,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk150_1(X1)))
    | hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9612]),
    [final] ).

cnf(i_0_17015,plain,
    ( X2 = esk482_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_10283]),
    [final] ).

cnf(i_0_17016,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_9812]),
    [final] ).

cnf(i_0_17017,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_10284]),
    [final] ).

cnf(i_0_17018,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_10285]),
    [final] ).

cnf(i_0_17019,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_10286]),
    [final] ).

cnf(i_0_17020,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_10287]),
    [final] ).

cnf(i_0_17021,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_9572]),
    [final] ).

cnf(i_0_17022,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_10134]),
    [final] ).

cnf(i_0_17023,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_10288]),
    [final] ).

cnf(i_0_17024,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_10133]),
    [final] ).

cnf(i_0_17025,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_10289]),
    [final] ).

cnf(i_0_17026,plain,
    hAPP(hAPP(c_Map_Omap__of(X1,X2),c_List_Olist_ONil(tc_prod(X1,X2))),X3) = c_Option_Ooption_ONone(X2),
    inference(split_conjunct,[status(thm)],[i_0_10290]),
    [final] ).

cnf(i_0_17027,plain,
    hAPP(hAPP(c_Map_Omap__of(X1,X2),c_List_Olist_ONil(tc_prod(X1,X2))),X3) = c_Option_Ooption_ONone(X2),
    inference(split_conjunct,[status(thm)],[i_0_10291]),
    [final] ).

cnf(i_0_17028,plain,
    ( hBOOL(hAPP(X1,esk309_2(X2,X1)))
    | ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_10292]),
    [final] ).

cnf(i_0_17029,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_10293]),
    [final] ).

cnf(i_0_17030,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_10294]),
    [final] ).

cnf(i_0_17031,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_10295]),
    [final] ).

cnf(i_0_17032,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_10296]),
    [final] ).

cnf(i_0_17033,plain,
    ( c_Smallcheck_Osmall_H(X3,X1,X2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7944]),
    [final] ).

cnf(i_0_17034,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_10297]),
    [final] ).

cnf(i_0_17035,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_10298]),
    [final] ).

cnf(i_0_17036,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_6862]),
    [final] ).

cnf(i_0_17037,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_6862]),
    [final] ).

cnf(i_0_17038,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_10299]),
    [final] ).

cnf(i_0_17039,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_10300]),
    [final] ).

cnf(i_0_17040,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_10301]),
    [final] ).

cnf(i_0_17041,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_10302]),
    [final] ).

cnf(i_0_17042,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_10303]),
    [final] ).

cnf(i_0_17043,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_10304]),
    [final] ).

cnf(i_0_17044,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_10305]),
    [final] ).

cnf(i_0_17045,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_10306]),
    [final] ).

cnf(i_0_17046,plain,
    c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,X1,X2) = c_Smallcheck_Ofull__small_H(X1,hAPP(c_Code__Numeral_Oint__of,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X2))),
    inference(split_conjunct,[status(thm)],[i_0_10307]),
    [final] ).

cnf(i_0_17047,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_10308]),
    [final] ).

cnf(i_0_17048,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_10297]),
    [final] ).

cnf(i_0_17049,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_10298]),
    [final] ).

cnf(i_0_17050,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_10309]),
    [final] ).

cnf(i_0_17051,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_10310]),
    [final] ).

cnf(i_0_17052,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_10311]),
    [final] ).

cnf(i_0_17053,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_10312]),
    [final] ).

cnf(i_0_17054,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_10313]),
    [final] ).

cnf(i_0_17055,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_10314]),
    [final] ).

cnf(i_0_17056,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_10315]),
    [final] ).

cnf(i_0_17057,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_10316,c_0_6209]),
    [final] ).

cnf(i_0_17058,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_10317]),
    [final] ).

cnf(i_0_17059,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_10318,c_0_6102]),c_0_6103]),c_0_6104]),
    [final] ).

cnf(i_0_17060,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_10319]),
    [final] ).

cnf(i_0_17061,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_10320]),
    [final] ).

cnf(i_0_17062,plain,
    ~ hBOOL(hAPP(hAPP(c_List_Oset(X1),c_List_Olist_ONil(X1)),X2)),
    inference(rw,[status(thm)],[i_0_10321,c_0_8412]),
    [final] ).

cnf(i_0_17063,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_10322]),
    [final] ).

cnf(i_0_17064,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_10154]),
    [final] ).

cnf(i_0_17065,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_10323]),
    [final] ).

cnf(i_0_17066,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_7931]),
    [final] ).

cnf(i_0_17067,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_7931]),
    [final] ).

cnf(i_0_17068,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_8672]),
    [final] ).

cnf(i_0_17069,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_8673]),
    [final] ).

cnf(i_0_17070,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_9776]),
    [final] ).

cnf(i_0_17071,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_10324,c_0_7157]),
    [final] ).

cnf(i_0_17072,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_17073,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_10325]),
    [final] ).

cnf(i_0_17074,plain,
    ( c_List_Olist__ex1(X2,X1,c_Enum_Oenum__class_Oenum(X2))
    | esk506_3(X1,X2,X3) != X3
    | ~ hBOOL(hAPP(X1,X3))
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9696]),
    [final] ).

cnf(i_0_17075,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_10326]),
    [final] ).

cnf(i_0_17076,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk400_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_9948]),
    [final] ).

cnf(i_0_17077,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_10327]),
    [final] ).

cnf(i_0_17078,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_10328]),
    [final] ).

cnf(i_0_17079,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_9922]),
    [final] ).

cnf(i_0_17080,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_10329]),
    [final] ).

cnf(i_0_17081,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_10330]),
    [final] ).

cnf(i_0_17082,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_10008]),
    [final] ).

cnf(i_0_17083,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_10009]),
    [final] ).

cnf(i_0_17084,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_10331]),
    [final] ).

cnf(i_0_17085,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_10332]),
    [final] ).

cnf(i_0_17086,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_10333]),
    [final] ).

cnf(i_0_17087,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_10334]),
    [final] ).

cnf(i_0_17088,plain,
    hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),X1),X2) = c_Smallcheck_Osmall_H(X1,hAPP(c_Code__Numeral_Oint__of,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X2))),
    inference(split_conjunct,[status(thm)],[i_0_10335]),
    [final] ).

cnf(i_0_17089,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_10336]),
    [final] ).

cnf(i_0_17090,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_10337]),
    [final] ).

cnf(i_0_17091,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_10338]),
    [final] ).

cnf(i_0_17092,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_10339]),
    [final] ).

cnf(i_0_17093,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_10340]),
    [final] ).

cnf(i_0_17094,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_10341]),
    [final] ).

cnf(i_0_17095,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_10342]),
    [final] ).

cnf(i_0_17096,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_10343]),
    [final] ).

cnf(i_0_17097,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_10344]),
    [final] ).

cnf(i_0_17098,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_10345]),
    [final] ).

cnf(i_0_17099,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_10346]),
    [final] ).

cnf(i_0_17100,plain,
    ( hAPP(hAPP(c_List_Onth(X1),X2),esk413_2(X2,X1)) = hAPP(hAPP(c_List_Onth(X1),X2),esk414_2(X2,X1))
    | hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8405]),
    [final] ).

cnf(i_0_17101,plain,
    ( hBOOL(hAPP(X3,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10347]),
    [final] ).

cnf(i_0_17102,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_10181]),
    [final] ).

cnf(i_0_17103,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_10184]),
    [final] ).

cnf(i_0_17104,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_10187]),
    [final] ).

cnf(i_0_17105,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_10190]),
    [final] ).

cnf(i_0_17106,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_10348,c_0_7157]),
    [final] ).

cnf(i_0_17107,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_10349]),
    [final] ).

cnf(i_0_17108,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10350]),
    [final] ).

cnf(i_0_17109,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_10351]),
    [final] ).

cnf(i_0_17110,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_10352]),
    [final] ).

cnf(i_0_17111,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_6908]),
    [final] ).

cnf(i_0_17112,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_6909]),
    [final] ).

cnf(i_0_17113,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_10353]),
    [final] ).

cnf(i_0_17114,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_10354]),
    [final] ).

cnf(i_0_17115,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_10355]),
    [final] ).

cnf(i_0_17116,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_10356]),
    [final] ).

cnf(i_0_17117,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_10357]),
    [final] ).

cnf(i_0_17118,plain,
    c_Map_Oran(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10358]),
    [final] ).

cnf(i_0_17119,plain,
    c_Map_Odom(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_10359]),
    [final] ).

cnf(i_0_17120,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_10360]),
    [final] ).

cnf(i_0_17121,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_9880]),
    [final] ).

cnf(i_0_17122,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_9881]),
    [final] ).

cnf(i_0_17123,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_9882]),
    [final] ).

cnf(i_0_17124,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_9883]),
    [final] ).

cnf(i_0_17125,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_9455]),
    [final] ).

cnf(i_0_17126,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_10361]),
    [final] ).

cnf(i_0_17127,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_10362]),
    [final] ).

cnf(i_0_17128,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_10363]),
    [final] ).

cnf(i_0_17129,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_10364]),
    [final] ).

cnf(i_0_17130,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_10365]),
    [final] ).

cnf(i_0_17131,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_10366]),
    [final] ).

cnf(i_0_17132,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_10367]),
    [final] ).

cnf(i_0_17133,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_10368]),
    [final] ).

cnf(i_0_17134,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_10369]),
    [final] ).

cnf(i_0_17135,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_10370]),
    [final] ).

cnf(i_0_17136,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_10052]),
    [final] ).

cnf(i_0_17137,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_10053]),
    [final] ).

cnf(i_0_17138,plain,
    ( X1 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk189_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_9937]),
    [final] ).

cnf(i_0_17139,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X3),c_Option_Oset(X2,X1)))
    | X1 != hAPP(c_Option_Ooption_OSome(X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10021]),
    [final] ).

cnf(i_0_17140,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_10045]),
    [final] ).

cnf(i_0_17141,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_10371]),
    [final] ).

cnf(i_0_17142,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_10372]),
    [final] ).

cnf(i_0_17143,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_10373]),
    [final] ).

cnf(i_0_17144,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_9674]),
    [final] ).

cnf(i_0_17145,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_10374]),
    [final] ).

cnf(i_0_17146,plain,
    ( hBOOL(hAPP(X1,esk153_1(X1)))
    | ~ hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9768]),
    [final] ).

cnf(i_0_17147,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_6013]),
    [final] ).

cnf(i_0_17148,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_17149,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_10375,c_0_7157]),
    [final] ).

cnf(i_0_17150,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_10376]),
    [final] ).

cnf(i_0_17151,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_10377]),
    [final] ).

cnf(i_0_17152,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_10162]),
    [final] ).

cnf(i_0_17153,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_10378]),
    [final] ).

cnf(i_0_17154,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_10379]),
    [final] ).

cnf(i_0_17155,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,esk145_1(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9860]),
    [final] ).

cnf(i_0_17156,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_10380]),
    [final] ).

cnf(i_0_17157,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_10381]),
    [final] ).

cnf(i_0_17158,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_10382]),
    [final] ).

cnf(i_0_17159,plain,
    ( X3 = hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))
    | c_Map_Odom(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_10383]),
    [final] ).

cnf(i_0_17160,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk111_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_10384]),
    [final] ).

cnf(i_0_17161,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_10385]),
    [final] ).

cnf(i_0_17162,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_10386]),
    [final] ).

cnf(i_0_17163,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_10387]),
    [final] ).

cnf(i_0_17164,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_10388]),
    [final] ).

cnf(i_0_17165,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_10177]),
    [final] ).

cnf(i_0_17166,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_10389]),
    [final] ).

cnf(i_0_17167,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_10178]),
    [final] ).

cnf(i_0_17168,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_10390]),
    [final] ).

cnf(i_0_17169,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_10391]),
    [final] ).

cnf(i_0_17170,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_10367]),
    [final] ).

cnf(i_0_17171,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_10368]),
    [final] ).

cnf(i_0_17172,plain,
    ( hBOOL(hAPP(X1,esk507_2(X1,X2)))
    | ~ c_List_Olist__ex1(X2,X1,c_Enum_Oenum__class_Oenum(X2))
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9696]),
    [final] ).

cnf(i_0_17173,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_10392]),
    [final] ).

cnf(i_0_17174,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_10393]),
    [final] ).

cnf(i_0_17175,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_10141]),
    [final] ).

cnf(i_0_17176,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_10394]),
    [final] ).

cnf(i_0_17177,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_10395]),
    [final] ).

cnf(i_0_17178,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_10396]),
    [final] ).

cnf(i_0_17179,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_10397]),
    [final] ).

cnf(i_0_17180,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_10398,c_0_6209]),
    [final] ).

cnf(i_0_17181,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_10098]),
    [final] ).

cnf(i_0_17182,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_17183,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_10399]),
    [final] ).

cnf(i_0_17184,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_10400]),
    [final] ).

cnf(i_0_17185,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_9467]),
    [final] ).

cnf(i_0_17186,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_9976]),
    [final] ).

cnf(i_0_17187,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_9977]),
    [final] ).

cnf(i_0_17188,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_10035]),
    [final] ).

cnf(i_0_17189,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_10401]),
    [final] ).

cnf(i_0_17190,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_10402]),
    [final] ).

cnf(i_0_17191,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_10403]),
    [final] ).

cnf(i_0_17192,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),esk116_3(X2,X3,X1)) = X2
    | hAPP(c_Finite__Set_Ocard(X1),X3) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8048]),
    [final] ).

cnf(i_0_17193,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_10404]),
    [final] ).

cnf(i_0_17194,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X2),X1))
    | ~ hBOOL(hAPP(X1,esk5_2(X1,X2)))
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10405]),
    [final] ).

cnf(i_0_17195,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X2),X1))
    | ~ hBOOL(hAPP(X1,esk4_2(X1,X2)))
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10406]),
    [final] ).

cnf(i_0_17196,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_10337]),
    [final] ).

cnf(i_0_17197,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_10338]),
    [final] ).

cnf(i_0_17198,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_10407]),
    [final] ).

cnf(i_0_17199,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_10408,c_0_6209]),
    [final] ).

cnf(i_0_17200,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_9849]),
    [final] ).

cnf(i_0_17201,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_9954]),
    [final] ).

cnf(i_0_17202,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_9746]),
    [final] ).

cnf(i_0_17203,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_10409]),
    [final] ).

cnf(i_0_17204,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_10410]),
    [final] ).

cnf(i_0_17205,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_10411]),
    [final] ).

cnf(i_0_17206,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_10218]),
    [final] ).

cnf(i_0_17207,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_10218]),
    [final] ).

cnf(i_0_17208,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_9799]),
    [final] ).

cnf(i_0_17209,plain,
    ( X2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk156_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_9849]),
    [final] ).

cnf(i_0_17210,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_17211,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_10412,c_0_7369]),
    [final] ).

cnf(i_0_17212,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_10413]),
    [final] ).

cnf(i_0_17213,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_10414]),
    [final] ).

cnf(i_0_17214,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_10414]),
    [final] ).

cnf(i_0_17215,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X1),X2),X3))
    | ~ class_HOL_Oequal(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10415]),
    [final] ).

cnf(i_0_17216,plain,
    hAPP(hAPP(c_Option_Omap(X1,X2),X3),hAPP(c_Option_Ooption_OSome(X1),X4)) = hAPP(c_Option_Ooption_OSome(X2),hAPP(X3,X4)),
    inference(split_conjunct,[status(thm)],[i_0_10416]),
    [final] ).

cnf(i_0_17217,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_10417]),
    [final] ).

cnf(i_0_17218,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_6197]),
    [final] ).

cnf(i_0_17219,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_6198]),
    [final] ).

cnf(i_0_17220,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_9921]),
    [final] ).

cnf(i_0_17221,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_10418]),
    [final] ).

cnf(i_0_17222,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_9593]),
    [final] ).

cnf(i_0_17223,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_10419]),
    [final] ).

cnf(i_0_17224,plain,
    ( c_Map_Odom(X3,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
    | X1 != hAPP(c_COMBK(tc_Option_Ooption(X2),X3),c_Option_Ooption_ONone(X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10383]),
    [final] ).

cnf(i_0_17225,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10420]),
    [final] ).

cnf(i_0_17226,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_9359]),
    [final] ).

cnf(i_0_17227,plain,
    ( hBOOL(hAPP(hAPP(X1,esk72_1(X1)),esk73_1(X1)))
    | hAPP(X1,esk72_1(X1)) = hAPP(X1,esk73_1(X1))
    | c_Equiv__Relations_Oequivp(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10035]),
    [final] ).

cnf(i_0_17228,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_10421]),
    [final] ).

cnf(i_0_17229,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_10422]),
    [final] ).

cnf(i_0_17230,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_10423]),
    [final] ).

cnf(i_0_17231,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_10424]),
    [final] ).

cnf(i_0_17232,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_10425]),
    [final] ).

cnf(i_0_17233,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_10426]),
    [final] ).

cnf(i_0_17234,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_10427]),
    [final] ).

cnf(i_0_17235,plain,
    ( X1 = X2
    | c_List_Oreplicate(X3,X1,X4) != c_List_Oreplicate(X3,X2,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_10413]),
    [final] ).

cnf(i_0_17236,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_10428]),
    [final] ).

cnf(i_0_17237,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_10428]),
    [final] ).

cnf(i_0_17238,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_10429]),
    [final] ).

cnf(i_0_17239,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_10430]),
    [final] ).

cnf(i_0_17240,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_10059]),
    [final] ).

cnf(i_0_17241,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_10431]),
    [final] ).

cnf(i_0_17242,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_10028]),
    [final] ).

cnf(i_0_17243,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_7123]),
    [final] ).

cnf(i_0_17244,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_10394]),
    [final] ).

cnf(i_0_17245,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_10395]),
    [final] ).

cnf(i_0_17246,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_10432]),
    [final] ).

cnf(i_0_17247,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))
    | 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_10350]),
    [final] ).

cnf(i_0_17248,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_10352]),
    [final] ).

cnf(i_0_17249,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_10311]),
    [final] ).

cnf(i_0_17250,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_9526]),
    [final] ).

cnf(i_0_17251,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_10433]),
    [final] ).

cnf(i_0_17252,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_10434]),
    [final] ).

cnf(i_0_17253,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_10435]),
    [final] ).

cnf(i_0_17254,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_10436]),
    [final] ).

cnf(i_0_17255,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_6494]),
    [final] ).

cnf(i_0_17256,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_10437]),
    [final] ).

cnf(i_0_17257,plain,
    ( hAPP(hAPP(c_Option_Omap(X2,X6),X4),X1) = hAPP(c_Option_Ooption_OSome(X6),X5)
    | X1 != hAPP(c_Option_Ooption_OSome(X2),X3)
    | hAPP(X4,X3) != X5 ),
    inference(split_conjunct,[status(thm)],[i_0_7319]),
    [final] ).

cnf(i_0_17258,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_10438]),
    [final] ).

cnf(i_0_17259,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_10215]),
    [final] ).

cnf(i_0_17260,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_10216]),
    [final] ).

cnf(i_0_17261,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),esk482_2(X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10283]),
    [final] ).

cnf(i_0_17262,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_10439]),
    [final] ).

cnf(i_0_17263,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_10234]),
    [final] ).

cnf(i_0_17264,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_10440]),
    [final] ).

cnf(i_0_17265,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_10441]),
    [final] ).

cnf(i_0_17266,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_10171]),
    [final] ).

cnf(i_0_17267,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_10442]),
    [final] ).

cnf(i_0_17268,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_10443]),
    [final] ).

cnf(i_0_17269,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk146_1(X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9784]),
    [final] ).

cnf(i_0_17270,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk470_2(X1,X2)),esk469_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_7416]),
    [final] ).

cnf(i_0_17271,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_10444]),
    [final] ).

cnf(i_0_17272,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_10444]),
    [final] ).

cnf(i_0_17273,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_10445]),
    [final] ).

cnf(i_0_17274,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_10446]),
    [final] ).

cnf(i_0_17275,plain,
    ( X2 = esk507_2(X1,X3)
    | ~ hBOOL(hAPP(X1,X2))
    | ~ c_List_Olist__ex1(X3,X1,c_Enum_Oenum__class_Oenum(X3))
    | ~ class_Enum_Oenum(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9696]),
    [final] ).

cnf(i_0_17276,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_10447]),
    [final] ).

cnf(i_0_17277,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_10404]),
    [final] ).

cnf(i_0_17278,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_9543]),
    [final] ).

cnf(i_0_17279,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_10448]),
    [final] ).

cnf(i_0_17280,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_9359]),
    [final] ).

cnf(i_0_17281,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_10449]),
    [final] ).

cnf(i_0_17282,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_17283,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_8796]),
    [final] ).

cnf(i_0_17284,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_10450]),
    [final] ).

cnf(i_0_17285,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_10451]),
    [final] ).

cnf(i_0_17286,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_10452]),
    [final] ).

cnf(i_0_17287,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_10453]),
    [final] ).

cnf(i_0_17288,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_10454,c_0_6768]),
    [final] ).

cnf(i_0_17289,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_10455]),
    [final] ).

cnf(i_0_17290,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_10456]),
    [final] ).

cnf(i_0_17291,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_10457]),
    [final] ).

cnf(i_0_17292,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_10458]),
    [final] ).

cnf(i_0_17293,plain,
    c_Predicate_Oconversep(X1,X2,c_Predicate_Oconversep(X2,X1,X3)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_10459]),
    [final] ).

cnf(i_0_17294,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_10460]),
    [final] ).

cnf(i_0_17295,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_9793]),
    [final] ).

cnf(i_0_17296,plain,
    ( hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(X1,esk150_1(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9612]),
    [final] ).

cnf(i_0_17297,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_10461]),
    [final] ).

cnf(i_0_17298,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_9824]),
    [final] ).

cnf(i_0_17299,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_9791]),
    [final] ).

cnf(i_0_17300,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_9792]),
    [final] ).

cnf(i_0_17301,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_10462]),
    [final] ).

cnf(i_0_17302,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_10463]),
    [final] ).

cnf(i_0_17303,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_10464]),
    [final] ).

cnf(i_0_17304,plain,
    ( X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk123_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_10465]),
    [final] ).

cnf(i_0_17305,plain,
    ( X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk133_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_10466]),
    [final] ).

cnf(i_0_17306,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_10467]),
    [final] ).

cnf(i_0_17307,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_10156]),
    [final] ).

cnf(i_0_17308,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | ~ c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10468]),
    [final] ).

cnf(i_0_17309,plain,
    ( X2 = esk524_3(X3,X4,X1)
    | c_FunDef_OTHE__default(X4,X3,X1) = X3
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8130]),
    [final] ).

cnf(i_0_17310,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_10123]),
    [final] ).

cnf(i_0_17311,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_10469]),
    [final] ).

cnf(i_0_17312,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_10470]),
    [final] ).

cnf(i_0_17313,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_10471]),
    [final] ).

cnf(i_0_17314,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_10472]),
    [final] ).

cnf(i_0_17315,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_10473]),
    [final] ).

cnf(i_0_17316,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_10360]),
    [final] ).

cnf(i_0_17317,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_10474]),
    [final] ).

cnf(i_0_17318,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_10475]),
    [final] ).

cnf(i_0_17319,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_10476]),
    [final] ).

cnf(i_0_17320,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_10477]),
    [final] ).

cnf(i_0_17321,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_10478]),
    [final] ).

cnf(i_0_17322,plain,
    ( hBOOL(hAPP(X2,esk35_2(X2,X1)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X2))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10479]),
    [final] ).

cnf(i_0_17323,plain,
    ( hBOOL(hAPP(X2,esk34_2(X2,X1)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X2))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10480]),
    [final] ).

cnf(i_0_17324,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_10481]),
    [final] ).

cnf(i_0_17325,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_10482]),
    [final] ).

cnf(i_0_17326,plain,
    ( X4 = c_Option_Ooption_ONone(X1)
    | hAPP(hAPP(c_Option_Omap(X1,X2),X3),X4) != c_Option_Ooption_ONone(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10483]),
    [final] ).

cnf(i_0_17327,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_10484]),
    [final] ).

cnf(i_0_17328,plain,
    c_Option_Oset(X1,hAPP(c_Option_Ooption_OSome(X1),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_10485]),
    [final] ).

cnf(i_0_17329,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10129]),
    [final] ).

cnf(i_0_17330,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_10486]),
    [final] ).

cnf(i_0_17331,plain,
    ( c_Orderings_Oorder__class_Omono(X2,X1,X3)
    | ~ class_Orderings_Oorder(X1)
    | ~ class_Orderings_Oorder(X2)
    | ~ c_Orderings_Oorder__class_Ostrict__mono(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10487]),
    [final] ).

cnf(i_0_17332,plain,
    ( hBOOL(hAPP(X1,c_Option_Ooption_ONone(X2)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X2)),X1))
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7569]),
    [final] ).

cnf(i_0_17333,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_10488]),
    [final] ).

cnf(i_0_17334,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_10489]),
    [final] ).

cnf(i_0_17335,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_10490]),
    [final] ).

cnf(i_0_17336,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_10491]),
    [final] ).

cnf(i_0_17337,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10347]),
    [final] ).

cnf(i_0_17338,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_10492]),
    [final] ).

cnf(i_0_17339,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_10493]),
    [final] ).

cnf(i_0_17340,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_10494]),
    [final] ).

cnf(i_0_17341,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_10495]),
    [final] ).

cnf(i_0_17342,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_10496]),
    [final] ).

cnf(i_0_17343,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_10008]),
    [final] ).

cnf(i_0_17344,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_10009]),
    [final] ).

cnf(i_0_17345,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_10497]),
    [final] ).

cnf(i_0_17346,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10108]),
    [final] ).

cnf(i_0_17347,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10498]),
    [final] ).

cnf(i_0_17348,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_10499]),
    [final] ).

cnf(i_0_17349,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10373]),
    [final] ).

cnf(i_0_17350,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_10373]),
    [final] ).

cnf(i_0_17351,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10111]),
    [final] ).

cnf(i_0_17352,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_10500,c_0_7157]),
    [final] ).

cnf(i_0_17353,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_10501]),
    [final] ).

cnf(i_0_17354,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_10502,c_0_7157]),
    [final] ).

cnf(i_0_17355,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_10503]),
    [final] ).

cnf(i_0_17356,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_10504]),
    [final] ).

cnf(i_0_17357,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_10505]),
    [final] ).

cnf(i_0_17358,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_10506]),
    [final] ).

cnf(i_0_17359,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_10507]),
    [final] ).

cnf(i_0_17360,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_10508]),
    [final] ).

cnf(i_0_17361,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_10509]),
    [final] ).

cnf(i_0_17362,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_10510]),
    [final] ).

cnf(i_0_17363,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_10511]),
    [final] ).

cnf(i_0_17364,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_10512]),
    [final] ).

cnf(i_0_17365,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_10513]),
    [final] ).

cnf(i_0_17366,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_10514]),
    [final] ).

cnf(i_0_17367,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_10515]),
    [final] ).

cnf(i_0_17368,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_10494]),
    [final] ).

cnf(i_0_17369,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_10495]),
    [final] ).

cnf(i_0_17370,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_10516]),
    [final] ).

cnf(i_0_17371,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_10517]),
    [final] ).

cnf(i_0_17372,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_10518]),
    [final] ).

cnf(i_0_17373,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_10495]),
    [final] ).

cnf(i_0_17374,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_10494]),
    [final] ).

cnf(i_0_17375,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_10519]),
    [final] ).

cnf(i_0_17376,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_10518]),
    [final] ).

cnf(i_0_17377,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_10517]),
    [final] ).

cnf(i_0_17378,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_10520]),
    [final] ).

cnf(i_0_17379,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_10521]),
    [final] ).

cnf(i_0_17380,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_10522]),
    [final] ).

cnf(i_0_17381,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_10523]),
    [final] ).

cnf(i_0_17382,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_10524]),
    [final] ).

cnf(i_0_17383,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_10525]),
    [final] ).

cnf(i_0_17384,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_10035]),
    [final] ).

cnf(i_0_17385,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_10303]),
    [final] ).

cnf(i_0_17386,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,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9860]),
    [final] ).

cnf(i_0_17387,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_10526]),
    [final] ).

cnf(i_0_17388,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10527]),
    [final] ).

cnf(i_0_17389,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10528]),
    [final] ).

cnf(i_0_17390,plain,
    ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,esk146_1(X1))))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9784]),
    [final] ).

cnf(i_0_17391,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_10529]),
    [final] ).

cnf(i_0_17392,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_10508]),
    [final] ).

cnf(i_0_17393,plain,
    ( c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2) = hAPP(X2,c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ c_Orderings_Oorder__class_Omono(X1,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10530]),
    [final] ).

cnf(i_0_17394,plain,
    ( c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2) = hAPP(X2,c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ c_Orderings_Oorder__class_Omono(X1,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10531]),
    [final] ).

cnf(i_0_17395,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_10159]),
    [final] ).

cnf(i_0_17396,plain,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_Orderings_Oorder__class_Ostrict__mono(X4,X5,X1)
    | ~ class_Orderings_Oorder(X5)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_10532]),
    [final] ).

cnf(i_0_17397,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_10533,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_17398,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_10534]),
    [final] ).

cnf(i_0_17399,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_10535]),
    [final] ).

cnf(i_0_17400,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_10536]),
    [final] ).

cnf(i_0_17401,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_10537]),
    [final] ).

cnf(i_0_17402,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_10538]),
    [final] ).

cnf(i_0_17403,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_10539]),
    [final] ).

cnf(i_0_17404,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_10540]),
    [final] ).

cnf(i_0_17405,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_9496]),
    [final] ).

cnf(i_0_17406,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_10541]),
    [final] ).

cnf(i_0_17407,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_8710]),
    [final] ).

cnf(i_0_17408,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_10542]),
    [final] ).

cnf(i_0_17409,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_10543]),
    [final] ).

cnf(i_0_17410,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_8712]),
    [final] ).

cnf(i_0_17411,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_10544]),
    [final] ).

cnf(i_0_17412,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_10545]),
    [final] ).

cnf(i_0_17413,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_10362]),
    [final] ).

cnf(i_0_17414,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_10546]),
    [final] ).

cnf(i_0_17415,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_10547]),
    [final] ).

cnf(i_0_17416,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_10548]),
    [final] ).

cnf(i_0_17417,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_10549]),
    [final] ).

cnf(i_0_17418,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_10550]),
    [final] ).

cnf(i_0_17419,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_10551]),
    [final] ).

cnf(i_0_17420,plain,
    ( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X2))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10552]),
    [final] ).

cnf(i_0_17421,plain,
    ( c_Wellfounded_Owf(X1,c_Wellfounded_Omlex__prod(X1,X3,X2))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10553]),
    [final] ).

cnf(i_0_17422,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_9828]),
    [final] ).

cnf(i_0_17423,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_10554]),
    [final] ).

cnf(i_0_17424,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_10391]),
    [final] ).

cnf(i_0_17425,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_10388]),
    [final] ).

cnf(i_0_17426,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X2)),X1))
    | ~ hBOOL(hAPP(X1,c_Option_Ooption_ONone(X2)))
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7600]),
    [final] ).

cnf(i_0_17427,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_10555]),
    [final] ).

cnf(i_0_17428,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_10556]),
    [final] ).

cnf(i_0_17429,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_10557]),
    [final] ).

cnf(i_0_17430,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_10558]),
    [final] ).

cnf(i_0_17431,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_10559]),
    [final] ).

cnf(i_0_17432,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_10560]),
    [final] ).

cnf(i_0_17433,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_10561]),
    [final] ).

cnf(i_0_17434,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_10562]),
    [final] ).

cnf(i_0_17435,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_10563]),
    [final] ).

cnf(i_0_17436,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_10564]),
    [final] ).

cnf(i_0_17437,plain,
    ( esk116_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_8048]),
    [final] ).

cnf(i_0_17438,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_10339]),
    [final] ).

cnf(i_0_17439,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_10565]),
    [final] ).

cnf(i_0_17440,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_10566]),
    [final] ).

cnf(i_0_17441,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_10567]),
    [final] ).

cnf(i_0_17442,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_10568]),
    [final] ).

cnf(i_0_17443,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_10569]),
    [final] ).

cnf(i_0_17444,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_10570]),
    [final] ).

cnf(i_0_17445,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_10571]),
    [final] ).

cnf(i_0_17446,plain,
    ( hBOOL(hAPP(X2,c_Orderings_Oord__class_OLeast(X1,X2)))
    | ~ class_Orderings_Owellorder(X1)
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10572]),
    [final] ).

cnf(i_0_17447,plain,
    ( hBOOL(hAPP(X2,c_Orderings_Oord__class_OLeast(X1,X2)))
    | ~ class_Orderings_Owellorder(X1)
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10573]),
    [final] ).

cnf(i_0_17448,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_10574]),
    [final] ).

cnf(i_0_17449,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_10565]),
    [final] ).

cnf(i_0_17450,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_10575]),
    [final] ).

cnf(i_0_17451,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_10576]),
    [final] ).

cnf(i_0_17452,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_10577]),
    [final] ).

cnf(i_0_17453,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_10578]),
    [final] ).

cnf(i_0_17454,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_10579]),
    [final] ).

cnf(i_0_17455,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_10308]),
    [final] ).

cnf(i_0_17456,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_10580]),
    [final] ).

cnf(i_0_17457,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    inference(split_conjunct,[status(thm)],[i_0_10581]),
    [final] ).

cnf(i_0_17458,plain,
    ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(split_conjunct,[status(thm)],[i_0_10582]),
    [final] ).

cnf(i_0_17459,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_10583]),
    [final] ).

cnf(i_0_17460,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_10584]),
    [final] ).

cnf(i_0_17461,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_10585]),
    [final] ).

cnf(i_0_17462,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_10586]),
    [final] ).

cnf(i_0_17463,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_10587]),
    [final] ).

cnf(i_0_17464,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_10294]),
    [final] ).

cnf(i_0_17465,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_10588]),
    [final] ).

cnf(i_0_17466,plain,
    hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10589]),
    [final] ).

cnf(i_0_17467,plain,
    hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10590]),
    [final] ).

cnf(i_0_17468,plain,
    hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10591]),
    [final] ).

cnf(i_0_17469,plain,
    hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10592]),
    [final] ).

cnf(i_0_17470,plain,
    hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10593]),
    [final] ).

cnf(i_0_17471,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_9791]),
    [final] ).

cnf(i_0_17472,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_9792]),
    [final] ).

cnf(i_0_17473,plain,
    ( X2 = hAPP(X3,X2)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | X2 != c_Inductive_Ocomplete__lattice__class_Olfp(X1,X3)
    | ~ c_Orderings_Oorder__class_Omono(X1,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10594]),
    [final] ).

cnf(i_0_17474,plain,
    ( X2 = hAPP(X3,X2)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | X2 != c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X3)
    | ~ c_Orderings_Oorder__class_Omono(X1,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10595]),
    [final] ).

cnf(i_0_17475,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_10596]),
    [final] ).

cnf(i_0_17476,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_10297]),
    [final] ).

cnf(i_0_17477,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_10298]),
    [final] ).

cnf(i_0_17478,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_10597]),
    [final] ).

cnf(i_0_17479,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_10598,c_0_8361]),
    [final] ).

cnf(i_0_17480,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_10599,c_0_8361]),
    [final] ).

cnf(i_0_17481,plain,
    ( hBOOL(X2)
    | ~ hBOOL(hAPP(hAPP(c_fimplies,X1),X2))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10600]),
    [final] ).

cnf(i_0_17482,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_10601]),
    [final] ).

cnf(i_0_17483,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_10602]),
    [final] ).

cnf(i_0_17484,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_10603]),
    [final] ).

cnf(i_0_17485,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_10604]),
    [final] ).

cnf(i_0_17486,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_10605]),
    [final] ).

cnf(i_0_17487,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_10606]),
    [final] ).

cnf(i_0_17488,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_10607]),
    [final] ).

cnf(i_0_17489,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_10608]),
    [final] ).

cnf(i_0_17490,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_10609]),
    [final] ).

cnf(i_0_17491,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_10610]),
    [final] ).

cnf(i_0_17492,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_10611]),
    [final] ).

cnf(i_0_17493,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_10612]),
    [final] ).

cnf(i_0_17494,plain,
    ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10613]),
    [final] ).

cnf(i_0_17495,plain,
    ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10614]),
    [final] ).

cnf(i_0_17496,plain,
    ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10615]),
    [final] ).

cnf(i_0_17497,plain,
    ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10292]),
    [final] ).

cnf(i_0_17498,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_10465]),
    [final] ).

cnf(i_0_17499,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_10466]),
    [final] ).

cnf(i_0_17500,plain,
    ( hBOOL(X1)
    | hBOOL(X2)
    | ~ hBOOL(hAPP(hAPP(c_fdisj,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10616]),
    [final] ).

cnf(i_0_17501,plain,
    ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ epred1_3(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7732]),
    [final] ).

cnf(i_0_17502,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_10340]),
    [final] ).

cnf(i_0_17503,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_10617]),
    [final] ).

cnf(i_0_17504,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_10618]),
    [final] ).

cnf(i_0_17505,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_10384]),
    [final] ).

cnf(i_0_17506,plain,
    ( X1 = X2
    | hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10619]),
    [final] ).

cnf(i_0_17507,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_10620]),
    [final] ).

cnf(i_0_17508,plain,
    ( hAPP(hAPP(X2,X4),X4) = X4
    | ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10621]),
    [final] ).

cnf(i_0_17509,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_10622]),
    [final] ).

cnf(i_0_17510,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_10297]),
    [final] ).

cnf(i_0_17511,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_10298]),
    [final] ).

cnf(i_0_17512,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_10623]),
    [final] ).

cnf(i_0_17513,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_10624]),
    [final] ).

cnf(i_0_17514,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_10577]),
    [final] ).

cnf(i_0_17515,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_10625]),
    [final] ).

cnf(i_0_17516,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_10626]),
    [final] ).

cnf(i_0_17517,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_10627]),
    [final] ).

cnf(i_0_17518,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_10628]),
    [final] ).

cnf(i_0_17519,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_10429]),
    [final] ).

cnf(i_0_17520,plain,
    ( hBOOL(X1)
    | ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10629]),
    [final] ).

cnf(i_0_17521,plain,
    ( hBOOL(X2)
    | ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10630]),
    [final] ).

cnf(i_0_17522,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_10631]),
    [final] ).

cnf(i_0_17523,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_10632]),
    [final] ).

cnf(i_0_17524,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_10633]),
    [final] ).

cnf(i_0_17525,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_10366]),
    [final] ).

cnf(i_0_17526,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_10045]),
    [final] ).

cnf(i_0_17527,plain,
    hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_10634]),
    [final] ).

cnf(i_0_17528,plain,
    hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10635]),
    [final] ).

cnf(i_0_17529,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_10636]),
    [final] ).

cnf(i_0_17530,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_10636]),
    [final] ).

cnf(i_0_17531,plain,
    ( hBOOL(hAPP(X2,X3))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ epred2_3(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7743]),
    [final] ).

cnf(i_0_17532,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_10637]),
    [final] ).

cnf(i_0_17533,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_10451]),
    [final] ).

cnf(i_0_17534,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_10453]),
    [final] ).

cnf(i_0_17535,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_10638]),
    [final] ).

cnf(i_0_17536,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_10639]),
    [final] ).

cnf(i_0_17537,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_fequal,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10640]),
    [final] ).

cnf(i_0_17538,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_10641]),
    [final] ).

cnf(i_0_17539,plain,
    ( hAPP(c_List_Oset(X1),esk482_2(X2,X1)) = X2
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10283]),
    [final] ).

cnf(i_0_17540,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_10439]),
    [final] ).

cnf(i_0_17541,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_10642]),
    [final] ).

cnf(i_0_17542,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_10643]),
    [final] ).

cnf(i_0_17543,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_10644]),
    [final] ).

cnf(i_0_17544,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_10645]),
    [final] ).

cnf(i_0_17545,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_10369]),
    [final] ).

cnf(i_0_17546,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_10646]),
    [final] ).

cnf(i_0_17547,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_10647]),
    [final] ).

cnf(i_0_17548,plain,
    hAPP(c_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_10648]),
    [final] ).

cnf(i_0_17549,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_10413]),
    [final] ).

cnf(i_0_17550,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_17551,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_10649]),
    [final] ).

cnf(i_0_17552,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_10650]),
    [final] ).

cnf(i_0_17553,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_10651]),
    [final] ).

cnf(i_0_17554,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_10652]),
    [final] ).

cnf(i_0_17555,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_10653]),
    [final] ).

cnf(i_0_17556,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_10611]),
    [final] ).

cnf(i_0_17557,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_10611]),
    [final] ).

cnf(i_0_17558,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_10654]),
    [final] ).

cnf(i_0_17559,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_10612]),
    [final] ).

cnf(i_0_17560,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_10612]),
    [final] ).

cnf(i_0_17561,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X3),X1),X2))
    | X1 != X2
    | ~ class_HOL_Oequal(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10415]),
    [final] ).

cnf(i_0_17562,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_9737]),
    [final] ).

cnf(i_0_17563,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_9737]),
    [final] ).

cnf(i_0_17564,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_10655]),
    [final] ).

cnf(i_0_17565,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_9953]),
    [final] ).

cnf(i_0_17566,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_10656]),
    [final] ).

cnf(i_0_17567,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_10657]),
    [final] ).

cnf(i_0_17568,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_10658]),
    [final] ).

cnf(i_0_17569,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_10659]),
    [final] ).

cnf(i_0_17570,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_10660]),
    [final] ).

cnf(i_0_17571,plain,
    c_Lazy__Sequence_Ohb__flat(X1,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1))))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10661]),
    [final] ).

cnf(i_0_17572,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_10662]),
    [final] ).

cnf(i_0_17573,plain,
    ( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))
    | ~ c_Wellfounded_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10468]),
    [final] ).

cnf(i_0_17574,plain,
    ( c_List_Olinorder__class_Osorted(X1,esk482_2(X2,X1))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10283]),
    [final] ).

cnf(i_0_17575,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_10439]),
    [final] ).

cnf(i_0_17576,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_10663]),
    [final] ).

cnf(i_0_17577,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_10664]),
    [final] ).

cnf(i_0_17578,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_10665]),
    [final] ).

cnf(i_0_17579,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_10431]),
    [final] ).

cnf(i_0_17580,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X1),X2),X2))
    | ~ class_HOL_Oequal(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10666]),
    [final] ).

cnf(i_0_17581,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10667]),
    [final] ).

cnf(i_0_17582,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_10664]),
    [final] ).

cnf(i_0_17583,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_10664]),
    [final] ).

cnf(i_0_17584,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_10668]),
    [final] ).

cnf(i_0_17585,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_17586,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_17587,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_17588,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_10669]),
    [final] ).

cnf(i_0_17589,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_10670]),
    [final] ).

cnf(i_0_17590,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_10671]),
    [final] ).

cnf(i_0_17591,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_10672]),
    [final] ).

cnf(i_0_17592,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_10673]),
    [final] ).

cnf(i_0_17593,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_10674]),
    [final] ).

cnf(i_0_17594,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_10675]),
    [final] ).

cnf(i_0_17595,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_10676]),
    [final] ).

cnf(i_0_17596,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_10677]),
    [final] ).

cnf(i_0_17597,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_10678]),
    [final] ).

cnf(i_0_17598,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_10679]),
    [final] ).

cnf(i_0_17599,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_10680]),
    [final] ).

cnf(i_0_17600,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_10681]),
    [final] ).

cnf(i_0_17601,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_10682]),
    [final] ).

cnf(i_0_17602,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_10683]),
    [final] ).

cnf(i_0_17603,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_9466]),
    [final] ).

cnf(i_0_17604,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_10305]),
    [final] ).

cnf(i_0_17605,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_10684]),
    [final] ).

cnf(i_0_17606,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_10685]),
    [final] ).

cnf(i_0_17607,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_10421]),
    [final] ).

cnf(i_0_17608,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_5256]),
    [final] ).

cnf(i_0_17609,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_5254]),
    [final] ).

cnf(i_0_17610,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_10686]),
    [final] ).

cnf(i_0_17611,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_10687]),
    [final] ).

cnf(i_0_17612,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_10688]),
    [final] ).

cnf(i_0_17613,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_5256]),
    [final] ).

cnf(i_0_17614,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_5254]),
    [final] ).

cnf(i_0_17615,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_10689]),
    [final] ).

cnf(i_0_17616,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_10689]),
    [final] ).

cnf(i_0_17617,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_10690,c_0_9036]),
    [final] ).

cnf(i_0_17618,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_10618]),
    [final] ).

cnf(i_0_17619,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_10691]),
    [final] ).

cnf(i_0_17620,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_10692]),
    [final] ).

cnf(i_0_17621,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_10693]),
    [final] ).

cnf(i_0_17622,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_10460]),
    [final] ).

cnf(i_0_17623,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_10694]),
    [final] ).

cnf(i_0_17624,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_10695]),
    [final] ).

cnf(i_0_17625,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_10696]),
    [final] ).

cnf(i_0_17626,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_10697]),
    [final] ).

cnf(i_0_17627,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_10698]),
    [final] ).

cnf(i_0_17628,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_10699]),
    [final] ).

cnf(i_0_17629,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_10700]),
    [final] ).

cnf(i_0_17630,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_10701]),
    [final] ).

cnf(i_0_17631,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_10702]),
    [final] ).

cnf(i_0_17632,plain,
    hAPP(hAPP(c_List_Omap(X1,X1),c_COMBI(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10703]),
    [final] ).

cnf(i_0_17633,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
    | ~ c_Wellfounded_OwfP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10704]),
    [final] ).

cnf(i_0_17634,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
    | ~ c_Wellfounded_OwfP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10212]),
    [final] ).

cnf(i_0_17635,plain,
    ( hBOOL(hAPP(hAPP(X2,X3),X3))
    | ~ c_Predicate_Oreflp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10705]),
    [final] ).

cnf(i_0_17636,plain,
    ( hBOOL(hAPP(hAPP(X2,X3),X3))
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10706]),
    [final] ).

cnf(i_0_17637,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_10494]),
    [final] ).

cnf(i_0_17638,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_10495]),
    [final] ).

cnf(i_0_17639,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_10405]),
    [final] ).

cnf(i_0_17640,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_10406]),
    [final] ).

cnf(i_0_17641,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_10611]),
    [final] ).

cnf(i_0_17642,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_10612]),
    [final] ).

cnf(i_0_17643,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_10481]),
    [final] ).

cnf(i_0_17644,plain,
    ( hAPP(hAPP(c_Option_Omap(X2,X3),X4),X1) = c_Option_Ooption_ONone(X3)
    | X1 != c_Option_Ooption_ONone(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10483]),
    [final] ).

cnf(i_0_17645,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_10482]),
    [final] ).

cnf(i_0_17646,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_10484]),
    [final] ).

cnf(i_0_17647,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_10707]),
    [final] ).

cnf(i_0_17648,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_10708]),
    [final] ).

cnf(i_0_17649,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_10709]),
    [final] ).

cnf(i_0_17650,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_10710]),
    [final] ).

cnf(i_0_17651,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,X2))
    | X3 != c_Hilbert__Choice_OEps(X4,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10711]),
    [final] ).

cnf(i_0_17652,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_10712]),
    [final] ).

cnf(i_0_17653,plain,
    hAPP(hAPP(c_Option_Omap(X1,X2),X3),c_Option_Ooption_ONone(X1)) = c_Option_Ooption_ONone(X2),
    inference(split_conjunct,[status(thm)],[i_0_10713]),
    [final] ).

cnf(i_0_17654,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_10714]),
    [final] ).

cnf(i_0_17655,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_10715]),
    [final] ).

cnf(i_0_17656,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_10716]),
    [final] ).

cnf(i_0_17657,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_10717]),
    [final] ).

cnf(i_0_17658,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_10718]),
    [final] ).

cnf(i_0_17659,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_10719]),
    [final] ).

cnf(i_0_17660,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_10720]),
    [final] ).

cnf(i_0_17661,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_10720]),
    [final] ).

cnf(i_0_17662,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_10721]),
    [final] ).

cnf(i_0_17663,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_10721]),
    [final] ).

cnf(i_0_17664,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_10722]),
    [final] ).

cnf(i_0_17665,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_10723]),
    [final] ).

cnf(i_0_17666,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_10724]),
    [final] ).

cnf(i_0_17667,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_10725]),
    [final] ).

cnf(i_0_17668,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_10726]),
    [final] ).

cnf(i_0_17669,plain,
    ( c_Inductive_Ocomplete__lattice__class_Olfp(X1,hAPP(c_COMBK(X1,X1),X2)) = X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10727]),
    [final] ).

cnf(i_0_17670,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_9641]),
    [final] ).

cnf(i_0_17671,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_10728,c_0_9036]),
    [final] ).

cnf(i_0_17672,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_9887]),
    [final] ).

cnf(i_0_17673,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_10729]),
    [final] ).

cnf(i_0_17674,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_10506]),
    [final] ).

cnf(i_0_17675,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_10507]),
    [final] ).

cnf(i_0_17676,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_10505]),
    [final] ).

cnf(i_0_17677,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_10730]),
    [final] ).

cnf(i_0_17678,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_10731]),
    [final] ).

cnf(i_0_17679,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10732]),
    [final] ).

cnf(i_0_17680,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10125]),
    [final] ).

cnf(i_0_17681,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10110]),
    [final] ).

cnf(i_0_17682,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_10479]),
    [final] ).

cnf(i_0_17683,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_10480]),
    [final] ).

cnf(i_0_17684,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_10733]),
    [final] ).

cnf(i_0_17685,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_10636]),
    [final] ).

cnf(i_0_17686,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_10734]),
    [final] ).

cnf(i_0_17687,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_10719]),
    [final] ).

cnf(i_0_17688,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_10719]),
    [final] ).

cnf(i_0_17689,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_10719]),
    [final] ).

cnf(i_0_17690,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_10719]),
    [final] ).

cnf(i_0_17691,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_10657]),
    [final] ).

cnf(i_0_17692,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_10735]),
    [final] ).

cnf(i_0_17693,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_10736]),
    [final] ).

cnf(i_0_17694,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_10737]),
    [final] ).

cnf(i_0_17695,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_10571]),
    [final] ).

cnf(i_0_17696,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_10738]),
    [final] ).

cnf(i_0_17697,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_10739]),
    [final] ).

cnf(i_0_17698,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_10740]),
    [final] ).

cnf(i_0_17699,plain,
    ~ c_List_Olist__ex1(X1,X2,c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10741]),
    [final] ).

cnf(i_0_17700,plain,
    ~ c_List_Olist__ex(X1,X2,c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10742]),
    [final] ).

cnf(i_0_17701,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_10743]),
    [final] ).

cnf(i_0_17702,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_17703,plain,
    hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10744]),
    [final] ).

cnf(i_0_17704,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10745]),
    [final] ).

cnf(i_0_17705,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10746]),
    [final] ).

cnf(i_0_17706,plain,
    hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1))),
    inference(split_conjunct,[status(thm)],[i_0_10747]),
    [final] ).

cnf(i_0_17707,plain,
    hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1))),
    inference(split_conjunct,[status(thm)],[i_0_10748]),
    [final] ).

cnf(i_0_17708,plain,
    hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_10749]),
    [final] ).

cnf(i_0_17709,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_10611]),
    [final] ).

cnf(i_0_17710,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_10611]),
    [final] ).

cnf(i_0_17711,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_10612]),
    [final] ).

cnf(i_0_17712,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_10612]),
    [final] ).

cnf(i_0_17713,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_10750]),
    [final] ).

cnf(i_0_17714,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_10750]),
    [final] ).

cnf(i_0_17715,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_10751]),
    [final] ).

cnf(i_0_17716,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_10751]),
    [final] ).

cnf(i_0_17717,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_10752,c_0_6242]),
    [final] ).

cnf(i_0_17718,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_10753,c_0_6104]),
    [final] ).

cnf(i_0_17719,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_10754,c_0_6209]),
    [final] ).

cnf(i_0_17720,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_10755]),
    [final] ).

cnf(i_0_17721,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_10756]),
    [final] ).

cnf(i_0_17722,plain,
    hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
    inference(split_conjunct,[status(thm)],[i_0_10757]),
    [final] ).

cnf(i_0_17723,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_10758,c_0_6209]),
    [final] ).

cnf(i_0_17724,plain,
    c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3) != c_Lazy__Sequence_Olazy__sequence_OEmpty(X1),
    inference(split_conjunct,[status(thm)],[i_0_10759]),
    [final] ).

cnf(i_0_17725,plain,
    c_Lazy__Sequence_Olazy__sequence_OEmpty(X1) != c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_10760]),
    [final] ).

cnf(i_0_17726,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_10761]),
    [final] ).

cnf(i_0_17727,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_10762]),
    [final] ).

cnf(i_0_17728,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_10763]),
    [final] ).

cnf(i_0_17729,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_10764]),
    [final] ).

cnf(i_0_17730,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_10765]),
    [final] ).

cnf(i_0_17731,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_10766]),
    [final] ).

cnf(i_0_17732,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_10767]),
    [final] ).

cnf(i_0_17733,plain,
    ( hBOOL(hAPP(hAPP(c_fconj,X1),X2))
    | ~ hBOOL(X1)
    | ~ hBOOL(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10768]),
    [final] ).

cnf(i_0_17734,plain,
    ( hBOOL(hAPP(X1,esk6_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_10638]),
    [final] ).

cnf(i_0_17735,plain,
    ( hBOOL(hAPP(X1,esk7_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_10639]),
    [final] ).

cnf(i_0_17736,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_10769]),
    [final] ).

cnf(i_0_17737,plain,
    ( X3 = c_List_Olist_ONil(X1)
    | hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10770]),
    [final] ).

cnf(i_0_17738,plain,
    ( X3 = c_List_Olist_ONil(X2)
    | X1 != hAPP(hAPP(c_List_Oappend(X2),X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10771]),
    [final] ).

cnf(i_0_17739,plain,
    ( X3 = c_List_Olist_ONil(X2)
    | X1 != hAPP(hAPP(c_List_Oappend(X2),X3),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10772]),
    [final] ).

cnf(i_0_17740,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_10773]),
    [final] ).

cnf(i_0_17741,plain,
    hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10774]),
    [final] ).

cnf(i_0_17742,plain,
    c_List_Olist_ONil(X1) != hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_10775]),
    [final] ).

cnf(i_0_17743,plain,
    hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_10776]),
    [final] ).

cnf(i_0_17744,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_10654]),
    [final] ).

cnf(i_0_17745,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_10777,c_0_6242]),
    [final] ).

cnf(i_0_17746,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X2),X1))
    | esk413_2(X1,X2) != esk414_2(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8405]),
    [final] ).

cnf(i_0_17747,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_10773]),
    [final] ).

cnf(i_0_17748,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_10778]),
    [final] ).

cnf(i_0_17749,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_10779]),
    [final] ).

cnf(i_0_17750,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_10780]),
    [final] ).

cnf(i_0_17751,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_10781]),
    [final] ).

cnf(i_0_17752,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_10782]),
    [final] ).

cnf(i_0_17753,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_10783]),
    [final] ).

cnf(i_0_17754,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_10784]),
    [final] ).

cnf(i_0_17755,plain,
    hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    inference(split_conjunct,[status(thm)],[fact_eq__int__code_I6_J]),
    [final] ).

cnf(i_0_17756,plain,
    hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(split_conjunct,[status(thm)],[fact_eq__int__code_I1_J]),
    [final] ).

cnf(i_0_17757,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_17758,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_17759,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_17760,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_17761,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_17762,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_10785]),
    [final] ).

cnf(i_0_17763,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_10786]),
    [final] ).

cnf(i_0_17764,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_10787]),
    [final] ).

cnf(i_0_17765,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_10788]),
    [final] ).

cnf(i_0_17766,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_10789]),
    [final] ).

cnf(i_0_17767,plain,
    hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
    inference(split_conjunct,[status(thm)],[i_0_10790]),
    [final] ).

cnf(i_0_17768,plain,
    X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
    inference(split_conjunct,[status(thm)],[i_0_10791]),
    [final] ).

cnf(i_0_17769,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_10792]),
    [final] ).

cnf(i_0_17770,plain,
    ( hBOOL(hAPP(hAPP(c_fdisj,X1),X2))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10793]),
    [final] ).

cnf(i_0_17771,plain,
    ( hBOOL(hAPP(hAPP(c_fdisj,X2),X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10794]),
    [final] ).

cnf(i_0_17772,plain,
    ( hBOOL(hAPP(hAPP(c_fimplies,X2),X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10795]),
    [final] ).

cnf(i_0_17773,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_10796]),
    [final] ).

cnf(i_0_17774,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_10797]),
    [final] ).

cnf(i_0_17775,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_10798]),
    [final] ).

cnf(i_0_17776,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_10799]),
    [final] ).

cnf(i_0_17777,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_10800]),
    [final] ).

cnf(i_0_17778,plain,
    ( c_List_Oremdups(X1,X2) = X2
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10801]),
    [final] ).

cnf(i_0_17779,plain,
    ( c_List_Oremdups(X1,X2) = X2
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10802]),
    [final] ).

cnf(i_0_17780,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_10803,c_0_8046]),
    [final] ).

cnf(i_0_17781,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_10804]),
    [final] ).

cnf(i_0_17782,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_10805]),
    [final] ).

cnf(i_0_17783,plain,
    ( hBOOL(X1)
    | hBOOL(hAPP(hAPP(c_fimplies,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10806]),
    [final] ).

cnf(i_0_17784,plain,
    c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10807]),
    [final] ).

cnf(i_0_17785,plain,
    c_Relation_Orefl__on(X1,X2,c_Relation_OId__on(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10808]),
    [final] ).

cnf(i_0_17786,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_10809]),
    [final] ).

cnf(i_0_17787,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_10809]),
    [final] ).

cnf(i_0_17788,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_10810]),
    [final] ).

cnf(i_0_17789,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_10810]),
    [final] ).

cnf(i_0_17790,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_10811]),
    [final] ).

cnf(i_0_17791,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_10811]),
    [final] ).

cnf(i_0_17792,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_10720]),
    [final] ).

cnf(i_0_17793,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_10721]),
    [final] ).

cnf(i_0_17794,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_10812]),
    [final] ).

cnf(i_0_17795,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_10813]),
    [final] ).

cnf(i_0_17796,plain,
    ( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10814]),
    [final] ).

cnf(i_0_17797,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_10815]),
    [final] ).

cnf(i_0_17798,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_10816]),
    [final] ).

cnf(i_0_17799,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_10817]),
    [final] ).

cnf(i_0_17800,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_10818]),
    [final] ).

cnf(i_0_17801,plain,
    ( c_Wellfounded_Owf(X2,X1)
    | esk311_2(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8294]),
    [final] ).

cnf(i_0_17802,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_10819]),
    [final] ).

cnf(i_0_17803,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_10820]),
    [final] ).

cnf(i_0_17804,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_10689]),
    [final] ).

cnf(i_0_17805,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_10821]),
    [final] ).

cnf(i_0_17806,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_10822]),
    [final] ).

cnf(i_0_17807,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_10823]),
    [final] ).

cnf(i_0_17808,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_10824]),
    [final] ).

cnf(i_0_17809,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_10494]),
    [final] ).

cnf(i_0_17810,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_10495]),
    [final] ).

cnf(i_0_17811,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_10825]),
    [final] ).

cnf(i_0_17812,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_10826]),
    [final] ).

cnf(i_0_17813,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_10827]),
    [final] ).

cnf(i_0_17814,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_10828]),
    [final] ).

cnf(i_0_17815,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_10829]),
    [final] ).

cnf(i_0_17816,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_10830]),
    [final] ).

cnf(i_0_17817,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_10831]),
    [final] ).

cnf(i_0_17818,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_10832]),
    [final] ).

cnf(i_0_17819,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_10833]),
    [final] ).

cnf(i_0_17820,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_10834]),
    [final] ).

cnf(i_0_17821,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_10835]),
    [final] ).

cnf(i_0_17822,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_10836]),
    [final] ).

cnf(i_0_17823,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_10837]),
    [final] ).

cnf(i_0_17824,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_10838]),
    [final] ).

cnf(i_0_17825,plain,
    ( c_List_Olinorder__class_Osorted(X1,esk469_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_7416]),
    [final] ).

cnf(i_0_17826,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_10839]),
    [final] ).

cnf(i_0_17827,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_10840]),
    [final] ).

cnf(i_0_17828,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_10422]),
    [final] ).

cnf(i_0_17829,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_10841]),
    [final] ).

cnf(i_0_17830,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_10842,c_0_6103]),
    [final] ).

cnf(i_0_17831,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_10843,c_0_6103]),
    [final] ).

cnf(i_0_17832,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_10844]),
    [final] ).

cnf(i_0_17833,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_10750]),
    [final] ).

cnf(i_0_17834,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_10751]),
    [final] ).

cnf(i_0_17835,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X1)),hAPP(c_Option_Ooption_OSome(X1),X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_10845]),
    [final] ).

cnf(i_0_17836,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_10846]),
    [final] ).

cnf(i_0_17837,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1) != c_Int_OMin,
    inference(rw,[status(thm)],[i_0_10847,c_0_6103]),
    [final] ).

cnf(i_0_17838,plain,
    c_Int_OMin != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1),
    inference(rw,[status(thm)],[i_0_10848,c_0_6103]),
    [final] ).

cnf(i_0_17839,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_10849]),
    [final] ).

cnf(i_0_17840,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_10850]),
    [final] ).

cnf(i_0_17841,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_10851]),
    [final] ).

cnf(i_0_17842,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_10852]),
    [final] ).

cnf(i_0_17843,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_10853]),
    [final] ).

cnf(i_0_17844,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_10854]),
    [final] ).

cnf(i_0_17845,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_10855]),
    [final] ).

cnf(i_0_17846,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_10856]),
    [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_10857]),
    [final] ).

cnf(i_0_17848,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_10858]),
    [final] ).

cnf(i_0_17849,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_10859]),
    [final] ).

cnf(i_0_17850,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_10860]),
    [final] ).

cnf(i_0_17851,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_10861]),
    [final] ).

cnf(i_0_17852,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_10862]),
    [final] ).

cnf(i_0_17853,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_10863]),
    [final] ).

cnf(i_0_17854,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_10864]),
    [final] ).

cnf(i_0_17855,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_10708]),
    [final] ).

cnf(i_0_17856,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_10865]),
    [final] ).

cnf(i_0_17857,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_10723]),
    [final] ).

cnf(i_0_17858,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_10618]),
    [final] ).

cnf(i_0_17859,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_10696]),
    [final] ).

cnf(i_0_17860,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_10696]),
    [final] ).

cnf(i_0_17861,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_10724]),
    [final] ).

cnf(i_0_17862,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_10866]),
    [final] ).

cnf(i_0_17863,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_10867]),
    [final] ).

cnf(i_0_17864,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_10868]),
    [final] ).

cnf(i_0_17865,plain,
    ( X2 = c_Option_Ooption_ONone(X1)
    | c_Option_Oset(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_10869]),
    [final] ).

cnf(i_0_17866,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_10870]),
    [final] ).

cnf(i_0_17867,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_10871]),
    [final] ).

cnf(i_0_17868,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_10872]),
    [final] ).

cnf(i_0_17869,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_10873]),
    [final] ).

cnf(i_0_17870,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_10874]),
    [final] ).

cnf(i_0_17871,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_10875]),
    [final] ).

cnf(i_0_17872,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_10876]),
    [final] ).

cnf(i_0_17873,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_10877]),
    [final] ).

cnf(i_0_17874,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X3),c_List_Olist_ONil(X3)),X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10878]),
    [final] ).

cnf(i_0_17875,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_10735]),
    [final] ).

cnf(i_0_17876,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_10865]),
    [final] ).

cnf(i_0_17877,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_10879]),
    [final] ).

cnf(i_0_17878,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_10880]),
    [final] ).

cnf(i_0_17879,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_10881]),
    [final] ).

cnf(i_0_17880,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_10882]),
    [final] ).

cnf(i_0_17881,plain,
    hAPP(c_Lazy__Sequence_Oyield(X1),c_Lazy__Sequence_Olazy__sequence_OEmpty(X1)) = c_Option_Ooption_ONone(tc_prod(X1,tc_Lazy__Sequence_Olazy__sequence(X1))),
    inference(split_conjunct,[status(thm)],[i_0_10883]),
    [final] ).

cnf(i_0_17882,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_10884]),
    [final] ).

cnf(i_0_17883,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_10885]),
    [final] ).

cnf(i_0_17884,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_10886]),
    [final] ).

cnf(i_0_17885,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_10887]),
    [final] ).

cnf(i_0_17886,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_10888]),
    [final] ).

cnf(i_0_17887,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_10889]),
    [final] ).

cnf(i_0_17888,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_10654]),
    [final] ).

cnf(i_0_17889,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_10730]),
    [final] ).

cnf(i_0_17890,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_10731]),
    [final] ).

cnf(i_0_17891,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_10605]),
    [final] ).

cnf(i_0_17892,plain,
    hAPP(c_Relation_ODomain(X1,X1),c_Relation_OId__on(X1,X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10890]),
    [final] ).

cnf(i_0_17893,plain,
    hAPP(c_Relation_ORange(X1,X1),c_Relation_OId__on(X1,X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10891]),
    [final] ).

cnf(i_0_17894,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_10892]),
    [final] ).

cnf(i_0_17895,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_10893]),
    [final] ).

cnf(i_0_17896,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_10894]),
    [final] ).

cnf(i_0_17897,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_10895]),
    [final] ).

cnf(i_0_17898,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_10896]),
    [final] ).

cnf(i_0_17899,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_10897]),
    [final] ).

cnf(i_0_17900,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_10898]),
    [final] ).

cnf(i_0_17901,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_10899]),
    [final] ).

cnf(i_0_17902,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_10900]),
    [final] ).

cnf(i_0_17903,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_10901]),
    [final] ).

cnf(i_0_17904,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_10902]),
    [final] ).

cnf(i_0_17905,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_10903]),
    [final] ).

cnf(i_0_17906,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_10904]),
    [final] ).

cnf(i_0_17907,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_10905]),
    [final] ).

cnf(i_0_17908,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_10906]),
    [final] ).

cnf(i_0_17909,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | c_List_Oremdups(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10801]),
    [final] ).

cnf(i_0_17910,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_10907]),
    [final] ).

cnf(i_0_17911,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_10908]),
    [final] ).

cnf(i_0_17912,plain,
    hAPP(c_List_Oset(X1),c_List_Oremdups(X1,X2)) = hAPP(c_List_Oset(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10909]),
    [final] ).

cnf(i_0_17913,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_10910]),
    [final] ).

cnf(i_0_17914,plain,
    ( X2 = X3
    | hAPP(c_List_Orev(X1),X2) != hAPP(c_List_Orev(X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10911]),
    [final] ).

cnf(i_0_17915,plain,
    ( X2 = X3
    | hAPP(c_Option_Ooption_OSome(X1),X2) != hAPP(c_Option_Ooption_OSome(X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10912]),
    [final] ).

cnf(i_0_17916,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_8366]),
    [final] ).

cnf(i_0_17917,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_10605]),
    [final] ).

cnf(i_0_17918,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_10913]),
    [final] ).

cnf(i_0_17919,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_10914]),
    [final] ).

cnf(i_0_17920,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_17921,plain,
    hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10915]),
    [final] ).

cnf(i_0_17922,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_10733]),
    [final] ).

cnf(i_0_17923,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_10916]),
    [final] ).

cnf(i_0_17924,plain,
    c_List_Osublist(X1,c_List_Olist_ONil(X1),X2) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10917]),
    [final] ).

cnf(i_0_17925,plain,
    c_List_OtakeWhile(X1,X2,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10918]),
    [final] ).

cnf(i_0_17926,plain,
    c_List_Oremove1(X1,X2,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10919]),
    [final] ).

cnf(i_0_17927,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_10736]),
    [final] ).

cnf(i_0_17928,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_10737]),
    [final] ).

cnf(i_0_17929,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_10920]),
    [final] ).

cnf(i_0_17930,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_10921]),
    [final] ).

cnf(i_0_17931,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_10922]),
    [final] ).

cnf(i_0_17932,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_10923]),
    [final] ).

cnf(i_0_17933,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_10924]),
    [final] ).

cnf(i_0_17934,plain,
    c_Option_Ooption_Ooption__size(X1,X2,c_Option_Ooption_ONone(X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_10925]),
    [final] ).

cnf(i_0_17935,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_10926]),
    [final] ).

cnf(i_0_17936,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_10927]),
    [final] ).

cnf(i_0_17937,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_10928]),
    [final] ).

cnf(i_0_17938,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_10733]),
    [final] ).

cnf(i_0_17939,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_10929]),
    [final] ).

cnf(i_0_17940,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_10929]),
    [final] ).

cnf(i_0_17941,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_10930]),
    [final] ).

cnf(i_0_17942,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_10930]),
    [final] ).

cnf(i_0_17943,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),c_Enum_Oenum__class_Oenum(X1)))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10931]),
    [final] ).

cnf(i_0_17944,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_10932]),
    [final] ).

cnf(i_0_17945,plain,
    ( hAPP(hAPP(c_List_Oappend(X2),X1),X3) = X3
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10769]),
    [final] ).

cnf(i_0_17946,plain,
    ( hAPP(hAPP(c_List_Oappend(X2),X3),X1) = X3
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10770]),
    [final] ).

cnf(i_0_17947,plain,
    ( X3 = hAPP(hAPP(c_List_Oappend(X2),X1),X3)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10772]),
    [final] ).

cnf(i_0_17948,plain,
    ( X3 = hAPP(hAPP(c_List_Oappend(X2),X3),X1)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10771]),
    [final] ).

cnf(i_0_17949,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_10933]),
    [final] ).

cnf(i_0_17950,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_10934]),
    [final] ).

cnf(i_0_17951,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_10935]),
    [final] ).

cnf(i_0_17952,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_10936]),
    [final] ).

cnf(i_0_17953,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_10937]),
    [final] ).

cnf(i_0_17954,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_10938]),
    [final] ).

cnf(i_0_17955,plain,
    c_List_Osplice(X1,c_List_Olist_ONil(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10939]),
    [final] ).

cnf(i_0_17956,plain,
    c_Lazy__Sequence_Oappend(X1,c_Lazy__Sequence_Olazy__sequence_OEmpty(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10940]),
    [final] ).

cnf(i_0_17957,plain,
    c_List_Osplice(X1,X2,c_List_Olist_ONil(X1)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10941]),
    [final] ).

cnf(i_0_17958,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_10942]),
    [final] ).

cnf(i_0_17959,plain,
    c_List_Olist__all(X1,X2,c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10943]),
    [final] ).

cnf(i_0_17960,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_10809]),
    [final] ).

cnf(i_0_17961,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_10719]),
    [final] ).

cnf(i_0_17962,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_10810]),
    [final] ).

cnf(i_0_17963,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_10811]),
    [final] ).

cnf(i_0_17964,plain,
    ( hAPP(c_List_Oset(X1),c_Enum_Oenum__class_Oenum(X1)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10944]),
    [final] ).

cnf(i_0_17965,plain,
    ( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_List_Oset(X1),c_Enum_Oenum__class_Oenum(X1))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10945]),
    [final] ).

cnf(i_0_17966,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10946]),
    [final] ).

cnf(i_0_17967,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10947]),
    [final] ).

cnf(i_0_17968,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10948]),
    [final] ).

cnf(i_0_17969,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10949]),
    [final] ).

cnf(i_0_17970,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_10950]),
    [final] ).

cnf(i_0_17971,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_10951]),
    [final] ).

cnf(i_0_17972,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_10952]),
    [final] ).

cnf(i_0_17973,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_10953]),
    [final] ).

cnf(i_0_17974,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2) = X2
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10954]),
    [final] ).

cnf(i_0_17975,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2) = X2
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10955]),
    [final] ).

cnf(i_0_17976,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_10956]),
    [final] ).

cnf(i_0_17977,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_10957]),
    [final] ).

cnf(i_0_17978,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_10958]),
    [final] ).

cnf(i_0_17979,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_10959]),
    [final] ).

cnf(i_0_17980,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_10960]),
    [final] ).

cnf(i_0_17981,plain,
    hAPP(c_New__DSequence_Opos__single(X1,X2),X3) = hAPP(c_Lazy__Sequence_Osingle(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10961]),
    [final] ).

cnf(i_0_17982,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_6250]),
    [final] ).

cnf(i_0_17983,plain,
    hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10962]),
    [final] ).

cnf(i_0_17984,plain,
    hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10963]),
    [final] ).

cnf(i_0_17985,plain,
    hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10964]),
    [final] ).

cnf(i_0_17986,plain,
    hAPP(c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10965]),
    [final] ).

cnf(i_0_17987,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_10966]),
    [final] ).

cnf(i_0_17988,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_10967]),
    [final] ).

cnf(i_0_17989,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_10968]),
    [final] ).

cnf(i_0_17990,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_17991,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_10969]),
    [final] ).

cnf(i_0_17992,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_10970]),
    [final] ).

cnf(i_0_17993,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_10971]),
    [final] ).

cnf(i_0_17994,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_10972]),
    [final] ).

cnf(i_0_17995,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_10973]),
    [final] ).

cnf(i_0_17996,plain,
    hAPP(c_Option_Omap(X1,X1),c_Fun_Oid(X1)) = c_Fun_Oid(tc_Option_Ooption(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10974]),
    [final] ).

cnf(i_0_17997,plain,
    hAPP(c_Option_Omap(X1,X1),c_COMBI(X1)) = c_Fun_Oid(tc_Option_Ooption(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10975]),
    [final] ).

cnf(i_0_17998,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_10976]),
    [final] ).

cnf(i_0_17999,plain,
    hAPP(c_List_Omap(X1,X1),c_COMBI(X1)) = c_Fun_Oid(tc_List_Olist(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10977]),
    [final] ).

cnf(i_0_18000,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_10978]),
    [final] ).

cnf(i_0_18001,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_10979]),
    [final] ).

cnf(i_0_18002,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_10817]),
    [final] ).

cnf(i_0_18003,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_10818]),
    [final] ).

cnf(i_0_18004,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_10980]),
    [final] ).

cnf(i_0_18005,plain,
    ( hAPP(c_List_Orev(X2),X1) = X3
    | X1 != hAPP(c_List_Orev(X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10981]),
    [final] ).

cnf(i_0_18006,plain,
    ( X2 = hAPP(c_List_Orev(X1),X3)
    | hAPP(c_List_Orev(X1),X2) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_10981]),
    [final] ).

cnf(i_0_18007,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_10982]),
    [final] ).

cnf(i_0_18008,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_10983]),
    [final] ).

cnf(i_0_18009,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_10984]),
    [final] ).

cnf(i_0_18010,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_10985]),
    [final] ).

cnf(i_0_18011,plain,
    hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olist_ONil(X1))),
    inference(split_conjunct,[status(thm)],[i_0_10986]),
    [final] ).

cnf(i_0_18012,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_9664]),
    [final] ).

cnf(i_0_18013,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_9626]),
    [final] ).

cnf(i_0_18014,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_9092]),
    [final] ).

cnf(i_0_18015,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_10789]),
    [final] ).

cnf(i_0_18016,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_10789]),
    [final] ).

cnf(i_0_18017,plain,
    hAPP(c_New__DSequence_Oneg__single(X1,X2),X3) = c_Lazy__Sequence_Ohb__single(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_10987]),
    [final] ).

cnf(i_0_18018,plain,
    c_List_Oremdups(X1,c_List_Oremdups(X1,X2)) = c_List_Oremdups(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_10988]),
    [final] ).

cnf(i_0_18019,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_10989]),
    [final] ).

cnf(i_0_18020,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_10990]),
    [final] ).

cnf(i_0_18021,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_10991]),
    [final] ).

cnf(i_0_18022,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_10992]),
    [final] ).

cnf(i_0_18023,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_10993]),
    [final] ).

cnf(i_0_18024,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_10994]),
    [final] ).

cnf(i_0_18025,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_10995]),
    [final] ).

cnf(i_0_18026,plain,
    c_Predicate_Oconversep(X1,X1,c_fequal) = c_fequal,
    inference(split_conjunct,[status(thm)],[i_0_10996]),
    [final] ).

cnf(i_0_18027,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_9179]),
    [final] ).

cnf(i_0_18028,plain,
    ( c_List_Otranspose(X2,X1) = c_List_Olist_ONil(tc_List_Olist(X2))
    | esk445_2(X1,X2) != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9318]),
    [final] ).

cnf(i_0_18029,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[i_0_10997]),
    [final] ).

cnf(i_0_18030,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[i_0_10998]),
    [final] ).

cnf(i_0_18031,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_10999]),
    [final] ).

cnf(i_0_18032,plain,
    ( X1 = c_Option_Ooption_ONone(X2)
    | X1 = hAPP(c_Option_Ooption_OSome(X2),esk68_2(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_11000]),
    [final] ).

cnf(i_0_18033,plain,
    ( X1 = hAPP(c_Option_Ooption_OSome(X2),esk67_2(X2,X1))
    | X1 = c_Option_Ooption_ONone(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11001]),
    [final] ).

cnf(i_0_18034,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_11002]),
    [final] ).

cnf(i_0_18035,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_11003]),
    [final] ).

cnf(i_0_18036,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_11004]),
    [final] ).

cnf(i_0_18037,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_10972]),
    [final] ).

cnf(i_0_18038,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_11005]),
    [final] ).

cnf(i_0_18039,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_11006]),
    [final] ).

cnf(i_0_18040,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_11007]),
    [final] ).

cnf(i_0_18041,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_11008]),
    [final] ).

cnf(i_0_18042,plain,
    ( ~ hBOOL(hAPP(c_fNot,X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11009]),
    [final] ).

cnf(i_0_18043,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_11010]),
    [final] ).

cnf(i_0_18044,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_11011]),
    [final] ).

cnf(i_0_18045,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_11012]),
    [final] ).

cnf(i_0_18046,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_11013]),
    [final] ).

cnf(i_0_18047,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_11014]),
    [final] ).

cnf(i_0_18048,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_11015]),
    [final] ).

cnf(i_0_18049,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_11016]),
    [final] ).

cnf(i_0_18050,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_11017]),
    [final] ).

cnf(i_0_18051,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_18052,plain,
    hAPP(c_List_Ofilter(X1,X2),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_11018]),
    [final] ).

cnf(i_0_18053,plain,
    c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),
    inference(split_conjunct,[status(thm)],[fact_mono__Suc]),
    [final] ).

cnf(i_0_18054,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts),
    inference(split_conjunct,[status(thm)],[conj_4]),
    [final] ).

cnf(i_0_18055,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,v_ts),
    inference(split_conjunct,[status(thm)],[conj_1]),
    [final] ).

cnf(i_0_18056,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11019]),
    [final] ).

cnf(i_0_18057,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11020]),
    [final] ).

cnf(i_0_18058,plain,
    ( c_Option_Oset(X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | X1 != c_Option_Ooption_ONone(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10869]),
    [final] ).

cnf(i_0_18059,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_11021]),
    [final] ).

cnf(i_0_18060,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_11022]),
    [final] ).

cnf(i_0_18061,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_18062,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_11023,c_0_6103]),
    [final] ).

cnf(i_0_18063,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_11024,c_0_6103]),
    [final] ).

cnf(i_0_18064,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_18065,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_11025]),
    [final] ).

cnf(i_0_18066,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_11026]),
    [final] ).

cnf(i_0_18067,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_10297]),
    [final] ).

cnf(i_0_18068,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_10298]),
    [final] ).

cnf(i_0_18069,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_11027]),
    [final] ).

cnf(i_0_18070,plain,
    c_Option_Oset(X1,c_Option_Ooption_ONone(X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_11028]),
    [final] ).

cnf(i_0_18071,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_11029]),
    [final] ).

cnf(i_0_18072,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_11030]),
    [final] ).

cnf(i_0_18073,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OPls) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11031]),
    [final] ).

cnf(i_0_18074,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OPls) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11032]),
    [final] ).

cnf(i_0_18075,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_11033]),
    [final] ).

cnf(i_0_18076,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_11034]),
    [final] ).

cnf(i_0_18077,plain,
    ( class_HOL_Oequal(tc_fun(X1,X2))
    | ~ class_Enum_Oenum(X1)
    | ~ class_HOL_Oequal(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11035]),
    [final] ).

cnf(i_0_18078,plain,
    ( class_Smallcheck_Osmall(tc_prod(X1,X2))
    | ~ class_Smallcheck_Osmall(X1)
    | ~ class_Smallcheck_Osmall(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11036]),
    [final] ).

cnf(i_0_18079,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_11037]),
    [final] ).

cnf(i_0_18080,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_11038]),
    [final] ).

cnf(i_0_18081,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_11039]),
    [final] ).

cnf(i_0_18082,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_11040]),
    [final] ).

cnf(i_0_18083,plain,
    ( class_Enum_Oenum(tc_sum(X1,X2))
    | ~ class_Enum_Oenum(X1)
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11041]),
    [final] ).

cnf(i_0_18084,plain,
    ( class_Enum_Oenum(tc_prod(X1,X2))
    | ~ class_Enum_Oenum(X1)
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11042]),
    [final] ).

cnf(i_0_18085,plain,
    ( class_Enum_Oenum(tc_fun(X1,X2))
    | ~ class_Enum_Oenum(X1)
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11043]),
    [final] ).

cnf(i_0_18086,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_18087,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_18088,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11044]),
    [final] ).

cnf(i_0_18089,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_10932]),
    [final] ).

cnf(i_0_18090,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_11045]),
    [final] ).

cnf(i_0_18091,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_11046]),
    [final] ).

cnf(i_0_18092,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_11047]),
    [final] ).

cnf(i_0_18093,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_10958]),
    [final] ).

cnf(i_0_18094,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_11048]),
    [final] ).

cnf(i_0_18095,plain,
    c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11049]),
    [final] ).

cnf(i_0_18096,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_11050]),
    [final] ).

cnf(i_0_18097,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_10308]),
    [final] ).

cnf(i_0_18098,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_10028]),
    [final] ).

cnf(i_0_18099,plain,
    ( X1 != hAPP(c_Option_Ooption_OSome(X2),X3)
    | X1 != c_Option_Ooption_ONone(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11000]),
    [final] ).

cnf(i_0_18100,plain,
    ( X1 != c_Option_Ooption_ONone(X2)
    | X1 != hAPP(c_Option_Ooption_OSome(X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_11001]),
    [final] ).

cnf(i_0_18101,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_11051,c_0_6242]),
    [final] ).

cnf(i_0_18102,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_11052,c_0_6103]),
    [final] ).

cnf(i_0_18103,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_11053,c_0_6104]),
    [final] ).

cnf(i_0_18104,plain,
    ( X1 = X2
    | hAPP(c_Code__Numeral_Onat__of,X1) != hAPP(c_Code__Numeral_Onat__of,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11054]),
    [final] ).

cnf(i_0_18105,plain,
    ( X1 = X2
    | hAPP(c_Code__Numeral_Onat__of,X1) != hAPP(c_Code__Numeral_Onat__of,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11055]),
    [final] ).

cnf(i_0_18106,plain,
    ( X1 = X2
    | hAPP(c_Code__Numeral_Oof__nat,X1) != hAPP(c_Code__Numeral_Oof__nat,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11056]),
    [final] ).

cnf(i_0_18107,plain,
    ( X1 = X2
    | hAPP(c_Int_ORep__Integ,X1) != hAPP(c_Int_ORep__Integ,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11057]),
    [final] ).

cnf(i_0_18108,plain,
    ( X1 = X2
    | hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11058]),
    [final] ).

cnf(i_0_18109,plain,
    ( X1 = X2
    | hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11059]),
    [final] ).

cnf(i_0_18110,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_11060]),
    [final] ).

cnf(i_0_18111,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_11061]),
    [final] ).

cnf(i_0_18112,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_11062]),
    [final] ).

cnf(i_0_18113,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X1)),c_Option_Ooption_ONone(X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_11063]),
    [final] ).

cnf(i_0_18114,plain,
    c_Wellfounded_Owf(X1,c_List_Omeasures(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11064]),
    [final] ).

cnf(i_0_18115,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_11007]),
    [final] ).

cnf(i_0_18116,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_11008]),
    [final] ).

cnf(i_0_18117,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_11006]),
    [final] ).

cnf(i_0_18118,plain,
    ( ~ class_Rings_Osemiring__1(X1)
    | ~ c_Int_Oiszero(X1,c_Groups_Oone__class_Oone(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_11065]),
    [final] ).

cnf(i_0_18119,plain,
    c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11066]),
    [final] ).

cnf(i_0_18120,plain,
    hAPP(c_Option_Ooption_OSome(X1),X2) != c_Option_Ooption_ONone(X1),
    inference(split_conjunct,[status(thm)],[i_0_11067]),
    [final] ).

cnf(i_0_18121,plain,
    c_Option_Ooption_ONone(X1) != hAPP(c_Option_Ooption_OSome(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_11068]),
    [final] ).

cnf(i_0_18122,plain,
    c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11069]),
    [final] ).

cnf(i_0_18123,plain,
    c_HOL_OThe(X1,hAPP(c_fequal,X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11070]),
    [final] ).

cnf(i_0_18124,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_11071]),
    [final] ).

cnf(i_0_18125,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_11072]),
    [final] ).

cnf(i_0_18126,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_11073]),
    [final] ).

cnf(i_0_18127,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_11074]),
    [final] ).

cnf(i_0_18128,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_11075]),
    [final] ).

cnf(i_0_18129,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_11076]),
    [final] ).

cnf(i_0_18130,plain,
    ( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
    | ~ class_Lattices_Obounded__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11077]),
    [final] ).

cnf(i_0_18131,plain,
    ( class_Groups_Ouminus(tc_fun(X2,X1))
    | ~ class_Groups_Ouminus(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11078]),
    [final] ).

cnf(i_0_18132,plain,
    ( class_Lattices_Oboolean__algebra(tc_fun(X2,X1))
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11079]),
    [final] ).

cnf(i_0_18133,plain,
    ( class_Lattices_Obounded__lattice__top(tc_fun(X2,X1))
    | ~ class_Lattices_Obounded__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11080]),
    [final] ).

cnf(i_0_18134,plain,
    ( class_Orderings_Otop(tc_fun(X2,X1))
    | ~ class_Orderings_Otop(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11081]),
    [final] ).

cnf(i_0_18135,plain,
    ( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11082]),
    [final] ).

cnf(i_0_18136,plain,
    ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11083]),
    [final] ).

cnf(i_0_18137,plain,
    ( class_Lattices_Osemilattice__inf(tc_fun(X2,X1))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11084]),
    [final] ).

cnf(i_0_18138,plain,
    ( class_Groups_Ominus(tc_fun(X2,X1))
    | ~ class_Groups_Ominus(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11085]),
    [final] ).

cnf(i_0_18139,plain,
    ( class_Lattices_Obounded__lattice__bot(tc_fun(X2,X1))
    | ~ class_Lattices_Obounded__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11086]),
    [final] ).

cnf(i_0_18140,plain,
    ( class_Lattices_Olattice(tc_fun(X2,X1))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11087]),
    [final] ).

cnf(i_0_18141,plain,
    ( class_Lattices_Osemilattice__sup(tc_fun(X2,X1))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11088]),
    [final] ).

cnf(i_0_18142,plain,
    ( class_Orderings_Oord(tc_fun(X2,X1))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11089]),
    [final] ).

cnf(i_0_18143,plain,
    ( class_Orderings_Oorder(tc_fun(X2,X1))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11090]),
    [final] ).

cnf(i_0_18144,plain,
    ( class_Orderings_Obot(tc_fun(X2,X1))
    | ~ class_Orderings_Obot(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11091]),
    [final] ).

cnf(i_0_18145,plain,
    ( class_Orderings_Opreorder(tc_fun(X2,X1))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11092]),
    [final] ).

cnf(i_0_18146,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_11021]),
    [final] ).

cnf(i_0_18147,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_5265]),
    [final] ).

cnf(i_0_18148,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_11022]),
    [final] ).

cnf(i_0_18149,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | ~ c_Nitpick_Owf_H(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10028]),
    [final] ).

cnf(i_0_18150,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11093]),
    [final] ).

cnf(i_0_18151,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_11029]),
    [final] ).

cnf(i_0_18152,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_11030]),
    [final] ).

cnf(i_0_18153,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_11094]),
    [final] ).

cnf(i_0_18154,plain,
    hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11095]),
    [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_11096]),
    [final] ).

cnf(i_0_18156,plain,
    hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11097]),
    [final] ).

cnf(i_0_18157,plain,
    hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11098]),
    [final] ).

cnf(i_0_18158,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_11099]),
    [final] ).

cnf(i_0_18159,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_11100]),
    [final] ).

cnf(i_0_18160,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_11101]),
    [final] ).

cnf(i_0_18161,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_11102]),
    [final] ).

cnf(i_0_18162,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_11103]),
    [final] ).

cnf(i_0_18163,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_11104]),
    [final] ).

cnf(i_0_18164,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_11105]),
    [final] ).

cnf(i_0_18165,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | c_List_Oremdups(X1,X2) != c_List_Olist_ONil(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11106]),
    [final] ).

cnf(i_0_18166,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | c_List_Olist_ONil(X1) != c_List_Oremdups(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11107]),
    [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_Groups_Osgn__if(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10141]),
    [final] ).

cnf(i_0_18168,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_11060]),
    [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_11045]),
    [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_11046]),
    [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_11047]),
    [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_11108]),
    [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_11109]),
    [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_11110]),
    [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_11111]),
    [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)
    | esk400_1(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_9948]),
    [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_11112]),
    [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_11113]),
    [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_9928]),
    [final] ).

cnf(i_0_18184,plain,
    class_Nat_Osize(tc_Nitpick_Opair__box(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11114]),
    [final] ).

cnf(i_0_18185,plain,
    class_Nat_Osize(tc_sum(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11115]),
    [final] ).

cnf(i_0_18186,plain,
    class_Nat_Osize(tc_prod(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11116]),
    [final] ).

cnf(i_0_18187,plain,
    class_HOL_Oequal(tc_Nitpick_Opair__box(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11117]),
    [final] ).

cnf(i_0_18188,plain,
    class_HOL_Oequal(tc_sum(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11118]),
    [final] ).

cnf(i_0_18189,plain,
    class_HOL_Oequal(tc_prod(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11119]),
    [final] ).

cnf(i_0_18190,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_7416]),
    [final] ).

cnf(i_0_18191,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_11099]),
    [final] ).

cnf(i_0_18192,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_11120]),
    [final] ).

cnf(i_0_18193,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_11121]),
    [final] ).

cnf(i_0_18194,plain,
    ( c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11122]),
    [final] ).

cnf(i_0_18195,plain,
    ( c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11123]),
    [final] ).

cnf(i_0_18196,plain,
    ( c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11124]),
    [final] ).

cnf(i_0_18197,plain,
    ( c_List_Oremdups(X2,X1) = c_List_Olist_ONil(X2)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11106]),
    [final] ).

cnf(i_0_18198,plain,
    ( c_List_Olist_ONil(X2) = c_List_Oremdups(X2,X1)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11107]),
    [final] ).

cnf(i_0_18199,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_11100]),
    [final] ).

cnf(i_0_18200,plain,
    hAPP(c_New__DSequence_Opos__empty(X1),X2) = c_Lazy__Sequence_Oempty(X1),
    inference(split_conjunct,[status(thm)],[i_0_11125]),
    [final] ).

cnf(i_0_18201,plain,
    c_List_Oremdups(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_11126]),
    [final] ).

cnf(i_0_18202,plain,
    c_List_Obutlast(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_11127]),
    [final] ).

cnf(i_0_18203,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_11128]),
    [final] ).

cnf(i_0_18204,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_11129]),
    [final] ).

cnf(i_0_18205,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_11130]),
    [final] ).

cnf(i_0_18206,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_11131]),
    [final] ).

cnf(i_0_18207,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_11132]),
    [final] ).

cnf(i_0_18208,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_11133]),
    [final] ).

cnf(i_0_18209,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_18210,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_18211,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_18212,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_18213,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_18214,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_18215,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_18216,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_11134]),
    [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_11135]),
    [final] ).

cnf(i_0_18218,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(split_conjunct,[status(thm)],[i_0_11136]),
    [final] ).

cnf(i_0_18219,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_11137]),
    [final] ).

cnf(i_0_18220,plain,
    hAPP(c_Fun_Oid(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11138]),
    [final] ).

cnf(i_0_18221,plain,
    hAPP(c_Fun_Oid(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11139]),
    [final] ).

cnf(i_0_18222,plain,
    hAPP(c_COMBI(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11140]),
    [final] ).

cnf(i_0_18223,plain,
    hAPP(c_Set_OCollect(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11141]),
    [final] ).

cnf(i_0_18224,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_10388]),
    [final] ).

cnf(i_0_18225,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_5292]),
    [final] ).

cnf(i_0_18226,plain,
    ( c_Nitpick_Onat__gcd(X2,X1) = X2
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10578]),
    [final] ).

cnf(i_0_18227,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_18228,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_11142]),
    [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_11143]),
    [final] ).

cnf(i_0_18230,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_10914]),
    [final] ).

cnf(i_0_18231,plain,
    X1 = hAPP(c_Int_OAbs__Integ,esk297_1(X1)),
    inference(split_conjunct,[status(thm)],[i_0_8946]),
    [final] ).

cnf(i_0_18232,plain,
    c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11144]),
    [final] ).

cnf(i_0_18233,plain,
    c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11145]),
    [final] ).

cnf(i_0_18234,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_18235,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_18236,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_18237,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_18238,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_18239,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_18240,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_18241,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_18242,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_18243,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_18244,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_18245,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_18246,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11146]),
    [final] ).

cnf(i_0_18247,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11147]),
    [final] ).

cnf(i_0_18248,plain,
    ( class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X1))
    | ~ class_Lazy__Sequence_Osmall__lazy(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11148]),
    [final] ).

cnf(i_0_18249,plain,
    ( class_Finite__Set_Ofinite(tc_Option_Ooption(X1))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11149]),
    [final] ).

cnf(i_0_18250,plain,
    ( class_Enum_Oenum(tc_Option_Ooption(X1))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11150]),
    [final] ).

cnf(i_0_18251,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_18252,plain,
    c_Equiv__Relations_Oequivp(X1,c_fequal),
    inference(split_conjunct,[status(thm)],[i_0_11151]),
    [final] ).

cnf(i_0_18253,plain,
    ( c_HOL_Oequal__class_Oequal(X1) = c_fequal
    | ~ class_HOL_Oequal(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11152]),
    [final] ).

cnf(i_0_18254,plain,
    ( c_fequal = c_HOL_Oequal__class_Oequal(X1)
    | ~ class_HOL_Oequal(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11153]),
    [final] ).

cnf(i_0_18255,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(split_conjunct,[status(thm)],[fact_wf__pred__nat]),
    [final] ).

cnf(i_0_18256,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(split_conjunct,[status(thm)],[fact_wf__less__than]),
    [final] ).

cnf(i_0_18257,plain,
    class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11154]),
    [final] ).

cnf(i_0_18258,plain,
    class_Nat_Osize(tc_List_Olist(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11155]),
    [final] ).

cnf(i_0_18259,plain,
    class_Nat_Osize(tc_Option_Ooption(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11156]),
    [final] ).

cnf(i_0_18260,plain,
    class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11157]),
    [final] ).

cnf(i_0_18261,plain,
    class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11158]),
    [final] ).

cnf(i_0_18262,plain,
    class_HOL_Oequal(tc_List_Olist(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11159]),
    [final] ).

cnf(i_0_18263,plain,
    class_HOL_Oequal(tc_Option_Ooption(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11160]),
    [final] ).

cnf(i_0_18264,plain,
    class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11161]),
    [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_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_18267,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_18268,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_18269,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_18270,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_18271,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_18272,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_18273,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_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_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_18276,plain,
    ~ hBOOL(c_fFalse),
    inference(split_conjunct,[status(thm)],[i_0_11162]),
    [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_Lazy__Sequence_Osmall__lazy(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lazy__Sequence_Osmall__lazy]),
    [final] ).

cnf(i_0_18279,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_18280,plain,
    class_Nat_Osize(tc_Code__Evaluation_Oterm),
    inference(split_conjunct,[status(thm)],[arity_Code____Evaluation__Oterm__Nat_Osize]),
    [final] ).

cnf(i_0_18281,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_18282,plain,
    class_Nat_Osize(tc_Product__Type_Ounit),
    inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Nat_Osize]),
    [final] ).

cnf(i_0_18283,plain,
    class_Nat_Osize(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Nat_Osize]),
    [final] ).

cnf(i_0_18284,plain,
    class_Nat_Osize(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Nat_Osize]),
    [final] ).

cnf(i_0_18285,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_18286,plain,
    class_Groups_Osemigroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osemigroup__add]),
    [final] ).

cnf(i_0_18287,plain,
    class_Groups_Osemigroup__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Osemigroup__add]),
    [final] ).

cnf(i_0_18288,plain,
    class_HOL_Oequal(tc_Code__Evaluation_Oterm),
    inference(split_conjunct,[status(thm)],[arity_Code____Evaluation__Oterm__HOL_Oequal]),
    [final] ).

cnf(i_0_18289,plain,
    class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__HOL_Oequal]),
    [final] ).

cnf(i_0_18290,plain,
    class_HOL_Oequal(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__HOL_Oequal]),
    [final] ).

cnf(i_0_18291,plain,
    class_HOL_Oequal(tc_Product__Type_Ounit),
    inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__HOL_Oequal]),
    [final] ).

cnf(i_0_18292,plain,
    class_HOL_Oequal(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__HOL_Oequal]),
    [final] ).

cnf(i_0_18293,plain,
    class_HOL_Oequal(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__HOL_Oequal]),
    [final] ).

cnf(i_0_18294,plain,
    class_Smallcheck_Osmall(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Smallcheck_Osmall]),
    [final] ).

cnf(i_0_18295,plain,
    class_Smallcheck_Osmall(tc_Product__Type_Ounit),
    inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Smallcheck_Osmall]),
    [final] ).

cnf(i_0_18296,plain,
    class_Groups_Oabs__if(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]),
    [final] ).

cnf(i_0_18297,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_18298,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_18299,plain,
    class_Groups_Osgn__if(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]),
    [final] ).

cnf(i_0_18300,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_18301,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_18302,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_18303,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_18304,plain,
    class_Rings_Osemiring__1(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]),
    [final] ).

cnf(i_0_18305,plain,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]),
    [final] ).

cnf(i_0_18306,plain,
    class_Int_Onumber__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]),
    [final] ).

cnf(i_0_18307,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_18308,plain,
    class_Int_Onumber(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber]),
    [final] ).

cnf(i_0_18309,plain,
    class_Int_Onumber(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Int_Onumber]),
    [final] ).

cnf(i_0_18310,plain,
    class_Divides_Oring__div(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Oring__div]),
    [final] ).

cnf(i_0_18311,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_18312,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]),
    [final] ).

cnf(i_0_18313,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]),
    [final] ).

cnf(i_0_18314,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_18315,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1]),
    [final] ).

cnf(i_0_18316,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_18317,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]),
    [final] ).

cnf(i_0_18318,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]),
    [final] ).

cnf(i_0_18319,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_18320,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Power_Opower]),
    [final] ).

cnf(i_0_18321,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Power_Opower]),
    [final] ).

cnf(i_0_18322,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_18323,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_18324,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_18325,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]),
    [final] ).

cnf(i_0_18326,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]),
    [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_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_18331,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_18332,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_18333,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_18334,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_18335,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_18336,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_18337,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]),
    [final] ).

cnf(i_0_18338,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]),
    [final] ).

cnf(i_0_18339,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_18340,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_18341,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_18342,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_18343,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_18344,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_18345,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]),
    [final] ).

cnf(i_0_18346,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_18347,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_18348,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_18349,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_18350,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_18351,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_18352,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_18353,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_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_Olinordered__ab__group__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__group__add]),
    [final] ).

cnf(i_0_18358,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_18359,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_18360,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_18361,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_18362,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]),
    [final] ).

cnf(i_0_18363,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
    [final] ).

cnf(i_0_18364,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_18365,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ozero]),
    [final] ).

cnf(i_0_18366,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
    [final] ).

cnf(i_0_18367,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_18368,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_18369,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_18370,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]),
    [final] ).

cnf(i_0_18371,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_18372,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring]),
    [final] ).

cnf(i_0_18373,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]),
    [final] ).

cnf(i_0_18374,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_18375,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]),
    [final] ).

cnf(i_0_18376,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]),
    [final] ).

cnf(i_0_18377,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_18378,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_18379,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_18380,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_18381,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_18382,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_18383,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_18384,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_18385,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_18386,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_18387,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_18388,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_18389,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_18390,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_18391,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_18392,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_18393,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_18394,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_18395,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_18396,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_18397,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_18398,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_18399,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_18400,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_18401,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_18402,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_18403,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]),
    [final] ).

cnf(i_0_18404,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
    [final] ).

cnf(i_0_18405,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_18406,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]),
    [final] ).

cnf(i_0_18407,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]),
    [final] ).

cnf(i_0_18408,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_18409,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_18410,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_18411,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_18412,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oone]),
    [final] ).

cnf(i_0_18413,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
    [final] ).

cnf(i_0_18414,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]),
    [final] ).

cnf(i_0_18415,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring]),
    [final] ).

cnf(i_0_18416,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oidom]),
    [final] ).

cnf(i_0_18417,plain,
    class_Groups_Ouminus(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ouminus]),
    [final] ).

cnf(i_0_18418,plain,
    class_Groups_Ouminus(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]),
    [final] ).

cnf(i_0_18419,plain,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]),
    [final] ).

cnf(i_0_18420,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]),
    [final] ).

cnf(i_0_18421,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_18422,plain,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]),
    [final] ).

cnf(i_0_18423,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_18424,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_18425,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_18426,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_18427,plain,
    class_Orderings_Otop(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]),
    [final] ).

cnf(i_0_18428,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_18429,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_18430,plain,
    class_Lattices_Odistrib__lattice(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Odistrib__lattice]),
    [final] ).

cnf(i_0_18431,plain,
    class_Lattices_Odistrib__lattice(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Odistrib__lattice]),
    [final] ).

cnf(i_0_18432,plain,
    class_Lattices_Odistrib__lattice(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Odistrib__lattice]),
    [final] ).

cnf(i_0_18433,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_18434,plain,
    class_Lattices_Osemilattice__inf(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__inf]),
    [final] ).

cnf(i_0_18435,plain,
    class_Lattices_Osemilattice__inf(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__inf]),
    [final] ).

cnf(i_0_18436,plain,
    class_Lattices_Osemilattice__inf(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__inf]),
    [final] ).

cnf(i_0_18437,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_18438,plain,
    class_Groups_Ominus(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ominus]),
    [final] ).

cnf(i_0_18439,plain,
    class_Groups_Ominus(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ominus]),
    [final] ).

cnf(i_0_18440,plain,
    class_Groups_Ominus(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ominus]),
    [final] ).

cnf(i_0_18441,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_18442,plain,
    class_Lattices_Olattice(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Olattice]),
    [final] ).

cnf(i_0_18443,plain,
    class_Lattices_Olattice(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Olattice]),
    [final] ).

cnf(i_0_18444,plain,
    class_Lattices_Olattice(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Olattice]),
    [final] ).

cnf(i_0_18445,plain,
    class_Lattices_Osemilattice__sup(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__sup]),
    [final] ).

cnf(i_0_18446,plain,
    class_Lattices_Osemilattice__sup(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__sup]),
    [final] ).

cnf(i_0_18447,plain,
    class_Lattices_Osemilattice__sup(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__sup]),
    [final] ).

cnf(i_0_18448,plain,
    class_Orderings_Owellorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Owellorder]),
    [final] ).

cnf(i_0_18449,plain,
    class_Enum_Oenum(tc_Product__Type_Ounit),
    inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Enum_Oenum]),
    [final] ).

cnf(i_0_18450,plain,
    class_Enum_Oenum(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Enum_Oenum]),
    [final] ).

cnf(i_0_18451,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_18452,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oord]),
    [final] ).

cnf(i_0_18453,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
    [final] ).

cnf(i_0_18454,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
    [final] ).

cnf(i_0_18455,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_18456,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oorder]),
    [final] ).

cnf(i_0_18457,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
    [final] ).

cnf(i_0_18458,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
    [final] ).

cnf(i_0_18459,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_18460,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]),
    [final] ).

cnf(i_0_18461,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
    [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_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder]),
    [final] ).

cnf(i_0_18465,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]),
    [final] ).

cnf(i_0_18466,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
    [final] ).

cnf(i_0_18467,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
    [final] ).

cnf(i_0_18468,plain,
    hBOOL(c_fTrue),
    inference(split_conjunct,[status(thm)],[help_c__fTrue__1]),
    [final] ).

cnf(i_0_18469,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_18470,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_18471,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[fact_Pls__def]),
    [final] ).

cnf(i_0_18472,plain,
    c_Int_OMin != c_Int_OPls,
    inference(split_conjunct,[status(thm)],[fact_rel__simps_I40_J]),
    [final] ).

cnf(i_0_18473,plain,
    c_Int_OPls != c_Int_OMin,
    inference(split_conjunct,[status(thm)],[fact_rel__simps_I37_J]),
    [final] ).

cnf(i_0_18474,axiom,
    X1 = X1 ).

cnf(i_0_18475,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_18476,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_18477,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_18478,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_18479,axiom,
    ( X1 != X2
    | c_Map_Omap__upds(X1,X3,X4,X5,X6) = c_Map_Omap__upds(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18480,axiom,
    ( X1 != X2
    | c_Map_Omap__upds(X3,X1,X4,X5,X6) = c_Map_Omap__upds(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18481,axiom,
    ( X1 != X2
    | c_Map_Omap__upds(X3,X4,X1,X5,X6) = c_Map_Omap__upds(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18482,axiom,
    ( X1 != X2
    | c_Map_Omap__upds(X3,X4,X5,X1,X6) = c_Map_Omap__upds(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18483,axiom,
    ( X1 != X2
    | c_Map_Omap__upds(X3,X4,X5,X6,X1) = c_Map_Omap__upds(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18484,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMin(X1,X3) = c_Big__Operators_Olinorder__class_OMin(X2,X3) ) ).

cnf(i_0_18485,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMin(X3,X1) = c_Big__Operators_Olinorder__class_OMin(X3,X2) ) ).

cnf(i_0_18486,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMax(X1,X3) = c_Big__Operators_Olinorder__class_OMax(X2,X3) ) ).

cnf(i_0_18487,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMax(X3,X1) = c_Big__Operators_Olinorder__class_OMax(X3,X2) ) ).

cnf(i_0_18488,axiom,
    ( X1 != X2
    | c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).

cnf(i_0_18489,axiom,
    ( X1 != X2
    | c_List_Olistrel(X1,X3) = c_List_Olistrel(X2,X3) ) ).

cnf(i_0_18490,axiom,
    ( X1 != X2
    | c_List_Olistrel(X3,X1) = c_List_Olistrel(X3,X2) ) ).

cnf(i_0_18491,axiom,
    ( X1 != X2
    | c_List_Opartition(X1,X3,X4) = c_List_Opartition(X2,X3,X4) ) ).

cnf(i_0_18492,axiom,
    ( X1 != X2
    | c_List_Opartition(X3,X1,X4) = c_List_Opartition(X3,X2,X4) ) ).

cnf(i_0_18493,axiom,
    ( X1 != X2
    | c_List_Opartition(X3,X4,X1) = c_List_Opartition(X3,X4,X2) ) ).

cnf(i_0_18494,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X1,X3,X4,X5) = c_Wellfounded_Olex__prod(X2,X3,X4,X5) ) ).

cnf(i_0_18495,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X1,X4,X5) = c_Wellfounded_Olex__prod(X3,X2,X4,X5) ) ).

cnf(i_0_18496,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X4,X1,X5) = c_Wellfounded_Olex__prod(X3,X4,X2,X5) ) ).

cnf(i_0_18497,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X4,X5,X1) = c_Wellfounded_Olex__prod(X3,X4,X5,X2) ) ).

cnf(i_0_18498,axiom,
    ( X1 != X2
    | c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).

cnf(i_0_18499,axiom,
    ( X1 != X2
    | c_List_Osublist(X1,X3,X4) = c_List_Osublist(X2,X3,X4) ) ).

cnf(i_0_18500,axiom,
    ( X1 != X2
    | c_List_Osublist(X3,X1,X4) = c_List_Osublist(X3,X2,X4) ) ).

cnf(i_0_18501,axiom,
    ( X1 != X2
    | c_List_Osublist(X3,X4,X1) = c_List_Osublist(X3,X4,X2) ) ).

cnf(i_0_18502,axiom,
    ( X1 != X2
    | c_List_Otranspose(X1,X3) = c_List_Otranspose(X2,X3) ) ).

cnf(i_0_18503,axiom,
    ( X1 != X2
    | c_List_Otranspose(X3,X1) = c_List_Otranspose(X3,X2) ) ).

cnf(i_0_18504,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int__rel(X1,X3) = c_Divides_Odivmod__int__rel(X2,X3) ) ).

cnf(i_0_18505,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int__rel(X3,X1) = c_Divides_Odivmod__int__rel(X3,X2) ) ).

cnf(i_0_18506,axiom,
    ( X1 != X2
    | c_Set_Othe__elem(X1,X3) = c_Set_Othe__elem(X2,X3) ) ).

cnf(i_0_18507,axiom,
    ( X1 != X2
    | c_Set_Othe__elem(X3,X1) = c_Set_Othe__elem(X3,X2) ) ).

cnf(i_0_18508,axiom,
    ( X1 != X2
    | c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).

cnf(i_0_18509,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X1,X3,X4,X5) = c_Nitpick_Osetsum_H(X2,X3,X4,X5) ) ).

cnf(i_0_18510,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X1,X4,X5) = c_Nitpick_Osetsum_H(X3,X2,X4,X5) ) ).

cnf(i_0_18511,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X4,X1,X5) = c_Nitpick_Osetsum_H(X3,X4,X2,X5) ) ).

cnf(i_0_18512,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X4,X5,X1) = c_Nitpick_Osetsum_H(X3,X4,X5,X2) ) ).

cnf(i_0_18513,axiom,
    ( X1 != X2
    | c_List_Omonoid__add__class_Olistsum(X1) = c_List_Omonoid__add__class_Olistsum(X2) ) ).

cnf(i_0_18514,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_OEps(X1,X3) = c_Hilbert__Choice_OEps(X2,X3) ) ).

cnf(i_0_18515,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_OEps(X3,X1) = c_Hilbert__Choice_OEps(X3,X2) ) ).

cnf(i_0_18516,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_18517,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_18518,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X1,X3,X4,X5) = c_Random__Sequence_ORandom(X2,X3,X4,X5) ) ).

cnf(i_0_18519,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X1,X4,X5) = c_Random__Sequence_ORandom(X3,X2,X4,X5) ) ).

cnf(i_0_18520,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X4,X1,X5) = c_Random__Sequence_ORandom(X3,X4,X2,X5) ) ).

cnf(i_0_18521,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X4,X5,X1) = c_Random__Sequence_ORandom(X3,X4,X5,X2) ) ).

cnf(i_0_18522,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__not__seq(X1) = c_Lazy__Sequence_Ohb__not__seq(X2) ) ).

cnf(i_0_18523,axiom,
    ( X1 != X2
    | c_Wellfounded_Omax__ext(X1,X3) = c_Wellfounded_Omax__ext(X2,X3) ) ).

cnf(i_0_18524,axiom,
    ( X1 != X2
    | c_Wellfounded_Omax__ext(X3,X1) = c_Wellfounded_Omax__ext(X3,X2) ) ).

cnf(i_0_18525,axiom,
    ( X1 != X2
    | c_Groups_Ominus__class_Ominus(X1) = c_Groups_Ominus__class_Ominus(X2) ) ).

cnf(i_0_18526,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).

cnf(i_0_18527,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).

cnf(i_0_18528,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).

cnf(i_0_18529,axiom,
    ( X1 != X2
    | c_Wellfounded_Omin__ext(X1,X3) = c_Wellfounded_Omin__ext(X2,X3) ) ).

cnf(i_0_18530,axiom,
    ( X1 != X2
    | c_Wellfounded_Omin__ext(X3,X1) = c_Wellfounded_Omin__ext(X3,X2) ) ).

cnf(i_0_18531,axiom,
    ( X1 != X2
    | c_Wellfounded_Ofinite__psubset(X1) = c_Wellfounded_Ofinite__psubset(X2) ) ).

cnf(i_0_18532,axiom,
    ( X1 != X2
    | c_Nitpick_Ocard_H(X1,X3) = c_Nitpick_Ocard_H(X2,X3) ) ).

cnf(i_0_18533,axiom,
    ( X1 != X2
    | c_Nitpick_Ocard_H(X3,X1) = c_Nitpick_Ocard_H(X3,X2) ) ).

cnf(i_0_18534,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_18535,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_18536,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_18537,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_18538,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_18539,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_18540,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_18541,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_18542,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_18543,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_18544,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_18545,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_18546,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_18547,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_18548,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_18549,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_18550,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_18551,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_18552,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_18553,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_18554,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_18555,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_18556,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_18557,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_18558,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X1,X3,X4) = c_Lazy__Sequence_Oappend(X2,X3,X4) ) ).

cnf(i_0_18559,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X3,X1,X4) = c_Lazy__Sequence_Oappend(X3,X2,X4) ) ).

cnf(i_0_18560,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X3,X4,X1) = c_Lazy__Sequence_Oappend(X3,X4,X2) ) ).

cnf(i_0_18561,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X1,X3,X4,X5) = c_Lazy__Sequence_Oproduct(X2,X3,X4,X5) ) ).

cnf(i_0_18562,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X1,X4,X5) = c_Lazy__Sequence_Oproduct(X3,X2,X4,X5) ) ).

cnf(i_0_18563,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X4,X1,X5) = c_Lazy__Sequence_Oproduct(X3,X4,X2,X5) ) ).

cnf(i_0_18564,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X4,X5,X1) = c_Lazy__Sequence_Oproduct(X3,X4,X5,X2) ) ).

cnf(i_0_18565,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oempty(X1) = c_Lazy__Sequence_Oempty(X2) ) ).

cnf(i_0_18566,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X1,X3) = c_Complete__Lattice_OSup__class_OSup(X2,X3) ) ).

cnf(i_0_18567,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X3,X1) = c_Complete__Lattice_OSup__class_OSup(X3,X2) ) ).

cnf(i_0_18568,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X1,X3) = c_Complete__Lattice_OInf__class_OInf(X2,X3) ) ).

cnf(i_0_18569,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X3,X1) = c_Complete__Lattice_OInf__class_OInf(X3,X2) ) ).

cnf(i_0_18570,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_18571,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_18572,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_18573,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_18574,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X1,X3,X4,X5) = c_New__DSequence_Oneg__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18575,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X1,X4,X5) = c_New__DSequence_Oneg__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18576,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X4,X1,X5) = c_New__DSequence_Oneg__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18577,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X4,X5,X1) = c_New__DSequence_Oneg__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18578,axiom,
    ( X1 != X2
    | esk342_5(X1,X3,X4,X5,X6) = esk342_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18579,axiom,
    ( X1 != X2
    | esk342_5(X3,X1,X4,X5,X6) = esk342_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18580,axiom,
    ( X1 != X2
    | esk342_5(X3,X4,X1,X5,X6) = esk342_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18581,axiom,
    ( X1 != X2
    | esk342_5(X3,X4,X5,X1,X6) = esk342_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18582,axiom,
    ( X1 != X2
    | esk342_5(X3,X4,X5,X6,X1) = esk342_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18583,axiom,
    ( X1 != X2
    | esk343_5(X1,X3,X4,X5,X6) = esk343_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18584,axiom,
    ( X1 != X2
    | esk343_5(X3,X1,X4,X5,X6) = esk343_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18585,axiom,
    ( X1 != X2
    | esk343_5(X3,X4,X1,X5,X6) = esk343_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18586,axiom,
    ( X1 != X2
    | esk343_5(X3,X4,X5,X1,X6) = esk343_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18587,axiom,
    ( X1 != X2
    | esk343_5(X3,X4,X5,X6,X1) = esk343_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18588,axiom,
    ( X1 != X2
    | c_Int_Onumber__class_Onumber__of(X1) = c_Int_Onumber__class_Onumber__of(X2) ) ).

cnf(i_0_18589,axiom,
    ( X1 != X2
    | esk341_5(X1,X3,X4,X5,X6) = esk341_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18590,axiom,
    ( X1 != X2
    | esk341_5(X3,X1,X4,X5,X6) = esk341_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18591,axiom,
    ( X1 != X2
    | esk341_5(X3,X4,X1,X5,X6) = esk341_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18592,axiom,
    ( X1 != X2
    | esk341_5(X3,X4,X5,X1,X6) = esk341_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18593,axiom,
    ( X1 != X2
    | esk341_5(X3,X4,X5,X6,X1) = esk341_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18594,axiom,
    ( X1 != X2
    | esk340_5(X1,X3,X4,X5,X6) = esk340_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18595,axiom,
    ( X1 != X2
    | esk340_5(X3,X1,X4,X5,X6) = esk340_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18596,axiom,
    ( X1 != X2
    | esk340_5(X3,X4,X1,X5,X6) = esk340_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18597,axiom,
    ( X1 != X2
    | esk340_5(X3,X4,X5,X1,X6) = esk340_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18598,axiom,
    ( X1 != X2
    | esk340_5(X3,X4,X5,X6,X1) = esk340_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18599,axiom,
    ( X1 != X2
    | c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).

cnf(i_0_18600,axiom,
    ( X1 != X2
    | c_Option_Ooption_ONone(X1) = c_Option_Ooption_ONone(X2) ) ).

cnf(i_0_18601,axiom,
    ( X1 != X2
    | c_HOL_OThe(X1,X3) = c_HOL_OThe(X2,X3) ) ).

cnf(i_0_18602,axiom,
    ( X1 != X2
    | c_HOL_OThe(X3,X1) = c_HOL_OThe(X3,X2) ) ).

cnf(i_0_18603,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_18604,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_18605,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_18606,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_18607,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X1,X3,X4,X5) = c_New__DSequence_Opos__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18608,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X1,X4,X5) = c_New__DSequence_Opos__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18609,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X4,X1,X5) = c_New__DSequence_Opos__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18610,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X4,X5,X1) = c_New__DSequence_Opos__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18611,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X1,X3,X4,X5) = c_Nitpick_Oprod(X2,X3,X4,X5) ) ).

cnf(i_0_18612,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X1,X4,X5) = c_Nitpick_Oprod(X3,X2,X4,X5) ) ).

cnf(i_0_18613,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X4,X1,X5) = c_Nitpick_Oprod(X3,X4,X2,X5) ) ).

cnf(i_0_18614,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X4,X5,X1) = c_Nitpick_Oprod(X3,X4,X5,X2) ) ).

cnf(i_0_18615,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X1,X3,X4) = c_List_OtakeWhile(X2,X3,X4) ) ).

cnf(i_0_18616,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X3,X1,X4) = c_List_OtakeWhile(X3,X2,X4) ) ).

cnf(i_0_18617,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X3,X4,X1) = c_List_OtakeWhile(X3,X4,X2) ) ).

cnf(i_0_18618,axiom,
    ( X1 != X2
    | esk242_6(X1,X3,X4,X5,X6,X7) = esk242_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18619,axiom,
    ( X1 != X2
    | esk242_6(X3,X1,X4,X5,X6,X7) = esk242_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18620,axiom,
    ( X1 != X2
    | esk242_6(X3,X4,X1,X5,X6,X7) = esk242_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18621,axiom,
    ( X1 != X2
    | esk242_6(X3,X4,X5,X1,X6,X7) = esk242_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18622,axiom,
    ( X1 != X2
    | esk242_6(X3,X4,X5,X6,X1,X7) = esk242_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18623,axiom,
    ( X1 != X2
    | esk242_6(X3,X4,X5,X6,X7,X1) = esk242_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18624,axiom,
    ( X1 != X2
    | esk241_6(X1,X3,X4,X5,X6,X7) = esk241_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18625,axiom,
    ( X1 != X2
    | esk241_6(X3,X1,X4,X5,X6,X7) = esk241_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18626,axiom,
    ( X1 != X2
    | esk241_6(X3,X4,X1,X5,X6,X7) = esk241_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18627,axiom,
    ( X1 != X2
    | esk241_6(X3,X4,X5,X1,X6,X7) = esk241_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18628,axiom,
    ( X1 != X2
    | esk241_6(X3,X4,X5,X6,X1,X7) = esk241_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18629,axiom,
    ( X1 != X2
    | esk241_6(X3,X4,X5,X6,X7,X1) = esk241_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18630,axiom,
    ( X1 != X2
    | c_Fun_Oid(X1) = c_Fun_Oid(X2) ) ).

cnf(i_0_18631,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X1,X3,X4) = c_Enum_On__lists(X2,X3,X4) ) ).

cnf(i_0_18632,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X3,X1,X4) = c_Enum_On__lists(X3,X2,X4) ) ).

cnf(i_0_18633,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X3,X4,X1) = c_Enum_On__lists(X3,X4,X2) ) ).

cnf(i_0_18634,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X1,X3,X4) = c_Nitpick_Otimes__frac(X2,X3,X4) ) ).

cnf(i_0_18635,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X3,X1,X4) = c_Nitpick_Otimes__frac(X3,X2,X4) ) ).

cnf(i_0_18636,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X3,X4,X1) = c_Nitpick_Otimes__frac(X3,X4,X2) ) ).

cnf(i_0_18637,axiom,
    ( X1 != X2
    | c_Divides_OnegDivAlg(X1,X3) = c_Divides_OnegDivAlg(X2,X3) ) ).

cnf(i_0_18638,axiom,
    ( X1 != X2
    | c_Divides_OnegDivAlg(X3,X1) = c_Divides_OnegDivAlg(X3,X2) ) ).

cnf(i_0_18639,axiom,
    ( X1 != X2
    | c_Divides_OposDivAlg(X1,X3) = c_Divides_OposDivAlg(X2,X3) ) ).

cnf(i_0_18640,axiom,
    ( X1 != X2
    | c_Divides_OposDivAlg(X3,X1) = c_Divides_OposDivAlg(X3,X2) ) ).

cnf(i_0_18641,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1) = c_Nat_Osemiring__1__class_Oof__nat(X2) ) ).

cnf(i_0_18642,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X1,X3,X4,X5) = c_Nat_Onat_Onat__case(X2,X3,X4,X5) ) ).

cnf(i_0_18643,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X1,X4,X5) = c_Nat_Onat_Onat__case(X3,X2,X4,X5) ) ).

cnf(i_0_18644,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X1,X5) = c_Nat_Onat_Onat__case(X3,X4,X2,X5) ) ).

cnf(i_0_18645,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X5,X1) = c_Nat_Onat_Onat__case(X3,X4,X5,X2) ) ).

cnf(i_0_18646,axiom,
    ( X1 != X2
    | c_List_Omap__filter(X1,X3,X4,X5) = c_List_Omap__filter(X2,X3,X4,X5) ) ).

cnf(i_0_18647,axiom,
    ( X1 != X2
    | c_List_Omap__filter(X3,X1,X4,X5) = c_List_Omap__filter(X3,X2,X4,X5) ) ).

cnf(i_0_18648,axiom,
    ( X1 != X2
    | c_List_Omap__filter(X3,X4,X1,X5) = c_List_Omap__filter(X3,X4,X2,X5) ) ).

cnf(i_0_18649,axiom,
    ( X1 != X2
    | c_List_Omap__filter(X3,X4,X5,X1) = c_List_Omap__filter(X3,X4,X5,X2) ) ).

cnf(i_0_18650,axiom,
    ( X1 != X2
    | c_Map_Odom(X1,X3,X4) = c_Map_Odom(X2,X3,X4) ) ).

cnf(i_0_18651,axiom,
    ( X1 != X2
    | c_Map_Odom(X3,X1,X4) = c_Map_Odom(X3,X2,X4) ) ).

cnf(i_0_18652,axiom,
    ( X1 != X2
    | c_Map_Odom(X3,X4,X1) = c_Map_Odom(X3,X4,X2) ) ).

cnf(i_0_18653,axiom,
    ( X1 != X2
    | c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).

cnf(i_0_18654,axiom,
    ( X1 != X2
    | c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).

cnf(i_0_18655,axiom,
    ( X1 != X2
    | c_Int_Oint__ge__less__than(X1) = c_Int_Oint__ge__less__than(X2) ) ).

cnf(i_0_18656,axiom,
    ( X1 != X2
    | c_List_Olistrel1(X1,X3) = c_List_Olistrel1(X2,X3) ) ).

cnf(i_0_18657,axiom,
    ( X1 != X2
    | c_List_Olistrel1(X3,X1) = c_List_Olistrel1(X3,X2) ) ).

cnf(i_0_18658,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X1,X3,X4) = c_Finite__Set_Ofold(X2,X3,X4) ) ).

cnf(i_0_18659,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X3,X1,X4) = c_Finite__Set_Ofold(X3,X2,X4) ) ).

cnf(i_0_18660,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X3,X4,X1) = c_Finite__Set_Ofold(X3,X4,X2) ) ).

cnf(i_0_18661,axiom,
    ( X1 != X2
    | c_Nitpick_Ouminus__frac(X1,X3) = c_Nitpick_Ouminus__frac(X2,X3) ) ).

cnf(i_0_18662,axiom,
    ( X1 != X2
    | c_Nitpick_Ouminus__frac(X3,X1) = c_Nitpick_Ouminus__frac(X3,X2) ) ).

cnf(i_0_18663,axiom,
    ( X1 != X2
    | c_Nitpick_OAbs__Frac(X1,X3) = c_Nitpick_OAbs__Frac(X2,X3) ) ).

cnf(i_0_18664,axiom,
    ( X1 != X2
    | c_Nitpick_OAbs__Frac(X3,X1) = c_Nitpick_OAbs__Frac(X3,X2) ) ).

cnf(i_0_18665,axiom,
    ( X1 != X2
    | esk439_4(X1,X3,X4,X5) = esk439_4(X2,X3,X4,X5) ) ).

cnf(i_0_18666,axiom,
    ( X1 != X2
    | esk439_4(X3,X1,X4,X5) = esk439_4(X3,X2,X4,X5) ) ).

cnf(i_0_18667,axiom,
    ( X1 != X2
    | esk439_4(X3,X4,X1,X5) = esk439_4(X3,X4,X2,X5) ) ).

cnf(i_0_18668,axiom,
    ( X1 != X2
    | esk439_4(X3,X4,X5,X1) = esk439_4(X3,X4,X5,X2) ) ).

cnf(i_0_18669,axiom,
    ( X1 != X2
    | esk438_4(X1,X3,X4,X5) = esk438_4(X2,X3,X4,X5) ) ).

cnf(i_0_18670,axiom,
    ( X1 != X2
    | esk438_4(X3,X1,X4,X5) = esk438_4(X3,X2,X4,X5) ) ).

cnf(i_0_18671,axiom,
    ( X1 != X2
    | esk438_4(X3,X4,X1,X5) = esk438_4(X3,X4,X2,X5) ) ).

cnf(i_0_18672,axiom,
    ( X1 != X2
    | esk438_4(X3,X4,X5,X1) = esk438_4(X3,X4,X5,X2) ) ).

cnf(i_0_18673,axiom,
    ( X1 != X2
    | c_Enum_Oenum__class_Oenum(X1) = c_Enum_Oenum__class_Oenum(X2) ) ).

cnf(i_0_18674,axiom,
    ( X1 != X2
    | c_Fun_Ooverride__on(X1,X3,X4,X5,X6) = c_Fun_Ooverride__on(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18675,axiom,
    ( X1 != X2
    | c_Fun_Ooverride__on(X3,X1,X4,X5,X6) = c_Fun_Ooverride__on(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18676,axiom,
    ( X1 != X2
    | c_Fun_Ooverride__on(X3,X4,X1,X5,X6) = c_Fun_Ooverride__on(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18677,axiom,
    ( X1 != X2
    | c_Fun_Ooverride__on(X3,X4,X5,X1,X6) = c_Fun_Ooverride__on(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18678,axiom,
    ( X1 != X2
    | c_Fun_Ooverride__on(X3,X4,X5,X6,X1) = c_Fun_Ooverride__on(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18679,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_18680,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X1,X3,X4,X5) = c_Hilbert__Choice_Oinv__into(X2,X3,X4,X5) ) ).

cnf(i_0_18681,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X1,X4,X5) = c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5) ) ).

cnf(i_0_18682,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X4,X1,X5) = c_Hilbert__Choice_Oinv__into(X3,X4,X2,X5) ) ).

cnf(i_0_18683,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X4,X5,X1) = c_Hilbert__Choice_Oinv__into(X3,X4,X5,X2) ) ).

cnf(i_0_18684,axiom,
    ( X1 != X2
    | c_List_Olistsp(X1,X3) = c_List_Olistsp(X2,X3) ) ).

cnf(i_0_18685,axiom,
    ( X1 != X2
    | c_List_Olistsp(X3,X1) = c_List_Olistsp(X3,X2) ) ).

cnf(i_0_18686,axiom,
    ( X1 != X2
    | c_List_Olists(X1,X3) = c_List_Olists(X2,X3) ) ).

cnf(i_0_18687,axiom,
    ( X1 != X2
    | c_List_Olists(X3,X1) = c_List_Olists(X3,X2) ) ).

cnf(i_0_18688,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omax(X1) = c_Orderings_Oord__class_Omax(X2) ) ).

cnf(i_0_18689,axiom,
    ( X1 != X2
    | c_Map_Oran(X1,X3,X4) = c_Map_Oran(X2,X3,X4) ) ).

cnf(i_0_18690,axiom,
    ( X1 != X2
    | c_Map_Oran(X3,X1,X4) = c_Map_Oran(X3,X2,X4) ) ).

cnf(i_0_18691,axiom,
    ( X1 != X2
    | c_Map_Oran(X3,X4,X1) = c_Map_Oran(X3,X4,X2) ) ).

cnf(i_0_18692,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X1,X3,X4) = c_Big__Operators_Olattice_OInf__fin(X2,X3,X4) ) ).

cnf(i_0_18693,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X3,X1,X4) = c_Big__Operators_Olattice_OInf__fin(X3,X2,X4) ) ).

cnf(i_0_18694,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X3,X4,X1) = c_Big__Operators_Olattice_OInf__fin(X3,X4,X2) ) ).

cnf(i_0_18695,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omin(X1) = c_Orderings_Oord__class_Omin(X2) ) ).

cnf(i_0_18696,axiom,
    ( X1 != X2
    | c_Int_Oint__ge__less__than2(X1) = c_Int_Oint__ge__less__than2(X2) ) ).

cnf(i_0_18697,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X1,X3,X4) = c_Nitpick_Oof__frac(X2,X3,X4) ) ).

cnf(i_0_18698,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X3,X1,X4) = c_Nitpick_Oof__frac(X3,X2,X4) ) ).

cnf(i_0_18699,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X3,X4,X1) = c_Nitpick_Oof__frac(X3,X4,X2) ) ).

cnf(i_0_18700,axiom,
    ( X1 != X2
    | c_List_Omeasures(X1,X3) = c_List_Omeasures(X2,X3) ) ).

cnf(i_0_18701,axiom,
    ( X1 != X2
    | c_List_Omeasures(X3,X1) = c_List_Omeasures(X3,X2) ) ).

cnf(i_0_18702,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X1,X3,X4,X5) = c_Random__Sequence_Omap(X2,X3,X4,X5) ) ).

cnf(i_0_18703,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X1,X4,X5) = c_Random__Sequence_Omap(X3,X2,X4,X5) ) ).

cnf(i_0_18704,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X4,X1,X5) = c_Random__Sequence_Omap(X3,X4,X2,X5) ) ).

cnf(i_0_18705,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X4,X5,X1) = c_Random__Sequence_Omap(X3,X4,X5,X2) ) ).

cnf(i_0_18706,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X1,X3,X4,X5) = c_Random__Sequence_Obind(X2,X3,X4,X5) ) ).

cnf(i_0_18707,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X1,X4,X5) = c_Random__Sequence_Obind(X3,X2,X4,X5) ) ).

cnf(i_0_18708,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X4,X1,X5) = c_Random__Sequence_Obind(X3,X4,X2,X5) ) ).

cnf(i_0_18709,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X4,X5,X1) = c_Random__Sequence_Obind(X3,X4,X5,X2) ) ).

cnf(i_0_18710,axiom,
    ( X1 != X2
    | c_Map_Orestrict__map(X1,X3,X4,X5) = c_Map_Orestrict__map(X2,X3,X4,X5) ) ).

cnf(i_0_18711,axiom,
    ( X1 != X2
    | c_Map_Orestrict__map(X3,X1,X4,X5) = c_Map_Orestrict__map(X3,X2,X4,X5) ) ).

cnf(i_0_18712,axiom,
    ( X1 != X2
    | c_Map_Orestrict__map(X3,X4,X1,X5) = c_Map_Orestrict__map(X3,X4,X2,X5) ) ).

cnf(i_0_18713,axiom,
    ( X1 != X2
    | c_Map_Orestrict__map(X3,X4,X5,X1) = c_Map_Orestrict__map(X3,X4,X5,X2) ) ).

cnf(i_0_18714,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).

cnf(i_0_18715,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).

cnf(i_0_18716,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).

cnf(i_0_18717,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X1,X3,X4) = c_Big__Operators_Olattice_OSup__fin(X2,X3,X4) ) ).

cnf(i_0_18718,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X3,X1,X4) = c_Big__Operators_Olattice_OSup__fin(X3,X2,X4) ) ).

cnf(i_0_18719,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X3,X4,X1) = c_Big__Operators_Olattice_OSup__fin(X3,X4,X2) ) ).

cnf(i_0_18720,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_OLeast(X1,X3) = c_Orderings_Oord__class_OLeast(X2,X3) ) ).

cnf(i_0_18721,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_OLeast(X3,X1) = c_Orderings_Oord__class_OLeast(X3,X2) ) ).

cnf(i_0_18722,axiom,
    ( X1 != X2
    | c_Lattices_Osemilattice__inf__class_Oinf(X1) = c_Lattices_Osemilattice__inf__class_Oinf(X2) ) ).

cnf(i_0_18723,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OSup__fin(X1,X3) = c_Big__Operators_Olattice__class_OSup__fin(X2,X3) ) ).

cnf(i_0_18724,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OSup__fin(X3,X1) = c_Big__Operators_Olattice__class_OSup__fin(X3,X2) ) ).

cnf(i_0_18725,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X1,X3,X4) = c_List_Olist_Olist__size(X2,X3,X4) ) ).

cnf(i_0_18726,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X3,X1,X4) = c_List_Olist_Olist__size(X3,X2,X4) ) ).

cnf(i_0_18727,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X3,X4,X1) = c_List_Olist_Olist__size(X3,X4,X2) ) ).

cnf(i_0_18728,axiom,
    ( X1 != X2
    | c_Lattices_Osemilattice__sup__class_Osup(X1) = c_Lattices_Osemilattice__sup__class_Osup(X2) ) ).

cnf(i_0_18729,axiom,
    ( X1 != X2
    | c_Enum_Osublists(X1,X3) = c_Enum_Osublists(X2,X3) ) ).

cnf(i_0_18730,axiom,
    ( X1 != X2
    | c_Enum_Osublists(X3,X1) = c_Enum_Osublists(X3,X2) ) ).

cnf(i_0_18731,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OInf__fin(X1,X3) = c_Big__Operators_Olattice__class_OInf__fin(X2,X3) ) ).

cnf(i_0_18732,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OInf__fin(X3,X1) = c_Big__Operators_Olattice__class_OInf__fin(X3,X2) ) ).

cnf(i_0_18733,axiom,
    ( X1 != X2
    | c_Random_Oselect__weight(X1,X3) = c_Random_Oselect__weight(X2,X3) ) ).

cnf(i_0_18734,axiom,
    ( X1 != X2
    | c_Random_Oselect__weight(X3,X1) = c_Random_Oselect__weight(X3,X2) ) ).

cnf(i_0_18735,axiom,
    ( X1 != X2
    | c_Random_Opick(X1,X3) = c_Random_Opick(X2,X3) ) ).

cnf(i_0_18736,axiom,
    ( X1 != X2
    | c_Random_Opick(X3,X1) = c_Random_Opick(X3,X2) ) ).

cnf(i_0_18737,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X1,X3,X4) = c_List_Oset__Cons(X2,X3,X4) ) ).

cnf(i_0_18738,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X3,X1,X4) = c_List_Oset__Cons(X3,X2,X4) ) ).

cnf(i_0_18739,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X3,X4,X1) = c_List_Oset__Cons(X3,X4,X2) ) ).

cnf(i_0_18740,axiom,
    ( X1 != X2
    | c_Sum__Type_Osum_Osum__case(X1,X3,X4,X5,X6) = c_Sum__Type_Osum_Osum__case(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18741,axiom,
    ( X1 != X2
    | c_Sum__Type_Osum_Osum__case(X3,X1,X4,X5,X6) = c_Sum__Type_Osum_Osum__case(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18742,axiom,
    ( X1 != X2
    | c_Sum__Type_Osum_Osum__case(X3,X4,X1,X5,X6) = c_Sum__Type_Osum_Osum__case(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18743,axiom,
    ( X1 != X2
    | c_Sum__Type_Osum_Osum__case(X3,X4,X5,X1,X6) = c_Sum__Type_Osum_Osum__case(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18744,axiom,
    ( X1 != X2
    | c_Sum__Type_Osum_Osum__case(X3,X4,X5,X6,X1) = c_Sum__Type_Osum_Osum__case(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18745,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X1,X3,X4) = c_Wellfounded_Omlex__prod(X2,X3,X4) ) ).

cnf(i_0_18746,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X3,X1,X4) = c_Wellfounded_Omlex__prod(X3,X2,X4) ) ).

cnf(i_0_18747,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X3,X4,X1) = c_Wellfounded_Omlex__prod(X3,X4,X2) ) ).

cnf(i_0_18748,axiom,
    ( X1 != X2
    | c_Nitpick_Onorm__frac(X1,X3) = c_Nitpick_Onorm__frac(X2,X3) ) ).

cnf(i_0_18749,axiom,
    ( X1 != X2
    | c_Nitpick_Onorm__frac(X3,X1) = c_Nitpick_Onorm__frac(X3,X2) ) ).

cnf(i_0_18750,axiom,
    ( X1 != X2
    | c_List_Oremove1(X1,X3,X4) = c_List_Oremove1(X2,X3,X4) ) ).

cnf(i_0_18751,axiom,
    ( X1 != X2
    | c_List_Oremove1(X3,X1,X4) = c_List_Oremove1(X3,X2,X4) ) ).

cnf(i_0_18752,axiom,
    ( X1 != X2
    | c_List_Oremove1(X3,X4,X1) = c_List_Oremove1(X3,X4,X2) ) ).

cnf(i_0_18753,axiom,
    ( X1 != X2
    | esk527_4(X1,X3,X4,X5) = esk527_4(X2,X3,X4,X5) ) ).

cnf(i_0_18754,axiom,
    ( X1 != X2
    | esk527_4(X3,X1,X4,X5) = esk527_4(X3,X2,X4,X5) ) ).

cnf(i_0_18755,axiom,
    ( X1 != X2
    | esk527_4(X3,X4,X1,X5) = esk527_4(X3,X4,X2,X5) ) ).

cnf(i_0_18756,axiom,
    ( X1 != X2
    | esk527_4(X3,X4,X5,X1) = esk527_4(X3,X4,X5,X2) ) ).

cnf(i_0_18757,axiom,
    ( X1 != X2
    | esk526_4(X1,X3,X4,X5) = esk526_4(X2,X3,X4,X5) ) ).

cnf(i_0_18758,axiom,
    ( X1 != X2
    | esk526_4(X3,X1,X4,X5) = esk526_4(X3,X2,X4,X5) ) ).

cnf(i_0_18759,axiom,
    ( X1 != X2
    | esk526_4(X3,X4,X1,X5) = esk526_4(X3,X4,X2,X5) ) ).

cnf(i_0_18760,axiom,
    ( X1 != X2
    | esk526_4(X3,X4,X5,X1) = esk526_4(X3,X4,X5,X2) ) ).

cnf(i_0_18761,axiom,
    ( X1 != X2
    | esk329_3(X1,X3,X4) = esk329_3(X2,X3,X4) ) ).

cnf(i_0_18762,axiom,
    ( X1 != X2
    | esk329_3(X3,X1,X4) = esk329_3(X3,X2,X4) ) ).

cnf(i_0_18763,axiom,
    ( X1 != X2
    | esk329_3(X3,X4,X1) = esk329_3(X3,X4,X2) ) ).

cnf(i_0_18764,axiom,
    ( X1 != X2
    | esk328_3(X1,X3,X4) = esk328_3(X2,X3,X4) ) ).

cnf(i_0_18765,axiom,
    ( X1 != X2
    | esk328_3(X3,X1,X4) = esk328_3(X3,X2,X4) ) ).

cnf(i_0_18766,axiom,
    ( X1 != X2
    | esk328_3(X3,X4,X1) = esk328_3(X3,X4,X2) ) ).

cnf(i_0_18767,axiom,
    ( X1 != X2
    | c_Smallcheck_Osmall_H(X1,X3,X4) = c_Smallcheck_Osmall_H(X2,X3,X4) ) ).

cnf(i_0_18768,axiom,
    ( X1 != X2
    | c_Smallcheck_Osmall_H(X3,X1,X4) = c_Smallcheck_Osmall_H(X3,X2,X4) ) ).

cnf(i_0_18769,axiom,
    ( X1 != X2
    | c_Smallcheck_Osmall_H(X3,X4,X1) = c_Smallcheck_Osmall_H(X3,X4,X2) ) ).

cnf(i_0_18770,axiom,
    ( X1 != X2
    | c_Random_Oselect(X1,X3) = c_Random_Oselect(X2,X3) ) ).

cnf(i_0_18771,axiom,
    ( X1 != X2
    | c_Random_Oselect(X3,X1) = c_Random_Oselect(X3,X2) ) ).

cnf(i_0_18772,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_18773,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_18774,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_18775,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_18776,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_18777,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold1(X1,X3) = c_Finite__Set_Ofold1(X2,X3) ) ).

cnf(i_0_18778,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold1(X3,X1) = c_Finite__Set_Ofold1(X3,X2) ) ).

cnf(i_0_18779,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_18780,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_18781,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_18782,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_18783,axiom,
    ( X1 != X2
    | c_HOL_Oequal__class_Oequal(X1) = c_HOL_Oequal__class_Oequal(X2) ) ).

cnf(i_0_18784,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_18785,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_18786,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_18787,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_18788,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_18789,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_18790,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_18791,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_18792,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_18793,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_18794,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int(X1,X3) = c_Divides_Odivmod__int(X2,X3) ) ).

cnf(i_0_18795,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int(X3,X1) = c_Divides_Odivmod__int(X3,X2) ) ).

cnf(i_0_18796,axiom,
    ( X1 != X2
    | esk41_5(X1,X3,X4,X5,X6) = esk41_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18797,axiom,
    ( X1 != X2
    | esk41_5(X3,X1,X4,X5,X6) = esk41_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18798,axiom,
    ( X1 != X2
    | esk41_5(X3,X4,X1,X5,X6) = esk41_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18799,axiom,
    ( X1 != X2
    | esk41_5(X3,X4,X5,X1,X6) = esk41_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18800,axiom,
    ( X1 != X2
    | esk41_5(X3,X4,X5,X6,X1) = esk41_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18801,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).

cnf(i_0_18802,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).

cnf(i_0_18803,axiom,
    ( X1 != X2
    | esk334_3(X1,X3,X4) = esk334_3(X2,X3,X4) ) ).

cnf(i_0_18804,axiom,
    ( X1 != X2
    | esk334_3(X3,X1,X4) = esk334_3(X3,X2,X4) ) ).

cnf(i_0_18805,axiom,
    ( X1 != X2
    | esk334_3(X3,X4,X1) = esk334_3(X3,X4,X2) ) ).

cnf(i_0_18806,axiom,
    ( X1 != X2
    | esk333_3(X1,X3,X4) = esk333_3(X2,X3,X4) ) ).

cnf(i_0_18807,axiom,
    ( X1 != X2
    | esk333_3(X3,X1,X4) = esk333_3(X3,X2,X4) ) ).

cnf(i_0_18808,axiom,
    ( X1 != X2
    | esk333_3(X3,X4,X1) = esk333_3(X3,X4,X2) ) ).

cnf(i_0_18809,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_18810,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_18811,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_18812,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_18813,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_18814,axiom,
    ( X1 != X2
    | esk476_2(X1,X3) = esk476_2(X2,X3) ) ).

cnf(i_0_18815,axiom,
    ( X1 != X2
    | esk476_2(X3,X1) = esk476_2(X3,X2) ) ).

cnf(i_0_18816,axiom,
    ( X1 != X2
    | esk477_2(X1,X3) = esk477_2(X2,X3) ) ).

cnf(i_0_18817,axiom,
    ( X1 != X2
    | esk477_2(X3,X1) = esk477_2(X3,X2) ) ).

cnf(i_0_18818,axiom,
    ( X1 != X2
    | c_Nitpick_Onat__gcd(X1,X3) = c_Nitpick_Onat__gcd(X2,X3) ) ).

cnf(i_0_18819,axiom,
    ( X1 != X2
    | c_Nitpick_Onat__gcd(X3,X1) = c_Nitpick_Onat__gcd(X3,X2) ) ).

cnf(i_0_18820,axiom,
    ( X1 != X2
    | c_Divides_Opdivmod(X1,X3) = c_Divides_Opdivmod(X2,X3) ) ).

cnf(i_0_18821,axiom,
    ( X1 != X2
    | c_Divides_Opdivmod(X3,X1) = c_Divides_Opdivmod(X3,X2) ) ).

cnf(i_0_18822,axiom,
    ( X1 != X2
    | c_List_Oremdups(X1,X3) = c_List_Oremdups(X2,X3) ) ).

cnf(i_0_18823,axiom,
    ( X1 != X2
    | c_List_Oremdups(X3,X1) = c_List_Oremdups(X3,X2) ) ).

cnf(i_0_18824,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X1,X3,X4) = c_Partial__Function_Oflat__lub(X2,X3,X4) ) ).

cnf(i_0_18825,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X3,X1,X4) = c_Partial__Function_Oflat__lub(X3,X2,X4) ) ).

cnf(i_0_18826,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X3,X4,X1) = c_Partial__Function_Oflat__lub(X3,X4,X2) ) ).

cnf(i_0_18827,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__flat(X1,X3) = c_Lazy__Sequence_Ohb__flat(X2,X3) ) ).

cnf(i_0_18828,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__flat(X3,X1) = c_Lazy__Sequence_Ohb__flat(X3,X2) ) ).

cnf(i_0_18829,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__map(X1,X3,X4,X5) = c_Lazy__Sequence_Ohb__map(X2,X3,X4,X5) ) ).

cnf(i_0_18830,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__map(X3,X1,X4,X5) = c_Lazy__Sequence_Ohb__map(X3,X2,X4,X5) ) ).

cnf(i_0_18831,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__map(X3,X4,X1,X5) = c_Lazy__Sequence_Ohb__map(X3,X4,X2,X5) ) ).

cnf(i_0_18832,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__map(X3,X4,X5,X1) = c_Lazy__Sequence_Ohb__map(X3,X4,X5,X2) ) ).

cnf(i_0_18833,axiom,
    ( X1 != X2
    | c_List_Olenlex(X1,X3) = c_List_Olenlex(X2,X3) ) ).

cnf(i_0_18834,axiom,
    ( X1 != X2
    | c_List_Olenlex(X3,X1) = c_List_Olenlex(X3,X2) ) ).

cnf(i_0_18835,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X1,X3,X4) = c_List_Oreplicate(X2,X3,X4) ) ).

cnf(i_0_18836,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X1,X4) = c_List_Oreplicate(X3,X2,X4) ) ).

cnf(i_0_18837,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X4,X1) = c_List_Oreplicate(X3,X4,X2) ) ).

cnf(i_0_18838,axiom,
    ( X1 != X2
    | c_List_Olex(X1,X3) = c_List_Olex(X2,X3) ) ).

cnf(i_0_18839,axiom,
    ( X1 != X2
    | c_List_Olex(X3,X1) = c_List_Olex(X3,X2) ) ).

cnf(i_0_18840,axiom,
    ( X1 != X2
    | esk253_3(X1,X3,X4) = esk253_3(X2,X3,X4) ) ).

cnf(i_0_18841,axiom,
    ( X1 != X2
    | esk253_3(X3,X1,X4) = esk253_3(X3,X2,X4) ) ).

cnf(i_0_18842,axiom,
    ( X1 != X2
    | esk253_3(X3,X4,X1) = esk253_3(X3,X4,X2) ) ).

cnf(i_0_18843,axiom,
    ( X1 != X2
    | esk39_3(X1,X3,X4) = esk39_3(X2,X3,X4) ) ).

cnf(i_0_18844,axiom,
    ( X1 != X2
    | esk39_3(X3,X1,X4) = esk39_3(X3,X2,X4) ) ).

cnf(i_0_18845,axiom,
    ( X1 != X2
    | esk39_3(X3,X4,X1) = esk39_3(X3,X4,X2) ) ).

cnf(i_0_18846,axiom,
    ( X1 != X2
    | esk522_4(X1,X3,X4,X5) = esk522_4(X2,X3,X4,X5) ) ).

cnf(i_0_18847,axiom,
    ( X1 != X2
    | esk522_4(X3,X1,X4,X5) = esk522_4(X3,X2,X4,X5) ) ).

cnf(i_0_18848,axiom,
    ( X1 != X2
    | esk522_4(X3,X4,X1,X5) = esk522_4(X3,X4,X2,X5) ) ).

cnf(i_0_18849,axiom,
    ( X1 != X2
    | esk522_4(X3,X4,X5,X1) = esk522_4(X3,X4,X5,X2) ) ).

cnf(i_0_18850,axiom,
    ( X1 != X2
    | esk509_4(X1,X3,X4,X5) = esk509_4(X2,X3,X4,X5) ) ).

cnf(i_0_18851,axiom,
    ( X1 != X2
    | esk509_4(X3,X1,X4,X5) = esk509_4(X3,X2,X4,X5) ) ).

cnf(i_0_18852,axiom,
    ( X1 != X2
    | esk509_4(X3,X4,X1,X5) = esk509_4(X3,X4,X2,X5) ) ).

cnf(i_0_18853,axiom,
    ( X1 != X2
    | esk509_4(X3,X4,X5,X1) = esk509_4(X3,X4,X5,X2) ) ).

cnf(i_0_18854,axiom,
    ( X1 != X2
    | esk234_4(X1,X3,X4,X5) = esk234_4(X2,X3,X4,X5) ) ).

cnf(i_0_18855,axiom,
    ( X1 != X2
    | esk234_4(X3,X1,X4,X5) = esk234_4(X3,X2,X4,X5) ) ).

cnf(i_0_18856,axiom,
    ( X1 != X2
    | esk234_4(X3,X4,X1,X5) = esk234_4(X3,X4,X2,X5) ) ).

cnf(i_0_18857,axiom,
    ( X1 != X2
    | esk234_4(X3,X4,X5,X1) = esk234_4(X3,X4,X5,X2) ) ).

cnf(i_0_18858,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X1,X3,X4,X5) = c_List_Ofoldl(X2,X3,X4,X5) ) ).

cnf(i_0_18859,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X1,X4,X5) = c_List_Ofoldl(X3,X2,X4,X5) ) ).

cnf(i_0_18860,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X1,X5) = c_List_Ofoldl(X3,X4,X2,X5) ) ).

cnf(i_0_18861,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X1) = c_List_Ofoldl(X3,X4,X5,X2) ) ).

cnf(i_0_18862,axiom,
    ( X1 != X2
    | esk236_4(X1,X3,X4,X5) = esk236_4(X2,X3,X4,X5) ) ).

cnf(i_0_18863,axiom,
    ( X1 != X2
    | esk236_4(X3,X1,X4,X5) = esk236_4(X3,X2,X4,X5) ) ).

cnf(i_0_18864,axiom,
    ( X1 != X2
    | esk236_4(X3,X4,X1,X5) = esk236_4(X3,X4,X2,X5) ) ).

cnf(i_0_18865,axiom,
    ( X1 != X2
    | esk236_4(X3,X4,X5,X1) = esk236_4(X3,X4,X5,X2) ) ).

cnf(i_0_18866,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X1,X3,X4,X5) = c_Enum_Oproduct(X2,X3,X4,X5) ) ).

cnf(i_0_18867,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X1,X4,X5) = c_Enum_Oproduct(X3,X2,X4,X5) ) ).

cnf(i_0_18868,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X4,X1,X5) = c_Enum_Oproduct(X3,X4,X2,X5) ) ).

cnf(i_0_18869,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X4,X5,X1) = c_Enum_Oproduct(X3,X4,X5,X2) ) ).

cnf(i_0_18870,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X1,X3,X4,X5,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18871,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X3,X1,X4,X5,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18872,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X3,X4,X1,X5,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18873,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X3,X4,X5,X1,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18874,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X3,X4,X5,X6,X1) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18875,axiom,
    ( X1 != X2
    | esk33_4(X1,X3,X4,X5) = esk33_4(X2,X3,X4,X5) ) ).

cnf(i_0_18876,axiom,
    ( X1 != X2
    | esk33_4(X3,X1,X4,X5) = esk33_4(X3,X2,X4,X5) ) ).

cnf(i_0_18877,axiom,
    ( X1 != X2
    | esk33_4(X3,X4,X1,X5) = esk33_4(X3,X4,X2,X5) ) ).

cnf(i_0_18878,axiom,
    ( X1 != X2
    | esk33_4(X3,X4,X5,X1) = esk33_4(X3,X4,X5,X2) ) ).

cnf(i_0_18879,axiom,
    ( X1 != X2
    | esk32_4(X1,X3,X4,X5) = esk32_4(X2,X3,X4,X5) ) ).

cnf(i_0_18880,axiom,
    ( X1 != X2
    | esk32_4(X3,X1,X4,X5) = esk32_4(X3,X2,X4,X5) ) ).

cnf(i_0_18881,axiom,
    ( X1 != X2
    | esk32_4(X3,X4,X1,X5) = esk32_4(X3,X4,X2,X5) ) ).

cnf(i_0_18882,axiom,
    ( X1 != X2
    | esk32_4(X3,X4,X5,X1) = esk32_4(X3,X4,X5,X2) ) ).

cnf(i_0_18883,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X1,X3,X4,X5) = c_Fun_Ocomp(X2,X3,X4,X5) ) ).

cnf(i_0_18884,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X1,X4,X5) = c_Fun_Ocomp(X3,X2,X4,X5) ) ).

cnf(i_0_18885,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X1,X5) = c_Fun_Ocomp(X3,X4,X2,X5) ) ).

cnf(i_0_18886,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X5,X1) = c_Fun_Ocomp(X3,X4,X5,X2) ) ).

cnf(i_0_18887,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_18888,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_18889,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_18890,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_18891,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_18892,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X1,X3,X4,X5) = c_Nitpick_Opair__box_OPairBox(X2,X3,X4,X5) ) ).

cnf(i_0_18893,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X3,X1,X4,X5) = c_Nitpick_Opair__box_OPairBox(X3,X2,X4,X5) ) ).

cnf(i_0_18894,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X3,X4,X1,X5) = c_Nitpick_Opair__box_OPairBox(X3,X4,X2,X5) ) ).

cnf(i_0_18895,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X1) = c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X2) ) ).

cnf(i_0_18896,axiom,
    ( X1 != X2
    | esk368_3(X1,X3,X4) = esk368_3(X2,X3,X4) ) ).

cnf(i_0_18897,axiom,
    ( X1 != X2
    | esk368_3(X3,X1,X4) = esk368_3(X3,X2,X4) ) ).

cnf(i_0_18898,axiom,
    ( X1 != X2
    | esk368_3(X3,X4,X1) = esk368_3(X3,X4,X2) ) ).

cnf(i_0_18899,axiom,
    ( X1 != X2
    | esk369_3(X1,X3,X4) = esk369_3(X2,X3,X4) ) ).

cnf(i_0_18900,axiom,
    ( X1 != X2
    | esk369_3(X3,X1,X4) = esk369_3(X3,X2,X4) ) ).

cnf(i_0_18901,axiom,
    ( X1 != X2
    | esk369_3(X3,X4,X1) = esk369_3(X3,X4,X2) ) ).

cnf(i_0_18902,axiom,
    ( X1 != X2
    | esk40_4(X1,X3,X4,X5) = esk40_4(X2,X3,X4,X5) ) ).

cnf(i_0_18903,axiom,
    ( X1 != X2
    | esk40_4(X3,X1,X4,X5) = esk40_4(X3,X2,X4,X5) ) ).

cnf(i_0_18904,axiom,
    ( X1 != X2
    | esk40_4(X3,X4,X1,X5) = esk40_4(X3,X4,X2,X5) ) ).

cnf(i_0_18905,axiom,
    ( X1 != X2
    | esk40_4(X3,X4,X5,X1) = esk40_4(X3,X4,X5,X2) ) ).

cnf(i_0_18906,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_18907,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_18908,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_18909,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_18910,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).

cnf(i_0_18911,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).

cnf(i_0_18912,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).

cnf(i_0_18913,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).

cnf(i_0_18914,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X1,X3,X4) = c_Nitpick_Oplus__frac(X2,X3,X4) ) ).

cnf(i_0_18915,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X3,X1,X4) = c_Nitpick_Oplus__frac(X3,X2,X4) ) ).

cnf(i_0_18916,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X3,X4,X1) = c_Nitpick_Oplus__frac(X3,X4,X2) ) ).

cnf(i_0_18917,axiom,
    ( X1 != X2
    | esk372_3(X1,X3,X4) = esk372_3(X2,X3,X4) ) ).

cnf(i_0_18918,axiom,
    ( X1 != X2
    | esk372_3(X3,X1,X4) = esk372_3(X3,X2,X4) ) ).

cnf(i_0_18919,axiom,
    ( X1 != X2
    | esk372_3(X3,X4,X1) = esk372_3(X3,X4,X2) ) ).

cnf(i_0_18920,axiom,
    ( X1 != X2
    | esk371_3(X1,X3,X4) = esk371_3(X2,X3,X4) ) ).

cnf(i_0_18921,axiom,
    ( X1 != X2
    | esk371_3(X3,X1,X4) = esk371_3(X3,X2,X4) ) ).

cnf(i_0_18922,axiom,
    ( X1 != X2
    | esk371_3(X3,X4,X1) = esk371_3(X3,X4,X2) ) ).

cnf(i_0_18923,axiom,
    ( X1 != X2
    | c_List_Oupto(X1,X3) = c_List_Oupto(X2,X3) ) ).

cnf(i_0_18924,axiom,
    ( X1 != X2
    | c_List_Oupto(X3,X1) = c_List_Oupto(X3,X2) ) ).

cnf(i_0_18925,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_18926,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_18927,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_18928,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_18929,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_18930,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_18931,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_18932,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_18933,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_18934,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_18935,axiom,
    ( X1 != X2
    | c_List_Olast(X1,X3) = c_List_Olast(X2,X3) ) ).

cnf(i_0_18936,axiom,
    ( X1 != X2
    | c_List_Olast(X3,X1) = c_List_Olast(X3,X2) ) ).

cnf(i_0_18937,axiom,
    ( X1 != X2
    | c_List_Obutlast(X1,X3) = c_List_Obutlast(X2,X3) ) ).

cnf(i_0_18938,axiom,
    ( X1 != X2
    | c_List_Obutlast(X3,X1) = c_List_Obutlast(X3,X2) ) ).

cnf(i_0_18939,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X3,X4) = c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X3,X4) ) ).

cnf(i_0_18940,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X1,X4) = c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X2,X4) ) ).

cnf(i_0_18941,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X4,X1) = c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X4,X2) ) ).

cnf(i_0_18942,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohit__bound(X1) = c_Lazy__Sequence_Ohit__bound(X2) ) ).

cnf(i_0_18943,axiom,
    ( X1 != X2
    | c_Nitpick_Oint__lcm(X1,X3) = c_Nitpick_Oint__lcm(X2,X3) ) ).

cnf(i_0_18944,axiom,
    ( X1 != X2
    | c_Nitpick_Oint__lcm(X3,X1) = c_Nitpick_Oint__lcm(X3,X2) ) ).

cnf(i_0_18945,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_18946,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_18947,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_18948,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_18949,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_18950,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__rec(X1,X3,X4,X5,X6) = c_Option_Ooption_Ooption__rec(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18951,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__rec(X3,X1,X4,X5,X6) = c_Option_Ooption_Ooption__rec(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18952,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__rec(X3,X4,X1,X5,X6) = c_Option_Ooption_Ooption__rec(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18953,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__rec(X3,X4,X5,X1,X6) = c_Option_Ooption_Ooption__rec(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18954,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__rec(X3,X4,X5,X6,X1) = c_Option_Ooption_Ooption__rec(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18955,axiom,
    ( X1 != X2
    | esk116_3(X1,X3,X4) = esk116_3(X2,X3,X4) ) ).

cnf(i_0_18956,axiom,
    ( X1 != X2
    | esk116_3(X3,X1,X4) = esk116_3(X3,X2,X4) ) ).

cnf(i_0_18957,axiom,
    ( X1 != X2
    | esk116_3(X3,X4,X1) = esk116_3(X3,X4,X2) ) ).

cnf(i_0_18958,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OEmpty(X1) = c_Lazy__Sequence_Olazy__sequence_OEmpty(X2) ) ).

cnf(i_0_18959,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy_H(X1,X3) = c_Lazy__Sequence_Osmall__lazy_H(X2,X3) ) ).

cnf(i_0_18960,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy_H(X3,X1) = c_Lazy__Sequence_Osmall__lazy_H(X3,X2) ) ).

cnf(i_0_18961,axiom,
    ( X1 != X2
    | esk523_4(X1,X3,X4,X5) = esk523_4(X2,X3,X4,X5) ) ).

cnf(i_0_18962,axiom,
    ( X1 != X2
    | esk523_4(X3,X1,X4,X5) = esk523_4(X3,X2,X4,X5) ) ).

cnf(i_0_18963,axiom,
    ( X1 != X2
    | esk523_4(X3,X4,X1,X5) = esk523_4(X3,X4,X2,X5) ) ).

cnf(i_0_18964,axiom,
    ( X1 != X2
    | esk523_4(X3,X4,X5,X1) = esk523_4(X3,X4,X5,X2) ) ).

cnf(i_0_18965,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X1,X3,X4) = c_FunDef_OTHE__default(X2,X3,X4) ) ).

cnf(i_0_18966,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X3,X1,X4) = c_FunDef_OTHE__default(X3,X2,X4) ) ).

cnf(i_0_18967,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X3,X4,X1) = c_FunDef_OTHE__default(X3,X4,X2) ) ).

cnf(i_0_18968,axiom,
    ( X1 != X2
    | c_List_Omaps(X1,X3,X4,X5) = c_List_Omaps(X2,X3,X4,X5) ) ).

cnf(i_0_18969,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X1,X4,X5) = c_List_Omaps(X3,X2,X4,X5) ) ).

cnf(i_0_18970,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X4,X1,X5) = c_List_Omaps(X3,X4,X2,X5) ) ).

cnf(i_0_18971,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X4,X5,X1) = c_List_Omaps(X3,X4,X5,X2) ) ).

cnf(i_0_18972,axiom,
    ( X1 != X2
    | esk311_2(X1,X3) = esk311_2(X2,X3) ) ).

cnf(i_0_18973,axiom,
    ( X1 != X2
    | esk311_2(X3,X1) = esk311_2(X3,X2) ) ).

cnf(i_0_18974,axiom,
    ( X1 != X2
    | esk448_2(X1,X3) = esk448_2(X2,X3) ) ).

cnf(i_0_18975,axiom,
    ( X1 != X2
    | esk448_2(X3,X1) = esk448_2(X3,X2) ) ).

cnf(i_0_18976,axiom,
    ( X1 != X2
    | esk449_2(X1,X3) = esk449_2(X2,X3) ) ).

cnf(i_0_18977,axiom,
    ( X1 != X2
    | esk449_2(X3,X1) = esk449_2(X3,X2) ) ).

cnf(i_0_18978,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_18979,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_18980,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_18981,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_18982,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X4) ) ).

cnf(i_0_18983,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X2,X4) ) ).

cnf(i_0_18984,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X2) ) ).

cnf(i_0_18985,axiom,
    ( X1 != X2
    | c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).

cnf(i_0_18986,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X4) ) ).

cnf(i_0_18987,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X2,X4) ) ).

cnf(i_0_18988,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X2) ) ).

cnf(i_0_18989,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_18990,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_18991,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_18992,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_18993,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).

cnf(i_0_18994,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).

cnf(i_0_18995,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).

cnf(i_0_18996,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X1,X3,X4,X5,X6) = c_Predicate_Opred__comp(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18997,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X1,X4,X5,X6) = c_Predicate_Opred__comp(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18998,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X1,X5,X6) = c_Predicate_Opred__comp(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18999,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X5,X1,X6) = c_Predicate_Opred__comp(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19000,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X5,X6,X1) = c_Predicate_Opred__comp(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19001,axiom,
    ( X1 != X2
    | esk433_2(X1,X3) = esk433_2(X2,X3) ) ).

cnf(i_0_19002,axiom,
    ( X1 != X2
    | esk433_2(X3,X1) = esk433_2(X3,X2) ) ).

cnf(i_0_19003,axiom,
    ( X1 != X2
    | esk233_3(X1,X3,X4) = esk233_3(X2,X3,X4) ) ).

cnf(i_0_19004,axiom,
    ( X1 != X2
    | esk233_3(X3,X1,X4) = esk233_3(X3,X2,X4) ) ).

cnf(i_0_19005,axiom,
    ( X1 != X2
    | esk233_3(X3,X4,X1) = esk233_3(X3,X4,X2) ) ).

cnf(i_0_19006,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).

cnf(i_0_19007,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).

cnf(i_0_19008,axiom,
    ( X1 != X2
    | esk235_3(X1,X3,X4) = esk235_3(X2,X3,X4) ) ).

cnf(i_0_19009,axiom,
    ( X1 != X2
    | esk235_3(X3,X1,X4) = esk235_3(X3,X2,X4) ) ).

cnf(i_0_19010,axiom,
    ( X1 != X2
    | esk235_3(X3,X4,X1) = esk235_3(X3,X4,X2) ) ).

cnf(i_0_19011,axiom,
    ( X1 != X2
    | esk24_3(X1,X3,X4) = esk24_3(X2,X3,X4) ) ).

cnf(i_0_19012,axiom,
    ( X1 != X2
    | esk24_3(X3,X1,X4) = esk24_3(X3,X2,X4) ) ).

cnf(i_0_19013,axiom,
    ( X1 != X2
    | esk24_3(X3,X4,X1) = esk24_3(X3,X4,X2) ) ).

cnf(i_0_19014,axiom,
    ( X1 != X2
    | esk23_3(X1,X3,X4) = esk23_3(X2,X3,X4) ) ).

cnf(i_0_19015,axiom,
    ( X1 != X2
    | esk23_3(X3,X1,X4) = esk23_3(X3,X2,X4) ) ).

cnf(i_0_19016,axiom,
    ( X1 != X2
    | esk23_3(X3,X4,X1) = esk23_3(X3,X4,X2) ) ).

cnf(i_0_19017,axiom,
    ( X1 != X2
    | c_Inductive_Ocomplete__lattice__class_Olfp(X1,X3) = c_Inductive_Ocomplete__lattice__class_Olfp(X2,X3) ) ).

cnf(i_0_19018,axiom,
    ( X1 != X2
    | c_Inductive_Ocomplete__lattice__class_Olfp(X3,X1) = c_Inductive_Ocomplete__lattice__class_Olfp(X3,X2) ) ).

cnf(i_0_19019,axiom,
    ( X1 != X2
    | esk521_3(X1,X3,X4) = esk521_3(X2,X3,X4) ) ).

cnf(i_0_19020,axiom,
    ( X1 != X2
    | esk521_3(X3,X1,X4) = esk521_3(X3,X2,X4) ) ).

cnf(i_0_19021,axiom,
    ( X1 != X2
    | esk521_3(X3,X4,X1) = esk521_3(X3,X4,X2) ) ).

cnf(i_0_19022,axiom,
    ( X1 != X2
    | esk508_3(X1,X3,X4) = esk508_3(X2,X3,X4) ) ).

cnf(i_0_19023,axiom,
    ( X1 != X2
    | esk508_3(X3,X1,X4) = esk508_3(X3,X2,X4) ) ).

cnf(i_0_19024,axiom,
    ( X1 != X2
    | esk508_3(X3,X4,X1) = esk508_3(X3,X4,X2) ) ).

cnf(i_0_19025,axiom,
    ( X1 != X2
    | c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X3) = c_Inductive_Ocomplete__lattice__class_Ogfp(X2,X3) ) ).

cnf(i_0_19026,axiom,
    ( X1 != X2
    | c_Inductive_Ocomplete__lattice__class_Ogfp(X3,X1) = c_Inductive_Ocomplete__lattice__class_Ogfp(X3,X2) ) ).

cnf(i_0_19027,axiom,
    ( X1 != X2
    | c_List_Osplice(X1,X3,X4) = c_List_Osplice(X2,X3,X4) ) ).

cnf(i_0_19028,axiom,
    ( X1 != X2
    | c_List_Osplice(X3,X1,X4) = c_List_Osplice(X3,X2,X4) ) ).

cnf(i_0_19029,axiom,
    ( X1 != X2
    | c_List_Osplice(X3,X4,X1) = c_List_Osplice(X3,X4,X2) ) ).

cnf(i_0_19030,axiom,
    ( X1 != X2
    | c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).

cnf(i_0_19031,axiom,
    ( X1 != X2
    | c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).

cnf(i_0_19032,axiom,
    ( X1 != X2
    | c_Random_Olog(X1,X3) = c_Random_Olog(X2,X3) ) ).

cnf(i_0_19033,axiom,
    ( X1 != X2
    | c_Random_Olog(X3,X1) = c_Random_Olog(X3,X2) ) ).

cnf(i_0_19034,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X1,X3,X4) = c_Random_Ominus__shift(X2,X3,X4) ) ).

cnf(i_0_19035,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X3,X1,X4) = c_Random_Ominus__shift(X3,X2,X4) ) ).

cnf(i_0_19036,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X3,X4,X1) = c_Random_Ominus__shift(X3,X4,X2) ) ).

cnf(i_0_19037,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X1,X3,X4) = c_Random__Sequence_Oempty(X2,X3,X4) ) ).

cnf(i_0_19038,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X3,X1,X4) = c_Random__Sequence_Oempty(X3,X2,X4) ) ).

cnf(i_0_19039,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X3,X4,X1) = c_Random__Sequence_Oempty(X3,X4,X2) ) ).

cnf(i_0_19040,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_19041,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_19042,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_19043,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_19044,axiom,
    ( X1 != X2
    | esk445_2(X1,X3) = esk445_2(X2,X3) ) ).

cnf(i_0_19045,axiom,
    ( X1 != X2
    | esk445_2(X3,X1) = esk445_2(X3,X2) ) ).

cnf(i_0_19046,axiom,
    ( X1 != X2
    | c_List_Olistset(X1,X3) = c_List_Olistset(X2,X3) ) ).

cnf(i_0_19047,axiom,
    ( X1 != X2
    | c_List_Olistset(X3,X1) = c_List_Olistset(X3,X2) ) ).

cnf(i_0_19048,axiom,
    ( X1 != X2
    | c_Code__Numeral_Odiv__mod__code__numeral(X1,X3) = c_Code__Numeral_Odiv__mod__code__numeral(X2,X3) ) ).

cnf(i_0_19049,axiom,
    ( X1 != X2
    | c_Code__Numeral_Odiv__mod__code__numeral(X3,X1) = c_Code__Numeral_Odiv__mod__code__numeral(X3,X2) ) ).

cnf(i_0_19050,axiom,
    ( X1 != X2
    | esk414_2(X1,X3) = esk414_2(X2,X3) ) ).

cnf(i_0_19051,axiom,
    ( X1 != X2
    | esk414_2(X3,X1) = esk414_2(X3,X2) ) ).

cnf(i_0_19052,axiom,
    ( X1 != X2
    | esk413_2(X1,X3) = esk413_2(X2,X3) ) ).

cnf(i_0_19053,axiom,
    ( X1 != X2
    | esk413_2(X3,X1) = esk413_2(X3,X2) ) ).

cnf(i_0_19054,axiom,
    ( X1 != X2
    | esk506_3(X1,X3,X4) = esk506_3(X2,X3,X4) ) ).

cnf(i_0_19055,axiom,
    ( X1 != X2
    | esk506_3(X3,X1,X4) = esk506_3(X3,X2,X4) ) ).

cnf(i_0_19056,axiom,
    ( X1 != X2
    | esk506_3(X3,X4,X1) = esk506_3(X3,X4,X2) ) ).

cnf(i_0_19057,axiom,
    ( X1 != X2
    | c_List_Oinsert(X1,X3,X4) = c_List_Oinsert(X2,X3,X4) ) ).

cnf(i_0_19058,axiom,
    ( X1 != X2
    | c_List_Oinsert(X3,X1,X4) = c_List_Oinsert(X3,X2,X4) ) ).

cnf(i_0_19059,axiom,
    ( X1 != X2
    | c_List_Oinsert(X3,X4,X1) = c_List_Oinsert(X3,X4,X2) ) ).

cnf(i_0_19060,axiom,
    ( X1 != X2
    | c_Int_Oring__1__class_Oof__int(X1) = c_Int_Oring__1__class_Oof__int(X2) ) ).

cnf(i_0_19061,axiom,
    ( X1 != X2
    | esk524_3(X1,X3,X4) = esk524_3(X2,X3,X4) ) ).

cnf(i_0_19062,axiom,
    ( X1 != X2
    | esk524_3(X3,X1,X4) = esk524_3(X3,X2,X4) ) ).

cnf(i_0_19063,axiom,
    ( X1 != X2
    | esk524_3(X3,X4,X1) = esk524_3(X3,X4,X2) ) ).

cnf(i_0_19064,axiom,
    ( X1 != X2
    | c_SMT_Oz3div(X1,X3) = c_SMT_Oz3div(X2,X3) ) ).

cnf(i_0_19065,axiom,
    ( X1 != X2
    | c_SMT_Oz3div(X3,X1) = c_SMT_Oz3div(X3,X2) ) ).

cnf(i_0_19066,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omin(X1,X3) = c_Orderings_Oord_Omin(X2,X3) ) ).

cnf(i_0_19067,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omin(X3,X1) = c_Orderings_Oord_Omin(X3,X2) ) ).

cnf(i_0_19068,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omax(X1,X3) = c_Orderings_Oord_Omax(X2,X3) ) ).

cnf(i_0_19069,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omax(X3,X1) = c_Orderings_Oord_Omax(X3,X2) ) ).

cnf(i_0_19070,axiom,
    ( X1 != X2
    | c_Option_Oset(X1,X3) = c_Option_Oset(X2,X3) ) ).

cnf(i_0_19071,axiom,
    ( X1 != X2
    | c_Option_Oset(X3,X1) = c_Option_Oset(X3,X2) ) ).

cnf(i_0_19072,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__single(X1,X3) = c_New__DSequence_Oneg__single(X2,X3) ) ).

cnf(i_0_19073,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__single(X3,X1) = c_New__DSequence_Oneg__single(X3,X2) ) ).

cnf(i_0_19074,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__single(X1,X3) = c_New__DSequence_Opos__single(X2,X3) ) ).

cnf(i_0_19075,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__single(X3,X1) = c_New__DSequence_Opos__single(X3,X2) ) ).

cnf(i_0_19076,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X1) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X2) ) ).

cnf(i_0_19077,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X1,X3,X4) = c_Predicate_Oconversep(X2,X3,X4) ) ).

cnf(i_0_19078,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X1,X4) = c_Predicate_Oconversep(X3,X2,X4) ) ).

cnf(i_0_19079,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X4,X1) = c_Predicate_Oconversep(X3,X4,X2) ) ).

cnf(i_0_19080,axiom,
    ( X1 != X2
    | c_SMT_Oz3mod(X1,X3) = c_SMT_Oz3mod(X2,X3) ) ).

cnf(i_0_19081,axiom,
    ( X1 != X2
    | c_SMT_Oz3mod(X3,X1) = c_SMT_Oz3mod(X3,X2) ) ).

cnf(i_0_19082,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__size(X1,X3,X4) = c_Option_Ooption_Ooption__size(X2,X3,X4) ) ).

cnf(i_0_19083,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__size(X3,X1,X4) = c_Option_Ooption_Ooption__size(X3,X2,X4) ) ).

cnf(i_0_19084,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__size(X3,X4,X1) = c_Option_Ooption_Ooption__size(X3,X4,X2) ) ).

cnf(i_0_19085,axiom,
    ( X1 != X2
    | esk482_2(X1,X3) = esk482_2(X2,X3) ) ).

cnf(i_0_19086,axiom,
    ( X1 != X2
    | esk482_2(X3,X1) = esk482_2(X3,X2) ) ).

cnf(i_0_19087,axiom,
    ( X1 != X2
    | c_Smallcheck_Ofull__small__class_Ofull__small(X1,X3,X4) = c_Smallcheck_Ofull__small__class_Ofull__small(X2,X3,X4) ) ).

cnf(i_0_19088,axiom,
    ( X1 != X2
    | c_Smallcheck_Ofull__small__class_Ofull__small(X3,X1,X4) = c_Smallcheck_Ofull__small__class_Ofull__small(X3,X2,X4) ) ).

cnf(i_0_19089,axiom,
    ( X1 != X2
    | c_Smallcheck_Ofull__small__class_Ofull__small(X3,X4,X1) = c_Smallcheck_Ofull__small__class_Ofull__small(X3,X4,X2) ) ).

cnf(i_0_19090,axiom,
    ( X1 != X2
    | c_Smallcheck_Ofull__small_H(X1,X3,X4) = c_Smallcheck_Ofull__small_H(X2,X3,X4) ) ).

cnf(i_0_19091,axiom,
    ( X1 != X2
    | c_Smallcheck_Ofull__small_H(X3,X1,X4) = c_Smallcheck_Ofull__small_H(X3,X2,X4) ) ).

cnf(i_0_19092,axiom,
    ( X1 != X2
    | c_Smallcheck_Ofull__small_H(X3,X4,X1) = c_Smallcheck_Ofull__small_H(X3,X4,X2) ) ).

cnf(i_0_19093,axiom,
    ( X1 != X2
    | esk400_1(X1) = esk400_1(X2) ) ).

cnf(i_0_19094,axiom,
    ( X1 != X2
    | esk507_2(X1,X3) = esk507_2(X2,X3) ) ).

cnf(i_0_19095,axiom,
    ( X1 != X2
    | esk507_2(X3,X1) = esk507_2(X3,X2) ) ).

cnf(i_0_19096,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).

cnf(i_0_19097,axiom,
    ( X1 != X2
    | c_Random_Oinc__shift(X1,X3) = c_Random_Oinc__shift(X2,X3) ) ).

cnf(i_0_19098,axiom,
    ( X1 != X2
    | c_Random_Oinc__shift(X3,X1) = c_Random_Oinc__shift(X3,X2) ) ).

cnf(i_0_19099,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__single(X1,X3) = c_Lazy__Sequence_Ohb__single(X2,X3) ) ).

cnf(i_0_19100,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__single(X3,X1) = c_Lazy__Sequence_Ohb__single(X3,X2) ) ).

cnf(i_0_19101,axiom,
    ( X1 != X2
    | c_HOL_Obool_Obool__size(X1) = c_HOL_Obool_Obool__size(X2) ) ).

cnf(i_0_19102,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X1,X3,X4,X5) = c_Option_Ooption_Ooption__case(X2,X3,X4,X5) ) ).

cnf(i_0_19103,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X1,X4,X5) = c_Option_Ooption_Ooption__case(X3,X2,X4,X5) ) ).

cnf(i_0_19104,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X4,X1,X5) = c_Option_Ooption_Ooption__case(X3,X4,X2,X5) ) ).

cnf(i_0_19105,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X4,X5,X1) = c_Option_Ooption_Ooption__case(X3,X4,X5,X2) ) ).

cnf(i_0_19106,axiom,
    ( X1 != X2
    | c_Divides_Oadjust(X1) = c_Divides_Oadjust(X2) ) ).

cnf(i_0_19107,axiom,
    ( X1 != X2
    | c_FunDef_Orp__inv__image(X1,X3) = c_FunDef_Orp__inv__image(X2,X3) ) ).

cnf(i_0_19108,axiom,
    ( X1 != X2
    | c_FunDef_Orp__inv__image(X3,X1) = c_FunDef_Orp__inv__image(X3,X2) ) ).

cnf(i_0_19109,axiom,
    ( X1 != X2
    | c_Map_Omap__add(X1,X3,X4,X5) = c_Map_Omap__add(X2,X3,X4,X5) ) ).

cnf(i_0_19110,axiom,
    ( X1 != X2
    | c_Map_Omap__add(X3,X1,X4,X5) = c_Map_Omap__add(X3,X2,X4,X5) ) ).

cnf(i_0_19111,axiom,
    ( X1 != X2
    | c_Map_Omap__add(X3,X4,X1,X5) = c_Map_Omap__add(X3,X4,X2,X5) ) ).

cnf(i_0_19112,axiom,
    ( X1 != X2
    | c_Map_Omap__add(X3,X4,X5,X1) = c_Map_Omap__add(X3,X4,X5,X2) ) ).

cnf(i_0_19113,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_19114,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | class_Groups_Ocomm__monoid__add(X2) ) ).

cnf(i_0_19115,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring(X1)
    | class_Rings_Olinordered__semiring(X2) ) ).

cnf(i_0_19116,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_19117,axiom,
    ( X1 != X2
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).

cnf(i_0_19118,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oreflp(X1,X3)
    | c_Predicate_Oreflp(X2,X3) ) ).

cnf(i_0_19119,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oreflp(X3,X1)
    | c_Predicate_Oreflp(X3,X2) ) ).

cnf(i_0_19120,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__comm__semiring__strict(X1)
    | class_Rings_Olinordered__comm__semiring__strict(X2) ) ).

cnf(i_0_19121,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__comm__semiring(X1)
    | class_Rings_Oordered__comm__semiring(X2) ) ).

cnf(i_0_19122,axiom,
    ( X1 != X2
    | ~ class_Divides_Oring__div(X1)
    | class_Divides_Oring__div(X2) ) ).

cnf(i_0_19123,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | class_Groups_Olinordered__ab__group__add(X2) ) ).

cnf(i_0_19124,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | class_Rings_Oordered__cancel__semiring(X2) ) ).

cnf(i_0_19125,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X4) ) ).

cnf(i_0_19126,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X4) ) ).

cnf(i_0_19127,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X1)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X2) ) ).

cnf(i_0_19128,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1(X1)
    | class_Rings_Oring__1(X2) ) ).

cnf(i_0_19129,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring__abs(X1)
    | class_Rings_Oordered__ring__abs(X2) ) ).

cnf(i_0_19130,axiom,
    ( X1 != X2
    | ~ class_Orderings_Owellorder(X1)
    | class_Orderings_Owellorder(X2) ) ).

cnf(i_0_19131,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oboolean__algebra(X1)
    | class_Lattices_Oboolean__algebra(X2) ) ).

cnf(i_0_19132,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring(X1)
    | class_Rings_Odivision__ring(X2) ) ).

cnf(i_0_19133,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring(X1)
    | class_Rings_Ocomm__semiring(X2) ) ).

cnf(i_0_19134,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder__class_Ostrict__mono(X1,X3,X4)
    | c_Orderings_Oorder__class_Ostrict__mono(X2,X3,X4) ) ).

cnf(i_0_19135,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder__class_Ostrict__mono(X3,X1,X4)
    | c_Orderings_Oorder__class_Ostrict__mono(X3,X2,X4) ) ).

cnf(i_0_19136,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder__class_Ostrict__mono(X3,X4,X1)
    | c_Orderings_Oorder__class_Ostrict__mono(X3,X4,X2) ) ).

cnf(i_0_19137,axiom,
    ( X1 != X2
    | ~ c_Partial__Function_Omk__less(X1,X3,X4,X5)
    | c_Partial__Function_Omk__less(X2,X3,X4,X5) ) ).

cnf(i_0_19138,axiom,
    ( X1 != X2
    | ~ c_Partial__Function_Omk__less(X3,X1,X4,X5)
    | c_Partial__Function_Omk__less(X3,X2,X4,X5) ) ).

cnf(i_0_19139,axiom,
    ( X1 != X2
    | ~ c_Partial__Function_Omk__less(X3,X4,X1,X5)
    | c_Partial__Function_Omk__less(X3,X4,X2,X5) ) ).

cnf(i_0_19140,axiom,
    ( X1 != X2
    | ~ c_Partial__Function_Omk__less(X3,X4,X5,X1)
    | c_Partial__Function_Omk__less(X3,X4,X5,X2) ) ).

cnf(i_0_19141,axiom,
    ( X1 != X2
    | ~ class_Groups_Ominus(X1)
    | class_Groups_Ominus(X2) ) ).

cnf(i_0_19142,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_19143,axiom,
    ( X1 != X2
    | ~ class_Groups_Ogroup__add(X1)
    | class_Groups_Ogroup__add(X2) ) ).

cnf(i_0_19144,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | class_Groups_Ocomm__monoid__mult(X2) ) ).

cnf(i_0_19145,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X1,X3,X4,X5)
    | c_Nat__Transfer_Otransfer__morphism(X2,X3,X4,X5) ) ).

cnf(i_0_19146,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X1,X4,X5)
    | c_Nat__Transfer_Otransfer__morphism(X3,X2,X4,X5) ) ).

cnf(i_0_19147,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X1,X5)
    | c_Nat__Transfer_Otransfer__morphism(X3,X4,X2,X5) ) ).

cnf(i_0_19148,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X1)
    | c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X2) ) ).

cnf(i_0_19149,axiom,
    ( X1 != X2
    | ~ class_Nat_Osemiring__char__0(X1)
    | class_Nat_Osemiring__char__0(X2) ) ).

cnf(i_0_19150,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Owf_H(X1,X3)
    | c_Nitpick_Owf_H(X2,X3) ) ).

cnf(i_0_19151,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Owf_H(X3,X1)
    | c_Nitpick_Owf_H(X3,X2) ) ).

cnf(i_0_19152,axiom,
    ( X1 != X2
    | ~ c_List_Onat__list(X1)
    | c_List_Onat__list(X2) ) ).

cnf(i_0_19153,axiom,
    ( X1 != X2
    | ~ class_Groups_Osgn__if(X1)
    | class_Groups_Osgn__if(X2) ) ).

cnf(i_0_19154,axiom,
    ( X1 != X2
    | ~ class_Power_Opower(X1)
    | class_Power_Opower(X2) ) ).

cnf(i_0_19155,axiom,
    ( X1 != X2
    | ~ class_Groups_Oabs__if(X1)
    | class_Groups_Oabs__if(X2) ) ).

cnf(i_0_19156,axiom,
    ( X1 != X2
    | ~ class_Groups_Ouminus(X1)
    | class_Groups_Ouminus(X2) ) ).

cnf(i_0_19157,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X1,X3,X4)
    | c_Big__Operators_Osemilattice__big(X2,X3,X4) ) ).

cnf(i_0_19158,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X3,X1,X4)
    | c_Big__Operators_Osemilattice__big(X3,X2,X4) ) ).

cnf(i_0_19159,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X3,X4,X1)
    | c_Big__Operators_Osemilattice__big(X3,X4,X2) ) ).

cnf(i_0_19160,axiom,
    ( X1 != X2
    | ~ class_Rings_Oidom(X1)
    | class_Rings_Oidom(X2) ) ).

cnf(i_0_19161,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oord(X1)
    | class_Orderings_Oord(X2) ) ).

cnf(i_0_19162,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__ring__1(X1)
    | class_Rings_Ocomm__ring__1(X2) ) ).

cnf(i_0_19163,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | class_Groups_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_19164,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__ab__semigroup__add(X1)
    | class_Groups_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_19165,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Ounknown(X1)
    | c_Nitpick_Ounknown(X2) ) ).

cnf(i_0_19166,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(X2) ) ).

cnf(i_0_19167,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_19168,axiom,
    ( X1 != X2
    | ~ class_Orderings_Otop(X1)
    | class_Orderings_Otop(X2) ) ).

cnf(i_0_19169,axiom,
    ( X1 != X2
    | ~ class_Rings_Omult__zero(X1)
    | class_Rings_Omult__zero(X2) ) ).

cnf(i_0_19170,axiom,
    ( X1 != X2
    | ~ class_Rings_Ozero__neq__one(X1)
    | class_Rings_Ozero__neq__one(X2) ) ).

cnf(i_0_19171,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | class_Rings_Oring__no__zero__divisors(X2) ) ).

cnf(i_0_19172,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__semigroup__add(X1)
    | class_Groups_Olinordered__ab__semigroup__add(X2) ) ).

cnf(i_0_19173,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice__top(X1)
    | class_Lattices_Obounded__lattice__top(X2) ) ).

cnf(i_0_19174,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice__bot(X1)
    | class_Lattices_Obounded__lattice__bot(X2) ) ).

cnf(i_0_19175,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring__inverse__zero(X1)
    | class_Rings_Odivision__ring__inverse__zero(X2) ) ).

cnf(i_0_19176,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice(X1)
    | class_Lattices_Obounded__lattice(X2) ) ).

cnf(i_0_19177,axiom,
    ( X1 != X2
    | ~ class_Nat_Osize(X1)
    | class_Nat_Osize(X2) ) ).

cnf(i_0_19178,axiom,
    ( X1 != X2
    | ~ class_Groups_Ozero(X1)
    | class_Groups_Ozero(X2) ) ).

cnf(i_0_19179,axiom,
    ( X1 != X2
    | ~ class_Groups_Oone(X1)
    | class_Groups_Oone(X2) ) ).

cnf(i_0_19180,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_19181,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_19182,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_19183,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_19184,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_19185,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_19186,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__idom(X1)
    | class_Rings_Olinordered__idom(X2) ) ).

cnf(i_0_19187,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_19188,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_19189,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_19190,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_19191,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_19192,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_19193,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_19194,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X1,X3,X4)
    | c_Relation_Orefl__on(X2,X3,X4) ) ).

cnf(i_0_19195,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X3,X1,X4)
    | c_Relation_Orefl__on(X3,X2,X4) ) ).

cnf(i_0_19196,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X3,X4,X1)
    | c_Relation_Orefl__on(X3,X4,X2) ) ).

cnf(i_0_19197,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_19198,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_19199,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_19200,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_19201,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_19202,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_19203,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X1,X3,X4,X5)
    | c_Wellfounded_Omax__extp(X2,X3,X4,X5) ) ).

cnf(i_0_19204,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X1,X4,X5)
    | c_Wellfounded_Omax__extp(X3,X2,X4,X5) ) ).

cnf(i_0_19205,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X4,X1,X5)
    | c_Wellfounded_Omax__extp(X3,X4,X2,X5) ) ).

cnf(i_0_19206,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X4,X5,X1)
    | c_Wellfounded_Omax__extp(X3,X4,X5,X2) ) ).

cnf(i_0_19207,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X1,X3,X4,X5)
    | c_List_Olistrelp(X2,X3,X4,X5) ) ).

cnf(i_0_19208,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X1,X4,X5)
    | c_List_Olistrelp(X3,X2,X4,X5) ) ).

cnf(i_0_19209,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X4,X1,X5)
    | c_List_Olistrelp(X3,X4,X2,X5) ) ).

cnf(i_0_19210,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X4,X5,X1)
    | c_List_Olistrelp(X3,X4,X5,X2) ) ).

cnf(i_0_19211,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequivp(X1,X3)
    | c_Equiv__Relations_Oequivp(X2,X3) ) ).

cnf(i_0_19212,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequivp(X3,X1)
    | c_Equiv__Relations_Oequivp(X3,X2) ) ).

cnf(i_0_19213,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Owf(X1,X3)
    | c_Wellfounded_Owf(X2,X3) ) ).

cnf(i_0_19214,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Owf(X3,X1)
    | c_Wellfounded_Owf(X3,X2) ) ).

cnf(i_0_19215,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_OwfP(X1,X3)
    | c_Wellfounded_OwfP(X2,X3) ) ).

cnf(i_0_19216,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_OwfP(X3,X1)
    | c_Wellfounded_OwfP(X3,X2) ) ).

cnf(i_0_19217,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X1,X3,X4)
    | c_Finite__Set_Ofun__left__comm(X2,X3,X4) ) ).

cnf(i_0_19218,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X3,X1,X4)
    | c_Finite__Set_Ofun__left__comm(X3,X2,X4) ) ).

cnf(i_0_19219,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X3,X4,X1)
    | c_Finite__Set_Ofun__left__comm(X3,X4,X2) ) ).

cnf(i_0_19220,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semidom(X1)
    | class_Rings_Olinordered__semidom(X2) ) ).

cnf(i_0_19221,axiom,
    ( X1 != X2
    | ~ class_Lazy__Sequence_Osmall__lazy(X1)
    | class_Lazy__Sequence_Osmall__lazy(X2) ) ).

cnf(i_0_19222,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_19223,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | class_Groups_Oordered__ab__group__add(X2) ) ).

cnf(i_0_19224,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X4)
    | c_Equiv__Relations_Oequiv(X2,X3,X4) ) ).

cnf(i_0_19225,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X3,X1,X4)
    | c_Equiv__Relations_Oequiv(X3,X2,X4) ) ).

cnf(i_0_19226,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X3,X4,X1)
    | c_Equiv__Relations_Oequiv(X3,X4,X2) ) ).

cnf(i_0_19227,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_19228,axiom,
    ( X1 != X2
    | ~ class_Smallcheck_Osmall(X1)
    | class_Smallcheck_Osmall(X2) ) ).

cnf(i_0_19229,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__mult(X1)
    | class_Groups_Omonoid__mult(X2) ) ).

cnf(i_0_19230,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__mult(X1)
    | class_Groups_Oab__semigroup__mult(X2) ) ).

cnf(i_0_19231,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__add(X1)
    | class_Groups_Omonoid__add(X2) ) ).

cnf(i_0_19232,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | class_Groups_Oordered__ab__semigroup__add(X2) ) ).

cnf(i_0_19233,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X1,X3,X4,X5,X6)
    | c_List_Olist__all2(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19234,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X1,X4,X5,X6)
    | c_List_Olist__all2(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19235,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X1,X5,X6)
    | c_List_Olist__all2(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19236,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X5,X1,X6)
    | c_List_Olist__all2(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19237,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X5,X6,X1)
    | c_List_Olist__all2(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19238,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_19239,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X1,X3,X4)
    | c_Finite__Set_Ofolding__one__idem(X2,X3,X4) ) ).

cnf(i_0_19240,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X3,X1,X4)
    | c_Finite__Set_Ofolding__one__idem(X3,X2,X4) ) ).

cnf(i_0_19241,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X3,X4,X1)
    | c_Finite__Set_Ofolding__one__idem(X3,X4,X2) ) ).

cnf(i_0_19242,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | class_Rings_Ocomm__semiring__1(X2) ) ).

cnf(i_0_19243,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring__0(X1)
    | class_Rings_Osemiring__0(X2) ) ).

cnf(i_0_19244,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring__1(X1)
    | class_Rings_Osemiring__1(X2) ) ).

cnf(i_0_19245,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X1,X3,X4)
    | c_Finite__Set_Ofolding__one(X2,X3,X4) ) ).

cnf(i_0_19246,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X3,X1,X4)
    | c_Finite__Set_Ofolding__one(X3,X2,X4) ) ).

cnf(i_0_19247,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X3,X4,X1)
    | c_Finite__Set_Ofolding__one(X3,X4,X2) ) ).

cnf(i_0_19248,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | class_Fields_Olinordered__field__inverse__zero(X2) ) ).

cnf(i_0_19249,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oreduction__pair(X1,X3)
    | c_FunDef_Oreduction__pair(X2,X3) ) ).

cnf(i_0_19250,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oreduction__pair(X3,X1)
    | c_FunDef_Oreduction__pair(X3,X2) ) ).

cnf(i_0_19251,axiom,
    ( X1 != X2
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | c_List_Olinorder__class_Osorted(X2,X3) ) ).

cnf(i_0_19252,axiom,
    ( X1 != X2
    | ~ c_List_Olinorder__class_Osorted(X3,X1)
    | c_List_Olinorder__class_Osorted(X3,X2) ) ).

cnf(i_0_19253,axiom,
    ( X1 != X2
    | ~ class_Enum_Oenum(X1)
    | class_Enum_Oenum(X2) ) ).

cnf(i_0_19254,axiom,
    ( X1 != X2
    | ~ c_Enum_Oex__n__lists(X1,X3,X4)
    | c_Enum_Oex__n__lists(X2,X3,X4) ) ).

cnf(i_0_19255,axiom,
    ( X1 != X2
    | ~ c_Enum_Oex__n__lists(X3,X1,X4)
    | c_Enum_Oex__n__lists(X3,X2,X4) ) ).

cnf(i_0_19256,axiom,
    ( X1 != X2
    | ~ c_Enum_Oex__n__lists(X3,X4,X1)
    | c_Enum_Oex__n__lists(X3,X4,X2) ) ).

cnf(i_0_19257,axiom,
    ( X1 != X2
    | ~ class_HOL_Oequal(X1)
    | class_HOL_Oequal(X2) ) ).

cnf(i_0_19258,axiom,
    ( X1 != X2
    | ~ c_Enum_Oall__n__lists(X1,X3,X4)
    | c_Enum_Oall__n__lists(X2,X3,X4) ) ).

cnf(i_0_19259,axiom,
    ( X1 != X2
    | ~ c_Enum_Oall__n__lists(X3,X1,X4)
    | c_Enum_Oall__n__lists(X3,X2,X4) ) ).

cnf(i_0_19260,axiom,
    ( X1 != X2
    | ~ c_Enum_Oall__n__lists(X3,X4,X1)
    | c_Enum_Oall__n__lists(X3,X4,X2) ) ).

cnf(i_0_19261,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Ois__nat(X1)
    | c_Nat__Transfer_Ois__nat(X2) ) ).

cnf(i_0_19262,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_19263,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_19264,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_19265,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_19266,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X1,X3,X4)
    | c_Nitpick_Oless__eq__frac(X2,X3,X4) ) ).

cnf(i_0_19267,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X3,X1,X4)
    | c_Nitpick_Oless__eq__frac(X3,X2,X4) ) ).

cnf(i_0_19268,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X3,X4,X1)
    | c_Nitpick_Oless__eq__frac(X3,X4,X2) ) ).

cnf(i_0_19269,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X1,X3,X4)
    | c_Nitpick_Oless__frac(X2,X3,X4) ) ).

cnf(i_0_19270,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X3,X1,X4)
    | c_Nitpick_Oless__frac(X3,X2,X4) ) ).

cnf(i_0_19271,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X3,X4,X1)
    | c_Nitpick_Oless__frac(X3,X4,X2) ) ).

cnf(i_0_19272,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | class_Groups_Oordered__comm__monoid__add(X2) ) ).

cnf(i_0_19273,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring(X1)
    | class_Rings_Oordered__ring(X2) ) ).

cnf(i_0_19274,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__group__add(X1)
    | class_Groups_Oab__group__add(X2) ) ).

cnf(i_0_19275,axiom,
    ( X1 != X2
    | ~ class_Rings_Oinverse(X1)
    | class_Rings_Oinverse(X2) ) ).

cnf(i_0_19276,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield(X1)
    | class_Fields_Ofield(X2) ) ).

cnf(i_0_19277,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X1,X3,X4)
    | c_List_Olist__ex1(X2,X3,X4) ) ).

cnf(i_0_19278,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X3,X1,X4)
    | c_List_Olist__ex1(X3,X2,X4) ) ).

cnf(i_0_19279,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X3,X4,X1)
    | c_List_Olist__ex1(X3,X4,X2) ) ).

cnf(i_0_19280,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X1,X3,X4)
    | c_List_Olist__all(X2,X3,X4) ) ).

cnf(i_0_19281,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X3,X1,X4)
    | c_List_Olist__all(X3,X2,X4) ) ).

cnf(i_0_19282,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X3,X4,X1)
    | c_List_Olist__all(X3,X4,X2) ) ).

cnf(i_0_19283,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_19284,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_19285,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_19286,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_19287,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_19288,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_19289,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_19290,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oinv__imagep(X1,X3,X4,X5,X6,X7)
    | c_Predicate_Oinv__imagep(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_19291,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oinv__imagep(X3,X1,X4,X5,X6,X7)
    | c_Predicate_Oinv__imagep(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_19292,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oinv__imagep(X3,X4,X1,X5,X6,X7)
    | c_Predicate_Oinv__imagep(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_19293,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oinv__imagep(X3,X4,X5,X1,X6,X7)
    | c_Predicate_Oinv__imagep(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_19294,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oinv__imagep(X3,X4,X5,X6,X1,X7)
    | c_Predicate_Oinv__imagep(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_19295,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oinv__imagep(X3,X4,X5,X6,X7,X1)
    | c_Predicate_Oinv__imagep(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_19296,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | class_Groups_Oordered__ab__group__add__abs(X2) ) ).

cnf(i_0_19297,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_19298,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_19299,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_19300,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_19301,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_19302,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | class_Rings_Oring__1__no__zero__divisors(X2) ) ).

cnf(i_0_19303,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Onat__set(X1)
    | c_Nat__Transfer_Onat__set(X2) ) ).

cnf(i_0_19304,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | class_Fields_Ofield__inverse__zero(X2) ) ).

cnf(i_0_19305,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_19306,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_19307,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_19308,axiom,
    ( X1 != X2
    | ~ class_Lattices_Osemilattice__sup(X1)
    | class_Lattices_Osemilattice__sup(X2) ) ).

cnf(i_0_19309,axiom,
    ( X1 != X2
    | ~ c_Int_Oiszero(X1,X3)
    | c_Int_Oiszero(X2,X3) ) ).

cnf(i_0_19310,axiom,
    ( X1 != X2
    | ~ c_Int_Oiszero(X3,X1)
    | c_Int_Oiszero(X3,X2) ) ).

cnf(i_0_19311,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X1,X3,X4)
    | c_Relation_Ototal__on(X2,X3,X4) ) ).

cnf(i_0_19312,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X3,X1,X4)
    | c_Relation_Ototal__on(X3,X2,X4) ) ).

cnf(i_0_19313,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X3,X4,X1)
    | c_Relation_Ototal__on(X3,X4,X2) ) ).

cnf(i_0_19314,axiom,
    ( X1 != X2
    | ~ class_Lattices_Odistrib__lattice(X1)
    | class_Lattices_Odistrib__lattice(X2) ) ).

cnf(i_0_19315,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X1,X3,X4)
    | c_Relation_Osingle__valued(X2,X3,X4) ) ).

cnf(i_0_19316,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X3,X1,X4)
    | c_Relation_Osingle__valued(X3,X2,X4) ) ).

cnf(i_0_19317,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X3,X4,X1)
    | c_Relation_Osingle__valued(X3,X4,X2) ) ).

cnf(i_0_19318,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber(X1)
    | class_Int_Onumber(X2) ) ).

cnf(i_0_19319,axiom,
    ( X1 != X2
    | ~ class_Divides_Osemiring__div(X1)
    | class_Divides_Osemiring__div(X2) ) ).

cnf(i_0_19320,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | class_Rings_Olinordered__ring__strict(X2) ) ).

cnf(i_0_19321,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_19322,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring(X1)
    | class_Rings_Olinordered__ring(X2) ) ).

cnf(i_0_19323,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X1,X3,X4,X5)
    | c_Finite__Set_Ofolding(X2,X3,X4,X5) ) ).

cnf(i_0_19324,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X1,X4,X5)
    | c_Finite__Set_Ofolding(X3,X2,X4,X5) ) ).

cnf(i_0_19325,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X4,X1,X5)
    | c_Finite__Set_Ofolding(X3,X4,X2,X5) ) ).

cnf(i_0_19326,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X4,X5,X1)
    | c_Finite__Set_Ofolding(X3,X4,X5,X2) ) ).

cnf(i_0_19327,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__1__strict(X1)
    | class_Rings_Olinordered__semiring__1__strict(X2) ) ).

cnf(i_0_19328,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__1(X1)
    | class_Rings_Olinordered__semiring__1(X2) ) ).

cnf(i_0_19329,axiom,
    ( X1 != X2
    | ~ class_Lattices_Osemilattice__inf(X1)
    | class_Lattices_Osemilattice__inf(X2) ) ).

cnf(i_0_19330,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder__class_Omono(X1,X3,X4)
    | c_Orderings_Oorder__class_Omono(X2,X3,X4) ) ).

cnf(i_0_19331,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder__class_Omono(X3,X1,X4)
    | c_Orderings_Oorder__class_Omono(X3,X2,X4) ) ).

cnf(i_0_19332,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder__class_Omono(X3,X4,X1)
    | c_Orderings_Oorder__class_Omono(X3,X4,X2) ) ).

cnf(i_0_19333,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field(X1)
    | class_Fields_Olinordered__field(X2) ) ).

cnf(i_0_19334,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oacyclic(X1,X3)
    | c_Wellfounded_Oacyclic(X2,X3) ) ).

cnf(i_0_19335,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oacyclic(X3,X1)
    | c_Wellfounded_Oacyclic(X3,X2) ) ).

cnf(i_0_19336,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1)
    | class_Lattices_Oab__semigroup__idem__mult(X2) ) ).

cnf(i_0_19337,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Orefl_H(X1,X3)
    | c_Nitpick_Orefl_H(X2,X3) ) ).

cnf(i_0_19338,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Orefl_H(X3,X1)
    | c_Nitpick_Orefl_H(X3,X2) ) ).

cnf(i_0_19339,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X1,X3,X4,X5)
    | c_Finite__Set_Ofolding__idem(X2,X3,X4,X5) ) ).

cnf(i_0_19340,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X1,X4,X5)
    | c_Finite__Set_Ofolding__idem(X3,X2,X4,X5) ) ).

cnf(i_0_19341,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X4,X1,X5)
    | c_Finite__Set_Ofolding__idem(X3,X4,X2,X5) ) ).

cnf(i_0_19342,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X4,X5,X1)
    | c_Finite__Set_Ofolding__idem(X3,X4,X5,X2) ) ).

cnf(i_0_19343,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_19344,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_19345,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_19346,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_19347,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_19348,axiom,
    ( X1 != X2
    | ~ class_Rings_Ono__zero__divisors(X1)
    | class_Rings_Ono__zero__divisors(X2) ) ).

cnf(i_0_19349,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X1,X3,X4,X5,X6)
    | c_Typedef_Otype__definition(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19350,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X1,X4,X5,X6)
    | c_Typedef_Otype__definition(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19351,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X1,X5,X6)
    | c_Typedef_Otype__definition(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19352,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X5,X1,X6)
    | c_Typedef_Otype__definition(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19353,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X1)
    | c_Typedef_Otype__definition(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19354,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring(X1)
    | class_Rings_Oring(X2) ) ).

cnf(i_0_19355,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring(X1)
    | class_Rings_Osemiring(X2) ) ).

cnf(i_0_19356,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X1,X3,X4,X5)
    | c_Equiv__Relations_Ocongruent(X2,X3,X4,X5) ) ).

cnf(i_0_19357,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X1,X4,X5)
    | c_Equiv__Relations_Ocongruent(X3,X2,X4,X5) ) ).

cnf(i_0_19358,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X4,X1,X5)
    | c_Equiv__Relations_Ocongruent(X3,X4,X2,X5) ) ).

cnf(i_0_19359,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X4,X5,X1)
    | c_Equiv__Relations_Ocongruent(X3,X4,X5,X2) ) ).

cnf(i_0_19360,axiom,
    ( X1 != X2
    | ~ class_Groups_Osemigroup__add(X1)
    | class_Groups_Osemigroup__add(X2) ) ).

cnf(i_0_19361,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X1,X3,X4)
    | c_List_Olist__ex(X2,X3,X4) ) ).

cnf(i_0_19362,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X3,X1,X4)
    | c_List_Olist__ex(X3,X2,X4) ) ).

cnf(i_0_19363,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X3,X4,X1)
    | c_List_Olist__ex(X3,X4,X2) ) ).

cnf(i_0_19364,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X1,X3,X4)
    | c_List_Oall__interval__int(X2,X3,X4) ) ).

cnf(i_0_19365,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X3,X1,X4)
    | c_List_Oall__interval__int(X3,X2,X4) ) ).

cnf(i_0_19366,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X3,X4,X1)
    | c_List_Oall__interval__int(X3,X4,X2) ) ).

cnf(i_0_19367,axiom,
    ( X1 != X2
    | ~ c_Relation_Oirrefl(X1,X3)
    | c_Relation_Oirrefl(X2,X3) ) ).

cnf(i_0_19368,axiom,
    ( X1 != X2
    | ~ c_Relation_Oirrefl(X3,X1)
    | c_Relation_Oirrefl(X3,X2) ) ).

cnf(i_0_19369,axiom,
    ( X1 != X2
    | ~ epred1_3(X1,X3,X4)
    | epred1_3(X2,X3,X4) ) ).

cnf(i_0_19370,axiom,
    ( X1 != X2
    | ~ epred1_3(X3,X1,X4)
    | epred1_3(X3,X2,X4) ) ).

cnf(i_0_19371,axiom,
    ( X1 != X2
    | ~ epred1_3(X3,X4,X1)
    | epred1_3(X3,X4,X2) ) ).

cnf(i_0_19372,axiom,
    ( X1 != X2
    | ~ epred2_3(X1,X3,X4)
    | epred2_3(X2,X3,X4) ) ).

cnf(i_0_19373,axiom,
    ( X1 != X2
    | ~ epred2_3(X3,X1,X4)
    | epred2_3(X3,X2,X4) ) ).

cnf(i_0_19374,axiom,
    ( X1 != X2
    | ~ epred2_3(X3,X4,X1)
    | epred2_3(X3,X4,X2) ) ).

cnf(i_0_19375,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__add(X1)
    | class_Groups_Oab__semigroup__add(X2) ) ).

cnf(i_0_19376,axiom,
    ( X1 != X2
    | ~ class_Int_Oring__char__0(X1)
    | class_Int_Oring__char__0(X2) ) ).

cnf(i_0_19377,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | class_Rings_Olinordered__semiring__strict(X2) ) ).

cnf(i_0_19378,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__semiring(X1)
    | class_Rings_Oordered__semiring(X2) ) ).

cnf(i_0_18474_001,axiom,
    X1 = X1 ).

cnf(i_0_18475_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_18476_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_18477_004,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_18478_005,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_18479_006,axiom,
    ( X1 != X2
    | c_Map_Omap__upds(X1,X3,X4,X5,X6) = c_Map_Omap__upds(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18480_007,axiom,
    ( X1 != X2
    | c_Map_Omap__upds(X3,X1,X4,X5,X6) = c_Map_Omap__upds(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18481_008,axiom,
    ( X1 != X2
    | c_Map_Omap__upds(X3,X4,X1,X5,X6) = c_Map_Omap__upds(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18482_009,axiom,
    ( X1 != X2
    | c_Map_Omap__upds(X3,X4,X5,X1,X6) = c_Map_Omap__upds(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18483_010,axiom,
    ( X1 != X2
    | c_Map_Omap__upds(X3,X4,X5,X6,X1) = c_Map_Omap__upds(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18484_011,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMin(X1,X3) = c_Big__Operators_Olinorder__class_OMin(X2,X3) ) ).

cnf(i_0_18485_012,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMin(X3,X1) = c_Big__Operators_Olinorder__class_OMin(X3,X2) ) ).

cnf(i_0_18486_013,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMax(X1,X3) = c_Big__Operators_Olinorder__class_OMax(X2,X3) ) ).

cnf(i_0_18487_014,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMax(X3,X1) = c_Big__Operators_Olinorder__class_OMax(X3,X2) ) ).

cnf(i_0_18488_015,axiom,
    ( X1 != X2
    | c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).

cnf(i_0_18489_016,axiom,
    ( X1 != X2
    | c_List_Olistrel(X1,X3) = c_List_Olistrel(X2,X3) ) ).

cnf(i_0_18490_017,axiom,
    ( X1 != X2
    | c_List_Olistrel(X3,X1) = c_List_Olistrel(X3,X2) ) ).

cnf(i_0_18491_018,axiom,
    ( X1 != X2
    | c_List_Opartition(X1,X3,X4) = c_List_Opartition(X2,X3,X4) ) ).

cnf(i_0_18492_019,axiom,
    ( X1 != X2
    | c_List_Opartition(X3,X1,X4) = c_List_Opartition(X3,X2,X4) ) ).

cnf(i_0_18493_020,axiom,
    ( X1 != X2
    | c_List_Opartition(X3,X4,X1) = c_List_Opartition(X3,X4,X2) ) ).

cnf(i_0_18494_021,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X1,X3,X4,X5) = c_Wellfounded_Olex__prod(X2,X3,X4,X5) ) ).

cnf(i_0_18495_022,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X1,X4,X5) = c_Wellfounded_Olex__prod(X3,X2,X4,X5) ) ).

cnf(i_0_18496_023,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X4,X1,X5) = c_Wellfounded_Olex__prod(X3,X4,X2,X5) ) ).

cnf(i_0_18497_024,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X4,X5,X1) = c_Wellfounded_Olex__prod(X3,X4,X5,X2) ) ).

cnf(i_0_18498_025,axiom,
    ( X1 != X2
    | c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).

cnf(i_0_18499_026,axiom,
    ( X1 != X2
    | c_List_Osublist(X1,X3,X4) = c_List_Osublist(X2,X3,X4) ) ).

cnf(i_0_18500_027,axiom,
    ( X1 != X2
    | c_List_Osublist(X3,X1,X4) = c_List_Osublist(X3,X2,X4) ) ).

cnf(i_0_18501_028,axiom,
    ( X1 != X2
    | c_List_Osublist(X3,X4,X1) = c_List_Osublist(X3,X4,X2) ) ).

cnf(i_0_18502_029,axiom,
    ( X1 != X2
    | c_List_Otranspose(X1,X3) = c_List_Otranspose(X2,X3) ) ).

cnf(i_0_18503_030,axiom,
    ( X1 != X2
    | c_List_Otranspose(X3,X1) = c_List_Otranspose(X3,X2) ) ).

cnf(i_0_18504_031,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int__rel(X1,X3) = c_Divides_Odivmod__int__rel(X2,X3) ) ).

cnf(i_0_18505_032,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int__rel(X3,X1) = c_Divides_Odivmod__int__rel(X3,X2) ) ).

cnf(i_0_18506_033,axiom,
    ( X1 != X2
    | c_Set_Othe__elem(X1,X3) = c_Set_Othe__elem(X2,X3) ) ).

cnf(i_0_18507_034,axiom,
    ( X1 != X2
    | c_Set_Othe__elem(X3,X1) = c_Set_Othe__elem(X3,X2) ) ).

cnf(i_0_18508_035,axiom,
    ( X1 != X2
    | c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).

cnf(i_0_18509_036,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X1,X3,X4,X5) = c_Nitpick_Osetsum_H(X2,X3,X4,X5) ) ).

cnf(i_0_18510_037,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X1,X4,X5) = c_Nitpick_Osetsum_H(X3,X2,X4,X5) ) ).

cnf(i_0_18511_038,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X4,X1,X5) = c_Nitpick_Osetsum_H(X3,X4,X2,X5) ) ).

cnf(i_0_18512_039,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X4,X5,X1) = c_Nitpick_Osetsum_H(X3,X4,X5,X2) ) ).

cnf(i_0_18513_040,axiom,
    ( X1 != X2
    | c_List_Omonoid__add__class_Olistsum(X1) = c_List_Omonoid__add__class_Olistsum(X2) ) ).

cnf(i_0_18514_041,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_OEps(X1,X3) = c_Hilbert__Choice_OEps(X2,X3) ) ).

cnf(i_0_18515_042,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_OEps(X3,X1) = c_Hilbert__Choice_OEps(X3,X2) ) ).

cnf(i_0_18516_043,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_18517_044,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_18518_045,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X1,X3,X4,X5) = c_Random__Sequence_ORandom(X2,X3,X4,X5) ) ).

cnf(i_0_18519_046,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X1,X4,X5) = c_Random__Sequence_ORandom(X3,X2,X4,X5) ) ).

cnf(i_0_18520_047,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X4,X1,X5) = c_Random__Sequence_ORandom(X3,X4,X2,X5) ) ).

cnf(i_0_18521_048,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X4,X5,X1) = c_Random__Sequence_ORandom(X3,X4,X5,X2) ) ).

cnf(i_0_18522_049,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__not__seq(X1) = c_Lazy__Sequence_Ohb__not__seq(X2) ) ).

cnf(i_0_18523_050,axiom,
    ( X1 != X2
    | c_Wellfounded_Omax__ext(X1,X3) = c_Wellfounded_Omax__ext(X2,X3) ) ).

cnf(i_0_18524_051,axiom,
    ( X1 != X2
    | c_Wellfounded_Omax__ext(X3,X1) = c_Wellfounded_Omax__ext(X3,X2) ) ).

cnf(i_0_18525_052,axiom,
    ( X1 != X2
    | c_Groups_Ominus__class_Ominus(X1) = c_Groups_Ominus__class_Ominus(X2) ) ).

cnf(i_0_18526_053,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).

cnf(i_0_18527_054,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).

cnf(i_0_18528_055,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).

cnf(i_0_18529_056,axiom,
    ( X1 != X2
    | c_Wellfounded_Omin__ext(X1,X3) = c_Wellfounded_Omin__ext(X2,X3) ) ).

cnf(i_0_18530_057,axiom,
    ( X1 != X2
    | c_Wellfounded_Omin__ext(X3,X1) = c_Wellfounded_Omin__ext(X3,X2) ) ).

cnf(i_0_18531_058,axiom,
    ( X1 != X2
    | c_Wellfounded_Ofinite__psubset(X1) = c_Wellfounded_Ofinite__psubset(X2) ) ).

cnf(i_0_18532_059,axiom,
    ( X1 != X2
    | c_Nitpick_Ocard_H(X1,X3) = c_Nitpick_Ocard_H(X2,X3) ) ).

cnf(i_0_18533_060,axiom,
    ( X1 != X2
    | c_Nitpick_Ocard_H(X3,X1) = c_Nitpick_Ocard_H(X3,X2) ) ).

cnf(i_0_18534_061,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_18535_062,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_18536_063,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_18537_064,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_18538_065,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_18539_066,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_18540_067,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_18541_068,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_18542_069,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_18543_070,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_18544_071,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_18545_072,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_18546_073,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_18547_074,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_18548_075,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_18549_076,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_18550_077,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_18551_078,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_18552_079,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_18553_080,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_18554_081,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_18555_082,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_18556_083,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_18557_084,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_18558_085,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X1,X3,X4) = c_Lazy__Sequence_Oappend(X2,X3,X4) ) ).

cnf(i_0_18559_086,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X3,X1,X4) = c_Lazy__Sequence_Oappend(X3,X2,X4) ) ).

cnf(i_0_18560_087,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X3,X4,X1) = c_Lazy__Sequence_Oappend(X3,X4,X2) ) ).

cnf(i_0_18561_088,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X1,X3,X4,X5) = c_Lazy__Sequence_Oproduct(X2,X3,X4,X5) ) ).

cnf(i_0_18562_089,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X1,X4,X5) = c_Lazy__Sequence_Oproduct(X3,X2,X4,X5) ) ).

cnf(i_0_18563_090,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X4,X1,X5) = c_Lazy__Sequence_Oproduct(X3,X4,X2,X5) ) ).

cnf(i_0_18564_091,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X4,X5,X1) = c_Lazy__Sequence_Oproduct(X3,X4,X5,X2) ) ).

cnf(i_0_18565_092,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oempty(X1) = c_Lazy__Sequence_Oempty(X2) ) ).

cnf(i_0_18566_093,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X1,X3) = c_Complete__Lattice_OSup__class_OSup(X2,X3) ) ).

cnf(i_0_18567_094,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X3,X1) = c_Complete__Lattice_OSup__class_OSup(X3,X2) ) ).

cnf(i_0_18568_095,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X1,X3) = c_Complete__Lattice_OInf__class_OInf(X2,X3) ) ).

cnf(i_0_18569_096,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X3,X1) = c_Complete__Lattice_OInf__class_OInf(X3,X2) ) ).

cnf(i_0_18570_097,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_18571_098,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_18572_099,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_18573_100,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_18574_101,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X1,X3,X4,X5) = c_New__DSequence_Oneg__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18575_102,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X1,X4,X5) = c_New__DSequence_Oneg__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18576_103,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X4,X1,X5) = c_New__DSequence_Oneg__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18577_104,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X4,X5,X1) = c_New__DSequence_Oneg__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18578_105,axiom,
    ( X1 != X2
    | esk342_5(X1,X3,X4,X5,X6) = esk342_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18579_106,axiom,
    ( X1 != X2
    | esk342_5(X3,X1,X4,X5,X6) = esk342_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18580_107,axiom,
    ( X1 != X2
    | esk342_5(X3,X4,X1,X5,X6) = esk342_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18581_108,axiom,
    ( X1 != X2
    | esk342_5(X3,X4,X5,X1,X6) = esk342_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18582_109,axiom,
    ( X1 != X2
    | esk342_5(X3,X4,X5,X6,X1) = esk342_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18583_110,axiom,
    ( X1 != X2
    | esk343_5(X1,X3,X4,X5,X6) = esk343_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18584_111,axiom,
    ( X1 != X2
    | esk343_5(X3,X1,X4,X5,X6) = esk343_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18585_112,axiom,
    ( X1 != X2
    | esk343_5(X3,X4,X1,X5,X6) = esk343_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18586_113,axiom,
    ( X1 != X2
    | esk343_5(X3,X4,X5,X1,X6) = esk343_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18587_114,axiom,
    ( X1 != X2
    | esk343_5(X3,X4,X5,X6,X1) = esk343_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18588_115,axiom,
    ( X1 != X2
    | c_Int_Onumber__class_Onumber__of(X1) = c_Int_Onumber__class_Onumber__of(X2) ) ).

cnf(i_0_18589_116,axiom,
    ( X1 != X2
    | esk341_5(X1,X3,X4,X5,X6) = esk341_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18590_117,axiom,
    ( X1 != X2
    | esk341_5(X3,X1,X4,X5,X6) = esk341_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18591_118,axiom,
    ( X1 != X2
    | esk341_5(X3,X4,X1,X5,X6) = esk341_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18592_119,axiom,
    ( X1 != X2
    | esk341_5(X3,X4,X5,X1,X6) = esk341_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18593_120,axiom,
    ( X1 != X2
    | esk341_5(X3,X4,X5,X6,X1) = esk341_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18594_121,axiom,
    ( X1 != X2
    | esk340_5(X1,X3,X4,X5,X6) = esk340_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18595_122,axiom,
    ( X1 != X2
    | esk340_5(X3,X1,X4,X5,X6) = esk340_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18596_123,axiom,
    ( X1 != X2
    | esk340_5(X3,X4,X1,X5,X6) = esk340_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18597_124,axiom,
    ( X1 != X2
    | esk340_5(X3,X4,X5,X1,X6) = esk340_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18598_125,axiom,
    ( X1 != X2
    | esk340_5(X3,X4,X5,X6,X1) = esk340_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18599_126,axiom,
    ( X1 != X2
    | c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).

cnf(i_0_18600_127,axiom,
    ( X1 != X2
    | c_Option_Ooption_ONone(X1) = c_Option_Ooption_ONone(X2) ) ).

cnf(i_0_18601_128,axiom,
    ( X1 != X2
    | c_HOL_OThe(X1,X3) = c_HOL_OThe(X2,X3) ) ).

cnf(i_0_18602_129,axiom,
    ( X1 != X2
    | c_HOL_OThe(X3,X1) = c_HOL_OThe(X3,X2) ) ).

cnf(i_0_18603_130,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_18604_131,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_18605_132,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_18606_133,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_18607_134,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X1,X3,X4,X5) = c_New__DSequence_Opos__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18608_135,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X1,X4,X5) = c_New__DSequence_Opos__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18609_136,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X4,X1,X5) = c_New__DSequence_Opos__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18610_137,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X4,X5,X1) = c_New__DSequence_Opos__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18611_138,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X1,X3,X4,X5) = c_Nitpick_Oprod(X2,X3,X4,X5) ) ).

cnf(i_0_18612_139,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X1,X4,X5) = c_Nitpick_Oprod(X3,X2,X4,X5) ) ).

cnf(i_0_18613_140,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X4,X1,X5) = c_Nitpick_Oprod(X3,X4,X2,X5) ) ).

cnf(i_0_18614_141,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X4,X5,X1) = c_Nitpick_Oprod(X3,X4,X5,X2) ) ).

cnf(i_0_18615_142,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X1,X3,X4) = c_List_OtakeWhile(X2,X3,X4) ) ).

cnf(i_0_18616_143,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X3,X1,X4) = c_List_OtakeWhile(X3,X2,X4) ) ).

cnf(i_0_18617_144,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X3,X4,X1) = c_List_OtakeWhile(X3,X4,X2) ) ).

cnf(i_0_18618_145,axiom,
    ( X1 != X2
    | esk242_6(X1,X3,X4,X5,X6,X7) = esk242_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18619_146,axiom,
    ( X1 != X2
    | esk242_6(X3,X1,X4,X5,X6,X7) = esk242_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18620_147,axiom,
    ( X1 != X2
    | esk242_6(X3,X4,X1,X5,X6,X7) = esk242_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18621_148,axiom,
    ( X1 != X2
    | esk242_6(X3,X4,X5,X1,X6,X7) = esk242_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18622_149,axiom,
    ( X1 != X2
    | esk242_6(X3,X4,X5,X6,X1,X7) = esk242_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18623_150,axiom,
    ( X1 != X2
    | esk242_6(X3,X4,X5,X6,X7,X1) = esk242_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18624_151,axiom,
    ( X1 != X2
    | esk241_6(X1,X3,X4,X5,X6,X7) = esk241_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18625_152,axiom,
    ( X1 != X2
    | esk241_6(X3,X1,X4,X5,X6,X7) = esk241_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18626_153,axiom,
    ( X1 != X2
    | esk241_6(X3,X4,X1,X5,X6,X7) = esk241_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18627_154,axiom,
    ( X1 != X2
    | esk241_6(X3,X4,X5,X1,X6,X7) = esk241_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18628_155,axiom,
    ( X1 != X2
    | esk241_6(X3,X4,X5,X6,X1,X7) = esk241_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18629_156,axiom,
    ( X1 != X2
    | esk241_6(X3,X4,X5,X6,X7,X1) = esk241_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18630_157,axiom,
    ( X1 != X2
    | c_Fun_Oid(X1) = c_Fun_Oid(X2) ) ).

cnf(i_0_18631_158,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X1,X3,X4) = c_Enum_On__lists(X2,X3,X4) ) ).

cnf(i_0_18632_159,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X3,X1,X4) = c_Enum_On__lists(X3,X2,X4) ) ).

cnf(i_0_18633_160,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X3,X4,X1) = c_Enum_On__lists(X3,X4,X2) ) ).

cnf(i_0_18634_161,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X1,X3,X4) = c_Nitpick_Otimes__frac(X2,X3,X4) ) ).

cnf(i_0_18635_162,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X3,X1,X4) = c_Nitpick_Otimes__frac(X3,X2,X4) ) ).

cnf(i_0_18636_163,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X3,X4,X1) = c_Nitpick_Otimes__frac(X3,X4,X2) ) ).

cnf(i_0_18637_164,axiom,
    ( X1 != X2
    | c_Divides_OnegDivAlg(X1,X3) = c_Divides_OnegDivAlg(X2,X3) ) ).

cnf(i_0_18638_165,axiom,
    ( X1 != X2
    | c_Divides_OnegDivAlg(X3,X1) = c_Divides_OnegDivAlg(X3,X2) ) ).

cnf(i_0_18639_166,axiom,
    ( X1 != X2
    | c_Divides_OposDivAlg(X1,X3) = c_Divides_OposDivAlg(X2,X3) ) ).

cnf(i_0_18640_167,axiom,
    ( X1 != X2
    | c_Divides_OposDivAlg(X3,X1) = c_Divides_OposDivAlg(X3,X2) ) ).

cnf(i_0_18641_168,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1) = c_Nat_Osemiring__1__class_Oof__nat(X2) ) ).

cnf(i_0_18642_169,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X1,X3,X4,X5) = c_Nat_Onat_Onat__case(X2,X3,X4,X5) ) ).

cnf(i_0_18643_170,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X1,X4,X5) = c_Nat_Onat_Onat__case(X3,X2,X4,X5) ) ).

cnf(i_0_18644_171,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X1,X5) = c_Nat_Onat_Onat__case(X3,X4,X2,X5) ) ).

cnf(i_0_18645_172,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X5,X1) = c_Nat_Onat_Onat__case(X3,X4,X5,X2) ) ).

cnf(i_0_18646_173,axiom,
    ( X1 != X2
    | c_List_Omap__filter(X1,X3,X4,X5) = c_List_Omap__filter(X2,X3,X4,X5) ) ).

cnf(i_0_18647_174,axiom,
    ( X1 != X2
    | c_List_Omap__filter(X3,X1,X4,X5) = c_List_Omap__filter(X3,X2,X4,X5) ) ).

cnf(i_0_18648_175,axiom,
    ( X1 != X2
    | c_List_Omap__filter(X3,X4,X1,X5) = c_List_Omap__filter(X3,X4,X2,X5) ) ).

cnf(i_0_18649_176,axiom,
    ( X1 != X2
    | c_List_Omap__filter(X3,X4,X5,X1) = c_List_Omap__filter(X3,X4,X5,X2) ) ).

cnf(i_0_18650_177,axiom,
    ( X1 != X2
    | c_Map_Odom(X1,X3,X4) = c_Map_Odom(X2,X3,X4) ) ).

cnf(i_0_18651_178,axiom,
    ( X1 != X2
    | c_Map_Odom(X3,X1,X4) = c_Map_Odom(X3,X2,X4) ) ).

cnf(i_0_18652_179,axiom,
    ( X1 != X2
    | c_Map_Odom(X3,X4,X1) = c_Map_Odom(X3,X4,X2) ) ).

cnf(i_0_18653_180,axiom,
    ( X1 != X2
    | c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).

cnf(i_0_18654_181,axiom,
    ( X1 != X2
    | c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).

cnf(i_0_18655_182,axiom,
    ( X1 != X2
    | c_Int_Oint__ge__less__than(X1) = c_Int_Oint__ge__less__than(X2) ) ).

cnf(i_0_18656_183,axiom,
    ( X1 != X2
    | c_List_Olistrel1(X1,X3) = c_List_Olistrel1(X2,X3) ) ).

cnf(i_0_18657_184,axiom,
    ( X1 != X2
    | c_List_Olistrel1(X3,X1) = c_List_Olistrel1(X3,X2) ) ).

cnf(i_0_18658_185,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X1,X3,X4) = c_Finite__Set_Ofold(X2,X3,X4) ) ).

cnf(i_0_18659_186,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X3,X1,X4) = c_Finite__Set_Ofold(X3,X2,X4) ) ).

cnf(i_0_18660_187,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X3,X4,X1) = c_Finite__Set_Ofold(X3,X4,X2) ) ).

cnf(i_0_18661_188,axiom,
    ( X1 != X2
    | c_Nitpick_Ouminus__frac(X1,X3) = c_Nitpick_Ouminus__frac(X2,X3) ) ).

cnf(i_0_18662_189,axiom,
    ( X1 != X2
    | c_Nitpick_Ouminus__frac(X3,X1) = c_Nitpick_Ouminus__frac(X3,X2) ) ).

cnf(i_0_18663_190,axiom,
    ( X1 != X2
    | c_Nitpick_OAbs__Frac(X1,X3) = c_Nitpick_OAbs__Frac(X2,X3) ) ).

cnf(i_0_18664_191,axiom,
    ( X1 != X2
    | c_Nitpick_OAbs__Frac(X3,X1) = c_Nitpick_OAbs__Frac(X3,X2) ) ).

cnf(i_0_18665_192,axiom,
    ( X1 != X2
    | esk439_4(X1,X3,X4,X5) = esk439_4(X2,X3,X4,X5) ) ).

cnf(i_0_18666_193,axiom,
    ( X1 != X2
    | esk439_4(X3,X1,X4,X5) = esk439_4(X3,X2,X4,X5) ) ).

cnf(i_0_18667_194,axiom,
    ( X1 != X2
    | esk439_4(X3,X4,X1,X5) = esk439_4(X3,X4,X2,X5) ) ).

cnf(i_0_18668_195,axiom,
    ( X1 != X2
    | esk439_4(X3,X4,X5,X1) = esk439_4(X3,X4,X5,X2) ) ).

cnf(i_0_18669_196,axiom,
    ( X1 != X2
    | esk438_4(X1,X3,X4,X5) = esk438_4(X2,X3,X4,X5) ) ).

cnf(i_0_18670_197,axiom,
    ( X1 != X2
    | esk438_4(X3,X1,X4,X5) = esk438_4(X3,X2,X4,X5) ) ).

cnf(i_0_18671_198,axiom,
    ( X1 != X2
    | esk438_4(X3,X4,X1,X5) = esk438_4(X3,X4,X2,X5) ) ).

cnf(i_0_18672_199,axiom,
    ( X1 != X2
    | esk438_4(X3,X4,X5,X1) = esk438_4(X3,X4,X5,X2) ) ).

cnf(i_0_18673_200,axiom,
    ( X1 != X2
    | c_Enum_Oenum__class_Oenum(X1) = c_Enum_Oenum__class_Oenum(X2) ) ).

cnf(i_0_18674_201,axiom,
    ( X1 != X2
    | c_Fun_Ooverride__on(X1,X3,X4,X5,X6) = c_Fun_Ooverride__on(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18675_202,axiom,
    ( X1 != X2
    | c_Fun_Ooverride__on(X3,X1,X4,X5,X6) = c_Fun_Ooverride__on(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18676_203,axiom,
    ( X1 != X2
    | c_Fun_Ooverride__on(X3,X4,X1,X5,X6) = c_Fun_Ooverride__on(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18677_204,axiom,
    ( X1 != X2
    | c_Fun_Ooverride__on(X3,X4,X5,X1,X6) = c_Fun_Ooverride__on(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18678_205,axiom,
    ( X1 != X2
    | c_Fun_Ooverride__on(X3,X4,X5,X6,X1) = c_Fun_Ooverride__on(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18679_206,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_18680_207,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X1,X3,X4,X5) = c_Hilbert__Choice_Oinv__into(X2,X3,X4,X5) ) ).

cnf(i_0_18681_208,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X1,X4,X5) = c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5) ) ).

cnf(i_0_18682_209,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X4,X1,X5) = c_Hilbert__Choice_Oinv__into(X3,X4,X2,X5) ) ).

cnf(i_0_18683_210,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X4,X5,X1) = c_Hilbert__Choice_Oinv__into(X3,X4,X5,X2) ) ).

cnf(i_0_18684_211,axiom,
    ( X1 != X2
    | c_List_Olistsp(X1,X3) = c_List_Olistsp(X2,X3) ) ).

cnf(i_0_18685_212,axiom,
    ( X1 != X2
    | c_List_Olistsp(X3,X1) = c_List_Olistsp(X3,X2) ) ).

cnf(i_0_18686_213,axiom,
    ( X1 != X2
    | c_List_Olists(X1,X3) = c_List_Olists(X2,X3) ) ).

cnf(i_0_18687_214,axiom,
    ( X1 != X2
    | c_List_Olists(X3,X1) = c_List_Olists(X3,X2) ) ).

cnf(i_0_18688_215,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omax(X1) = c_Orderings_Oord__class_Omax(X2) ) ).

cnf(i_0_18689_216,axiom,
    ( X1 != X2
    | c_Map_Oran(X1,X3,X4) = c_Map_Oran(X2,X3,X4) ) ).

cnf(i_0_18690_217,axiom,
    ( X1 != X2
    | c_Map_Oran(X3,X1,X4) = c_Map_Oran(X3,X2,X4) ) ).

cnf(i_0_18691_218,axiom,
    ( X1 != X2
    | c_Map_Oran(X3,X4,X1) = c_Map_Oran(X3,X4,X2) ) ).

cnf(i_0_18692_219,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X1,X3,X4) = c_Big__Operators_Olattice_OInf__fin(X2,X3,X4) ) ).

cnf(i_0_18693_220,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X3,X1,X4) = c_Big__Operators_Olattice_OInf__fin(X3,X2,X4) ) ).

cnf(i_0_18694_221,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X3,X4,X1) = c_Big__Operators_Olattice_OInf__fin(X3,X4,X2) ) ).

cnf(i_0_18695_222,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omin(X1) = c_Orderings_Oord__class_Omin(X2) ) ).

cnf(i_0_18696_223,axiom,
    ( X1 != X2
    | c_Int_Oint__ge__less__than2(X1) = c_Int_Oint__ge__less__than2(X2) ) ).

cnf(i_0_18697_224,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X1,X3,X4) = c_Nitpick_Oof__frac(X2,X3,X4) ) ).

cnf(i_0_18698_225,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X3,X1,X4) = c_Nitpick_Oof__frac(X3,X2,X4) ) ).

cnf(i_0_18699_226,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X3,X4,X1) = c_Nitpick_Oof__frac(X3,X4,X2) ) ).

cnf(i_0_18700_227,axiom,
    ( X1 != X2
    | c_List_Omeasures(X1,X3) = c_List_Omeasures(X2,X3) ) ).

cnf(i_0_18701_228,axiom,
    ( X1 != X2
    | c_List_Omeasures(X3,X1) = c_List_Omeasures(X3,X2) ) ).

cnf(i_0_18702_229,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X1,X3,X4,X5) = c_Random__Sequence_Omap(X2,X3,X4,X5) ) ).

cnf(i_0_18703_230,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X1,X4,X5) = c_Random__Sequence_Omap(X3,X2,X4,X5) ) ).

cnf(i_0_18704_231,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X4,X1,X5) = c_Random__Sequence_Omap(X3,X4,X2,X5) ) ).

cnf(i_0_18705_232,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X4,X5,X1) = c_Random__Sequence_Omap(X3,X4,X5,X2) ) ).

cnf(i_0_18706_233,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X1,X3,X4,X5) = c_Random__Sequence_Obind(X2,X3,X4,X5) ) ).

cnf(i_0_18707_234,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X1,X4,X5) = c_Random__Sequence_Obind(X3,X2,X4,X5) ) ).

cnf(i_0_18708_235,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X4,X1,X5) = c_Random__Sequence_Obind(X3,X4,X2,X5) ) ).

cnf(i_0_18709_236,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X4,X5,X1) = c_Random__Sequence_Obind(X3,X4,X5,X2) ) ).

cnf(i_0_18710_237,axiom,
    ( X1 != X2
    | c_Map_Orestrict__map(X1,X3,X4,X5) = c_Map_Orestrict__map(X2,X3,X4,X5) ) ).

cnf(i_0_18711_238,axiom,
    ( X1 != X2
    | c_Map_Orestrict__map(X3,X1,X4,X5) = c_Map_Orestrict__map(X3,X2,X4,X5) ) ).

cnf(i_0_18712_239,axiom,
    ( X1 != X2
    | c_Map_Orestrict__map(X3,X4,X1,X5) = c_Map_Orestrict__map(X3,X4,X2,X5) ) ).

cnf(i_0_18713_240,axiom,
    ( X1 != X2
    | c_Map_Orestrict__map(X3,X4,X5,X1) = c_Map_Orestrict__map(X3,X4,X5,X2) ) ).

cnf(i_0_18714_241,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).

cnf(i_0_18715_242,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).

cnf(i_0_18716_243,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).

cnf(i_0_18717_244,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X1,X3,X4) = c_Big__Operators_Olattice_OSup__fin(X2,X3,X4) ) ).

cnf(i_0_18718_245,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X3,X1,X4) = c_Big__Operators_Olattice_OSup__fin(X3,X2,X4) ) ).

cnf(i_0_18719_246,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X3,X4,X1) = c_Big__Operators_Olattice_OSup__fin(X3,X4,X2) ) ).

cnf(i_0_18720_247,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_OLeast(X1,X3) = c_Orderings_Oord__class_OLeast(X2,X3) ) ).

cnf(i_0_18721_248,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_OLeast(X3,X1) = c_Orderings_Oord__class_OLeast(X3,X2) ) ).

cnf(i_0_18722_249,axiom,
    ( X1 != X2
    | c_Lattices_Osemilattice__inf__class_Oinf(X1) = c_Lattices_Osemilattice__inf__class_Oinf(X2) ) ).

cnf(i_0_18723_250,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OSup__fin(X1,X3) = c_Big__Operators_Olattice__class_OSup__fin(X2,X3) ) ).

cnf(i_0_18724_251,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OSup__fin(X3,X1) = c_Big__Operators_Olattice__class_OSup__fin(X3,X2) ) ).

cnf(i_0_18725_252,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X1,X3,X4) = c_List_Olist_Olist__size(X2,X3,X4) ) ).

cnf(i_0_18726_253,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X3,X1,X4) = c_List_Olist_Olist__size(X3,X2,X4) ) ).

cnf(i_0_18727_254,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X3,X4,X1) = c_List_Olist_Olist__size(X3,X4,X2) ) ).

cnf(i_0_18728_255,axiom,
    ( X1 != X2
    | c_Lattices_Osemilattice__sup__class_Osup(X1) = c_Lattices_Osemilattice__sup__class_Osup(X2) ) ).

cnf(i_0_18729_256,axiom,
    ( X1 != X2
    | c_Enum_Osublists(X1,X3) = c_Enum_Osublists(X2,X3) ) ).

cnf(i_0_18730_257,axiom,
    ( X1 != X2
    | c_Enum_Osublists(X3,X1) = c_Enum_Osublists(X3,X2) ) ).

cnf(i_0_18731_258,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OInf__fin(X1,X3) = c_Big__Operators_Olattice__class_OInf__fin(X2,X3) ) ).

cnf(i_0_18732_259,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OInf__fin(X3,X1) = c_Big__Operators_Olattice__class_OInf__fin(X3,X2) ) ).

cnf(i_0_18733_260,axiom,
    ( X1 != X2
    | c_Random_Oselect__weight(X1,X3) = c_Random_Oselect__weight(X2,X3) ) ).

cnf(i_0_18734_261,axiom,
    ( X1 != X2
    | c_Random_Oselect__weight(X3,X1) = c_Random_Oselect__weight(X3,X2) ) ).

cnf(i_0_18735_262,axiom,
    ( X1 != X2
    | c_Random_Opick(X1,X3) = c_Random_Opick(X2,X3) ) ).

cnf(i_0_18736_263,axiom,
    ( X1 != X2
    | c_Random_Opick(X3,X1) = c_Random_Opick(X3,X2) ) ).

cnf(i_0_18737_264,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X1,X3,X4) = c_List_Oset__Cons(X2,X3,X4) ) ).

cnf(i_0_18738_265,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X3,X1,X4) = c_List_Oset__Cons(X3,X2,X4) ) ).

cnf(i_0_18739_266,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X3,X4,X1) = c_List_Oset__Cons(X3,X4,X2) ) ).

cnf(i_0_18740_267,axiom,
    ( X1 != X2
    | c_Sum__Type_Osum_Osum__case(X1,X3,X4,X5,X6) = c_Sum__Type_Osum_Osum__case(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18741_268,axiom,
    ( X1 != X2
    | c_Sum__Type_Osum_Osum__case(X3,X1,X4,X5,X6) = c_Sum__Type_Osum_Osum__case(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18742_269,axiom,
    ( X1 != X2
    | c_Sum__Type_Osum_Osum__case(X3,X4,X1,X5,X6) = c_Sum__Type_Osum_Osum__case(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18743_270,axiom,
    ( X1 != X2
    | c_Sum__Type_Osum_Osum__case(X3,X4,X5,X1,X6) = c_Sum__Type_Osum_Osum__case(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18744_271,axiom,
    ( X1 != X2
    | c_Sum__Type_Osum_Osum__case(X3,X4,X5,X6,X1) = c_Sum__Type_Osum_Osum__case(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18745_272,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X1,X3,X4) = c_Wellfounded_Omlex__prod(X2,X3,X4) ) ).

cnf(i_0_18746_273,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X3,X1,X4) = c_Wellfounded_Omlex__prod(X3,X2,X4) ) ).

cnf(i_0_18747_274,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X3,X4,X1) = c_Wellfounded_Omlex__prod(X3,X4,X2) ) ).

cnf(i_0_18748_275,axiom,
    ( X1 != X2
    | c_Nitpick_Onorm__frac(X1,X3) = c_Nitpick_Onorm__frac(X2,X3) ) ).

cnf(i_0_18749_276,axiom,
    ( X1 != X2
    | c_Nitpick_Onorm__frac(X3,X1) = c_Nitpick_Onorm__frac(X3,X2) ) ).

cnf(i_0_18750_277,axiom,
    ( X1 != X2
    | c_List_Oremove1(X1,X3,X4) = c_List_Oremove1(X2,X3,X4) ) ).

cnf(i_0_18751_278,axiom,
    ( X1 != X2
    | c_List_Oremove1(X3,X1,X4) = c_List_Oremove1(X3,X2,X4) ) ).

cnf(i_0_18752_279,axiom,
    ( X1 != X2
    | c_List_Oremove1(X3,X4,X1) = c_List_Oremove1(X3,X4,X2) ) ).

cnf(i_0_18753_280,axiom,
    ( X1 != X2
    | esk527_4(X1,X3,X4,X5) = esk527_4(X2,X3,X4,X5) ) ).

cnf(i_0_18754_281,axiom,
    ( X1 != X2
    | esk527_4(X3,X1,X4,X5) = esk527_4(X3,X2,X4,X5) ) ).

cnf(i_0_18755_282,axiom,
    ( X1 != X2
    | esk527_4(X3,X4,X1,X5) = esk527_4(X3,X4,X2,X5) ) ).

cnf(i_0_18756_283,axiom,
    ( X1 != X2
    | esk527_4(X3,X4,X5,X1) = esk527_4(X3,X4,X5,X2) ) ).

cnf(i_0_18757_284,axiom,
    ( X1 != X2
    | esk526_4(X1,X3,X4,X5) = esk526_4(X2,X3,X4,X5) ) ).

cnf(i_0_18758_285,axiom,
    ( X1 != X2
    | esk526_4(X3,X1,X4,X5) = esk526_4(X3,X2,X4,X5) ) ).

cnf(i_0_18759_286,axiom,
    ( X1 != X2
    | esk526_4(X3,X4,X1,X5) = esk526_4(X3,X4,X2,X5) ) ).

cnf(i_0_18760_287,axiom,
    ( X1 != X2
    | esk526_4(X3,X4,X5,X1) = esk526_4(X3,X4,X5,X2) ) ).

cnf(i_0_18761_288,axiom,
    ( X1 != X2
    | esk329_3(X1,X3,X4) = esk329_3(X2,X3,X4) ) ).

cnf(i_0_18762_289,axiom,
    ( X1 != X2
    | esk329_3(X3,X1,X4) = esk329_3(X3,X2,X4) ) ).

cnf(i_0_18763_290,axiom,
    ( X1 != X2
    | esk329_3(X3,X4,X1) = esk329_3(X3,X4,X2) ) ).

cnf(i_0_18764_291,axiom,
    ( X1 != X2
    | esk328_3(X1,X3,X4) = esk328_3(X2,X3,X4) ) ).

cnf(i_0_18765_292,axiom,
    ( X1 != X2
    | esk328_3(X3,X1,X4) = esk328_3(X3,X2,X4) ) ).

cnf(i_0_18766_293,axiom,
    ( X1 != X2
    | esk328_3(X3,X4,X1) = esk328_3(X3,X4,X2) ) ).

cnf(i_0_18767_294,axiom,
    ( X1 != X2
    | c_Smallcheck_Osmall_H(X1,X3,X4) = c_Smallcheck_Osmall_H(X2,X3,X4) ) ).

cnf(i_0_18768_295,axiom,
    ( X1 != X2
    | c_Smallcheck_Osmall_H(X3,X1,X4) = c_Smallcheck_Osmall_H(X3,X2,X4) ) ).

cnf(i_0_18769_296,axiom,
    ( X1 != X2
    | c_Smallcheck_Osmall_H(X3,X4,X1) = c_Smallcheck_Osmall_H(X3,X4,X2) ) ).

cnf(i_0_18770_297,axiom,
    ( X1 != X2
    | c_Random_Oselect(X1,X3) = c_Random_Oselect(X2,X3) ) ).

cnf(i_0_18771_298,axiom,
    ( X1 != X2
    | c_Random_Oselect(X3,X1) = c_Random_Oselect(X3,X2) ) ).

cnf(i_0_18772_299,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_18773_300,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_18774_301,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_18775_302,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_18776_303,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_18777_304,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold1(X1,X3) = c_Finite__Set_Ofold1(X2,X3) ) ).

cnf(i_0_18778_305,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold1(X3,X1) = c_Finite__Set_Ofold1(X3,X2) ) ).

cnf(i_0_18779_306,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_18780_307,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_18781_308,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_18782_309,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_18783_310,axiom,
    ( X1 != X2
    | c_HOL_Oequal__class_Oequal(X1) = c_HOL_Oequal__class_Oequal(X2) ) ).

cnf(i_0_18784_311,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_18785_312,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_18786_313,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_18787_314,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_18788_315,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_18789_316,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_18790_317,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_18791_318,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_18792_319,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_18793_320,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_18794_321,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int(X1,X3) = c_Divides_Odivmod__int(X2,X3) ) ).

cnf(i_0_18795_322,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int(X3,X1) = c_Divides_Odivmod__int(X3,X2) ) ).

cnf(i_0_18796_323,axiom,
    ( X1 != X2
    | esk41_5(X1,X3,X4,X5,X6) = esk41_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18797_324,axiom,
    ( X1 != X2
    | esk41_5(X3,X1,X4,X5,X6) = esk41_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18798_325,axiom,
    ( X1 != X2
    | esk41_5(X3,X4,X1,X5,X6) = esk41_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18799_326,axiom,
    ( X1 != X2
    | esk41_5(X3,X4,X5,X1,X6) = esk41_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18800_327,axiom,
    ( X1 != X2
    | esk41_5(X3,X4,X5,X6,X1) = esk41_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18801_328,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).

cnf(i_0_18802_329,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).

cnf(i_0_18803_330,axiom,
    ( X1 != X2
    | esk334_3(X1,X3,X4) = esk334_3(X2,X3,X4) ) ).

cnf(i_0_18804_331,axiom,
    ( X1 != X2
    | esk334_3(X3,X1,X4) = esk334_3(X3,X2,X4) ) ).

cnf(i_0_18805_332,axiom,
    ( X1 != X2
    | esk334_3(X3,X4,X1) = esk334_3(X3,X4,X2) ) ).

cnf(i_0_18806_333,axiom,
    ( X1 != X2
    | esk333_3(X1,X3,X4) = esk333_3(X2,X3,X4) ) ).

cnf(i_0_18807_334,axiom,
    ( X1 != X2
    | esk333_3(X3,X1,X4) = esk333_3(X3,X2,X4) ) ).

cnf(i_0_18808_335,axiom,
    ( X1 != X2
    | esk333_3(X3,X4,X1) = esk333_3(X3,X4,X2) ) ).

cnf(i_0_18809_336,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_18810_337,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_18811_338,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_18812_339,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_18813_340,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_18814_341,axiom,
    ( X1 != X2
    | esk476_2(X1,X3) = esk476_2(X2,X3) ) ).

cnf(i_0_18815_342,axiom,
    ( X1 != X2
    | esk476_2(X3,X1) = esk476_2(X3,X2) ) ).

cnf(i_0_18816_343,axiom,
    ( X1 != X2
    | esk477_2(X1,X3) = esk477_2(X2,X3) ) ).

cnf(i_0_18817_344,axiom,
    ( X1 != X2
    | esk477_2(X3,X1) = esk477_2(X3,X2) ) ).

cnf(i_0_18818_345,axiom,
    ( X1 != X2
    | c_Nitpick_Onat__gcd(X1,X3) = c_Nitpick_Onat__gcd(X2,X3) ) ).

cnf(i_0_18819_346,axiom,
    ( X1 != X2
    | c_Nitpick_Onat__gcd(X3,X1) = c_Nitpick_Onat__gcd(X3,X2) ) ).

cnf(i_0_18820_347,axiom,
    ( X1 != X2
    | c_Divides_Opdivmod(X1,X3) = c_Divides_Opdivmod(X2,X3) ) ).

cnf(i_0_18821_348,axiom,
    ( X1 != X2
    | c_Divides_Opdivmod(X3,X1) = c_Divides_Opdivmod(X3,X2) ) ).

cnf(i_0_18822_349,axiom,
    ( X1 != X2
    | c_List_Oremdups(X1,X3) = c_List_Oremdups(X2,X3) ) ).

cnf(i_0_18823_350,axiom,
    ( X1 != X2
    | c_List_Oremdups(X3,X1) = c_List_Oremdups(X3,X2) ) ).

cnf(i_0_18824_351,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X1,X3,X4) = c_Partial__Function_Oflat__lub(X2,X3,X4) ) ).

cnf(i_0_18825_352,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X3,X1,X4) = c_Partial__Function_Oflat__lub(X3,X2,X4) ) ).

cnf(i_0_18826_353,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X3,X4,X1) = c_Partial__Function_Oflat__lub(X3,X4,X2) ) ).

cnf(i_0_18827_354,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__flat(X1,X3) = c_Lazy__Sequence_Ohb__flat(X2,X3) ) ).

cnf(i_0_18828_355,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__flat(X3,X1) = c_Lazy__Sequence_Ohb__flat(X3,X2) ) ).

cnf(i_0_18829_356,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__map(X1,X3,X4,X5) = c_Lazy__Sequence_Ohb__map(X2,X3,X4,X5) ) ).

cnf(i_0_18830_357,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__map(X3,X1,X4,X5) = c_Lazy__Sequence_Ohb__map(X3,X2,X4,X5) ) ).

cnf(i_0_18831_358,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__map(X3,X4,X1,X5) = c_Lazy__Sequence_Ohb__map(X3,X4,X2,X5) ) ).

cnf(i_0_18832_359,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__map(X3,X4,X5,X1) = c_Lazy__Sequence_Ohb__map(X3,X4,X5,X2) ) ).

cnf(i_0_18833_360,axiom,
    ( X1 != X2
    | c_List_Olenlex(X1,X3) = c_List_Olenlex(X2,X3) ) ).

cnf(i_0_18834_361,axiom,
    ( X1 != X2
    | c_List_Olenlex(X3,X1) = c_List_Olenlex(X3,X2) ) ).

cnf(i_0_18835_362,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X1,X3,X4) = c_List_Oreplicate(X2,X3,X4) ) ).

cnf(i_0_18836_363,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X1,X4) = c_List_Oreplicate(X3,X2,X4) ) ).

cnf(i_0_18837_364,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X4,X1) = c_List_Oreplicate(X3,X4,X2) ) ).

cnf(i_0_18838_365,axiom,
    ( X1 != X2
    | c_List_Olex(X1,X3) = c_List_Olex(X2,X3) ) ).

cnf(i_0_18839_366,axiom,
    ( X1 != X2
    | c_List_Olex(X3,X1) = c_List_Olex(X3,X2) ) ).

cnf(i_0_18840_367,axiom,
    ( X1 != X2
    | esk253_3(X1,X3,X4) = esk253_3(X2,X3,X4) ) ).

cnf(i_0_18841_368,axiom,
    ( X1 != X2
    | esk253_3(X3,X1,X4) = esk253_3(X3,X2,X4) ) ).

cnf(i_0_18842_369,axiom,
    ( X1 != X2
    | esk253_3(X3,X4,X1) = esk253_3(X3,X4,X2) ) ).

cnf(i_0_18843_370,axiom,
    ( X1 != X2
    | esk39_3(X1,X3,X4) = esk39_3(X2,X3,X4) ) ).

cnf(i_0_18844_371,axiom,
    ( X1 != X2
    | esk39_3(X3,X1,X4) = esk39_3(X3,X2,X4) ) ).

cnf(i_0_18845_372,axiom,
    ( X1 != X2
    | esk39_3(X3,X4,X1) = esk39_3(X3,X4,X2) ) ).

cnf(i_0_18846_373,axiom,
    ( X1 != X2
    | esk522_4(X1,X3,X4,X5) = esk522_4(X2,X3,X4,X5) ) ).

cnf(i_0_18847_374,axiom,
    ( X1 != X2
    | esk522_4(X3,X1,X4,X5) = esk522_4(X3,X2,X4,X5) ) ).

cnf(i_0_18848_375,axiom,
    ( X1 != X2
    | esk522_4(X3,X4,X1,X5) = esk522_4(X3,X4,X2,X5) ) ).

cnf(i_0_18849_376,axiom,
    ( X1 != X2
    | esk522_4(X3,X4,X5,X1) = esk522_4(X3,X4,X5,X2) ) ).

cnf(i_0_18850_377,axiom,
    ( X1 != X2
    | esk509_4(X1,X3,X4,X5) = esk509_4(X2,X3,X4,X5) ) ).

cnf(i_0_18851_378,axiom,
    ( X1 != X2
    | esk509_4(X3,X1,X4,X5) = esk509_4(X3,X2,X4,X5) ) ).

cnf(i_0_18852_379,axiom,
    ( X1 != X2
    | esk509_4(X3,X4,X1,X5) = esk509_4(X3,X4,X2,X5) ) ).

cnf(i_0_18853_380,axiom,
    ( X1 != X2
    | esk509_4(X3,X4,X5,X1) = esk509_4(X3,X4,X5,X2) ) ).

cnf(i_0_18854_381,axiom,
    ( X1 != X2
    | esk234_4(X1,X3,X4,X5) = esk234_4(X2,X3,X4,X5) ) ).

cnf(i_0_18855_382,axiom,
    ( X1 != X2
    | esk234_4(X3,X1,X4,X5) = esk234_4(X3,X2,X4,X5) ) ).

cnf(i_0_18856_383,axiom,
    ( X1 != X2
    | esk234_4(X3,X4,X1,X5) = esk234_4(X3,X4,X2,X5) ) ).

cnf(i_0_18857_384,axiom,
    ( X1 != X2
    | esk234_4(X3,X4,X5,X1) = esk234_4(X3,X4,X5,X2) ) ).

cnf(i_0_18858_385,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X1,X3,X4,X5) = c_List_Ofoldl(X2,X3,X4,X5) ) ).

cnf(i_0_18859_386,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X1,X4,X5) = c_List_Ofoldl(X3,X2,X4,X5) ) ).

cnf(i_0_18860_387,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X1,X5) = c_List_Ofoldl(X3,X4,X2,X5) ) ).

cnf(i_0_18861_388,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X1) = c_List_Ofoldl(X3,X4,X5,X2) ) ).

cnf(i_0_18862_389,axiom,
    ( X1 != X2
    | esk236_4(X1,X3,X4,X5) = esk236_4(X2,X3,X4,X5) ) ).

cnf(i_0_18863_390,axiom,
    ( X1 != X2
    | esk236_4(X3,X1,X4,X5) = esk236_4(X3,X2,X4,X5) ) ).

cnf(i_0_18864_391,axiom,
    ( X1 != X2
    | esk236_4(X3,X4,X1,X5) = esk236_4(X3,X4,X2,X5) ) ).

cnf(i_0_18865_392,axiom,
    ( X1 != X2
    | esk236_4(X3,X4,X5,X1) = esk236_4(X3,X4,X5,X2) ) ).

cnf(i_0_18866_393,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X1,X3,X4,X5) = c_Enum_Oproduct(X2,X3,X4,X5) ) ).

cnf(i_0_18867_394,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X1,X4,X5) = c_Enum_Oproduct(X3,X2,X4,X5) ) ).

cnf(i_0_18868_395,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X4,X1,X5) = c_Enum_Oproduct(X3,X4,X2,X5) ) ).

cnf(i_0_18869_396,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X4,X5,X1) = c_Enum_Oproduct(X3,X4,X5,X2) ) ).

cnf(i_0_18870_397,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X1,X3,X4,X5,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18871_398,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X3,X1,X4,X5,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18872_399,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X3,X4,X1,X5,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18873_400,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X3,X4,X5,X1,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18874_401,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X3,X4,X5,X6,X1) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18875_402,axiom,
    ( X1 != X2
    | esk33_4(X1,X3,X4,X5) = esk33_4(X2,X3,X4,X5) ) ).

cnf(i_0_18876_403,axiom,
    ( X1 != X2
    | esk33_4(X3,X1,X4,X5) = esk33_4(X3,X2,X4,X5) ) ).

cnf(i_0_18877_404,axiom,
    ( X1 != X2
    | esk33_4(X3,X4,X1,X5) = esk33_4(X3,X4,X2,X5) ) ).

cnf(i_0_18878_405,axiom,
    ( X1 != X2
    | esk33_4(X3,X4,X5,X1) = esk33_4(X3,X4,X5,X2) ) ).

cnf(i_0_18879_406,axiom,
    ( X1 != X2
    | esk32_4(X1,X3,X4,X5) = esk32_4(X2,X3,X4,X5) ) ).

cnf(i_0_18880_407,axiom,
    ( X1 != X2
    | esk32_4(X3,X1,X4,X5) = esk32_4(X3,X2,X4,X5) ) ).

cnf(i_0_18881_408,axiom,
    ( X1 != X2
    | esk32_4(X3,X4,X1,X5) = esk32_4(X3,X4,X2,X5) ) ).

cnf(i_0_18882_409,axiom,
    ( X1 != X2
    | esk32_4(X3,X4,X5,X1) = esk32_4(X3,X4,X5,X2) ) ).

cnf(i_0_18883_410,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X1,X3,X4,X5) = c_Fun_Ocomp(X2,X3,X4,X5) ) ).

cnf(i_0_18884_411,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X1,X4,X5) = c_Fun_Ocomp(X3,X2,X4,X5) ) ).

cnf(i_0_18885_412,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X1,X5) = c_Fun_Ocomp(X3,X4,X2,X5) ) ).

cnf(i_0_18886_413,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X5,X1) = c_Fun_Ocomp(X3,X4,X5,X2) ) ).

cnf(i_0_18887_414,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_18888_415,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_18889_416,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_18890_417,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_18891_418,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_18892_419,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X1,X3,X4,X5) = c_Nitpick_Opair__box_OPairBox(X2,X3,X4,X5) ) ).

cnf(i_0_18893_420,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X3,X1,X4,X5) = c_Nitpick_Opair__box_OPairBox(X3,X2,X4,X5) ) ).

cnf(i_0_18894_421,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X3,X4,X1,X5) = c_Nitpick_Opair__box_OPairBox(X3,X4,X2,X5) ) ).

cnf(i_0_18895_422,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X1) = c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X2) ) ).

cnf(i_0_18896_423,axiom,
    ( X1 != X2
    | esk368_3(X1,X3,X4) = esk368_3(X2,X3,X4) ) ).

cnf(i_0_18897_424,axiom,
    ( X1 != X2
    | esk368_3(X3,X1,X4) = esk368_3(X3,X2,X4) ) ).

cnf(i_0_18898_425,axiom,
    ( X1 != X2
    | esk368_3(X3,X4,X1) = esk368_3(X3,X4,X2) ) ).

cnf(i_0_18899_426,axiom,
    ( X1 != X2
    | esk369_3(X1,X3,X4) = esk369_3(X2,X3,X4) ) ).

cnf(i_0_18900_427,axiom,
    ( X1 != X2
    | esk369_3(X3,X1,X4) = esk369_3(X3,X2,X4) ) ).

cnf(i_0_18901_428,axiom,
    ( X1 != X2
    | esk369_3(X3,X4,X1) = esk369_3(X3,X4,X2) ) ).

cnf(i_0_18902_429,axiom,
    ( X1 != X2
    | esk40_4(X1,X3,X4,X5) = esk40_4(X2,X3,X4,X5) ) ).

cnf(i_0_18903_430,axiom,
    ( X1 != X2
    | esk40_4(X3,X1,X4,X5) = esk40_4(X3,X2,X4,X5) ) ).

cnf(i_0_18904_431,axiom,
    ( X1 != X2
    | esk40_4(X3,X4,X1,X5) = esk40_4(X3,X4,X2,X5) ) ).

cnf(i_0_18905_432,axiom,
    ( X1 != X2
    | esk40_4(X3,X4,X5,X1) = esk40_4(X3,X4,X5,X2) ) ).

cnf(i_0_18906_433,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_18907_434,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_18908_435,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_18909_436,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_18910_437,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).

cnf(i_0_18911_438,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).

cnf(i_0_18912_439,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).

cnf(i_0_18913_440,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).

cnf(i_0_18914_441,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X1,X3,X4) = c_Nitpick_Oplus__frac(X2,X3,X4) ) ).

cnf(i_0_18915_442,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X3,X1,X4) = c_Nitpick_Oplus__frac(X3,X2,X4) ) ).

cnf(i_0_18916_443,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X3,X4,X1) = c_Nitpick_Oplus__frac(X3,X4,X2) ) ).

cnf(i_0_18917_444,axiom,
    ( X1 != X2
    | esk372_3(X1,X3,X4) = esk372_3(X2,X3,X4) ) ).

cnf(i_0_18918_445,axiom,
    ( X1 != X2
    | esk372_3(X3,X1,X4) = esk372_3(X3,X2,X4) ) ).

cnf(i_0_18919_446,axiom,
    ( X1 != X2
    | esk372_3(X3,X4,X1) = esk372_3(X3,X4,X2) ) ).

cnf(i_0_18920_447,axiom,
    ( X1 != X2
    | esk371_3(X1,X3,X4) = esk371_3(X2,X3,X4) ) ).

cnf(i_0_18921_448,axiom,
    ( X1 != X2
    | esk371_3(X3,X1,X4) = esk371_3(X3,X2,X4) ) ).

cnf(i_0_18922_449,axiom,
    ( X1 != X2
    | esk371_3(X3,X4,X1) = esk371_3(X3,X4,X2) ) ).

cnf(i_0_18923_450,axiom,
    ( X1 != X2
    | c_List_Oupto(X1,X3) = c_List_Oupto(X2,X3) ) ).

cnf(i_0_18924_451,axiom,
    ( X1 != X2
    | c_List_Oupto(X3,X1) = c_List_Oupto(X3,X2) ) ).

cnf(i_0_18925_452,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_18926_453,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_18927_454,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_18928_455,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_18929_456,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_18930_457,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_18931_458,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_18932_459,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_18933_460,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_18934_461,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_18935_462,axiom,
    ( X1 != X2
    | c_List_Olast(X1,X3) = c_List_Olast(X2,X3) ) ).

cnf(i_0_18936_463,axiom,
    ( X1 != X2
    | c_List_Olast(X3,X1) = c_List_Olast(X3,X2) ) ).

cnf(i_0_18937_464,axiom,
    ( X1 != X2
    | c_List_Obutlast(X1,X3) = c_List_Obutlast(X2,X3) ) ).

cnf(i_0_18938_465,axiom,
    ( X1 != X2
    | c_List_Obutlast(X3,X1) = c_List_Obutlast(X3,X2) ) ).

cnf(i_0_18939_466,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X3,X4) = c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X3,X4) ) ).

cnf(i_0_18940_467,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X1,X4) = c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X2,X4) ) ).

cnf(i_0_18941_468,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X4,X1) = c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X4,X2) ) ).

cnf(i_0_18942_469,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohit__bound(X1) = c_Lazy__Sequence_Ohit__bound(X2) ) ).

cnf(i_0_18943_470,axiom,
    ( X1 != X2
    | c_Nitpick_Oint__lcm(X1,X3) = c_Nitpick_Oint__lcm(X2,X3) ) ).

cnf(i_0_18944_471,axiom,
    ( X1 != X2
    | c_Nitpick_Oint__lcm(X3,X1) = c_Nitpick_Oint__lcm(X3,X2) ) ).

cnf(i_0_18945_472,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_18946_473,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_18947_474,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_18948_475,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_18949_476,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_18950_477,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__rec(X1,X3,X4,X5,X6) = c_Option_Ooption_Ooption__rec(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18951_478,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__rec(X3,X1,X4,X5,X6) = c_Option_Ooption_Ooption__rec(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18952_479,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__rec(X3,X4,X1,X5,X6) = c_Option_Ooption_Ooption__rec(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18953_480,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__rec(X3,X4,X5,X1,X6) = c_Option_Ooption_Ooption__rec(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18954_481,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__rec(X3,X4,X5,X6,X1) = c_Option_Ooption_Ooption__rec(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18955_482,axiom,
    ( X1 != X2
    | esk116_3(X1,X3,X4) = esk116_3(X2,X3,X4) ) ).

cnf(i_0_18956_483,axiom,
    ( X1 != X2
    | esk116_3(X3,X1,X4) = esk116_3(X3,X2,X4) ) ).

cnf(i_0_18957_484,axiom,
    ( X1 != X2
    | esk116_3(X3,X4,X1) = esk116_3(X3,X4,X2) ) ).

cnf(i_0_18958_485,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OEmpty(X1) = c_Lazy__Sequence_Olazy__sequence_OEmpty(X2) ) ).

cnf(i_0_18959_486,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy_H(X1,X3) = c_Lazy__Sequence_Osmall__lazy_H(X2,X3) ) ).

cnf(i_0_18960_487,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy_H(X3,X1) = c_Lazy__Sequence_Osmall__lazy_H(X3,X2) ) ).

cnf(i_0_18961_488,axiom,
    ( X1 != X2
    | esk523_4(X1,X3,X4,X5) = esk523_4(X2,X3,X4,X5) ) ).

cnf(i_0_18962_489,axiom,
    ( X1 != X2
    | esk523_4(X3,X1,X4,X5) = esk523_4(X3,X2,X4,X5) ) ).

cnf(i_0_18963_490,axiom,
    ( X1 != X2
    | esk523_4(X3,X4,X1,X5) = esk523_4(X3,X4,X2,X5) ) ).

cnf(i_0_18964_491,axiom,
    ( X1 != X2
    | esk523_4(X3,X4,X5,X1) = esk523_4(X3,X4,X5,X2) ) ).

cnf(i_0_18965_492,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X1,X3,X4) = c_FunDef_OTHE__default(X2,X3,X4) ) ).

cnf(i_0_18966_493,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X3,X1,X4) = c_FunDef_OTHE__default(X3,X2,X4) ) ).

cnf(i_0_18967_494,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X3,X4,X1) = c_FunDef_OTHE__default(X3,X4,X2) ) ).

cnf(i_0_18968_495,axiom,
    ( X1 != X2
    | c_List_Omaps(X1,X3,X4,X5) = c_List_Omaps(X2,X3,X4,X5) ) ).

cnf(i_0_18969_496,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X1,X4,X5) = c_List_Omaps(X3,X2,X4,X5) ) ).

cnf(i_0_18970_497,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X4,X1,X5) = c_List_Omaps(X3,X4,X2,X5) ) ).

cnf(i_0_18971_498,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X4,X5,X1) = c_List_Omaps(X3,X4,X5,X2) ) ).

cnf(i_0_18972_499,axiom,
    ( X1 != X2
    | esk311_2(X1,X3) = esk311_2(X2,X3) ) ).

cnf(i_0_18973_500,axiom,
    ( X1 != X2
    | esk311_2(X3,X1) = esk311_2(X3,X2) ) ).

cnf(i_0_18974_501,axiom,
    ( X1 != X2
    | esk448_2(X1,X3) = esk448_2(X2,X3) ) ).

cnf(i_0_18975_502,axiom,
    ( X1 != X2
    | esk448_2(X3,X1) = esk448_2(X3,X2) ) ).

cnf(i_0_18976_503,axiom,
    ( X1 != X2
    | esk449_2(X1,X3) = esk449_2(X2,X3) ) ).

cnf(i_0_18977_504,axiom,
    ( X1 != X2
    | esk449_2(X3,X1) = esk449_2(X3,X2) ) ).

cnf(i_0_18978_505,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_18979_506,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_18980_507,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_18981_508,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_18982_509,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X4) ) ).

cnf(i_0_18983_510,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X2,X4) ) ).

cnf(i_0_18984_511,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X2) ) ).

cnf(i_0_18985_512,axiom,
    ( X1 != X2
    | c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).

cnf(i_0_18986_513,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X4) ) ).

cnf(i_0_18987_514,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X2,X4) ) ).

cnf(i_0_18988_515,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X2) ) ).

cnf(i_0_18989_516,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_18990_517,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_18991_518,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_18992_519,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_18993_520,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).

cnf(i_0_18994_521,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).

cnf(i_0_18995_522,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).

cnf(i_0_18996_523,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X1,X3,X4,X5,X6) = c_Predicate_Opred__comp(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18997_524,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X1,X4,X5,X6) = c_Predicate_Opred__comp(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18998_525,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X1,X5,X6) = c_Predicate_Opred__comp(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18999_526,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X5,X1,X6) = c_Predicate_Opred__comp(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19000_527,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X5,X6,X1) = c_Predicate_Opred__comp(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19001_528,axiom,
    ( X1 != X2
    | esk433_2(X1,X3) = esk433_2(X2,X3) ) ).

cnf(i_0_19002_529,axiom,
    ( X1 != X2
    | esk433_2(X3,X1) = esk433_2(X3,X2) ) ).

cnf(i_0_19003_530,axiom,
    ( X1 != X2
    | esk233_3(X1,X3,X4) = esk233_3(X2,X3,X4) ) ).

cnf(i_0_19004_531,axiom,
    ( X1 != X2
    | esk233_3(X3,X1,X4) = esk233_3(X3,X2,X4) ) ).

cnf(i_0_19005_532,axiom,
    ( X1 != X2
    | esk233_3(X3,X4,X1) = esk233_3(X3,X4,X2) ) ).

cnf(i_0_19006_533,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).

cnf(i_0_19007_534,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).

cnf(i_0_19008_535,axiom,
    ( X1 != X2
    | esk235_3(X1,X3,X4) = esk235_3(X2,X3,X4) ) ).

cnf(i_0_19009_536,axiom,
    ( X1 != X2
    | esk235_3(X3,X1,X4) = esk235_3(X3,X2,X4) ) ).

cnf(i_0_19010_537,axiom,
    ( X1 != X2
    | esk235_3(X3,X4,X1) = esk235_3(X3,X4,X2) ) ).

cnf(i_0_19011_538,axiom,
    ( X1 != X2
    | esk24_3(X1,X3,X4) = esk24_3(X2,X3,X4) ) ).

cnf(i_0_19012_539,axiom,
    ( X1 != X2
    | esk24_3(X3,X1,X4) = esk24_3(X3,X2,X4) ) ).

cnf(i_0_19013_540,axiom,
    ( X1 != X2
    | esk24_3(X3,X4,X1) = esk24_3(X3,X4,X2) ) ).

cnf(i_0_19014_541,axiom,
    ( X1 != X2
    | esk23_3(X1,X3,X4) = esk23_3(X2,X3,X4) ) ).

cnf(i_0_19015_542,axiom,
    ( X1 != X2
    | esk23_3(X3,X1,X4) = esk23_3(X3,X2,X4) ) ).

cnf(i_0_19016_543,axiom,
    ( X1 != X2
    | esk23_3(X3,X4,X1) = esk23_3(X3,X4,X2) ) ).

cnf(i_0_19017_544,axiom,
    ( X1 != X2
    | c_Inductive_Ocomplete__lattice__class_Olfp(X1,X3) = c_Inductive_Ocomplete__lattice__class_Olfp(X2,X3) ) ).

cnf(i_0_19018_545,axiom,
    ( X1 != X2
    | c_Inductive_Ocomplete__lattice__class_Olfp(X3,X1) = c_Inductive_Ocomplete__lattice__class_Olfp(X3,X2) ) ).

cnf(i_0_19019_546,axiom,
    ( X1 != X2
    | esk521_3(X1,X3,X4) = esk521_3(X2,X3,X4) ) ).

cnf(i_0_19020_547,axiom,
    ( X1 != X2
    | esk521_3(X3,X1,X4) = esk521_3(X3,X2,X4) ) ).

cnf(i_0_19021_548,axiom,
    ( X1 != X2
    | esk521_3(X3,X4,X1) = esk521_3(X3,X4,X2) ) ).

cnf(i_0_19022_549,axiom,
    ( X1 != X2
    | esk508_3(X1,X3,X4) = esk508_3(X2,X3,X4) ) ).

cnf(i_0_19023_550,axiom,
    ( X1 != X2
    | esk508_3(X3,X1,X4) = esk508_3(X3,X2,X4) ) ).

cnf(i_0_19024_551,axiom,
    ( X1 != X2
    | esk508_3(X3,X4,X1) = esk508_3(X3,X4,X2) ) ).

cnf(i_0_19025_552,axiom,
    ( X1 != X2
    | c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X3) = c_Inductive_Ocomplete__lattice__class_Ogfp(X2,X3) ) ).

cnf(i_0_19026_553,axiom,
    ( X1 != X2
    | c_Inductive_Ocomplete__lattice__class_Ogfp(X3,X1) = c_Inductive_Ocomplete__lattice__class_Ogfp(X3,X2) ) ).

cnf(i_0_19027_554,axiom,
    ( X1 != X2
    | c_List_Osplice(X1,X3,X4) = c_List_Osplice(X2,X3,X4) ) ).

cnf(i_0_19028_555,axiom,
    ( X1 != X2
    | c_List_Osplice(X3,X1,X4) = c_List_Osplice(X3,X2,X4) ) ).

cnf(i_0_19029_556,axiom,
    ( X1 != X2
    | c_List_Osplice(X3,X4,X1) = c_List_Osplice(X3,X4,X2) ) ).

cnf(i_0_19030_557,axiom,
    ( X1 != X2
    | c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).

cnf(i_0_19031_558,axiom,
    ( X1 != X2
    | c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).

cnf(i_0_19032_559,axiom,
    ( X1 != X2
    | c_Random_Olog(X1,X3) = c_Random_Olog(X2,X3) ) ).

cnf(i_0_19033_560,axiom,
    ( X1 != X2
    | c_Random_Olog(X3,X1) = c_Random_Olog(X3,X2) ) ).

cnf(i_0_19034_561,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X1,X3,X4) = c_Random_Ominus__shift(X2,X3,X4) ) ).

cnf(i_0_19035_562,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X3,X1,X4) = c_Random_Ominus__shift(X3,X2,X4) ) ).

cnf(i_0_19036_563,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X3,X4,X1) = c_Random_Ominus__shift(X3,X4,X2) ) ).

cnf(i_0_19037_564,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X1,X3,X4) = c_Random__Sequence_Oempty(X2,X3,X4) ) ).

cnf(i_0_19038_565,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X3,X1,X4) = c_Random__Sequence_Oempty(X3,X2,X4) ) ).

cnf(i_0_19039_566,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X3,X4,X1) = c_Random__Sequence_Oempty(X3,X4,X2) ) ).

cnf(i_0_19040_567,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_19041_568,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_19042_569,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_19043_570,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_19044_571,axiom,
    ( X1 != X2
    | esk445_2(X1,X3) = esk445_2(X2,X3) ) ).

cnf(i_0_19045_572,axiom,
    ( X1 != X2
    | esk445_2(X3,X1) = esk445_2(X3,X2) ) ).

cnf(i_0_19046_573,axiom,
    ( X1 != X2
    | c_List_Olistset(X1,X3) = c_List_Olistset(X2,X3) ) ).

cnf(i_0_19047_574,axiom,
    ( X1 != X2
    | c_List_Olistset(X3,X1) = c_List_Olistset(X3,X2) ) ).

cnf(i_0_19048_575,axiom,
    ( X1 != X2
    | c_Code__Numeral_Odiv__mod__code__numeral(X1,X3) = c_Code__Numeral_Odiv__mod__code__numeral(X2,X3) ) ).

cnf(i_0_19049_576,axiom,
    ( X1 != X2
    | c_Code__Numeral_Odiv__mod__code__numeral(X3,X1) = c_Code__Numeral_Odiv__mod__code__numeral(X3,X2) ) ).

cnf(i_0_19050_577,axiom,
    ( X1 != X2
    | esk414_2(X1,X3) = esk414_2(X2,X3) ) ).

cnf(i_0_19051_578,axiom,
    ( X1 != X2
    | esk414_2(X3,X1) = esk414_2(X3,X2) ) ).

cnf(i_0_19052_579,axiom,
    ( X1 != X2
    | esk413_2(X1,X3) = esk413_2(X2,X3) ) ).

cnf(i_0_19053_580,axiom,
    ( X1 != X2
    | esk413_2(X3,X1) = esk413_2(X3,X2) ) ).

cnf(i_0_19054_581,axiom,
    ( X1 != X2
    | esk506_3(X1,X3,X4) = esk506_3(X2,X3,X4) ) ).

cnf(i_0_19055_582,axiom,
    ( X1 != X2
    | esk506_3(X3,X1,X4) = esk506_3(X3,X2,X4) ) ).

cnf(i_0_19056_583,axiom,
    ( X1 != X2
    | esk506_3(X3,X4,X1) = esk506_3(X3,X4,X2) ) ).

cnf(i_0_19057_584,axiom,
    ( X1 != X2
    | c_List_Oinsert(X1,X3,X4) = c_List_Oinsert(X2,X3,X4) ) ).

cnf(i_0_19058_585,axiom,
    ( X1 != X2
    | c_List_Oinsert(X3,X1,X4) = c_List_Oinsert(X3,X2,X4) ) ).

cnf(i_0_19059_586,axiom,
    ( X1 != X2
    | c_List_Oinsert(X3,X4,X1) = c_List_Oinsert(X3,X4,X2) ) ).

cnf(i_0_19060_587,axiom,
    ( X1 != X2
    | c_Int_Oring__1__class_Oof__int(X1) = c_Int_Oring__1__class_Oof__int(X2) ) ).

cnf(i_0_19061_588,axiom,
    ( X1 != X2
    | esk524_3(X1,X3,X4) = esk524_3(X2,X3,X4) ) ).

cnf(i_0_19062_589,axiom,
    ( X1 != X2
    | esk524_3(X3,X1,X4) = esk524_3(X3,X2,X4) ) ).

cnf(i_0_19063_590,axiom,
    ( X1 != X2
    | esk524_3(X3,X4,X1) = esk524_3(X3,X4,X2) ) ).

cnf(i_0_19064_591,axiom,
    ( X1 != X2
    | c_SMT_Oz3div(X1,X3) = c_SMT_Oz3div(X2,X3) ) ).

cnf(i_0_19065_592,axiom,
    ( X1 != X2
    | c_SMT_Oz3div(X3,X1) = c_SMT_Oz3div(X3,X2) ) ).

cnf(i_0_19066_593,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omin(X1,X3) = c_Orderings_Oord_Omin(X2,X3) ) ).

cnf(i_0_19067_594,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omin(X3,X1) = c_Orderings_Oord_Omin(X3,X2) ) ).

cnf(i_0_19068_595,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omax(X1,X3) = c_Orderings_Oord_Omax(X2,X3) ) ).

cnf(i_0_19069_596,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omax(X3,X1) = c_Orderings_Oord_Omax(X3,X2) ) ).

cnf(i_0_19070_597,axiom,
    ( X1 != X2
    | c_Option_Oset(X1,X3) = c_Option_Oset(X2,X3) ) ).

cnf(i_0_19071_598,axiom,
    ( X1 != X2
    | c_Option_Oset(X3,X1) = c_Option_Oset(X3,X2) ) ).

cnf(i_0_19072_599,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__single(X1,X3) = c_New__DSequence_Oneg__single(X2,X3) ) ).

cnf(i_0_19073_600,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__single(X3,X1) = c_New__DSequence_Oneg__single(X3,X2) ) ).

cnf(i_0_19074_601,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__single(X1,X3) = c_New__DSequence_Opos__single(X2,X3) ) ).

cnf(i_0_19075_602,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__single(X3,X1) = c_New__DSequence_Opos__single(X3,X2) ) ).

cnf(i_0_19076_603,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X1) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X2) ) ).

cnf(i_0_19077_604,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X1,X3,X4) = c_Predicate_Oconversep(X2,X3,X4) ) ).

cnf(i_0_19078_605,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X1,X4) = c_Predicate_Oconversep(X3,X2,X4) ) ).

cnf(i_0_19079_606,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X4,X1) = c_Predicate_Oconversep(X3,X4,X2) ) ).

cnf(i_0_19080_607,axiom,
    ( X1 != X2
    | c_SMT_Oz3mod(X1,X3) = c_SMT_Oz3mod(X2,X3) ) ).

cnf(i_0_19081_608,axiom,
    ( X1 != X2
    | c_SMT_Oz3mod(X3,X1) = c_SMT_Oz3mod(X3,X2) ) ).

cnf(i_0_19082_609,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__size(X1,X3,X4) = c_Option_Ooption_Ooption__size(X2,X3,X4) ) ).

cnf(i_0_19083_610,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__size(X3,X1,X4) = c_Option_Ooption_Ooption__size(X3,X2,X4) ) ).

cnf(i_0_19084_611,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__size(X3,X4,X1) = c_Option_Ooption_Ooption__size(X3,X4,X2) ) ).

cnf(i_0_19085_612,axiom,
    ( X1 != X2
    | esk482_2(X1,X3) = esk482_2(X2,X3) ) ).

cnf(i_0_19086_613,axiom,
    ( X1 != X2
    | esk482_2(X3,X1) = esk482_2(X3,X2) ) ).

cnf(i_0_19087_614,axiom,
    ( X1 != X2
    | c_Smallcheck_Ofull__small__class_Ofull__small(X1,X3,X4) = c_Smallcheck_Ofull__small__class_Ofull__small(X2,X3,X4) ) ).

cnf(i_0_19088_615,axiom,
    ( X1 != X2
    | c_Smallcheck_Ofull__small__class_Ofull__small(X3,X1,X4) = c_Smallcheck_Ofull__small__class_Ofull__small(X3,X2,X4) ) ).

cnf(i_0_19089_616,axiom,
    ( X1 != X2
    | c_Smallcheck_Ofull__small__class_Ofull__small(X3,X4,X1) = c_Smallcheck_Ofull__small__class_Ofull__small(X3,X4,X2) ) ).

cnf(i_0_19090_617,axiom,
    ( X1 != X2
    | c_Smallcheck_Ofull__small_H(X1,X3,X4) = c_Smallcheck_Ofull__small_H(X2,X3,X4) ) ).

cnf(i_0_19091_618,axiom,
    ( X1 != X2
    | c_Smallcheck_Ofull__small_H(X3,X1,X4) = c_Smallcheck_Ofull__small_H(X3,X2,X4) ) ).

cnf(i_0_19092_619,axiom,
    ( X1 != X2
    | c_Smallcheck_Ofull__small_H(X3,X4,X1) = c_Smallcheck_Ofull__small_H(X3,X4,X2) ) ).

cnf(i_0_19093_620,axiom,
    ( X1 != X2
    | esk400_1(X1) = esk400_1(X2) ) ).

cnf(i_0_19094_621,axiom,
    ( X1 != X2
    | esk507_2(X1,X3) = esk507_2(X2,X3) ) ).

cnf(i_0_19095_622,axiom,
    ( X1 != X2
    | esk507_2(X3,X1) = esk507_2(X3,X2) ) ).

cnf(i_0_19096_623,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).

cnf(i_0_19097_624,axiom,
    ( X1 != X2
    | c_Random_Oinc__shift(X1,X3) = c_Random_Oinc__shift(X2,X3) ) ).

cnf(i_0_19098_625,axiom,
    ( X1 != X2
    | c_Random_Oinc__shift(X3,X1) = c_Random_Oinc__shift(X3,X2) ) ).

cnf(i_0_19099_626,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__single(X1,X3) = c_Lazy__Sequence_Ohb__single(X2,X3) ) ).

cnf(i_0_19100_627,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__single(X3,X1) = c_Lazy__Sequence_Ohb__single(X3,X2) ) ).

cnf(i_0_19101_628,axiom,
    ( X1 != X2
    | c_HOL_Obool_Obool__size(X1) = c_HOL_Obool_Obool__size(X2) ) ).

cnf(i_0_19102_629,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X1,X3,X4,X5) = c_Option_Ooption_Ooption__case(X2,X3,X4,X5) ) ).

cnf(i_0_19103_630,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X1,X4,X5) = c_Option_Ooption_Ooption__case(X3,X2,X4,X5) ) ).

cnf(i_0_19104_631,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X4,X1,X5) = c_Option_Ooption_Ooption__case(X3,X4,X2,X5) ) ).

cnf(i_0_19105_632,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X4,X5,X1) = c_Option_Ooption_Ooption__case(X3,X4,X5,X2) ) ).

cnf(i_0_19106_633,axiom,
    ( X1 != X2
    | c_Divides_Oadjust(X1) = c_Divides_Oadjust(X2) ) ).

cnf(i_0_19107_634,axiom,
    ( X1 != X2
    | c_FunDef_Orp__inv__image(X1,X3) = c_FunDef_Orp__inv__image(X2,X3) ) ).

cnf(i_0_19108_635,axiom,
    ( X1 != X2
    | c_FunDef_Orp__inv__image(X3,X1) = c_FunDef_Orp__inv__image(X3,X2) ) ).

cnf(i_0_19109_636,axiom,
    ( X1 != X2
    | c_Map_Omap__add(X1,X3,X4,X5) = c_Map_Omap__add(X2,X3,X4,X5) ) ).

cnf(i_0_19110_637,axiom,
    ( X1 != X2
    | c_Map_Omap__add(X3,X1,X4,X5) = c_Map_Omap__add(X3,X2,X4,X5) ) ).

cnf(i_0_19111_638,axiom,
    ( X1 != X2
    | c_Map_Omap__add(X3,X4,X1,X5) = c_Map_Omap__add(X3,X4,X2,X5) ) ).

cnf(i_0_19112_639,axiom,
    ( X1 != X2
    | c_Map_Omap__add(X3,X4,X5,X1) = c_Map_Omap__add(X3,X4,X5,X2) ) ).

cnf(i_0_19113_640,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_19114_641,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | class_Groups_Ocomm__monoid__add(X2) ) ).

cnf(i_0_19115_642,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring(X1)
    | class_Rings_Olinordered__semiring(X2) ) ).

cnf(i_0_19116_643,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_19117_644,axiom,
    ( X1 != X2
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).

cnf(i_0_19118_645,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oreflp(X1,X3)
    | c_Predicate_Oreflp(X2,X3) ) ).

cnf(i_0_19119_646,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oreflp(X3,X1)
    | c_Predicate_Oreflp(X3,X2) ) ).

cnf(i_0_19120_647,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__comm__semiring__strict(X1)
    | class_Rings_Olinordered__comm__semiring__strict(X2) ) ).

cnf(i_0_19121_648,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__comm__semiring(X1)
    | class_Rings_Oordered__comm__semiring(X2) ) ).

cnf(i_0_19122_649,axiom,
    ( X1 != X2
    | ~ class_Divides_Oring__div(X1)
    | class_Divides_Oring__div(X2) ) ).

cnf(i_0_19123_650,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | class_Groups_Olinordered__ab__group__add(X2) ) ).

cnf(i_0_19124_651,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | class_Rings_Oordered__cancel__semiring(X2) ) ).

cnf(i_0_19125_652,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X4) ) ).

cnf(i_0_19126_653,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X4) ) ).

cnf(i_0_19127_654,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X1)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X2) ) ).

cnf(i_0_19128_655,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1(X1)
    | class_Rings_Oring__1(X2) ) ).

cnf(i_0_19129_656,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring__abs(X1)
    | class_Rings_Oordered__ring__abs(X2) ) ).

cnf(i_0_19130_657,axiom,
    ( X1 != X2
    | ~ class_Orderings_Owellorder(X1)
    | class_Orderings_Owellorder(X2) ) ).

cnf(i_0_19131_658,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oboolean__algebra(X1)
    | class_Lattices_Oboolean__algebra(X2) ) ).

cnf(i_0_19132_659,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring(X1)
    | class_Rings_Odivision__ring(X2) ) ).

cnf(i_0_19133_660,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring(X1)
    | class_Rings_Ocomm__semiring(X2) ) ).

cnf(i_0_19134_661,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder__class_Ostrict__mono(X1,X3,X4)
    | c_Orderings_Oorder__class_Ostrict__mono(X2,X3,X4) ) ).

cnf(i_0_19135_662,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder__class_Ostrict__mono(X3,X1,X4)
    | c_Orderings_Oorder__class_Ostrict__mono(X3,X2,X4) ) ).

cnf(i_0_19136_663,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder__class_Ostrict__mono(X3,X4,X1)
    | c_Orderings_Oorder__class_Ostrict__mono(X3,X4,X2) ) ).

cnf(i_0_19137_664,axiom,
    ( X1 != X2
    | ~ c_Partial__Function_Omk__less(X1,X3,X4,X5)
    | c_Partial__Function_Omk__less(X2,X3,X4,X5) ) ).

cnf(i_0_19138_665,axiom,
    ( X1 != X2
    | ~ c_Partial__Function_Omk__less(X3,X1,X4,X5)
    | c_Partial__Function_Omk__less(X3,X2,X4,X5) ) ).

cnf(i_0_19139_666,axiom,
    ( X1 != X2
    | ~ c_Partial__Function_Omk__less(X3,X4,X1,X5)
    | c_Partial__Function_Omk__less(X3,X4,X2,X5) ) ).

cnf(i_0_19140_667,axiom,
    ( X1 != X2
    | ~ c_Partial__Function_Omk__less(X3,X4,X5,X1)
    | c_Partial__Function_Omk__less(X3,X4,X5,X2) ) ).

cnf(i_0_19141_668,axiom,
    ( X1 != X2
    | ~ class_Groups_Ominus(X1)
    | class_Groups_Ominus(X2) ) ).

cnf(i_0_19142_669,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_19143_670,axiom,
    ( X1 != X2
    | ~ class_Groups_Ogroup__add(X1)
    | class_Groups_Ogroup__add(X2) ) ).

cnf(i_0_19144_671,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | class_Groups_Ocomm__monoid__mult(X2) ) ).

cnf(i_0_19145_672,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X1,X3,X4,X5)
    | c_Nat__Transfer_Otransfer__morphism(X2,X3,X4,X5) ) ).

cnf(i_0_19146_673,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X1,X4,X5)
    | c_Nat__Transfer_Otransfer__morphism(X3,X2,X4,X5) ) ).

cnf(i_0_19147_674,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X1,X5)
    | c_Nat__Transfer_Otransfer__morphism(X3,X4,X2,X5) ) ).

cnf(i_0_19148_675,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X1)
    | c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X2) ) ).

cnf(i_0_19149_676,axiom,
    ( X1 != X2
    | ~ class_Nat_Osemiring__char__0(X1)
    | class_Nat_Osemiring__char__0(X2) ) ).

cnf(i_0_19150_677,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Owf_H(X1,X3)
    | c_Nitpick_Owf_H(X2,X3) ) ).

cnf(i_0_19151_678,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Owf_H(X3,X1)
    | c_Nitpick_Owf_H(X3,X2) ) ).

cnf(i_0_19152_679,axiom,
    ( X1 != X2
    | ~ c_List_Onat__list(X1)
    | c_List_Onat__list(X2) ) ).

cnf(i_0_19153_680,axiom,
    ( X1 != X2
    | ~ class_Groups_Osgn__if(X1)
    | class_Groups_Osgn__if(X2) ) ).

cnf(i_0_19154_681,axiom,
    ( X1 != X2
    | ~ class_Power_Opower(X1)
    | class_Power_Opower(X2) ) ).

cnf(i_0_19155_682,axiom,
    ( X1 != X2
    | ~ class_Groups_Oabs__if(X1)
    | class_Groups_Oabs__if(X2) ) ).

cnf(i_0_19156_683,axiom,
    ( X1 != X2
    | ~ class_Groups_Ouminus(X1)
    | class_Groups_Ouminus(X2) ) ).

cnf(i_0_19157_684,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X1,X3,X4)
    | c_Big__Operators_Osemilattice__big(X2,X3,X4) ) ).

cnf(i_0_19158_685,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X3,X1,X4)
    | c_Big__Operators_Osemilattice__big(X3,X2,X4) ) ).

cnf(i_0_19159_686,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X3,X4,X1)
    | c_Big__Operators_Osemilattice__big(X3,X4,X2) ) ).

cnf(i_0_19160_687,axiom,
    ( X1 != X2
    | ~ class_Rings_Oidom(X1)
    | class_Rings_Oidom(X2) ) ).

cnf(i_0_19161_688,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oord(X1)
    | class_Orderings_Oord(X2) ) ).

cnf(i_0_19162_689,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__ring__1(X1)
    | class_Rings_Ocomm__ring__1(X2) ) ).

cnf(i_0_19163_690,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | class_Groups_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_19164_691,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__ab__semigroup__add(X1)
    | class_Groups_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_19165_692,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Ounknown(X1)
    | c_Nitpick_Ounknown(X2) ) ).

cnf(i_0_19166_693,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(X2) ) ).

cnf(i_0_19167_694,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_19168_695,axiom,
    ( X1 != X2
    | ~ class_Orderings_Otop(X1)
    | class_Orderings_Otop(X2) ) ).

cnf(i_0_19169_696,axiom,
    ( X1 != X2
    | ~ class_Rings_Omult__zero(X1)
    | class_Rings_Omult__zero(X2) ) ).

cnf(i_0_19170_697,axiom,
    ( X1 != X2
    | ~ class_Rings_Ozero__neq__one(X1)
    | class_Rings_Ozero__neq__one(X2) ) ).

cnf(i_0_19171_698,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | class_Rings_Oring__no__zero__divisors(X2) ) ).

cnf(i_0_19172_699,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__semigroup__add(X1)
    | class_Groups_Olinordered__ab__semigroup__add(X2) ) ).

cnf(i_0_19173_700,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice__top(X1)
    | class_Lattices_Obounded__lattice__top(X2) ) ).

cnf(i_0_19174_701,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice__bot(X1)
    | class_Lattices_Obounded__lattice__bot(X2) ) ).

cnf(i_0_19175_702,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring__inverse__zero(X1)
    | class_Rings_Odivision__ring__inverse__zero(X2) ) ).

cnf(i_0_19176_703,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice(X1)
    | class_Lattices_Obounded__lattice(X2) ) ).

cnf(i_0_19177_704,axiom,
    ( X1 != X2
    | ~ class_Nat_Osize(X1)
    | class_Nat_Osize(X2) ) ).

cnf(i_0_19178_705,axiom,
    ( X1 != X2
    | ~ class_Groups_Ozero(X1)
    | class_Groups_Ozero(X2) ) ).

cnf(i_0_19179_706,axiom,
    ( X1 != X2
    | ~ class_Groups_Oone(X1)
    | class_Groups_Oone(X2) ) ).

cnf(i_0_19180_707,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_19181_708,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_19182_709,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_19183_710,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_19184_711,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_19185_712,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_19186_713,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__idom(X1)
    | class_Rings_Olinordered__idom(X2) ) ).

cnf(i_0_19187_714,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_19188_715,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_19189_716,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_19190_717,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_19191_718,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_19192_719,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_19193_720,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_19194_721,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X1,X3,X4)
    | c_Relation_Orefl__on(X2,X3,X4) ) ).

cnf(i_0_19195_722,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X3,X1,X4)
    | c_Relation_Orefl__on(X3,X2,X4) ) ).

cnf(i_0_19196_723,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X3,X4,X1)
    | c_Relation_Orefl__on(X3,X4,X2) ) ).

cnf(i_0_19197_724,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_19198_725,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_19199_726,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_19200_727,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_19201_728,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_19202_729,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_19203_730,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X1,X3,X4,X5)
    | c_Wellfounded_Omax__extp(X2,X3,X4,X5) ) ).

cnf(i_0_19204_731,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X1,X4,X5)
    | c_Wellfounded_Omax__extp(X3,X2,X4,X5) ) ).

cnf(i_0_19205_732,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X4,X1,X5)
    | c_Wellfounded_Omax__extp(X3,X4,X2,X5) ) ).

cnf(i_0_19206_733,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X4,X5,X1)
    | c_Wellfounded_Omax__extp(X3,X4,X5,X2) ) ).

cnf(i_0_19207_734,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X1,X3,X4,X5)
    | c_List_Olistrelp(X2,X3,X4,X5) ) ).

cnf(i_0_19208_735,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X1,X4,X5)
    | c_List_Olistrelp(X3,X2,X4,X5) ) ).

cnf(i_0_19209_736,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X4,X1,X5)
    | c_List_Olistrelp(X3,X4,X2,X5) ) ).

cnf(i_0_19210_737,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X4,X5,X1)
    | c_List_Olistrelp(X3,X4,X5,X2) ) ).

cnf(i_0_19211_738,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequivp(X1,X3)
    | c_Equiv__Relations_Oequivp(X2,X3) ) ).

cnf(i_0_19212_739,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequivp(X3,X1)
    | c_Equiv__Relations_Oequivp(X3,X2) ) ).

cnf(i_0_19213_740,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Owf(X1,X3)
    | c_Wellfounded_Owf(X2,X3) ) ).

cnf(i_0_19214_741,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Owf(X3,X1)
    | c_Wellfounded_Owf(X3,X2) ) ).

cnf(i_0_19215_742,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_OwfP(X1,X3)
    | c_Wellfounded_OwfP(X2,X3) ) ).

cnf(i_0_19216_743,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_OwfP(X3,X1)
    | c_Wellfounded_OwfP(X3,X2) ) ).

cnf(i_0_19217_744,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X1,X3,X4)
    | c_Finite__Set_Ofun__left__comm(X2,X3,X4) ) ).

cnf(i_0_19218_745,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X3,X1,X4)
    | c_Finite__Set_Ofun__left__comm(X3,X2,X4) ) ).

cnf(i_0_19219_746,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X3,X4,X1)
    | c_Finite__Set_Ofun__left__comm(X3,X4,X2) ) ).

cnf(i_0_19220_747,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semidom(X1)
    | class_Rings_Olinordered__semidom(X2) ) ).

cnf(i_0_19221_748,axiom,
    ( X1 != X2
    | ~ class_Lazy__Sequence_Osmall__lazy(X1)
    | class_Lazy__Sequence_Osmall__lazy(X2) ) ).

cnf(i_0_19222_749,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_19223_750,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | class_Groups_Oordered__ab__group__add(X2) ) ).

cnf(i_0_19224_751,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X4)
    | c_Equiv__Relations_Oequiv(X2,X3,X4) ) ).

cnf(i_0_19225_752,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X3,X1,X4)
    | c_Equiv__Relations_Oequiv(X3,X2,X4) ) ).

cnf(i_0_19226_753,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X3,X4,X1)
    | c_Equiv__Relations_Oequiv(X3,X4,X2) ) ).

cnf(i_0_19227_754,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_19228_755,axiom,
    ( X1 != X2
    | ~ class_Smallcheck_Osmall(X1)
    | class_Smallcheck_Osmall(X2) ) ).

cnf(i_0_19229_756,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__mult(X1)
    | class_Groups_Omonoid__mult(X2) ) ).

cnf(i_0_19230_757,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__mult(X1)
    | class_Groups_Oab__semigroup__mult(X2) ) ).

cnf(i_0_19231_758,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__add(X1)
    | class_Groups_Omonoid__add(X2) ) ).

cnf(i_0_19232_759,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | class_Groups_Oordered__ab__semigroup__add(X2) ) ).

cnf(i_0_19233_760,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X1,X3,X4,X5,X6)
    | c_List_Olist__all2(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19234_761,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X1,X4,X5,X6)
    | c_List_Olist__all2(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19235_762,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X1,X5,X6)
    | c_List_Olist__all2(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19236_763,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X5,X1,X6)
    | c_List_Olist__all2(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19237_764,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X5,X6,X1)
    | c_List_Olist__all2(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19238_765,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_19239_766,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X1,X3,X4)
    | c_Finite__Set_Ofolding__one__idem(X2,X3,X4) ) ).

cnf(i_0_19240_767,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X3,X1,X4)
    | c_Finite__Set_Ofolding__one__idem(X3,X2,X4) ) ).

cnf(i_0_19241_768,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X3,X4,X1)
    | c_Finite__Set_Ofolding__one__idem(X3,X4,X2) ) ).

cnf(i_0_19242_769,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | class_Rings_Ocomm__semiring__1(X2) ) ).

cnf(i_0_19243_770,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring__0(X1)
    | class_Rings_Osemiring__0(X2) ) ).

cnf(i_0_19244_771,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring__1(X1)
    | class_Rings_Osemiring__1(X2) ) ).

cnf(i_0_19245_772,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X1,X3,X4)
    | c_Finite__Set_Ofolding__one(X2,X3,X4) ) ).

cnf(i_0_19246_773,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X3,X1,X4)
    | c_Finite__Set_Ofolding__one(X3,X2,X4) ) ).

cnf(i_0_19247_774,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X3,X4,X1)
    | c_Finite__Set_Ofolding__one(X3,X4,X2) ) ).

cnf(i_0_19248_775,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | class_Fields_Olinordered__field__inverse__zero(X2) ) ).

cnf(i_0_19249_776,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oreduction__pair(X1,X3)
    | c_FunDef_Oreduction__pair(X2,X3) ) ).

cnf(i_0_19250_777,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oreduction__pair(X3,X1)
    | c_FunDef_Oreduction__pair(X3,X2) ) ).

cnf(i_0_19251_778,axiom,
    ( X1 != X2
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | c_List_Olinorder__class_Osorted(X2,X3) ) ).

cnf(i_0_19252_779,axiom,
    ( X1 != X2
    | ~ c_List_Olinorder__class_Osorted(X3,X1)
    | c_List_Olinorder__class_Osorted(X3,X2) ) ).

cnf(i_0_19253_780,axiom,
    ( X1 != X2
    | ~ class_Enum_Oenum(X1)
    | class_Enum_Oenum(X2) ) ).

cnf(i_0_19254_781,axiom,
    ( X1 != X2
    | ~ c_Enum_Oex__n__lists(X1,X3,X4)
    | c_Enum_Oex__n__lists(X2,X3,X4) ) ).

cnf(i_0_19255_782,axiom,
    ( X1 != X2
    | ~ c_Enum_Oex__n__lists(X3,X1,X4)
    | c_Enum_Oex__n__lists(X3,X2,X4) ) ).

cnf(i_0_19256_783,axiom,
    ( X1 != X2
    | ~ c_Enum_Oex__n__lists(X3,X4,X1)
    | c_Enum_Oex__n__lists(X3,X4,X2) ) ).

cnf(i_0_19257_784,axiom,
    ( X1 != X2
    | ~ class_HOL_Oequal(X1)
    | class_HOL_Oequal(X2) ) ).

cnf(i_0_19258_785,axiom,
    ( X1 != X2
    | ~ c_Enum_Oall__n__lists(X1,X3,X4)
    | c_Enum_Oall__n__lists(X2,X3,X4) ) ).

cnf(i_0_19259_786,axiom,
    ( X1 != X2
    | ~ c_Enum_Oall__n__lists(X3,X1,X4)
    | c_Enum_Oall__n__lists(X3,X2,X4) ) ).

cnf(i_0_19260_787,axiom,
    ( X1 != X2
    | ~ c_Enum_Oall__n__lists(X3,X4,X1)
    | c_Enum_Oall__n__lists(X3,X4,X2) ) ).

cnf(i_0_19261_788,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Ois__nat(X1)
    | c_Nat__Transfer_Ois__nat(X2) ) ).

cnf(i_0_19262_789,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_19263_790,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_19264_791,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_19265_792,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_19266_793,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X1,X3,X4)
    | c_Nitpick_Oless__eq__frac(X2,X3,X4) ) ).

cnf(i_0_19267_794,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X3,X1,X4)
    | c_Nitpick_Oless__eq__frac(X3,X2,X4) ) ).

cnf(i_0_19268_795,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X3,X4,X1)
    | c_Nitpick_Oless__eq__frac(X3,X4,X2) ) ).

cnf(i_0_19269_796,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X1,X3,X4)
    | c_Nitpick_Oless__frac(X2,X3,X4) ) ).

cnf(i_0_19270_797,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X3,X1,X4)
    | c_Nitpick_Oless__frac(X3,X2,X4) ) ).

cnf(i_0_19271_798,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X3,X4,X1)
    | c_Nitpick_Oless__frac(X3,X4,X2) ) ).

cnf(i_0_19272_799,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | class_Groups_Oordered__comm__monoid__add(X2) ) ).

cnf(i_0_19273_800,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring(X1)
    | class_Rings_Oordered__ring(X2) ) ).

cnf(i_0_19274_801,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__group__add(X1)
    | class_Groups_Oab__group__add(X2) ) ).

cnf(i_0_19275_802,axiom,
    ( X1 != X2
    | ~ class_Rings_Oinverse(X1)
    | class_Rings_Oinverse(X2) ) ).

cnf(i_0_19276_803,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield(X1)
    | class_Fields_Ofield(X2) ) ).

cnf(i_0_19277_804,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X1,X3,X4)
    | c_List_Olist__ex1(X2,X3,X4) ) ).

cnf(i_0_19278_805,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X3,X1,X4)
    | c_List_Olist__ex1(X3,X2,X4) ) ).

cnf(i_0_19279_806,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X3,X4,X1)
    | c_List_Olist__ex1(X3,X4,X2) ) ).

cnf(i_0_19280_807,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X1,X3,X4)
    | c_List_Olist__all(X2,X3,X4) ) ).

cnf(i_0_19281_808,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X3,X1,X4)
    | c_List_Olist__all(X3,X2,X4) ) ).

cnf(i_0_19282_809,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X3,X4,X1)
    | c_List_Olist__all(X3,X4,X2) ) ).

cnf(i_0_19283_810,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_19284_811,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_19285_812,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_19286_813,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_19287_814,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_19288_815,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_19289_816,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_19290_817,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oinv__imagep(X1,X3,X4,X5,X6,X7)
    | c_Predicate_Oinv__imagep(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_19291_818,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oinv__imagep(X3,X1,X4,X5,X6,X7)
    | c_Predicate_Oinv__imagep(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_19292_819,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oinv__imagep(X3,X4,X1,X5,X6,X7)
    | c_Predicate_Oinv__imagep(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_19293_820,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oinv__imagep(X3,X4,X5,X1,X6,X7)
    | c_Predicate_Oinv__imagep(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_19294_821,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oinv__imagep(X3,X4,X5,X6,X1,X7)
    | c_Predicate_Oinv__imagep(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_19295_822,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oinv__imagep(X3,X4,X5,X6,X7,X1)
    | c_Predicate_Oinv__imagep(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_19296_823,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | class_Groups_Oordered__ab__group__add__abs(X2) ) ).

cnf(i_0_19297_824,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_19298_825,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_19299_826,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_19300_827,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_19301_828,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_19302_829,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | class_Rings_Oring__1__no__zero__divisors(X2) ) ).

cnf(i_0_19303_830,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Onat__set(X1)
    | c_Nat__Transfer_Onat__set(X2) ) ).

cnf(i_0_19304_831,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | class_Fields_Ofield__inverse__zero(X2) ) ).

cnf(i_0_19305_832,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_19306_833,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_19307_834,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_19308_835,axiom,
    ( X1 != X2
    | ~ class_Lattices_Osemilattice__sup(X1)
    | class_Lattices_Osemilattice__sup(X2) ) ).

cnf(i_0_19309_836,axiom,
    ( X1 != X2
    | ~ c_Int_Oiszero(X1,X3)
    | c_Int_Oiszero(X2,X3) ) ).

cnf(i_0_19310_837,axiom,
    ( X1 != X2
    | ~ c_Int_Oiszero(X3,X1)
    | c_Int_Oiszero(X3,X2) ) ).

cnf(i_0_19311_838,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X1,X3,X4)
    | c_Relation_Ototal__on(X2,X3,X4) ) ).

cnf(i_0_19312_839,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X3,X1,X4)
    | c_Relation_Ototal__on(X3,X2,X4) ) ).

cnf(i_0_19313_840,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X3,X4,X1)
    | c_Relation_Ototal__on(X3,X4,X2) ) ).

cnf(i_0_19314_841,axiom,
    ( X1 != X2
    | ~ class_Lattices_Odistrib__lattice(X1)
    | class_Lattices_Odistrib__lattice(X2) ) ).

cnf(i_0_19315_842,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X1,X3,X4)
    | c_Relation_Osingle__valued(X2,X3,X4) ) ).

cnf(i_0_19316_843,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X3,X1,X4)
    | c_Relation_Osingle__valued(X3,X2,X4) ) ).

cnf(i_0_19317_844,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X3,X4,X1)
    | c_Relation_Osingle__valued(X3,X4,X2) ) ).

cnf(i_0_19318_845,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber(X1)
    | class_Int_Onumber(X2) ) ).

cnf(i_0_19319_846,axiom,
    ( X1 != X2
    | ~ class_Divides_Osemiring__div(X1)
    | class_Divides_Osemiring__div(X2) ) ).

cnf(i_0_19320_847,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | class_Rings_Olinordered__ring__strict(X2) ) ).

cnf(i_0_19321_848,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_19322_849,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring(X1)
    | class_Rings_Olinordered__ring(X2) ) ).

cnf(i_0_19323_850,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X1,X3,X4,X5)
    | c_Finite__Set_Ofolding(X2,X3,X4,X5) ) ).

cnf(i_0_19324_851,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X1,X4,X5)
    | c_Finite__Set_Ofolding(X3,X2,X4,X5) ) ).

cnf(i_0_19325_852,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X4,X1,X5)
    | c_Finite__Set_Ofolding(X3,X4,X2,X5) ) ).

cnf(i_0_19326_853,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X4,X5,X1)
    | c_Finite__Set_Ofolding(X3,X4,X5,X2) ) ).

cnf(i_0_19327_854,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__1__strict(X1)
    | class_Rings_Olinordered__semiring__1__strict(X2) ) ).

cnf(i_0_19328_855,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__1(X1)
    | class_Rings_Olinordered__semiring__1(X2) ) ).

cnf(i_0_19329_856,axiom,
    ( X1 != X2
    | ~ class_Lattices_Osemilattice__inf(X1)
    | class_Lattices_Osemilattice__inf(X2) ) ).

cnf(i_0_19330_857,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder__class_Omono(X1,X3,X4)
    | c_Orderings_Oorder__class_Omono(X2,X3,X4) ) ).

cnf(i_0_19331_858,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder__class_Omono(X3,X1,X4)
    | c_Orderings_Oorder__class_Omono(X3,X2,X4) ) ).

cnf(i_0_19332_859,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder__class_Omono(X3,X4,X1)
    | c_Orderings_Oorder__class_Omono(X3,X4,X2) ) ).

cnf(i_0_19333_860,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field(X1)
    | class_Fields_Olinordered__field(X2) ) ).

cnf(i_0_19334_861,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oacyclic(X1,X3)
    | c_Wellfounded_Oacyclic(X2,X3) ) ).

cnf(i_0_19335_862,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oacyclic(X3,X1)
    | c_Wellfounded_Oacyclic(X3,X2) ) ).

cnf(i_0_19336_863,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1)
    | class_Lattices_Oab__semigroup__idem__mult(X2) ) ).

cnf(i_0_19337_864,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Orefl_H(X1,X3)
    | c_Nitpick_Orefl_H(X2,X3) ) ).

cnf(i_0_19338_865,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Orefl_H(X3,X1)
    | c_Nitpick_Orefl_H(X3,X2) ) ).

cnf(i_0_19339_866,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X1,X3,X4,X5)
    | c_Finite__Set_Ofolding__idem(X2,X3,X4,X5) ) ).

cnf(i_0_19340_867,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X1,X4,X5)
    | c_Finite__Set_Ofolding__idem(X3,X2,X4,X5) ) ).

cnf(i_0_19341_868,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X4,X1,X5)
    | c_Finite__Set_Ofolding__idem(X3,X4,X2,X5) ) ).

cnf(i_0_19342_869,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X4,X5,X1)
    | c_Finite__Set_Ofolding__idem(X3,X4,X5,X2) ) ).

cnf(i_0_19343_870,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_19344_871,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_19345_872,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_19346_873,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_19347_874,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_19348_875,axiom,
    ( X1 != X2
    | ~ class_Rings_Ono__zero__divisors(X1)
    | class_Rings_Ono__zero__divisors(X2) ) ).

cnf(i_0_19349_876,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X1,X3,X4,X5,X6)
    | c_Typedef_Otype__definition(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19350_877,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X1,X4,X5,X6)
    | c_Typedef_Otype__definition(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19351_878,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X1,X5,X6)
    | c_Typedef_Otype__definition(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19352_879,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X5,X1,X6)
    | c_Typedef_Otype__definition(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19353_880,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X1)
    | c_Typedef_Otype__definition(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19354_881,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring(X1)
    | class_Rings_Oring(X2) ) ).

cnf(i_0_19355_882,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring(X1)
    | class_Rings_Osemiring(X2) ) ).

cnf(i_0_19356_883,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X1,X3,X4,X5)
    | c_Equiv__Relations_Ocongruent(X2,X3,X4,X5) ) ).

cnf(i_0_19357_884,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X1,X4,X5)
    | c_Equiv__Relations_Ocongruent(X3,X2,X4,X5) ) ).

cnf(i_0_19358_885,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X4,X1,X5)
    | c_Equiv__Relations_Ocongruent(X3,X4,X2,X5) ) ).

cnf(i_0_19359_886,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X4,X5,X1)
    | c_Equiv__Relations_Ocongruent(X3,X4,X5,X2) ) ).

cnf(i_0_19360_887,axiom,
    ( X1 != X2
    | ~ class_Groups_Osemigroup__add(X1)
    | class_Groups_Osemigroup__add(X2) ) ).

cnf(i_0_19361_888,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X1,X3,X4)
    | c_List_Olist__ex(X2,X3,X4) ) ).

cnf(i_0_19362_889,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X3,X1,X4)
    | c_List_Olist__ex(X3,X2,X4) ) ).

cnf(i_0_19363_890,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X3,X4,X1)
    | c_List_Olist__ex(X3,X4,X2) ) ).

cnf(i_0_19364_891,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X1,X3,X4)
    | c_List_Oall__interval__int(X2,X3,X4) ) ).

cnf(i_0_19365_892,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X3,X1,X4)
    | c_List_Oall__interval__int(X3,X2,X4) ) ).

cnf(i_0_19366_893,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X3,X4,X1)
    | c_List_Oall__interval__int(X3,X4,X2) ) ).

cnf(i_0_19367_894,axiom,
    ( X1 != X2
    | ~ c_Relation_Oirrefl(X1,X3)
    | c_Relation_Oirrefl(X2,X3) ) ).

cnf(i_0_19368_895,axiom,
    ( X1 != X2
    | ~ c_Relation_Oirrefl(X3,X1)
    | c_Relation_Oirrefl(X3,X2) ) ).

cnf(i_0_19369_896,axiom,
    ( X1 != X2
    | ~ epred1_3(X1,X3,X4)
    | epred1_3(X2,X3,X4) ) ).

cnf(i_0_19370_897,axiom,
    ( X1 != X2
    | ~ epred1_3(X3,X1,X4)
    | epred1_3(X3,X2,X4) ) ).

cnf(i_0_19371_898,axiom,
    ( X1 != X2
    | ~ epred1_3(X3,X4,X1)
    | epred1_3(X3,X4,X2) ) ).

cnf(i_0_19372_899,axiom,
    ( X1 != X2
    | ~ epred2_3(X1,X3,X4)
    | epred2_3(X2,X3,X4) ) ).

cnf(i_0_19373_900,axiom,
    ( X1 != X2
    | ~ epred2_3(X3,X1,X4)
    | epred2_3(X3,X2,X4) ) ).

cnf(i_0_19374_901,axiom,
    ( X1 != X2
    | ~ epred2_3(X3,X4,X1)
    | epred2_3(X3,X4,X2) ) ).

cnf(i_0_19375_902,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__add(X1)
    | class_Groups_Oab__semigroup__add(X2) ) ).

cnf(i_0_19376_903,axiom,
    ( X1 != X2
    | ~ class_Int_Oring__char__0(X1)
    | class_Int_Oring__char__0(X2) ) ).

cnf(i_0_19377_904,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | class_Rings_Olinordered__semiring__strict(X2) ) ).

cnf(i_0_19378_905,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__semiring(X1)
    | class_Rings_Oordered__semiring(X2) ) ).

cnf(i_0_19379,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),esk64_7(X4,X4,X6,X5,X3,X2,X1)),esk65_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,[],[11190]) ).

cnf(i_0_19380,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),esk324_8(X6,X7,hAPP(c_Set_Oimage(X1,X2,X3),X4),X4,X3,X2,X1,X5)),X4)) ),
    inference(equality_inference,[],[11204]) ).

cnf(i_0_19381,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),esk186_8(X6,X7,hAPP(c_Set_Oimage(X1,X2,X3),X4),X4,X3,X2,X1,X5)),X4)) ),
    inference(equality_inference,[],[11205]) ).

cnf(i_0_19382,plain,
    ( ~ c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2)
    | hBOOL(hAPP(hAPP(c_member(X1),X3),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X2)),X4))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X2)))))) ),
    inference(equality_inference,[],[11211]) ).

cnf(i_0_19383,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)),esk401_4(X3,X2,X2,X1))) ),
    inference(equality_inference,[],[11231]) ).

cnf(i_0_19384,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),esk65_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,[],[11279]) ).

cnf(i_0_19385,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),esk64_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,[],[11280]) ).

cnf(i_0_19386,plain,
    X1 = X1,
    inference(equality_inference,[],[11314]) ).

cnf(i_0_19387,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,esk64_7(X1,X1,X6,X5,X4,X3,X2)) = hAPP(X6,esk65_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,[],[11325]) ).

cnf(i_0_19388,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,esk245_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,[],[11379]) ).

cnf(i_0_19389,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),esk245_6(X5,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X3),X4,X3,X2,X1)),X3)) ),
    inference(equality_inference,[],[11439]) ).

cnf(i_0_19390,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | ~ hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),esk481_5(X2,X3,X1,X3,X1))),hAPP(hAPP(c_List_Onth(X1),X3),esk481_5(X2,X3,X1,X3,X1)))) ),
    inference(equality_inference,[],[11441]) ).

cnf(i_0_19391,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | ~ hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),esk472_5(X3,X3,X2,X1,X1))),hAPP(hAPP(c_List_Onth(X1),X3),esk472_5(X3,X3,X2,X1,X1)))) ),
    inference(equality_inference,[],[11442]) ).

cnf(i_0_19392,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),esk452_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,[],[11450]) ).

cnf(i_0_19393,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),esk417_4(X3,X2,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk417_4(X3,X2,X2,X1)))),X3)) ),
    inference(equality_inference,[],[11462]) ).

cnf(i_0_19394,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,[],[11505]) ).

cnf(i_0_19395,plain,
    hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4)) = hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4)),
    inference(equality_inference,[],[11513]) ).

cnf(i_0_19396,plain,
    hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4)) = hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4)),
    inference(equality_inference,[],[11514]) ).

cnf(i_0_19397,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_19398,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,[],[11581]) ).

cnf(i_0_19399,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,[],[11582]) ).

cnf(i_0_19400,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,[],[11603]) ).

cnf(i_0_19401,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,[],[11672]) ).

cnf(i_0_19402,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,[],[11675]) ).

cnf(i_0_19403,plain,
    ( ~ c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_OCollect(X1)),X2))
    | hBOOL(hAPP(hAPP(c_member(X1),X3),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_OCollect(X1)),X2))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X4))
    | hBOOL(hAPP(hAPP(c_member(X1),esk25_5(X4,X3,X2,X1,c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_OCollect(X1)),X2)))),X4)) ),
    inference(equality_inference,[],[11734]) ).

cnf(i_0_19404,plain,
    ( ~ c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_OCollect(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_OCollect(X1)),X2)))),esk25_5(X3,X4,X2,X1,c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_OCollect(X1)),X2)))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | hBOOL(hAPP(hAPP(c_member(X1),X4),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_OCollect(X1)),X2)))) ),
    inference(equality_inference,[],[11738]) ).

cnf(i_0_19405,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,[],[11782]) ).

cnf(i_0_19406,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk473_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,[],[11783]) ).

cnf(i_0_19407,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk468_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,[],[11784]) ).

cnf(i_0_19408,plain,
    ( ~ c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2)
    | hBOOL(hAPP(X3,X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),X2)))
    | hBOOL(hAPP(hAPP(c_member(X1),esk28_5(X3,X4,X2,X1,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),X2))),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),X2)),hAPP(c_Set_OCollect(X1),X3))))) ),
    inference(equality_inference,[],[11794]) ).

cnf(i_0_19409,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,[],[11802]) ).

cnf(i_0_19410,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk481_5(X2,X3,X1,X3,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))) ),
    inference(equality_inference,[],[11807]) ).

cnf(i_0_19411,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk472_5(X3,X3,X2,X1,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))) ),
    inference(equality_inference,[],[11808]) ).

cnf(i_0_19412,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,[],[11851]) ).

cnf(i_0_19413,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),esk426_5(X2,X3,X2,X3,X1)),X2) = X2
    | X2 = hAPP(hAPP(c_List_Oappend(X1),esk427_5(X2,X3,X2,X3,X1)),X2) ),
    inference(equality_inference,[],[11894]) ).

cnf(i_0_19414,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),esk473_5(X2,X3,X3,X1,X1))) ),
    inference(equality_inference,[],[11900]) ).

cnf(i_0_19415,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),esk468_5(X3,X3,X2,X1,X1))) ),
    inference(equality_inference,[],[11901]) ).

cnf(i_0_19416,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,esk37_4(X4,X1,X2,hAPP(c_Set_Oimage(X1,X2,X3),X4))),hAPP(c_Set_Oimage(X1,X2,X3),X4))),X4)) ),
    inference(equality_inference,[],[11915]) ).

cnf(i_0_19417,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,[],[11943]) ).

cnf(i_0_19418,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,[],[11955]) ).

cnf(i_0_19419,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,[],[11956]) ).

cnf(i_0_19420,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,[],[11957]) ).

cnf(i_0_19421,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,[],[11958]) ).

cnf(i_0_19422,plain,
    ( ~ c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2)
    | hBOOL(hAPP(X3,X4))
    | ~ hBOOL(hAPP(X3,esk28_5(X3,X4,X2,X1,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),X2))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),X2))) ),
    inference(equality_inference,[],[11985]) ).

cnf(i_0_19423,plain,
    hAPP(hAPP(c_List_Omap(X1,X2),X3),X4) = hAPP(hAPP(c_List_Omap(X1,X2),X3),X4),
    inference(equality_inference,[],[11995]) ).

cnf(i_0_19424,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),X2),esk427_5(X3,X2,X3,X2,X1)) = X2
    | hAPP(hAPP(c_List_Oappend(X1),esk426_5(X3,X2,X3,X2,X1)),X3) = X3 ),
    inference(equality_inference,[],[12018]) ).

cnf(i_0_19425,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),X1),esk426_5(X3,X1,X3,X1,X2))
    | X3 = hAPP(hAPP(c_List_Oappend(X2),esk427_5(X3,X1,X3,X1,X2)),X3) ),
    inference(equality_inference,[],[12019]) ).

cnf(i_0_19426,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,[],[12053]) ).

cnf(i_0_19427,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,[],[12057]) ).

cnf(i_0_19428,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,[],[12058]) ).

cnf(i_0_19429,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,[],[12059]) ).

cnf(i_0_19430,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,[],[12060]) ).

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)),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,[],[12061]) ).

cnf(i_0_19432,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,[],[12081]) ).

cnf(i_0_19433,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,[],[12126]) ).

cnf(i_0_19434,plain,
    ( c_Map_Orestrict__map(X1,X1,c_Map_Omap__upds(X1,X1,X2,X3,X3),X4) = c_Map_Omap__upds(X1,X1,c_Map_Orestrict__map(X1,X1,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(c_List_Oset(X1),X3))),X3,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X3)),X4)) ),
    inference(equality_inference,[],[12127]) ).

cnf(i_0_19435,plain,
    ( hAPP(c_Map_Omap__of(X1,X2),X3) = hAPP(c_Map_Omap__of(X1,X2),X3)
    | hBOOL(hAPP(hAPP(c_member(X1),esk479_4(X3,X3,X2,X1)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)))) ),
    inference(equality_inference,[],[12130]) ).

cnf(i_0_19436,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,[],[12134]) ).

cnf(i_0_19437,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,[],[12189]) ).

cnf(i_0_19438,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,[],[12201]) ).

cnf(i_0_19439,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,[],[12206]) ).

cnf(i_0_19440,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,[],[12207]) ).

cnf(i_0_19441,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,[],[12208]) ).

cnf(i_0_19442,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)),esk254_5(X4,X3,X1,X1,X2))) ),
    inference(equality_inference,[],[12219]) ).

cnf(i_0_19443,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)),esk251_5(X4,X3,X1,X1,X2))) ),
    inference(equality_inference,[],[12220]) ).

cnf(i_0_19444,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),X1),esk426_5(X3,X1,X3,X1,X2))
    | hAPP(hAPP(c_List_Oappend(X2),X1),esk427_5(X3,X1,X3,X1,X2)) = X1 ),
    inference(equality_inference,[],[12224]) ).

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),X2)),c_List_Olistrel(X1,X3)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk401_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,[],[12227]) ).

cnf(i_0_19446,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,[],[12316]) ).

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)),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,[],[12319]) ).

cnf(i_0_19448,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,[],[12361]) ).

cnf(i_0_19449,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),esk417_4(X3,X2,X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
    inference(equality_inference,[],[12366]) ).

cnf(i_0_19450,plain,
    X1 = X1,
    inference(equality_inference,[],[12400]) ).

cnf(i_0_19451,plain,
    X1 = X1,
    inference(equality_inference,[],[12401]) ).

cnf(i_0_19452,plain,
    ( hAPP(c_Map_Omap__of(X1,X2),X3) = hAPP(c_Map_Omap__of(X1,X2),X3)
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))) ),
    inference(equality_inference,[],[12441]) ).

cnf(i_0_19453,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,[],[12447]) ).

cnf(i_0_19454,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,[],[12448]) ).

cnf(i_0_19455,plain,
    ( hAPP(c_List_Oset(tc_prod(X1,X2)),X3) = hAPP(c_List_Oset(tc_prod(X1,X2)),X3)
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))) ),
    inference(equality_inference,[],[12454]) ).

cnf(i_0_19456,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,[],[12466]) ).

cnf(i_0_19457,plain,
    ( hAPP(hAPP(c_Map_Omap__of(X1,X1),hAPP(hAPP(c_List_Ozip(X1,X1),X2),X2)),X3) = hAPP(c_Option_Ooption_OSome(X1),esk405_5(X3,X2,X1,X2,X1))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))) ),
    inference(equality_inference,[],[12525]) ).

cnf(i_0_19458,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,[],[12530]) ).

cnf(i_0_19459,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,[],[12546]) ).

cnf(i_0_19460,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,[],[12587]) ).

cnf(i_0_19461,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,[],[12588]) ).

cnf(i_0_19462,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,[],[12598]) ).

cnf(i_0_19463,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,[],[12622]) ).

cnf(i_0_19464,plain,
    ( ~ c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2)
    | hBOOL(hAPP(hAPP(c_member(X1),X3),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X2))))) ),
    inference(equality_inference,[],[12677]) ).

cnf(i_0_19465,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),esk212_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,[],[12747]) ).

cnf(i_0_19466,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),esk210_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,[],[12748]) ).

cnf(i_0_19467,plain,
    c_Map_Omap__upds(X1,X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4),X3) = c_Map_Omap__upds(X1,X1,X2,X3,X3),
    inference(equality_inference,[],[12781]) ).

cnf(i_0_19468,plain,
    c_Map_Omap__upds(X1,X1,X2,X3,hAPP(hAPP(c_List_Oappend(X1),X3),X4)) = c_Map_Omap__upds(X1,X1,X2,X3,X3),
    inference(equality_inference,[],[12782]) ).

cnf(i_0_19469,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,[],[12792]) ).

cnf(i_0_19470,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,[],[12796]) ).

cnf(i_0_19471,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,[],[12834]) ).

cnf(i_0_19472,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,[],[12846]) ).

cnf(i_0_19473,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),esk234_4(c_Nat_OSuc,X2,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
    inference(equality_inference,[],[12849]) ).

cnf(i_0_19474,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),esk213_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1)),X3)) ),
    inference(equality_inference,[],[12851]) ).

cnf(i_0_19475,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),esk211_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1)),X3)) ),
    inference(equality_inference,[],[12852]) ).

cnf(i_0_19476,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,[],[12898]) ).

cnf(i_0_19477,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,[],[12910]) ).

cnf(i_0_19478,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),esk471_4(hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),X1,X3,X2)),hAPP(c_List_Oset(X1),X3))) ),
    inference(equality_inference,[],[12933]) ).

cnf(i_0_19479,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,[],[12935]) ).

cnf(i_0_19480,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,[],[12937]) ).

cnf(i_0_19481,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,[],[12972]) ).

cnf(i_0_19482,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,[],[12973]) ).

cnf(i_0_19483,plain,
    hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)),X3) = hAPP(c_Option_Ooption_OSome(X2),X4),
    inference(equality_inference,[],[12979]) ).

cnf(i_0_19484,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,[],[12986]) ).

cnf(i_0_19485,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,[],[13034]) ).

cnf(i_0_19486,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,[],[13035]) ).

cnf(i_0_19487,plain,
    ( X1 = esk40_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,[],[13107]) ).

cnf(i_0_19488,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,[],[13145]) ).

cnf(i_0_19489,plain,
    ( X1 = X1
    | ~ c_Typedef_Otype__definition(X2,X3,X4,X5,X6) ),
    inference(equality_inference,[],[13152]) ).

cnf(i_0_19490,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,[],[13156]) ).

cnf(i_0_19491,plain,
    ( ~ class_HOL_Oequal(X1)
    | ~ class_Enum_Oenum(X2)
    | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X2,X1)),X3),X3)) ),
    inference(equality_inference,[],[13161]) ).

cnf(i_0_19492,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),esk213_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1)),esk212_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,[],[13162]) ).

cnf(i_0_19493,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),esk211_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1)),esk210_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,[],[13163]) ).

cnf(i_0_19494,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,[],[13182]) ).

cnf(i_0_19495,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,[],[13183]) ).

cnf(i_0_19496,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,[],[13193]) ).

cnf(i_0_19497,plain,
    ( X1 = X1
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),esk404_3(X2,X1,X1)),hAPP(c_List_Oset(tc_prod(X2,X2)),hAPP(hAPP(c_List_Ozip(X2,X2),X1),X1)))) ),
    inference(equality_inference,[],[13195]) ).

cnf(i_0_19498,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),esk471_4(hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2),X1,X2,X3))) ),
    inference(equality_inference,[],[13201]) ).

cnf(i_0_19499,plain,
    ( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ c_Orderings_Oorder__class_Omono(X1,X1,X2)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2)),X3))),X3)) ),
    inference(equality_inference,[],[13208]) ).

cnf(i_0_19500,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,[],[13238]) ).

cnf(i_0_19501,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,[],[13239]) ).

cnf(i_0_19502,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,[],[13256]) ).

cnf(i_0_19503,plain,
    hAPP(X1,hAPP(X2,X3)) = hAPP(X1,hAPP(X2,X3)),
    inference(equality_inference,[],[13335]) ).

cnf(i_0_19504,plain,
    hAPP(c_Fun_Oid(X1),hAPP(X2,X3)) = hAPP(X2,X3),
    inference(equality_inference,[],[13339]) ).

cnf(i_0_19505,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,[],[13346]) ).

cnf(i_0_19506,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,[],[13364]) ).

cnf(i_0_19507,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,[],[13365]) ).

cnf(i_0_19508,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,[],[13366]) ).

cnf(i_0_19509,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,[],[13498]) ).

cnf(i_0_19510,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,[],[13554]) ).

cnf(i_0_19511,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,[],[13579]) ).

cnf(i_0_19512,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,[],[13598]) ).

cnf(i_0_19513,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,[],[13620]) ).

cnf(i_0_19514,plain,
    c_Map_Odom(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))),X3),hAPP(c_Option_Ooption_OSome(X2),X4))) = hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
    inference(equality_inference,[],[13697]) ).

cnf(i_0_19515,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,[],[13727]) ).

cnf(i_0_19516,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,[],[13759]) ).

cnf(i_0_19517,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,[],[13809]) ).

cnf(i_0_19518,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,[],[13830]) ).

cnf(i_0_19519,plain,
    c_List_Olist__all2(X1,X2,X3,c_List_Olist_ONil(X1),c_List_Olist_ONil(X2)),
    inference(equality_inference,[],[13832]) ).

cnf(i_0_19520,plain,
    c_List_Olist__all2(X1,X2,X3,c_List_Olist_ONil(X1),c_List_Olist_ONil(X2)),
    inference(equality_inference,[],[13833]) ).

cnf(i_0_19521,plain,
    ( X1 = X1
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X2,tc_HOL_Obool),c_fequal),esk404_3(X2,X1,X1))) ),
    inference(equality_inference,[],[13847]) ).

cnf(i_0_19522,plain,
    c_List_Olist__all2(X1,X1,c_fequal,X2,X2),
    inference(equality_inference,[],[13855]) ).

cnf(i_0_19523,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,[],[13908]) ).

cnf(i_0_19524,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,[],[13911]) ).

cnf(i_0_19525,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,[],[13927]) ).

cnf(i_0_19526,plain,
    ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X2 = X3
    | X4 = X4 ),
    inference(equality_inference,[],[13950]) ).

cnf(i_0_19527,plain,
    ( ~ class_Enum_Oenum(X1)
    | hAPP(hAPP(c_Map_Omap__of(X1,X1),hAPP(hAPP(c_List_Ozip(X1,X1),c_Enum_Oenum__class_Oenum(X1)),c_Enum_Oenum__class_Oenum(X1))),X2) = hAPP(c_Option_Ooption_OSome(X1),esk436_4(X2,c_Enum_Oenum__class_Oenum(X1),X1,X1)) ),
    inference(equality_inference,[],[13956]) ).

cnf(i_0_19528,plain,
    ( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ c_Orderings_Oorder__class_Omono(X1,X1,X2)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2))))) ),
    inference(equality_inference,[],[13990]) ).

cnf(i_0_19529,plain,
    c_Map_Odom(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),c_Option_Ooption_ONone(X2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
    inference(equality_inference,[],[13996]) ).

cnf(i_0_19530,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,[],[14008]) ).

cnf(i_0_19531,plain,
    X1 = X1,
    inference(equality_inference,[],[14010]) ).

cnf(i_0_19532,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,[],[14035]) ).

cnf(i_0_19533,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,[],[14054]) ).

cnf(i_0_19534,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,[],[14056]) ).

cnf(i_0_19535,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,[],[14057]) ).

cnf(i_0_19536,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,[],[14083]) ).

cnf(i_0_19537,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,[],[14100]) ).

cnf(i_0_19538,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,[],[14154]) ).

cnf(i_0_19539,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,[],[14167]) ).

cnf(i_0_19540,plain,
    ( X1 = X1
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X4)) ),
    inference(equality_inference,[],[14212]) ).

cnf(i_0_19541,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,[],[14258]) ).

cnf(i_0_19542,plain,
    ( c_Fun_Oinj__on(X1,X2,esk37_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,[],[14269]) ).

cnf(i_0_19543,plain,
    ( ~ epred2_3(X1,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4))
    | 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,[],[14271]) ).

cnf(i_0_19544,plain,
    ( ~ epred1_3(X1,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4))
    | 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,[],[14272]) ).

cnf(i_0_19545,plain,
    ( ~ epred2_3(X1,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4))
    | 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,[],[14320]) ).

cnf(i_0_19546,plain,
    ( ~ epred1_3(X1,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4))
    | 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,[],[14321]) ).

cnf(i_0_19547,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,[],[14382]) ).

cnf(i_0_19548,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,[],[14394]) ).

cnf(i_0_19549,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,[],[14395]) ).

cnf(i_0_19550,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,[],[14409]) ).

cnf(i_0_19551,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,[],[14438]) ).

cnf(i_0_19552,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,[],[14463]) ).

cnf(i_0_19553,plain,
    X1 = X1,
    inference(equality_inference,[],[14466]) ).

cnf(i_0_19554,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,[],[14502]) ).

cnf(i_0_19555,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,[],[14522]) ).

cnf(i_0_19556,plain,
    hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)) = hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)),
    inference(equality_inference,[],[14535]) ).

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,[],[14554]) ).

cnf(i_0_19558,plain,
    hAPP(X1,hAPP(X2,X3)) = hAPP(hAPP(c_Fun_Ocomp(X4,X5,X6,X1),X2),X3),
    inference(equality_inference,[],[14555]) ).

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,[],[14595]) ).

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,[],[14601]) ).

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,[],[14618]) ).

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,[],[14619]) ).

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,[],[14632]) ).

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,[],[14634]) ).

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,[],[14635]) ).

cnf(i_0_19566,plain,
    ( X1 = X2
    | X1 = X1 ),
    inference(equality_inference,[],[14636]) ).

cnf(i_0_19567,plain,
    ( X1 = X2
    | X1 = X1 ),
    inference(equality_inference,[],[14637]) ).

cnf(i_0_19568,plain,
    ( X1 = X2
    | X2 = X2 ),
    inference(equality_inference,[],[14638]) ).

cnf(i_0_19569,plain,
    ( X1 = X2
    | X2 = X2 ),
    inference(equality_inference,[],[14639]) ).

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,[],[14642]) ).

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,[],[14695]) ).

cnf(i_0_19572,plain,
    X1 = X1,
    inference(equality_inference,[],[14742]) ).

cnf(i_0_19573,plain,
    X1 = X1,
    inference(equality_inference,[],[14743]) ).

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),esk433_2(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_List_Oset(tc_Nat_Onat),X1))) ),
    inference(equality_inference,[],[14746]) ).

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,[],[14747]) ).

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,[],[14750]) ).

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,[],[14759]) ).

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,[],[14765]) ).

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,[],[14776]) ).

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,[],[14811]) ).

cnf(i_0_19581,plain,
    ( X1 = X1
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk410_3(X2,X1,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1))) ),
    inference(equality_inference,[],[14820]) ).

cnf(i_0_19582,plain,
    ( hAPP(hAPP(c_Map_Omap__of(X1,X1),hAPP(hAPP(c_List_Ozip(X1,X1),X2),X2)),X3) = c_Option_Ooption_ONone(X1)
    | hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))) ),
    inference(equality_inference,[],[14848]) ).

cnf(i_0_19583,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,[],[14895]) ).

cnf(i_0_19584,plain,
    X1 = X1,
    inference(equality_inference,[],[14947]) ).

cnf(i_0_19585,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,[],[14969]) ).

cnf(i_0_19586,plain,
    ( ~ hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | c_Map_Odom(X1,X1,hAPP(c_Map_Omap__of(X1,X1),hAPP(hAPP(c_List_Ozip(X1,X1),X2),X2))) = hAPP(c_List_Oset(X1),X2) ),
    inference(equality_inference,[],[15021]) ).

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,[],[15042]) ).

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),esk310_3(X1,X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)) ),
    inference(equality_inference,[],[15070]) ).

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,[],[15099]) ).

cnf(i_0_19590,plain,
    ( X1 = X2
    | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X4)),c_Option_Ooption_OSome(X4)),X2),hAPP(c_Option_Ooption_OSome(X4),X5)),X1) = hAPP(c_Option_Ooption_OSome(X4),X1) ),
    inference(equality_inference,[],[15114]) ).

cnf(i_0_19591,plain,
    hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X2,c_Option_Ooption_ONone(X1),X3),hAPP(c_Option_Ooption_OSome(X2),X4)) = hAPP(X3,X4),
    inference(equality_inference,[],[15190]) ).

cnf(i_0_19592,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,[],[15234]) ).

cnf(i_0_19593,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,[],[15244]) ).

cnf(i_0_19594,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,[],[15256]) ).

cnf(i_0_19595,plain,
    ( hAPP(X1,X2) = hAPP(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4))) ),
    inference(equality_inference,[],[15260]) ).

cnf(i_0_19596,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,[],[15309]) ).

cnf(i_0_19597,plain,
    hAPP(c_Map_Omap__add(X1,X2,X3,c_Option_Ooption_OSome(X2)),X4) = hAPP(c_Option_Ooption_OSome(X2),X4),
    inference(equality_inference,[],[15354]) ).

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,[],[15393]) ).

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,[],[15401]) ).

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,[],[15415]) ).

cnf(i_0_19601,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,[],[15416]) ).

cnf(i_0_19602,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,[],[15417]) ).

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,[],[15422]) ).

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,[],[15436]) ).

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,[],[15531]) ).

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,[],[15532]) ).

cnf(i_0_19607,plain,
    X1 = X1,
    inference(equality_inference,[],[15552]) ).

cnf(i_0_19608,plain,
    X1 = X1,
    inference(equality_inference,[],[15553]) ).

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,[],[15567]) ).

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,[],[15584]) ).

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,[],[15592]) ).

cnf(i_0_19612,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,[],[15595]) ).

cnf(i_0_19613,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,[],[15596]) ).

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,[],[15695]) ).

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,[],[15720]) ).

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,[],[15746]) ).

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,[],[15747]) ).

cnf(i_0_19618,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
    inference(equality_inference,[],[15787]) ).

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,[],[15800]) ).

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,[],[15843]) ).

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,[],[15871]) ).

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,[],[15886]) ).

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,[],[15895]) ).

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,[],[15922]) ).

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,[],[15927]) ).

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,[],[15935]) ).

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,[],[15943]) ).

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,[],[15944]) ).

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,[],[16023]) ).

cnf(i_0_19630,plain,
    hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5),X4) = X5,
    inference(equality_inference,[],[16031]) ).

cnf(i_0_19631,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,[],[16055]) ).

cnf(i_0_19632,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,[],[16099]) ).

cnf(i_0_19633,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,[],[16114]) ).

cnf(i_0_19634,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,[],[16115]) ).

cnf(i_0_19635,plain,
    X1 = X1,
    inference(equality_inference,[],[16124]) ).

cnf(i_0_19636,plain,
    ( X1 = X1
    | hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
    | hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
    inference(equality_inference,[],[16135]) ).

cnf(i_0_19637,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,[],[16136]) ).

cnf(i_0_19638,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,[],[16138]) ).

cnf(i_0_19639,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,[],[16151]) ).

cnf(i_0_19640,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Oran(X3,X1,c_Option_Ooption_OSome(X1)))),
    inference(equality_inference,[],[16160]) ).

cnf(i_0_19641,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,c_Option_Ooption_OSome(X3)))),
    inference(equality_inference,[],[16161]) ).

cnf(i_0_19642,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,[],[16168]) ).

cnf(i_0_19643,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,[],[16171]) ).

cnf(i_0_19644,plain,
    ( ~ c_Nat__Transfer_Onat__set(X1)
    | ~ c_Nat__Transfer_Onat__set(X1)
    | X1 = X1 ),
    inference(equality_inference,[],[16182]) ).

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,[],[16199]) ).

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,[],[16249]) ).

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,[],[16254]) ).

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,[],[16255]) ).

cnf(i_0_19649,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,[],[16306]) ).

cnf(i_0_19650,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,[],[16336]) ).

cnf(i_0_19651,plain,
    X1 = X1,
    inference(equality_inference,[],[16352]) ).

cnf(i_0_19652,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,[],[16366]) ).

cnf(i_0_19653,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,[],[16393]) ).

cnf(i_0_19654,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,[],[16416]) ).

cnf(i_0_19655,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))),
    inference(equality_inference,[],[16420]) ).

cnf(i_0_19656,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,[],[16440]) ).

cnf(i_0_19657,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,[],[16446]) ).

cnf(i_0_19658,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
    inference(equality_inference,[],[16522]) ).

cnf(i_0_19659,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
    inference(equality_inference,[],[16523]) ).

cnf(i_0_19660,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,[],[16524]) ).

cnf(i_0_19661,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,[],[16529]) ).

cnf(i_0_19662,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,[],[16531]) ).

cnf(i_0_19663,plain,
    X1 = X1,
    inference(equality_inference,[],[16532]) ).

cnf(i_0_19664,plain,
    X1 = X1,
    inference(equality_inference,[],[16534]) ).

cnf(i_0_19665,plain,
    X1 = X1,
    inference(equality_inference,[],[16536]) ).

cnf(i_0_19666,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,[],[16540]) ).

cnf(i_0_19667,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,[],[16562]) ).

cnf(i_0_19668,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,[],[16564]) ).

cnf(i_0_19669,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,[],[16565]) ).

cnf(i_0_19670,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,[],[16628]) ).

cnf(i_0_19671,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,[],[16629]) ).

cnf(i_0_19672,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,[],[16665]) ).

cnf(i_0_19673,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,[],[16689]) ).

cnf(i_0_19674,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,[],[16690]) ).

cnf(i_0_19675,plain,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Map_Odom(X1,X3,c_Option_Ooption_OSome(X3))) = c_Map_Odom(X1,X3,c_Option_Ooption_OSome(X3)),
    inference(equality_inference,[],[16695]) ).

cnf(i_0_19676,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,[],[16713]) ).

cnf(i_0_19677,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,[],[16724]) ).

cnf(i_0_19678,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,[],[16725]) ).

cnf(i_0_19679,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,[],[16742]) ).

cnf(i_0_19680,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,[],[16757]) ).

cnf(i_0_19681,plain,
    X1 = X1,
    inference(equality_inference,[],[16758]) ).

cnf(i_0_19682,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,[],[16770]) ).

cnf(i_0_19683,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,[],[16807]) ).

cnf(i_0_19684,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,[],[16833]) ).

cnf(i_0_19685,plain,
    hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)),
    inference(equality_inference,[],[16840]) ).

cnf(i_0_19686,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,[],[16865]) ).

cnf(i_0_19687,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,[],[16866]) ).

cnf(i_0_19688,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,[],[16916]) ).

cnf(i_0_19689,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,[],[16917]) ).

cnf(i_0_19690,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,[],[16936]) ).

cnf(i_0_19691,plain,
    hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),hAPP(X3,X4)) = X3,
    inference(equality_inference,[],[16968]) ).

cnf(i_0_19692,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,[],[16978]) ).

cnf(i_0_19693,plain,
    hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olists(X1,X2))),
    inference(equality_inference,[],[16997]) ).

cnf(i_0_19694,plain,
    ( ~ c_List_Olinorder__class_Osorted(X1,X2)
    | ~ class_Orderings_Olinorder(X1)
    | X2 = esk482_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,[],[17015]) ).

cnf(i_0_19695,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,[],[17021]) ).

cnf(i_0_19696,plain,
    ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
    inference(equality_inference,[],[17024]) ).

cnf(i_0_19697,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,[],[17034]) ).

cnf(i_0_19698,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,[],[17035]) ).

cnf(i_0_19699,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,[],[17036]) ).

cnf(i_0_19700,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,[],[17037]) ).

cnf(i_0_19701,plain,
    X1 = X1,
    inference(equality_inference,[],[17038]) ).

cnf(i_0_19702,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,[],[17047]) ).

cnf(i_0_19703,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,[],[17048]) ).

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,[],[17049]) ).

cnf(i_0_19705,plain,
    ( ~ class_Rings_Oidom(X1)
    | X2 = X2
    | X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) ),
    inference(equality_inference,[],[17127]) ).

cnf(i_0_19706,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,[],[17131]) ).

cnf(i_0_19707,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,[],[17132]) ).

cnf(i_0_19708,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,[],[17133]) ).

cnf(i_0_19709,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,[],[17136]) ).

cnf(i_0_19710,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,[],[17137]) ).

cnf(i_0_19711,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Option_Oset(X1,hAPP(c_Option_Ooption_OSome(X1),X2)))),
    inference(equality_inference,[],[17139]) ).

cnf(i_0_19712,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,[],[17200]) ).

cnf(i_0_19713,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[17203]) ).

cnf(i_0_19714,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[17205]) ).

cnf(i_0_19715,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[17206]) ).

cnf(i_0_19716,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[17207]) ).

cnf(i_0_19717,plain,
    ( X1 = X1
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(equality_inference,[],[17212]) ).

cnf(i_0_19718,plain,
    c_Map_Odom(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(equality_inference,[],[17224]) ).

cnf(i_0_19719,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,[],[17229]) ).

cnf(i_0_19720,plain,
    ( ~ class_Groups_Ocancel__semigroup__add(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17231]) ).

cnf(i_0_19721,plain,
    ( X1 = X1
    | ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
    inference(equality_inference,[],[17232]) ).

cnf(i_0_19722,plain,
    ( ~ class_Groups_Ocancel__semigroup__add(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17234]) ).

cnf(i_0_19723,plain,
    X1 = X1,
    inference(equality_inference,[],[17235]) ).

cnf(i_0_19724,plain,
    X1 = X1,
    inference(equality_inference,[],[17236]) ).

cnf(i_0_19725,plain,
    X1 = X1,
    inference(equality_inference,[],[17237]) ).

cnf(i_0_19726,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,[],[17243]) ).

cnf(i_0_19727,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,[],[17244]) ).

cnf(i_0_19728,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,[],[17245]) ).

cnf(i_0_19729,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,[],[17258]) ).

cnf(i_0_19730,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,[],[17259]) ).

cnf(i_0_19731,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,[],[17260]) ).

cnf(i_0_19732,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,[],[17263]) ).

cnf(i_0_19733,plain,
    X1 = X1,
    inference(equality_inference,[],[17271]) ).

cnf(i_0_19734,plain,
    X1 = X1,
    inference(equality_inference,[],[17272]) ).

cnf(i_0_19735,plain,
    X1 = X1,
    inference(equality_inference,[],[17273]) ).

cnf(i_0_19736,plain,
    X1 = X1,
    inference(equality_inference,[],[17274]) ).

cnf(i_0_19737,plain,
    c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = X3,
    inference(equality_inference,[],[17298]) ).

cnf(i_0_19738,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,[],[17307]) ).

cnf(i_0_19739,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
    inference(equality_inference,[],[17329]) ).

cnf(i_0_19740,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(equality_inference,[],[17338]) ).

cnf(i_0_19741,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X1)),
    inference(equality_inference,[],[17346]) ).

cnf(i_0_19742,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(equality_inference,[],[17350]) ).

cnf(i_0_19743,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(equality_inference,[],[17351]) ).

cnf(i_0_19744,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,[],[17354]) ).

cnf(i_0_19745,plain,
    ( X1 = X1
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(equality_inference,[],[17357]) ).

cnf(i_0_19746,plain,
    ( X1 = X1
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(equality_inference,[],[17359]) ).

cnf(i_0_19747,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,[],[17360]) ).

cnf(i_0_19748,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,[],[17368]) ).

cnf(i_0_19749,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,[],[17369]) ).

cnf(i_0_19750,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,[],[17371]) ).

cnf(i_0_19751,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,[],[17372]) ).

cnf(i_0_19752,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,[],[17373]) ).

cnf(i_0_19753,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,[],[17374]) ).

cnf(i_0_19754,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,[],[17376]) ).

cnf(i_0_19755,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,[],[17377]) ).

cnf(i_0_19756,plain,
    ( ~ c_Equiv__Relations_Oequivp(X1,X2)
    | hBOOL(hAPP(hAPP(X2,X3),X3)) ),
    inference(equality_inference,[],[17384]) ).

cnf(i_0_19757,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ class_Orderings_Olinorder(X2)
    | X3 = X3
    | ~ c_Orderings_Oorder__class_Ostrict__mono(X2,X1,X4) ),
    inference(equality_inference,[],[17396]) ).

cnf(i_0_19758,plain,
    X1 = X1,
    inference(equality_inference,[],[17397]) ).

cnf(i_0_19759,plain,
    X1 = X1,
    inference(equality_inference,[],[17398]) ).

cnf(i_0_19760,plain,
    X1 = X1,
    inference(equality_inference,[],[17399]) ).

cnf(i_0_19761,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,[],[17405]) ).

cnf(i_0_19762,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,[],[17413]) ).

cnf(i_0_19763,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
    inference(equality_inference,[],[17422]) ).

cnf(i_0_19764,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,[],[17438]) ).

cnf(i_0_19765,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,[],[17440]) ).

cnf(i_0_19766,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,[],[17445]) ).

cnf(i_0_19767,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,[],[17455]) ).

cnf(i_0_19768,plain,
    ( ~ c_Orderings_Oorder__class_Omono(X1,X1,X2)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2) = hAPP(X2,c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2)) ),
    inference(equality_inference,[],[17473]) ).

cnf(i_0_19769,plain,
    ( ~ c_Orderings_Oorder__class_Omono(X1,X1,X2)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2) = hAPP(X2,c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2)) ),
    inference(equality_inference,[],[17474]) ).

cnf(i_0_19770,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,[],[17476]) ).

cnf(i_0_19771,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,[],[17477]) ).

cnf(i_0_19772,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,[],[17498]) ).

cnf(i_0_19773,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,[],[17499]) ).

cnf(i_0_19774,plain,
    ( ~ epred1_3(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(equality_inference,[],[17501]) ).

cnf(i_0_19775,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,[],[17502]) ).

cnf(i_0_19776,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,[],[17505]) ).

cnf(i_0_19777,plain,
    X1 = X1,
    inference(equality_inference,[],[17506]) ).

cnf(i_0_19778,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,[],[17510]) ).

cnf(i_0_19779,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,[],[17511]) ).

cnf(i_0_19780,plain,
    c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))) = X2,
    inference(equality_inference,[],[17514]) ).

cnf(i_0_19781,plain,
    ( ~ epred2_3(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | hBOOL(hAPP(X1,X2)) ),
    inference(equality_inference,[],[17531]) ).

cnf(i_0_19782,plain,
    ( ~ class_HOL_Oequal(X1)
    | hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X1),X2),X2)) ),
    inference(equality_inference,[],[17561]) ).

cnf(i_0_19783,plain,
    ( ~ class_Orderings_Oorder(X1)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2)) ),
    inference(equality_inference,[],[17563]) ).

cnf(i_0_19784,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2)) ),
    inference(equality_inference,[],[17564]) ).

cnf(i_0_19785,plain,
    ( ~ class_Orderings_Oorder(X1)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2)) ),
    inference(equality_inference,[],[17565]) ).

cnf(i_0_19786,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,[],[17609]) ).

cnf(i_0_19787,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,[],[17614]) ).

cnf(i_0_19788,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,[],[17618]) ).

cnf(i_0_19789,plain,
    hAPP(hAPP(c_List_Olist__update(X1,c_List_Olist_ONil(X1)),X2),X3) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[17643]) ).

cnf(i_0_19790,plain,
    hAPP(hAPP(c_Option_Omap(X1,X2),X3),c_Option_Ooption_ONone(X1)) = c_Option_Ooption_ONone(X2),
    inference(equality_inference,[],[17644]) ).

cnf(i_0_19791,plain,
    hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X2),
    inference(equality_inference,[],[17645]) ).

cnf(i_0_19792,plain,
    c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Olist_ONil(X2)),
    inference(equality_inference,[],[17646]) ).

cnf(i_0_19793,plain,
    ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(equality_inference,[],[17651]) ).

cnf(i_0_19794,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,[],[17671]) ).

cnf(i_0_19795,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,[],[17675]) ).

cnf(i_0_19796,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,[],[17676]) ).

cnf(i_0_19797,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)),
    inference(equality_inference,[],[17681]) ).

cnf(i_0_19798,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,[],[17685]) ).

cnf(i_0_19799,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,[],[17691]) ).

cnf(i_0_19800,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,[],[17723]) ).

cnf(i_0_19801,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,[],[17740]) ).

cnf(i_0_19802,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,[],[17744]) ).

cnf(i_0_19803,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17794]) ).

cnf(i_0_19804,plain,
    hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
    inference(equality_inference,[],[17796]) ).

cnf(i_0_19805,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17839]) ).

cnf(i_0_19806,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17840]) ).

cnf(i_0_19807,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17841]) ).

cnf(i_0_19808,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17842]) ).

cnf(i_0_19809,plain,
    ( ~ class_Nat_Osemiring__char__0(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17843]) ).

cnf(i_0_19810,plain,
    ( ~ class_Int_Oring__char__0(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17844]) ).

cnf(i_0_19811,plain,
    ( ~ class_Lattices_Oboolean__algebra(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17845]) ).

cnf(i_0_19812,plain,
    ( ~ class_Groups_Ogroup__add(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17846]) ).

cnf(i_0_19813,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,[],[17855]) ).

cnf(i_0_19814,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,[],[17856]) ).

cnf(i_0_19815,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,[],[17857]) ).

cnf(i_0_19816,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,[],[17858]) ).

cnf(i_0_19817,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,[],[17859]) ).

cnf(i_0_19818,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,[],[17860]) ).

cnf(i_0_19819,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,[],[17861]) ).

cnf(i_0_19820,plain,
    X1 = hAPP(hAPP(c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1),
    inference(equality_inference,[],[17874]) ).

cnf(i_0_19821,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,[],[17875]) ).

cnf(i_0_19822,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,[],[17888]) ).

cnf(i_0_19823,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,[],[17889]) ).

cnf(i_0_19824,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,[],[17890]) ).

cnf(i_0_19825,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,[],[17891]) ).

cnf(i_0_19826,plain,
    X1 = X1,
    inference(equality_inference,[],[17914]) ).

cnf(i_0_19827,plain,
    X1 = X1,
    inference(equality_inference,[],[17915]) ).

cnf(i_0_19828,plain,
    hAPP(hAPP(c_List_Otake(X1),X2),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[17922]) ).

cnf(i_0_19829,plain,
    c_List_Oreplicate(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[17927]) ).

cnf(i_0_19830,plain,
    c_List_Olist_ONil(X1) = c_List_Oreplicate(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2),
    inference(equality_inference,[],[17928]) ).

cnf(i_0_19831,plain,
    hAPP(hAPP(c_List_Otake(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[17938]) ).

cnf(i_0_19832,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,[],[17940]) ).

cnf(i_0_19833,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,[],[17942]) ).

cnf(i_0_19834,plain,
    hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) = X2,
    inference(equality_inference,[],[17945]) ).

cnf(i_0_19835,plain,
    hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
    inference(equality_inference,[],[17946]) ).

cnf(i_0_19836,plain,
    X1 = hAPP(hAPP(c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1),
    inference(equality_inference,[],[17947]) ).

cnf(i_0_19837,plain,
    X1 = hAPP(hAPP(c_List_Oappend(X2),X1),c_List_Olist_ONil(X2)),
    inference(equality_inference,[],[17948]) ).

cnf(i_0_19838,plain,
    X1 = X1,
    inference(equality_inference,[],[18001]) ).

cnf(i_0_19839,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,[],[18002]) ).

cnf(i_0_19840,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,[],[18003]) ).

cnf(i_0_19841,plain,
    hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
    inference(equality_inference,[],[18005]) ).

cnf(i_0_19842,plain,
    X1 = hAPP(c_List_Orev(X2),hAPP(c_List_Orev(X2),X1)),
    inference(equality_inference,[],[18006]) ).

cnf(i_0_19843,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,[],[18012]) ).

cnf(i_0_19844,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,[],[18013]) ).

cnf(i_0_19845,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,[],[18015]) ).

cnf(i_0_19846,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,[],[18016]) ).

cnf(i_0_19847,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = X1,
    inference(equality_inference,[],[18027]) ).

cnf(i_0_19848,plain,
    c_Option_Oset(X1,c_Option_Ooption_ONone(X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
    inference(equality_inference,[],[18058]) ).

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,[],[18062]) ).

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,[],[18063]) ).

cnf(i_0_19851,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,[],[18093]) ).

cnf(i_0_19852,plain,
    X1 = hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),
    inference(equality_inference,[],[18097]) ).

cnf(i_0_19853,plain,
    X1 = X1,
    inference(equality_inference,[],[18105]) ).

cnf(i_0_19854,plain,
    X1 = X1,
    inference(equality_inference,[],[18106]) ).

cnf(i_0_19855,plain,
    X1 = X1,
    inference(equality_inference,[],[18107]) ).

cnf(i_0_19856,plain,
    X1 = X1,
    inference(equality_inference,[],[18109]) ).

cnf(i_0_19857,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,[],[18115]) ).

cnf(i_0_19858,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,[],[18116]) ).

cnf(i_0_19859,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,[],[18117]) ).

cnf(i_0_19860,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,[],[18146]) ).

cnf(i_0_19861,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,[],[18147]) ).

cnf(i_0_19862,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,[],[18148]) ).

cnf(i_0_19863,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,[],[18151]) ).

cnf(i_0_19864,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,[],[18152]) ).

cnf(i_0_19865,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,[],[18167]) ).

cnf(i_0_19866,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,[],[18168]) ).

cnf(i_0_19867,plain,
    hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[18169]) ).

cnf(i_0_19868,plain,
    hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[18170]) ).

cnf(i_0_19869,plain,
    c_List_Olist_ONil(X1) = hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1)),
    inference(equality_inference,[],[18171]) ).

cnf(i_0_19870,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1)) ),
    inference(equality_inference,[],[18190]) ).

cnf(i_0_19871,plain,
    ( ~ class_Rings_Osemiring__1(X1)
    | c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(equality_inference,[],[18191]) ).

cnf(i_0_19872,plain,
    c_List_Oremdups(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[18197]) ).

cnf(i_0_19873,plain,
    c_List_Olist_ONil(X1) = c_List_Oremdups(X1,c_List_Olist_ONil(X1)),
    inference(equality_inference,[],[18198]) ).

cnf(i_0_19874,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,[],[18199]) ).

cnf(i_0_19875,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,[],[18224]) ).

cnf(i_0_19876,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,[],[18225]) ).

cnf(i_0_19877,plain,
    c_Nitpick_Onat__gcd(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
    inference(equality_inference,[],[18226]) ).

cnf(i_0_19878,plain,
    c_Random_Oinc__shift(X1,X1) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),
    inference(equality_inference,[],[18230]) ).

cnf(i_0_19879,plain,
    $false,
    inference(scs_inference,[],[i_0_16703,i_0_16485,i_0_18054,i_0_14549]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWW312+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
% 0.15/0.33  % Computer : n010.cluster.edu
% 0.15/0.33  % Model    : x86_64 x86_64
% 0.15/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33  % Memory   : 8042.1875MB
% 0.15/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33  % CPULimit   : 300
% 0.15/0.33  % WCLimit    : 300
% 0.15/0.33  % DateTime   : Tue May  5 06:36:21 EDT 2026
% 0.15/0.33  % CPUTime    : 
% 0.15/0.34  % start to proof: theBenchmark
% 31.75/17.27  % Version  : CSE_E---1.7
% 31.75/17.27  % Problem  : theBenchmark.p
% 31.75/17.27  % SZS status Theorem for theBenchmark.p
% 31.75/17.27  % SZS output start CNFRefutation
% See solution above
% 32.73/17.73  % Total time : 16.901s
%------------------------------------------------------------------------------